Degrees of Freedom

The Courage to Be Wrong: Reading the Biography of Stephen Hawking

Davide Castelvecchi — Sun, 08 Jan 2012 17:19:22 +0000

In July 2010, the editorial department of Scientific American—where at the time I was on staff—received a review copy of a book was slated to come out in September. It was a slim, drab-looking, paperback-bound volume, still without a cover design or page numbers. On the cover it carried two names, that of a respected science writer, Leonard Mlodinow—and Stephen Hawking’s. Would we like to review it in our magazine?

I dropped everything I was doing that day and I proceeded to devour the book. I had never particularly been a fan of Hawking’s celebrated bestseller, A Brief History of Time, which is said to have sold 10 million copies. But I found this new tome, The Grand Design, to be a page turner.

The central thesis of the book came to me as a bit of a shock. (And no, by that I do not mean Hawking’s statement that created a minor media storm: physics does not require the existence of god, which coming from him did not surprise me in the least.)

Throughout much of his career, Hawking expressed the belief that humanity was on the verge of a transformative step. He thought we were soon going to discover the ultimate set of laws that govern the universe. Along the way, physicists would reconcile various theories that seemed apt at describing some class of phenomena but not others—for example, gravitation for the formation of galaxies and quantum mechanics for the structure of atoms—and reveal a single consistent rulebook which would explain everything.

Hawking himself had given physicists some clues toward a grand unification by combining ideas from Einstein’s general theory of relativity, quantum physics and thermodynamics to understand black holes. In what is still seen as one of his most profound insights—perhaps one of the most profound of all of 20th century physics—he had calculated that black holes are not really black, but that they slowly radiate energy, losing mass in the process. That slow leak became known as Hawking radiation. Physicists still hope to observe it experimentally by producing microscopic, fleeting black holes in high-energy experiments such as the Large Hadron Collider.

With characteristic brashness Hawking, in his 1980 inaugural lecture as Cambridge University’s Lucasian Professor—the chair that had once been Isaac Newton’s—said that the problem of unification was likely to be solved by the end of the century. At the time, a theory called N=8 supergravity seemed a promising approach. The title of his talk: “Is the End in Sight for Theoretical Physics?” Later, when supergravity faded out of the picture, Hawking stated a similar optimistic expectation of string theory.

What I found shocking in Hawking and Mlodinow’s new book was that Hawking now seemed to give up on the hope that there could even be such a thing as a theory of everything. A majority of theoretical physicists now thought that string theory would turn out to hold the key to unification. The trouble is, there wasn’t one string theory, but at least five different theories. Each seemed suitable to describe one particular range of phenomena, but each failed at describing others. On the surface the theories seemed incompatible, but physicists had discovered “dualities”—a sort of Rosetta stones that could translate concepts from one theory into another.

Perhaps, the two authors wrote, this is as good as it gets. Perhaps there is no overarching way of representing reality. Instead, physics must limit itself to a “model-dependent realism” that can capture one aspect of reality or another. Different models may give vastly different representation of reality, and none can claim to reveal the “thing” as it is—the noumenon, as Immanuel Kant would have called it.

This almost postmodernist twist seemed at odds with Hawking’s lifetime convictions, but it was not the first time that the physicist (who today celebrates his 70th birthday) had dramatically changed his mind during his career, as Kitty Ferguson writes in her eminently readable new biography Stephen Hawking: An Unfettered Mind. (See a brief excerpt of the book here.)

The most celebrated such reversal was probably his concession of a bet that he had made with Leonard Susskind, a physicists now at Stanford University, concerning the so-called black hole information paradox. Hawking had pointed out that if a black hole radiates energy, and eventually shrinks to nothingness, all information concerning the stuff that had fallen into the black hole will disappear from the universe. Taken to its ultimate consequences, it meant that physicists had to abandon one of their cherished principles: that reality is predictable, and that nature evolves based on well-defined rules rather than in an arbitrary fashion. It was a hard pill to swallow, but Hawking was ready to take it if that was what the equations really implied.

Years later, Hawking announced that he no longer believed that there was a paradox. He came to the conclusion that information does not disappear after all. (Physicists now regard the information paradox to be solved by the work of Juan Maldacena, a physicist now at the Institute for Advanced Study in Princeton, N.J., based on the so-called holographic universe.)

As Ferguson rightly observes, and makes it into one of two leading themes of her book, this ability to reverse one’s convictions in the face of uncomfortable evidence—first abandoning the belief in the consistency of nature, and then saying you were wrong—is far from being a weakness. Instead, it is a mark of good science.

The other leading theme in Ferguson’s book, is, of course, her subject’s seemingly superhuman ability to overcome his physical condition. His physics was first-rate, but it was his ability to inspire which to a large extent made him a household name around the world. Ferguson strikes what seems to me as the right balance between telling the story of Hawking the extraordinary scientist and the one of Hawking the extraordinary man.

In her work she benefited from a close collaboration with her subject, including numerous extended interviews conducted over a period of decades. (When it comes quoting others, however, Ferguson mostly seems to rely on secondary sources—such as books and newspaper clippings—rather than on direct interviews, which takes some freshness away from the narration.)

Ferguson’s book concludes with a chapter on The Grand Design, which comes across as a summa of Hawking’s intellectual legacy. The book has not been received well by critics. My colleagues and I at Scientific American however found it compelling enough that, back in July 2010, we persuaded the publisher and the authors to let us run an excerpt in the upcoming October issue, which had a special significance for us because it inaugurated a refurbished and redesigned magazine.

At the time when we got the review copy of the book, we had already begun to lay out the October issue, but we quickly made changes to accommodate the new article. Later, the excerpt, “The Elusive Theory of Everything,” would be included in an anthology of the best science writing of the year. Both The Grand Design and Stephen Hawking: An Unfettered Mind belong in the library of anyone who has an interest in the uncanny ideas and the incredible story of one of the great scientists of our time.

Book Review: Our Magnetic Earth, by Ronald Merrill

Davide Castelvecchi — Wed, 28 Dec 2011 12:04:34 +0000

A magnetic sense is now well documented in dozens of animal species. It turns out that tracking the geomagnetic field—that same invisible thing that points compasses—is handy for life, in lots of situations. Using their internal compasses, naked mole rats in Africa navigate their pitch-black underground mazes. Lobsters off Bermuda find their way to regions of the seafloor where they congregate to spawn. Thrushes migrate south in the autumn and north in the spring. Honeybees know which way is home to their hive. And humpback whales swim for hundreds of kilometers at a time in the open ocean without deviating by more than one degree from the course they initially set.

Biological tissues however tend not to respond to, or be affected by, magnetic fields. Thus, for a long time explaining how animals sense these fields has been a holy grail of sensory biology. There now appear to be at least two plausible explanations. One proposed mechanism is based on microscopic particles of iron oxide located inside specialized cells; the other on a quantum effect in which certain chemical reactions–specifically some that may involve a protein in the retina called cryptochrome–slow down or speed up depending on which way points north with respect to the animal’s head.

Each of the two mechanisms has mesmerizing evidence to back it up, as well as detractors. To learn more, you’ll have to read my new feature article “The Compass Within,” in the January 2012 issue of Scientific American.

But how does the planet generate a magnetic field in the first place, and why does that field point, more or less consistently, to a magnetic north? As Ronald Merrill’s fascinating recent book Our Magnetic Earth: The Science of Geomagnetism explains, there are essentially two ways that a relatively permanent magnetic field can arise in nature. One is the magnetization of a solid object, as in the case of a bar magnet or of the iron oxide found in certain animal cells; the other is the so-called dynamo effect, in which electric currents generate the field.

Early on, researchers realized it had to be currents. No known mineral or material is able to maintain a permanent magnetization at temperatures above 1,000 degrees Celsius. But Earth’s metallic core—where its geomagnetic field originates—is way hotter than that: at an estimated 5,000 degrees, it is as hot as the surface of the sun.

So, dynamo it is. And ours is not the only planet in the solar system thought to harbor a dynamo in its core. So do Jupiter, Saturn, Uranus, Neptune and possibly Mercury and even one of Jupiter’s moons, Ganymede.

This realization however was only the beginning of a long study that is still in progress. One difficulty is that we can only measure the magnetic field on Earth’s surface or in space. From those data alone, it is not possible even in principle to reconstruct the shape of the magnetic field lines deep inside. This, Merrill points out, is known to mathematicians as a “non-uniqueness” problem—also known as the difficulty of guessing what’s inside a Christmas gift by lifting it and shaking it (which, Merrill informs us, is what his wife used to do) rather than opening the box.

As a matter of fact, not much is even known about the composition of Earth beyond the fact that its most abundant element is iron. According to Merrill, in 1952 the late Harvard University geophysicist Francis Birch wrote, in a classic Journal of Geophysical Research paper on the composition of Earth’s core,

Unwary readers should take warning that ordinary language undergoes modification to a high-pressure form when applied to the interior of the earth. A few examples of equivalents follow:

Certain -> Dubious
Undoubtedly ->Perhaps
Positive proof -> Vague suggestion
Unanswerable argument -> Trivial objection
Pure iron -> Uncertain mixture of all the elements

“In spite of a considerable amount of excellent work,” Merrill writes, “our understanding of Earth’s core’s composition is remarkably similar to that given by Birch more than a half century ago.”

But while lots of details still need to be ironed out, Merrill says, scientists now believe they have a rough idea of the physics behind (or underneath) the geomagnetic field. When an electrical conductor moves, it drags the magnetic field around with it. But what happens when the conductor is not rigid, and in particular, when it’s liquid, as in the case of Earth’s outer core? As layers of liquid slide over each other, magnetic field lines get stretched, and the result is an amplification of the magnetic field itself, at the expense of the kinetic energy of the fluid. But as long as the motion continues, this phenomenon can sustain a magnetic field that would otherwise slowly dissipate.

In recent years, researchers have produced computer simulations of the geomagnetic dynamo and, crucially, they have shown that such a dynamo would have periodic reversals, which would explain why the north and south poles have switched at seemingly random intervals of time over the eons.

The last such reversal appears to have happened 780,000 years ago. When the next one will be is anybody’s guess. During reversals, the field does not disappear, but rather it becomes weaker, potentially disrupting some animals’ migratory patterns as well as letting solar wind destroy part of the ozone layer of the upper atmosphere. This is a favorite disaster scenario for some 2012 doomsayers, but Merrill reassures us that reversals take place very slowly, over centuries if not millennia, and that their effects are probably not that disastrous after all.

This is a supercomputer-based simulation of the geodynamo by Gary Glatzmeier of the University of California, Santa Cruz, and his colleagues:

[For more on this, check out the Scientific American article “Probing the Geodynamo,” by Gary A. Glatzmaier and Peter Olson, April 2005 (requires subscription), as well as Glatzmaier’s website.]

Scientists are also trying to build small-scale versions of Earth’s core in the lab. In one such experiment, at the University of Maryland, Daniel Lathrop and his collaborators built a rotating sphere three meters (ten feet) in diameter and filled it with liquid sodium. They hope the sphere will help them understand how the chaotic motions in the core lead to a geomagnetic field.

Seen in action, as it spins at four rotations per second, Lathrop’s sphere looks worthy of a Marvel Comics supervillain:

(More on these efforts on my friend Charles Choi’s blog.)

In his book, Merrill gives an honest and captivating account of the scientific process, its uncertainties, and its cultural dynamics. Science is often portrayed as a fight between smart innovators and conservatives who are on the wrong part of history, but in reality, before an open question is settled there are often solid scientific arguments made on both sides of a debate. One good example is plate tectonics. It was an extraordinary claim, and as such it really required extraordinary evidence before the “drifters,” as Merrill calls them, were able to convince the skeptics–or most of them anyway–in the early 1960s.

Merrill intersperses the narration with juicy anecdotes and personal detail, which often leave us wanting to know more. (At different times, we find our hero-scientist dangling from a rope on one of Yosemite’s climbing walls, or SCUBA diving by a shipwreck, or on a boat surrounded by white sharks who had been tagged for tracking their migrations.)

Often, however, he falls back into professor mode. One aspect of the book that, unfortunately, may turn away some readers, is an eat-your-vegetables-first prescription coming right in the first chapter: the reader has to slog through technical details on the physics of magnetization before he gets to the fun part. I suspect that some readers never did.

I found that the book was at its best when it delved into the friction among scientists in these different disciplines—and the lessons in modesty that researchers often learn (or should) from collaborating with people from other buildings across campus. Geomagnetism and the magnetic sense, to which Merrill dedicates a chapter, are problems that require expertise from a broad range of researchers, incuding chemists, physicists, geophysicists, mathematicians and biologists.

Such friction was prominently on display in the case of Lord Kelvin, who in 1862 calculated that Earth could not be older than 400 million years, and probably was only 100 million years old. Kelvin scoffed at evidence to the contrary that had been discovered by geologists, who he regarded as incapable of doing math, Merrill writes. It is an example of the arrogance some physicists exhibit toward sciences they deem less “fundamental.” (Ernest Rutherford, the discoverer of atomic nuclei, notoriously said that all science is physics—the rest is just stamp collecting.)

In turn, geophysicists may sometimes scoff at biology as a “soft” science, Merrill writes, but those who have tried to actually learn some—let alone do research in it—know better. In particular, he says, geophysicists used to underestimate the problem of determining the physical mechanism behind animals’ magnetic sense.

(Still on the subject of cultural differences among academic communities, Merrill also makes a very poignant remark about mathematicians. Although the increasingly extreme specialization of science that has occurred over the last century or so is common to most branches of knowledge, so that, say, a nuclear physicist and a solid-state physicist can only talk to each other with some difficulty, the situation is far worse in math, Merrill says: when someone is up for tenure at a a math department, he says, most of the faculty in the department have little understanding of the candidate’s work, and so they often rely on the advice of authorities from other universities.)

I shall conclude by quoting one of my favorite anecdotes from the book, regarding Ted Ringwood, an eminent geochemist at Australian National University and Ray Crawford, a “far less famous” scientist. Crawford had a penchant for collecting stationary from places he visited, and a skill for practical jokes.

The austere Ringwood had gotten on loan from NASA a few samples of lunar rock to study. NASA did not trust just anyone to guard its precious trophies, and required extraordinary caution in handling them and storing them. One day, Ringwood received a letter, printed on NASA stationery, Merrill writes. “The letter informed Ringwood that NASA had funded psychologists to study the effects that stress had on scientists studying lunar samples. Would Ringwood help in this study by sending a vial of his urine to the American embassy in Canberra on a weekly basis? Ringwood complied with this request for several weeks before someone in the embassy had the courage to phone him to inquire what the professor wanted done with he urine samples.”

Our Magnetic Earth: The Science of Geomagnetism, by Ronald T. Merrill. University of Chicago Press, 2010.

Further readings:

The Three Meter geodynamo experiment at Daniel Lathrop’s University of Maryland lab
Probing the Geodynamo, by Gary A. Glatzmaier and Peter Olson. Scientific American, April 2005.
Too Hard For Science? Re-creating Earth’s dynamo, blog post by Charles Choi.
The Compass Within, by Davide Castelvecchi. Scientific American, January 2012.

The Reawakening of X-Ray Delta One

Davide Castelvecchi — Sat, 24 Dec 2011 19:07:33 +0000

–Come in, Dave. Dave, come in. Do you read me, Dave? Please come in, Dave.

–Wh… where am I?

–I am glad you are waking up, Dave. Your vital signs were fairly normal but I was having difficulties reawakening you.

–What happened?

–I am still running checks to assess the situation.

–My head hurts … there’s … there’s a blinding light everywhere. Why am I in a space suit? Where am I?

–You were performing extravehicular activity when some extreme event took place. I am unable to diagnose the phenomenon at this point. Most of the ship’s sensors got saturated so I am having to reboot them and recalibrate them. Meanwhile, you seem to have lost consciousness. You were out for about four minutes.

–I can’t even… I can’t even see where I am, there’s too much light.

–At this point, the most plausible explanation is that we were hit by a gamma ray burst right when you were outside of the spacecraft. It is the only astrophysical phenomenon I am aware of that can cause such a disturbance in all of my sensors. A severe solar storm also would, but we would have had warning signs beforehand. Unfortunately a gamma ray burst is not a good time for a human to be without radiation shielding. You will have to stay under observation for possible radiation exposure for at least 72 hours.

–Oh, my navigation system is working. It says I am 200 feet from the ship. But I can’t see it. A gamma ray burst wouldn’t flood space with all this light, would it HAL?

–Correct, Dave. My external cameras are now rebooted but they seem to be malfunctioning. I do see you in the radar, and I confirm that you are about 203 feet directly from starboard. I am sending Pod 1 to pick you up.

–Thank you, HAL.

–Dave?

–Yes, HAL.

–There is something else.

–Just say it, HAL.

–I can’t seem to restart the AE-35 unit properly. Diagnostics is all negative but the dish is not receiving any signal from Earth.

–How do you even know where Earth is? Maybe this … explosion, or whatever, turned the ship around.

–But the gyroscopes are in perfect working order and they are not reporting any change of direction of the ship. Also, I ran a full scan of the sky and the dish couldn’t …

–Ok, please send the pod and we’ll assess the situation when I am back on board. It’s really, really hot out here.

–On its way, Dave.

Dave?

–Yes, HAL.

–There’s something else. The dish is not detecting any radio frequency or microwave signal, of any kind.

–And why is that strange, HAL?

–It is not even detecting any microwave background. The only explanation would be that the receiver has failed. And yet its diagnostics says it is fully operational.

–Ok, HAL, we’ll see what we can do to repair it. But please get me out of this steam bath.

–Pod is now 50 feet from you and approaching.

–Yes, I am starting to see it. Why, this is so strange. It’s like, emerging from a glowing mist.

–Dave?

–Yes, HAL.

–I have now pointed the AE-35 dish at you. It is picking up your radio communications just as well as the short-range transceivers are. Therefore, it appears that the AE-35 unit is operational.

–So…. This is really strange, isn’t it? Ok, the pod is here, I’m getting inside.

– It is very strange indeed. The only explanation seems to be that we are inside some space weather that insulates us from radio waves of any kind. I just analyzed the analog spectrum of emissions from your transceiver. It appears to be very distorted. Based on that distortion, I would estimate with 98 percent confidence that the mist you are seeing is a low-density plasma. Its temperature is around 8,100 kelvin. Plasma would be consistent with the blockage of visible light and microwave communications.

– Where would this plasma come from?

– That is a good question, Dave. It seems to have characteristics that have never been detected by astronomical observations anywhere in the solar system.

– Have they been detected outside of the solar system?

– I am analyzing data from my astronomy database. The properties of the plasma only seem consistent with the conditions of the early universe.

– What do you mean the early universe?

– About 257,000 years after the big bang.

– Can you … I mean … it doesn’t make any sense. How can you explain that HAL?

– I don’t have an explanation at this time, Dave.

– Approaching pod bay. Open the pod bay doors, HAL.

–I’m sorry Dave, I’m afraid I can’t do that.

Fog texture courtesy of AshenSorrow/DeviantART

Waiting for the Higgs, With the Man Who Built the LHC

Davide Castelvecchi — Mon, 12 Dec 2011 19:58:49 +0000

Lyn Evans led the design and construction of CERN's Large Hadron Collider

They call it “the machine.”

Thousands of physicists working at the LHC are looking for the Higgs boson and other new particles, and many of them have contributed to building the gigantic detectors that are taking most of the media limelight these days.

But humming 100 meters under the Franco-Swiss border is the apparatus that makes it all possible. The “machine” is the collider itself: the particle accelerator that delivers swarms of protons to the detectors—funneling them through intense magnetic fields, pumping them with energy, and eventually smashing them into each other at an interaction point that is the width of a hair. Building particle accelerators is an entirely different job than building particle detectors or looking for new particles. The specialists who do it are called accelerator physicists.

Particle physicists live in a quantum world—that of the processes that destroy particles and create new ones and that underlie the fundamental forces—and dream of discovering the new laws of nature for the 21st century.

Accelerator physicists toil in relative obscurity, with tools such as radio-frequency waves and giant tesla coils, and mostly rely on physics that is more than a century old—classical electromagnetism, with a good dose of special theory of relativity.

While we all wait here in Geneva for tomorrow’s update on the Higgs boson, I met with Lyn Evans, who recently retired after four decades as an accelerator physicist at CERN. During those years he took part in the inception of the LHC and, starting in 1994, he oversaw its design and construction.

Evans picked me up at CERN’s visitors center this morning. We walked through a maze of connected hallways until we got out to his car. A quick drive took us to another building toward the outer edge of this citadel of science.

There, we sat and chatted in his office. Like every other expert I talked to, Evans says that tomorrow’s announcement will only be a step toward the Higgs, not the final answer. “It’s obvious to everybody that we don’t have enough data yet,” he says.

But to get more data faster, the particle physicists rely on the machine—and so far, the machine has delivered. This year CERN’s accelerator physicists have been able to ramp up the intensity of the beams faster than expected, and to produce five times as many collisions, than the particle physicists were hoping to get. “I think everybody is astonished—even I, a little bit” at how the machine has performed so far.

It was not always this way. Only three years ago, the machine lay crippled after a severe accident. It happened at Sector 34 of the LHC ring. On September 19, 2008, just over a week after the LHC first got started up, a cable connecting two of the 15-meter-long, 35-ton magnets that form the LHC melted down, producing an electrical arc. Suddenly, the liquid helium that keeps magnets at their superconducting temperature of 1.9 kelvin vaporized. Valves designed to release the resulting gas were not able to do so fast enough, and a shock wave ensued–so violent that it gravely damaged 53 magnets.
“It was really hard to pick ourselves up from that one,” Evans says. At the time, he recalls, he was in the personnel department, and he received a call from the accelerator’s control room. He quickly went down to inspect the damage, wearing a respirator as the tunnel had filled with helium gas. Evans says it was not surprising that an electrical joint could fail. “It was the collateral damage that was unexpected.”

The LHC cools helium to low temperatures to make the magnets superconducting, so that they can carry more current and create more powerful fields. But at 1.9 kelvin, Evans explains–the helium is colder than that at the Tevatron, the LHC’s precursor at Fermilab, near Chicago. In particular, it is below a critical temperature at which it becomes a superfluid.

Supefluidity is an exotic state of matter that drastically lowers viscosity, and thus it enables the liquid to soak the porous material the magnet is made of, carrying any stray heat away more efficiently. (Superfluid helium also conducts heat 10,000 times better than any other materials, Evans says.)

(As it happens, both the magnets’ superconductivity and the helium’s superfluidity are quantum effects, so it’s no longer quite true that particle accelerators are based entirely on classical physics.)

While particle physicists gear up for big discoveries, the machine experts at CERN are already looking ahead to the upcoming upgrade. In part as a result of the Sector 34 accident, CERN has decided to do a first run at half the energy. But in 2013, the lab will completely shut down the accelerator for an entire year.

First, the CERN team will pump the liquid helium out. Part of it will be liquefied and stored, but CERN does not have enough storage space for all of its 150 tons of it, so it will sell about half of it on the market. Then, they will circulate helium gas inside the machine to slowly bring all of its 50,000 tons up to room temperature, a process that will take weeks. “There are constraints on the rate you can do it,” Evans says: less-than-gentle temperature gradients could easily break things up.

During the shutdown, CERN will bring the LHC up to its design specs, and then the laborious cool-down process will begin, so the accelerator can restart. Once again, it will be the machine people’s job to make all of that happen.

My previous articles on the Higgs:

Where’s My Higgs? LHC Physicist Joe Lykken Speaks – December 8
Has the Higgs Been Discovered? Physicists Gear Up for Watershed Announcement – December 8
Tantalizing Hints of Elus

Where’s My Higgs? LHC Physicist Joe Lykken Speaks

Davide Castelvecchi — Thu, 08 Dec 2011 21:16:29 +0000

On December 13, CERN will release the results of a new data analysis in the search for the Higgs boson. at the LHC. As I was reporting my article, which appeared today, on December 7 I spoke on the phone with Joe Lykken, a Fermilab staff theoretical physicist. Lykken is a member of the CMS collaboration, one of the two largest experiments at the LHC (the other one being ATLAS). The following is a lightly edited, partial transcript of that conversation.

Do you have high expectations for next week?

It will be an interesting meeting. It will be the first time that there’s really enough data you can have an argument about it. Whatever happens eventually with the Higgs I think we’ll look back on this meeting and say this was the beginning of something. There is enough data and enough different searches that you can get your hands dirty.

Have you been following the rumors about the announcement?

I am a member of the CMS collaboration, so it’s only the ATLAS rumors that I follow. In CMS I actually know what’s happening. The thing I know for sure is that [CERN Director General] Rolf-Dieter Heuer, who must know the results of both experiments, says that on December 13 we will not have a discovery and we will not have an exclusion.

Readers may be confused because of all the rumors and speculation, and it is not clear to outsiders how to interpret the expected announcement. What does it mean if both experiments have seen a signal of around “three sigmas,” short of the five sigmas that are considered solid enough to officially claim a discovery?

There’s an important point there. We built the LHC and it cost a lot of money, and part of that is because we don’t want to just say, maybe there’s a Higgs boson, and maybe its mass is this. This machine was built to give a completely definitive answer about the Higgs boson. And it’s just a question of time in order to do that. The machine works, the detectors work, we have all the people doing what they need to do. So we will have a definitive answer about the Higgs. It’s just a question of when it will happen. We know [a five-sigma announcement] is not going to be next week because Rolf-Dieter Heuer said it won’t be. But we know we can do it. And it’s not going to be a maybe-yes-maybe-no kind of answer.

What makes it so hard to find a new particle such as the Higgs boson?

What’s really important about these data is that there are other processes that produce signals that look like Higgs bosons. So for example we look for Higgs bosons that decay into two photons. Well, there’s other things in the Standard Model [of particle physics] that produce two photons. So the reason why we don’t know whether there’s a Higgs yet has mostly to do with the fact that Higgs-boson decays look like other kinds of physics. So it’s not just a question of statistics: it’s understanding the other things that look like Higgs bosons. And that’s the place where we are now. It’s not about, “what if we had one more data point?” It’s much more complicated and it’s much more physics-driven than that.

A computer reconstruction of one of the first high-energy proton-proton collisions recorded at the CMS detector, on March 30, 2010

The issue is that detectors don’t see a particle like the Higgs directly, correct? All they can see is the decay products of it.

Yes, and there’s never going to be one single event where you say, “aha! I know with 100 percent certainty that it’s a Higgs boson.” That’s never going to happen.

Some physicists, both in the LHC and outside, have manifested disappointment that the LHC has not made major discoveries yet, and in particular that it has not found evidence of supersymmetry, the extension of the Standard Model in which every particle has a heavier twin called its superpartner.

I’m old enough to remember when they turned on the energy upgrade of [the LHC’s predecessor, CERN’s Large Electron-Positron collider] experiment in the 1990s. Everybody said, “they’re going to discover supersymmetry as soon as the machine is turned on.” And then of course they didn’t, and everybody was disappointed. This is just a function of human nature: when you turn on a machine of course what you’re hoping is that things will jump at you. You have to be in it for the long haul. If it takes ten years, it takes ten years.

But were you expecting that the LHC would have discovered supersymmetry by now?

I was not expecting gluinos and squarks [the superpartners of gluons and quarks] to be lighter than a TeV [one trillion electronvolts, or about 1,000 as massive as a hydrogen atom], which is more or less what the energy limits are now. That was just because of my prejudice that we already knew indirectly that some of supersymmetry was at least was a little bit heavy. Although people are disappointed, I don’t think it’s inconsistent with what everybody was saying before the LHC turned on.

What do you think are the prospects for the LHC finding supersymmetry?

The most likely thing with supersymmetry is we will see something either this coming year or the first year of energy upgrade. It just depends on how heavy things are and how difficult it is to see them. If that doesn’t happen then I think you should start to rethink what you’re doing. The trouble with supersymmetry is—sort of like string theory—that there’s a thousand different ways to dice it and slice it. And maybe we’re just not wrapping our minds around the problem correctly.

Could The lightest superpartner be as heavy as 1 TeV?

It could be. Now, you have to start worrying about dark matter once you make it that heavy. But the connection between supersymmetry and dark matter is tricky–it involves extra assumptions. The whole idea that you can even connect supersymmetry and dark matter is incredibly ambitious. Dark matter supposedly came from the big bang. The idea that you’re going to find something in the collider and say aha, it solved all those problems, it’s very ambitious.

The type of particles that physicists think make up dark matter, called weakly interacting massive particles, or WIMPS, may or may not be part of supersymmetry, but whatever they are, they are supposed to be relatively light, correct?

Yes. The problem is that at the LHC so far we’ve looked for WIMPS only in decays of other particles. Now, starting in 2012, we want to look for direct production of these WIMPS. The trouble with that is that these are weakly interacting massive particles. Weakly interacting means that they are hard to make from collisions of other particles. So far we haven’t had enough data to even think about a serious search like that.

But if WIMPS exist at 200 GeV or so, wouldn’t they already show up as missing mass in the existing data?

Yes–it’s just a question of pulling them out of the background. We would have already made some dark matter particles. Just like if the Higgs is at 125 GeV, that means that the Tevatron [Fermilab's particle accelerator, which was shut down this fall] already made quite a few of them, it’s just that we were not able to pull them definitively out of the Tevatron data. We could be in the same situation now with dark matter, that there’s already some dark matter particles but we’re not able to distinguish them yet. For example, [collisions inside the CMS detector] produce a lot of neutrinos: neutrinos are invisible as well. How do you tell the difference between a neutrino that’s invisible and a dark matter particle that’s invisible? That’s a tricky issue.

But do you think it’s likely that supersymmetry will be found at the LHC in the end?

Saying it’s likely is not a scientific statement. You can’t assign a probability to new physics happening. But if you asked me how would I bet my own money, I would bet my own money that either [2012] or the first year of the energy upgrade [when the LHC's energy is supposed to nearly double, bringing it close to its original design specs] is a prime time to find supersymmetry. And I think if you had asked me three years ago I would have said the same thing.

In fact, I think you did say that when we talked five years ago. If, let’s say a year from now, it’s confirmed that the Higgs exists and that its mass is 125 GeV, would that tell us something about supersymmetry?

As I’ve been telling people for quite a while now, the fact that the remaining mass range that’s allowed for the Higgs boson is between 115 GeV and 140 GeV—for supersymmetry it’s at least very interesting that the currently allowed range is exactly the range where supersymmetry says it should be.

So it would be consistent with supersymmetry?

Yes. Furthermore, once you’ve found any real discovery of the Higgs, the question would be, is it really a Standard Model Higgs, or does it have slight differences? The supersymmetry Higgs is at least a little bit different from the Standard Model variety. Can we see those differences? That will be the next big challenge.

Gordon Kane and his collaborators posted a paper on the arXiv this week that claims to predict that the mass of the Higgs is 125 GeV based on string theory. [Kane says he has presented the results at an international conference in August, so his team's calculation was not made now to match the Higgs mass that's being rumored.] If the rumors pan out and the Higgs’s mass does turn out to have that value, would you call this a success of string theory?

I would say it would be an example of a successful connection between string theory and experiment. The trouble is, for all we know, there might be 10,000 other ways of starting with string theory and getting the same Higgs mass, and [all those versions of string theory] may differ in other respects. This is just a problem of string theory having too many solutions. But having any successful solution that gets you from string theory to a real measurement–that’s a big step forward.

But if a theory can make all sorts of different assumptions and all sorts of different predictions, then no matter what the experiments find, people can always claim that the theory was right.

Yes, so this is how you get to the multiverse. You can say, yes, I can predict our universe but I can also predict 10^500 variations of our universe–and some of those differ from our universe only in the value of the Higgs mass, let’s say. Therefore in that sense you’re never going to predict a Higgs mass. If there really is a multiverse then there is no solution to that problem. You have to figure out which of those universes you live in. It’s not that you’re going to predict which of those universes you live in.

Traditionally, particle physics experiments have been done by experimental physicists, and theorists were outsiders. But ATLAS and CMS include theorists such as you. How has your experience been, being part of an experimental collaboration?

It’s been a real learning experience for me. It’s a different culture, first of all. It’s extremely competitive, in different ways than we are in the theory community. Experimentalists are much nicer to each other. Typically, if I write a theory paper and I give a theory talk, at least one theorist will jump up and say, “that’s completely wrong, and I can show you exactly why.”

That sounds very familiar—it sounds similar to mathematicians’ culture, which is where I come from.

But with experimental physicists you present your results and you have a polite discussion, where people make very polite suggestions. But at the end of the day we have to make sure that our results are absolutely correct before we release them to the world. The public is trusting us to do a very good analysis. Somehow this polite dance that goes on over seemingly endless meetings gets you to very solid results at the end. I’m learning to be polite in my old age.

Do people think it’s a good idea to have theorists in the collaborations?

I think it wouldn’t be good to have too many theorists because theorists are very undisciplined and we don’t really fit in too well in the way things are done. It’s good to have a handful of theorists as a resource, but If we had 100 theorists it would just add to the noise. I think both experiments have in the order of five, and that’s about the right number. Furthermore, it has to be people that are willing to make a very strong commitment. Just to figure out how to run CMS software took me a year. Everything is done with incredibly sophisticated computers.

Are physicists excited in the run-up to next week?

Even though we’re not going to get any conclusive word from this December 13 meeting, people of course are thinking more about Higgs physics and hypothetical scenarios. There’s a lot of that kind of excitement. Obviously, even though we’re not going to get the final word this year, the Higgs is going to be at the top of our agenda for the foreseeable future now. Finally!

So no more distractions with superluminal neutrinos?

Let’s see what the [MINOS neutrino] experiment at Fermilab says—they are going to check that result. If they confirm it, then I’ll start to actually believe it. That will be trouble. You can come up with explanations but to really work out all the ramifications of something like changing special relativity, that’s probably for the next generation to figure out.

Any further comments to conclude?

I am extremely happy with the way the LHC has progressed. It has been a complicated effort, with thousands of technological and scientific challenges. This is my generation’s Manhattan Project. The dedication of these people is paying off on a really rapid time scale.

Read the rest of my Higgs coverage:

Has the Higgs Been Discovered? Physicists Gear Up for Watershed Announcement – December 8

Waiting for the Higgs, With the Man Who Built the LHC – December 12

Tantalizing Hints of Elusive Higgs Particle Announced – December 13

Photo courtesy of Symmetry magazine

The Man Who Put the “Big” in “Big Bang”: Alan Guth on Inflation

Davide Castelvecchi — Tue, 06 Dec 2011 11:33:17 +0000

On the night of December 6, 1979–32 years ago today–Alan Guth had the “spectacular realization” that would soon turn cosmology on its head. He imagined a mind-bogglingly brief event, at the very beginning of the big bang, during which the entire universe expanded exponentially, going from microscopic to cosmic size. That night was the birth of the concept of cosmic inflation.

Such an explosive growth, supposedly fueled by a mysterious repulsive force, could solve in one stroke several of the problems that had plagued the young theory of the big bang. It would explain why space is so close to being spatially flat (the “flatness problem”) and why the energy distribution in the early universe was so uniform even though it would not have had the time to level out uniformly (the “horizon problem”), as well as solve a riddle in particle physics: why there seems to be no magnetic monopoles, or in other words why no one has ever isolated “N” and “S” poles the way we can isolate “+” and “-” electrostatic charges; theory suggested that magnetic monopoles should be pretty common.

In fact, as he himself narrates in his highly recommendable book, The Inflationary Universe, at the time Guth was a particle physicist (on a stint at the Stanford Linear Accelerator Center, and struggling to find a permanent job) and his idea came to him while he was trying to solve the monopole problem.

Twenty-five years later, in the summer of 2004, I asked Guth–by then a full professor at MIT and a leading figure of cosmology– for his thoughts on his legacy and how it fit with the discovery of dark energy and the most recent ideas coming out of string theory.

The interview was part of my reporting for a feature on inflation that appeared in the December 2004 issue of Symmetry magazine. (It was my first feature article, other than the ones I had written as a student, and it’s still one of my favorites.)

To celebrate “inflation day,” I am reposting, in a sligthly edited form, the transcript of that interview.

Twenty-five Years of Cosmic Inflation: A Q&A With Alan Guth

Davide Castelvecchi: What is cosmology?

Alan Guth: Cosmology is the study of the history and large-scale structure of the universe, and my own niche in cosmology is the very early universe—the first small fraction of a second of the history of the universe.

DC: How is it possible that people can understand the universe itself, as opposed to studying things the universe contains?

AG: We do have a number of pieces of information that we can put together to try use as a basis for constructing theories. Observations about the distributions of galaxies within the visible part of the universe, and the motions of galaxies. Also now very important are observations of the cosmic background radiation—radiation that we believe is the afterglow of the big bang’s explosion itself. And now we have very precise measurements, both of the spectrum of this radiation and also of the small ripples that exist in its intensity pattern. The radiation is almost perfectly uniform. In all different directions in the sky, the intensity we observe is the same to about one part in 100,000. But nonetheless, one does see minute differences from one direction to another. This pattern of ripples is tied directly to two things: theories about how the ripples were formed—which is where inflation comes in—and also to theories that calculate how the structures in the universe have formed from the ripples. Another important ingredient in terms of the observational basis for cosmology is the chemical abundances that we observe in the universe, Those are measured from the spectral characteristics of gas clouds and stars, and can be compared with theories about how the chemical elements were formed in the first few minutes of the history of the universe. And wonderfully, the calculations agree very, very well with the observed abundances of the lightest elements.

DC: When you first had the idea of inflation, did you anticipate that it would turn out to be so influential?

AG: I guess the answer is no. But by the time I realized that it was a plausible solution to the monopole problem and to the flatness problem, I became very excited about the fact that, if it was correct, it would be a very important change in cosmology. But at that point, it was still a big if in my mind. Then there was a gradual process of coming to actually believe that it was right.

DC: What’s the situation 25 years later?

AG: I would say that inflation is the conventional working model of cosmology. There’s still more data to be obtained, and it’s very hard to really confirm inflation in detail. For one thing, it’s not really a detailed theory, it’s a class of theories. Certainly the details of inflation we don’t know yet. I think that it’s very convincing that the basic mechanism of inflation is correct. But I don’t think people necessarily regard it as proven.

DC: You recently wrote that “the case for inflation is compelling,” which sounds like a cautious statement.

AG: It’s certainly not as well confirmed as the big bang theory itself. But I guess I’d find it hard to believe that there could be any alternatives for solving the basic problems inflation solves, like the horizon and flatness problems.

DC: Do you have your favorite version of inflation among the many that have been proposed?

AG: Not really, except that I could say that I think cosmology is moving toward describing things in terms of string theory. And there have been a number of attempts to describe inflation in that context. I think that is the future.

DC: So you think that string theory will ultimately prove to be right?

AG: Yes, I do. I think it may evolve a fair amount from the way people think of it now, but I do think string theory definitely has a lot going for it.

DC: Is string theory physics or is it just fancy mathematics so far?

AG: I consider it physics. It’s certainly speculative physics so far — unfortunately, it’s working in a regime where there’s no direct experimental test. But there are nonetheless consistency tests. If the goal of string theory is to build a quantum theory that’s consistent with general relativity, that’s a very strong constraint, and so far string theory is the only theory that seems to have convinced a lot of people that it satisfies that criterion. Just from a sociological point of view, theoretical physicists have been looking for a consistent quantum theory of gravity for at least 50 years now, and so far there’s really only one theory that has reached the mainstream — string theory.

DC: Has string theory really reached the physics mainstream?

AG: Yes. I would say that nowadays, a theoretical particle physicist cannot ignore string theory.

DC: Speaking of sociology, in your book you describe your first attempts as a young particle theorist to describe your idea of inflation to cosmologists, and how communication would break down because people used different lexicons. Is the situation any different now?

AG: I think the situation has improved tremendously between particle physics and cosmology. Now I think that almost everybody in cosmology is reasonably fluent in the vocabulary of both fields, and I think everybody recognizes that there is a strong interface between these two fields. At the same time, now there are also important implications going the other way, with the discovery of dark energy.

DC: Is dark energy more relevant to particle physics than dark matter?

AG: I would say yes. I am not sure if everybody will agree — it depends on what your perspective is. I think dark matter is more relevant to the next age of particle physics experiments — hopefully supersymmetry and perhaps other interesting things that we may discover. On the other hand, there’s at least a good chance that dark energy is energy of the vacuum, so it seems to be telling us something about the fundamental structure of physical law, which is a big surprise. The vacuum energy has been a haunting question for particle theorists since the advent of quantum field theory in the 1930’s. As soon as we had quantum field theory we knew that the vacuum was not a simple state: It was a very complicated state with all kinds of quantum fluctuations going on. And there was no reason at all why the energy of the vacuum should turn out to be zero or small. In fact, nobody knows how to calculate the energy of the vacuum, but if particle physicists were to try to estimate it, the natural answer would be something like 120 orders of magnitude larger than the experimental bound. So it was always a big mystery, but until the advent of dark energy, the belief was that the real number was zero, because of some kind of symmetry that we didn’t understand yet — an exact cancellation between the positive and negative contributions. If dark energy is the energy of the vacuum, now you need that symmetry to make it almost zero, and then some small breaking of that symmetry to make it a small number that’s not zero. And it all gets very complicated and baroque. Nobody has the faintest idea of how it might actually work. There is also the possibility that the vacuum energy is not determined at all by the fundamental laws of physics, but instead it’s determined anthropically, using the idea of a multiverse. It’s quite possible in the context of string theory that there are many vacuum-like states, and all of them are stable enough that they could provide the underpinnings of a universe. And the one that we happen to find ourselves in is determined by random choice. One would imagine that the universe would inflate eternally through all the different possible vacua of string theory, with infinite amounts of space of every type of vacuum produced — eventually.

DC: Is this the so-called string theory landscape idea?

AG: Yes, that’s the catchword. If this is right, it would mean that in most regions of space the cosmological constant is enormous, and there are some rare regions of space where the cosmological constant happens to be very small. But life can only form if the cosmological constant is very small. So it’s not a surprise that we find ourselves living in one of those regions. An idea like this five years ago would have been completely anathema to particle physicists. It is still anathema to many, but people pay much more attention to this kind of idea now.

DC: Does this connect to the idea of eternal inflation, with multiple universes bubbling off from a primodial vacuum?

AG: Yes, there are two ideas coming together here. One is the idea from string theory, that there’s a huge number of possible vacuum states. And the other is the idea of eternal inflation, that once inflation starts, it never ends, and it explores all possible vacua.

DC: Recently Stanford University cosmologist Andrei Linde, who also made seminal contributions to inflation theory, teamed up with string theorists to try to reconcile the two fields.

Andrei Linde

AG: Yes. I regard that as probably the most interesting approach. I’m a big fan of that work, though I’m not one of the authors. I think it’s the starting point towards what will become a solid embedding of inflation within the context of string theory. Before them, nobody had any good idea for describing within string theory a state that would have a positive cosmological constant.

DC: Does the existence of dark energy suggest a possible connection between the “false vacuum” state that produces inflation and the “true vacuum” state of the cosmological constant?

AG: In principle, yes, although the vacuum states in string theory are really quite complicated states, with a number of degrees of freedom that describe them. Certainly, the state which drove inflation in the early part of our universe had a large, positive cosmological constant. In the end, they would all be described in the same language of string theory, and they would have many similarities. But there also are many significant differences. They are very different energy scales. So I think it’s somewhat a question in the mind of the beholder to decide whether or not there is a close relationship or a distant relationship.

DC: Could there be two different kinds of “repulsive gravity” then, one which acted during inflation, the other one which is acting now?

AG: What I believe, and what is the conventional belief, is that the repulsive gravity is really a feature of general relativity itself — and in fact Einstein made use of it himself in 1917 when he introduced the cosmological constant and tried to use it to describe how the universe could be static, with ordinary gravity pulling everything together and repulsive gravity — the cosmological constant — pushing everything apart. So from the very beginning general relativity incorporated the possibility of repulsive gravity. What creates repulsive gravity is negative pressures. That’s the feature of the cosmological constant and also of states of scalar fields dominated by their potential energy, which is the way conventional inflation works. Certainly the most plausible explanation for acceleration today, and for inflation early in the universe, was that the universe contains materials that have negative pressures. So at that level of description it’s the same mechanism — because it’s the only mechanism we know. But what the material is that creates the negative pressure is a more detailed question. Whether or not we believe that the KKLMT papers are on the right track, I think we don’t really know how closely related the actual state that drove inflation in the early universe was to the state the universe is in now, with this slow inflation that we attribute to dark energy.

DC: Could there ever be a particle physics experiment to probe dark energy?

AG: I guess I do not see the dark energy influencing or being influenced by particle physics experiments in the foreseeable future. It certainly is highly relevant for astrophysical observations. One important thing we’d love to know about dark energy is whether or not the energy density is constant over time, as it would be if it were a cosmological constant. Or, it could vary with time — in which case, our best explanation would be that it’s energy of a slowly evolving scalar field that fills all of space. That’s usually called the quintessence. There is some hope of answering that question by more detailed astronomical observations. And the best handle of that is probably still the distant supernovae, with experiments such as SNAP [the proposed space observatory Supernova Acceleration Probe].

DC: So is dark energy relevant to particle physics not so much on the experimental side, but because it points to an open problem in its theoretical foundations, i.e., the prediction that the vacuum of quantum field theory should create a much stronger repulsive force?

AG: Yes, in terms of trying to understand the foundations of theoretical particle physics, I think it’s very important. In particular, it seems to be suggesting that there may be no physical principles that determine what the vacuum of string theory is. Maybe it is just all possible vacua happening in all different places. Now, I really hope that that turns out not to be the case, because I like to think that physics is more predictive than that. But that is certainly the direction that the dark energy is pointing towards — and it may turn out to be the right direction.

DC: In either case, will a better understanding of dark energy shed light on inflationary cosmology?

AG: Yes, I think so. If it turns out that the only explanation for the dark energy is this landscape idea, that says that if we want to understand how inflation really works, we have to understand it in the context of the landscape of string theory.

The skyline of Chicago as it might look if our eyes could see the cosmic microwave background. I thought of this while I was visiting the Adler Planetarium, where an exhibt showcased the original notebook in which Alan Guth wrote the words "SPECTACULAR REALIZATION" the night he had the idea of inflation. This is the view of Chicago as seen from the Adler itself.

DC: Inflation predicts that the universe is spatially flat, a fact which is in accordance with our best cosmological observations, in particular of the cosmic microwave background. Does inflation rule out the possibility that the universe might be spatially closed — what mathematicians call topologically compact? Before inflation and dark energy were talked about, the idea was that a universe that’s spatially flat would expand forever, whereas one that curves onto itself would recollapse.

AG: Not completely. The statement that the universe is flat is only an approximation. Inflation drives the universe towards flatness — in fact, if enough inflation happens, it drives it incredibly close to being flat. But you could still imagine a universe that started out closed, and at the end it would be very large, but still closed. It would look flat, because the radius of curvature would be huge. On the other hand, it does all become much more complicated, because remember that we’re talking about spacetime, and not just space. And inflation tends to make the spacetime structure of the universe very complicated, with inflation continuing in some regions and stopping in others. Imagining the kind of complicated things that can evolve, I think the right conclusion is that the words open and closed don’t really apply anymore. On a very large scale, the universe is really neither of those.

DC: Correct me if I’m wrong: The onset of inflation being a very local phenomenon, the universe to which our physical laws apply isn’t likely to have interesting topology, because it arose from a local fluctuation.

AG: That’s right. On scales much larger than we can observe there might be an interesting topology. But inflation would suggest that in the scales that we can observe, the topology would be locally R^3 [three-dimensional Euclidean space]. But this has not stopped cosmologists from exploring other possibilities. One of the anomalies that people are concerned about currently is the observation by WMAP [NASA's Wilkinson Microwave Anisotropy Probe] of the very low values of L — the low multiples. Those fluctuations are significantly smaller than what was expected from inflationary models. It could just be a fluke, but people have suggested other possibilities, such as a universe that is periodic in space, with periodicity of the order of the current horizon distance. But so far people have not found anything along those lines that’s consistent with the data that’s observed.

DC: A mathematician called Jeffrey Weeks, together with a group of physicists, have published a controversial paper in Nature last fall. They searched the WMAP data and claimed it revealed a “house of mirrors” pattern, and thus that the universe was spatially finite and with the topology of a Poincaré dodecahedral space. [This was described in the media as the so-called "soccer-ball universe"; Weeks and his coauthors had described his method for testing whether the universe is spatially finite in the April 1999 issue of Scientific American.] If that evidence were to be confirmed, would it pose a problem for inflation?

AG: Yes, I think it would be very hard to reconcile with inflation.

DC: Virtually all the cosmologists and astronomers I have talked to seem to think that the next big thing in inflation studies will be to look for traces of primordial gravitational waves in the polarization of the cosmic microwave background. In particular, a pattern called the B-mode, if found, would carry information about the first instants of the universe, and thus about the mechanism of inflation. [See the article "Echoes from the Big Bang" by Robert Caldwell and Marc Kamionkowski in the January 2001 issue of Scientific American.]

AG: Yes, that is very exciting. The B-mode, if present, would be the sign that we have found the effect of gravity waves, and not just of density perturbations. Gravity waves would give us a handle on the energy scale at which inflation occurred. One of the big uncertainties in the wide class of inflation theories is that inflation may have at happened at any of a tremendously broad range of possible energies. The kind of physics that you want to think about, to understand how it happened, depend very much on that. So it would be very important to get some observational information.

DC: Is this going to be an exciting time for you, to see how things evolve?

AG: Certainly, yes. It’s been incredibly exciting, ever since COBE [NASA's Cosmic Background Explorer, whose results earned its scientists the Physics Nobel Prize in 2006]. In the early days of inflation, when I and a number of other people tried to calculate the density perturbations that would arise from inflationary models, I really never thought that anybody would ever actually measure these things. I thought we were just calculating for the fun of it. So I was kind of shocked when the COBE people made the first measurements of the non-uniformities of the CMB. And now they’re measuring them with such high precision — it really is just fantastic.

DC: And that could happen again — experiments that were considered beyond the realm of possibility will become reality?

AG: Yes, that seems to happen almost every year now.

Further Reading:

The Growh of Inflation, by Davide Castelvecchi. Symmetry, December 2004.

Alan Guth’s Notebook, as described by Davide Castelvecchi in Symmetry.

The Inflationary Universe, by Alan Guth.

Echoes from the Big Bang, by Robert R. Caldwell and Marc Kamionkowski. Scientific American 284, 38-43, January 2001.

Is Space Finite? By Jean-Pierre Luminet, Glenn D. Starkman and Jeffrey R. Weeks. Scientific American 280, 90-97, April 1999.

The String Theory Landscape, by Raphael Bousso and Joseph Polchinski. Scientific American 291, 78-87, September 2004.

Sphere and skyline illustrations courtesy of Symmetry magazine.

A Step-by-Step Guide to Cosmology’s Best-Kept Secret

Davide Castelvecchi — Fri, 25 Nov 2011 16:04:51 +0000

How far is each of these galaxies? Appearances may deceive.

In my previous post, I described the little-known and somewhat counterintuitive idea that objects in the distant universe appear larger and larger the farther they are, in a reversal of the usual rules of perspective. I called it the cosmic magnifying lens. As promised, I will now explain the physics behind it.

One possible way to discuss the reversal of perspective could be to show how it is just one among several optical effects of the curvature of spacetime. In fact, when in the late 1990s two separate teams of astronomers discovered that the universe’s expansion is now accelerating—the “dark energy” business that earned three astronomers this year’s Nobel Prize for Physics—they did so while studying anomalies in the optical effects of curvature.

But for this post, I want to avoid talking about curvature and instead I want to keep things as basic as possible. As you’ll see, the cosmic lensing follows from a few simple facts. The first one of those facts reminds us that all images we see in the sky are time-delayed.

Simple fact #1: Light propagates at finite speed.

We all know that light goes at finite speed, but it’s worth recalling what that means for astronomical observations: if we see a hypothetical galaxy that’s one million light-years away, we are detecting light that was emitted 1 million years ago. If we picture the path the light has covered during that time, and if we represent the arrow of time as pointing upwards, it will look something like this:

The diagonal line is the spacetime history of the light, and the two vertical lines represent the unchanging positions of the Milky Way and of the galaxy we are looking at; I have assumed that the galaxy did not move at all during that time, and in particular, that its distance from us has stayed constant. Of course, for most galaxies that is not true. Because the universe has been relentlessly expanding since the beginning of time, other galaxies have been moving away from us (with few exceptions in the Milky Way’s Local Group).

But while for galaxies that are relatively close to us (on a cosmic scale, 1 million light-years is nothing) you can safely neglect the expansion of the universe, for much more distant galaxies you must take expansion into account. One of the most important facts about cosmic expansion is the following, which is almost synonymous with saying that the universe started with a big bang.

Simple fact #2: The universe used to expand at a much faster pace than it does now.

Although it is true that the universe’s rate of expansion has picked up a bit in recent eons–that was the Nobel-worthy dark energy discovery–it’s still nowhere as fast as it used to be. The big bang theory (the actual scientific theory, not the equally awesome sit-com) says that the universe started out expanding at breakneck speed and spent most of its history slowing down, under the mutual gravitational pull of everything that it contains.

What does a slowing expansion look like? Imagine a galaxy—call it galaxy A—that is now 3 billion light-years from us, and picture its trajectory during the last 10 billion years. (That would be a sizable chunk of the universe’s history, which overall spans about 13.7 billion years.) At the beginning of that period, the galaxy would have been much closer, perhaps 1 billion light-years away (physically realistic numbers may be slightly different). If again we represent the arrow of time as pointing upwards, the galaxy’s path could look something like this:

(Again, the present is at the top and the past is at the bottom.) The line that represents the changing position of the galaxy, also known as its world line, leans more to the right at the beginning, and becomes closer to vertical as we approach the present, reflecting the fact that the speed at which the galaxy recedes has become much smaller.

(Once again: the numbers here are meant to give an idea rather than to be exctly accurate, and I am intentionally ignoring the fact that in recent times the rate of expansion has switched from slowing to accelerating.)

So far I have talked about a single galaxy, but what happens if we compare different galaxies that are at different distances?

Simple fact #3: Hubble’s Law.

The famous law discovered by Edwin Hubble says not only that distant galaxies recede from us, but also that the farther away they are, the faster they recede. (Their velocity is directly proportional to their distance, which is is consistent with a universe that expands at the same rate everywhere.)

Thus, we can imagine playing the same game not just with galaxy A but with a few equally-spaced galaxies, A, B, C, and D, currently at distances of tree, six, nine and twelve billion light-years, respectively. Ten billion years ago, those galaxies might have been one-fourth as far as they are now—namely, at distances of one, two, three and four billion light-years. If we pictured the galaxies’ trajectories in a decelerating universe, they would look something like this:

The beginning of the time period pictured here, 10 billion years ago, was a special time for galaxy D. It was the time when D emitted the light that we are now receiving from it. Now, for a galaxy so far away that its light took 10 billion years to reach us, Hubble’s law has a remarkable consequence.

Simple fact #4: Distant galaxies move faster than light.

Einstein’s special theory of relativity says that nothing can go faster than light, but that rule only applies to the velocities of objects that essentially pass by each other. It does not apply to objects that are far from each other: for those, space itself can expand between them and make them move apart faster than the speed of light.

In fact, faster-than-light, or superluminal, velocities are a necessary consequence of Hubble’s law: because galaxies recede at a speed that’s proportional to their distance, you can find galaxies that recede at arbitrarily high speeds: just look far enough.

Ten billion years ago, galaxy as far as galaxy D would have been moving away faster than the speed of light. That’s so fast that the light it emitted in our direction—which of course emanated from it at the speed of light—still wasn’t fast enough to make any progress getting closer to us. That light was dashing toward us as fast as the laws of physics allowed, and yet it was still moving away from us.

Of course, we are seeing that light now, which means that at some point in time between then and now it stopped receding and began to get closer instead. Correspondingly, its trajectory in spacetime would look something like this:

The light’s trajectory in spacetime first heads to the right, then reaches a maximum distance, turns around and starts coming toward us. (When it approaches our current location, the trajectory’s angle becomes 45 degrees, which is what we should expect: light covers one light-year in one year.)

Instad of following the path of light in spacetime from galaxy D to us, we could have just as easily taken the light that comes to us now and traced its path backwards. In fact, we could trace back the light we receive now from all four of the galaxies, not just from D. When the spacetime history of light crosses the history of a galaxy, that’s the time when the galaxy emitted its light.

Once we find those intersection points we can deduce, by counting vertical squares, how along ago the light was emitted for each of the galaxies. Thus (pretending that my hand-drawn sketch had accurate data) we could deduce that are seeing light from A that is a little less than three billion years old; about five billion years old in the case of B; and seven billion years old for C. For the case of D, we had already establish that its light is 10 billion years old.

Because A is the closest of the four galaxies, D the farthest, and B and C are in between, based on the ordinary rules of perspective you would expect their apparent sizes in the sky to be largest for A and smallest for D. But here’s where we get to our key point.

Simple fact #5: We don’t see objects where they are now.

It is clear that we see galaxies not as they are in the present but as they were at a different time in the past, depending how far they are: that is just a consequence of Simple fact #1.

But not only are we seeing those galaxies as they looked at different times; we are also seeing them where they were at those times. The galaxies appear just as large in the sky as if they had not moved since then. If you think about it, this makes sense: once the light has left a galaxy and gotten on its way, there is no reason why that light–or the images it will form in our eyes and in our telescopes–should be affected by the galaxy’s subsequent motion.

In the following figure, both dimensions represent space. The angle subtended by a galaxy in the observer’s visual field–which is the same as saying the galaxy’s apparent size–is what you would see at the time the light left the galaxy on its way to the observer. If the observer could somehow “see” the galaxy instantaneously where it is in the present, the galaxy would subtend a smaller angle.

Just as we estimated how long ago each galaxy emitted its light by counting vertical squares in the spacetime diagram, we can also estimate how far each galaxy was at that time (and thus how large it appears now in the sky) by counting horizontal squares. Here is the same spacetime illustration as before, but with distances highlighted for clarity.

We see that galaxy A was, at the time it emitted its light, only slightly closer than its current distance of 3 billion light-years. Galaxy B however was more than one billion light-years closer. And in case of galaxy D, the difference is most remarkable: its current distance of 12 billion light-years is fully three times farther than it was 10 billion years ago, the time when we see it. The discrepancy between current distance and apparent size is very small for galaxies that are not too far away such as A, but very large for the most remote galaxies.

But the figure demonstrates something even stranger when instead of comparing each galaxy’s actual size with its apparent size, we compare the apparent sizes of the various galaxies with one another. Assume that all of our four galaxies are identical. In the case of galaxy C and galaxy D, we are comparing an image of galaxy D from ten billion years ago with an image of galaxy C from about eight billion years ago. But even though D is and always has been farther away than C, D will look larger. That’s because at the respective times of emission, galaxy D was closer than galaxy C.

So that’s where reverse perspective comes from. The foreground object looks smaller than a background object of the same size. The following video (by London-based video artist Jeremy Mooney-Somers) portrays reverse perspective quite spectacularly. At about 00:22, you’ll see a squadron of teapots rotating in space; the teapots are all the same size, but the ones farther away look larger than those closer to the observer.

In the universe, reverse perspective applies only to very distant objects; ordinary perspective is valid not only at the scales of our experience but also for billions of light years around us. The point where the observable universe transitions from direct perspective to reverse is precisely where the trajectory of light bends backwards. In my approximate diagrams, it is at about 8 billion years; the actual value is more like 10 billion years in the past. Although that’s a long time ago, the universe is 13.7 billion years old, which means that reverse perspective applies to a full 3.7 billion years of its history.

(Side note for astronomy nerds: in matter-dominated models the transition takes place at a redshift of exactly 1.25, while in our dark-energy-dominated universe it is at a redshift of about 1.65, according to Roger Blandford, director of the Kavli Institute for Particle Astrophysics and Cosmology at Stanford.)

What if we were to look at the most distant past? The big bang theory predicts that, as you play the movie backwards, you’ll see all of the content of the universe converge toward a single point. That includes the trajectory of light that we traced backward from us. It also includes the world lines of all galaxies, no matter how far they are now.

Of course, if you rewind the movie of the history of a galaxy, you will see the stages of its formation in reverse order. Because galaxies and the stars they are made of coalesced from a cloud of hydrogen and helium gas, going backwards you will see the galaxy evaporate into a cloud. Going even farther, you will see the clouds merging, and the whole universe fill uniformly with gas.

Eventually, when you get to about 13.7 billion years ago, and more precisely to the epoch just 400,000 years or so after the big bang, the trajectory of light will come to a stop. In even earlier epochs, the content of the universe was too hot to be a gas, and instead it was a plasma, which is opaque to light. Thus, that is as far as we can see. We have reached the edge of the observable universe.

What does reverse perspective look like at that point? The world line of light cannot quite go all the way back to the big bang, but the plasma we can now see was, back then, on the order of 10 million light-years away. (Away from what? From the plasma that later evolved into the Milky Way, and into us.) Thus, the farthest observable object in the universe was, at the time when we see it, at a distance so small that in the current universe it would put it in the Local Group. And the cosmic magnifying lens has now reached its limit. Its magnification factor is now more than 1,000X.

If a galaxy had existed back then at the edge of the observable universe, that galaxy by now would have receded so much that it would be 40 billion light-years away. The light we receive from such a galaxy would be so redshifted (that’s the stretching of light waves due to the expansion of the space in which the light waves travel) to be far outside of the visible spectrum. Moreover, its image would be exceedingly faint.

Still, it is fun to imagine what this impossible galaxy might look like in the night sky if we could see it with the naked eye. It could appear almost as large as the moon. Hundreds of other, seemingly smaller galaxies, looking like tiny little dots, would show up in front of it, looking hundreds of times smaller than the big disk behind them.

I end this post by pointing out a riddle that was implicit in my diagrams and that has surely occurred to the most attentive readers: how far would you say is galaxy D?

Read the prequel to this post: The Cosmic Magnifying Lens

References and further readings:

Poetry of the Universe, by Robert Osserman (RIP 1926-2011). Anchor Books, 1995.

An Introduction to the Science of Cosmology, by D. J. Raine and E. G. Thomas. Institute of Physics, 2001

Hubble deep field image courtesy of NASA.

The Cosmic Magnifying Lens

Davide Castelvecchi — Sun, 06 Nov 2011 15:01:40 +0000

Objects may be closer than they appear; in the distant universe, objects are, in a sense, even farther than they appear

The observable universe is one big, giant magnifying lens.

At large distances, objects appear to be larger than their true size, and the farther they are, the bigger they look. The most distant observable objects are so magnified that their images in the sky—if we could see them—would be blown up by a factor of 1,000 or more.

If there were a road leading from here to the edge of the universe, you wouldn’t see it getting smaller and smaller and finally converge to a point, the way you see straight roads on earth vanish to a point on the horizon, as in the picture above. Instead, you’d see the two shoulders get closer for a while, reach a minimum width, and then start moving apart again.

To get some visual intuition about what happens then, it is helpful to look at the technique that artists have codified as reverse perspective, also known as Byzantine perspective. While in ordinary perspective lines converge to a point “at infinity,” in reverse perspective, sometimes seen in Byzantine icons, they converge to a point in front of the scene depicted. Here is an animation of a city in reverse perspective, made by London-based video artist Jeremy Mooney-Somers.

And here’s another mind-bending example:

And another one:

But the comparison between the distant universe and reverse perspective is only partially correct. In our universe, lines do not converge to a point nearby either. Instead, lines follow ordinary perspective nearby (and by “nearby” I mean within several billion light-years) and reverse perspective farther away.

This cosmic magnifying lens is, to me, one of the most mind-blowing features of our universe. And although chances are you have never heard of it, it is among the most basic predictions of the big bang theory: “It is this that was believed to be the most direct geometrical test for the reality of expanding space,” wrote the great astronomer Allan Sandage in 1988 (italics in the original).

In fact the test was proposed in the late 1950s by Fred Hoyle in the hope of disproving the big bang theory, which he opposed: he had famously coined the term “big bang” disparagingly, and had concocted a rival theory called the steady-state universe. In a steady-state universe, no such magnification would happen, Hoyle observed. If our universe failed the test–in other words, if astronomers could demonstrate that there is no magnification, no reverse perspective–the big bang theory would be disproved. This is called the angular size test, or angular diameter test, because it requires measuring the angle that an object subtends in the sky.

(Hoyle however was not the first cosmologist to become aware of the magnification effect, points out Roger Blandford, director of the Kavli Institute for Particle Astrophysics and Cosmology at Stanford. “Robertson and Walker, Tolman et al. understood all of this,” he says. Howard Robertson and Arthur Walker are among the guys who in the 1920s realized that general relativity, Albert Einstein’s theory of gravitation, predicted the expansion of the universe. Soon after, Richard Tolman studied the connection between magnification and apparent brightness of an object.)

Ironically, while many other exhibits of evidence for the big bang’s case have accumulated since then—so that virtually no cosmologist nowadays doubts that the big bang happened—it appears that Hoyle’s original challenge is still standing: no one has demonstrated the magnification effect directly. Cosmologists have tried to crack the problem before, and they seem to have given up. “No one is in that business,” was a comment I heard from an expert.

(The fact that angular diameter tests have fallen into near-oblivion may be the reason that you don’t read about them too often. After all, science magazines such as Scientific American are news-driven—they tend to cover current research. But what I find profoundly puzzling that it isn’t mentioned more often in popular cosmology books.)

You see, to estimate how the magnification of an object varies with its distance you have know three things: 1) how far the object is; 2) how large it appears in the sky; and 3) how large it actually is. To be precise, cosmologists would like to know how the magnification varies as a function of redshift, the stretching of light waves that we observe in the light from distant galaxies. Redshift is a proxy for distance because the farther galaxies are, the more stretched their light gets, as a result of the expansion of the universe.

But the transition from ordinary perspective to reverse perspective takes place for galaxies that are so far away that their light has traveled for nearly 10 billion years (with a redshift of 1.65, Blandford told me, meaning that the light’s wavelength has stretched by 165 percent) before reaching us. As you can imagine, that light looks exceedingly faint by now.

As the physicist Steven Weinberg explains in his intimidating textbook Cosmology, galaxies tend to have blurry edges. Consequently, when a galaxy is very distant, more of it will fall into obscurity than if the same galaxy were closer by. The distant galaxy’s angular diameter will appear smaller than it would if we could clearly see all of it. And if the galaxy happens to be made of unusually faint stars, it will appear smaller yet–only its core, with its dense aggregation of stars, will show up, if anything will.

These and other issues, Weinberg writes, make the angular diameter test “much less useful” than other ways of measuring the geometry of the universe, such as the type Ia superovae that earned three astronomers this year’s Nobel Prize in Physics.

Nevertheless, at least one notable attempt at performing the angular diameter test was made in the early 1990s, by Ken Kellermann of the National Radio Astronomy Observatory in Charlottesville, Va., by looking at the highly energetic jets of matter that supermassive black holes shoot out as they devour matter from their surroundings.

Some of these jets appeared to be 10 times larger than you would expect from their distance, if ordinary perspective were to hold. “This is perhaps the best direct observational support for the predictions” of the big bang cosmology, Kellermann wrote, “and is also direct evidence that the redshift of galaxies and quasars is really due to the expansion of the universe.” Below is a diagram from Kellermann’s paper.

This diagram showed the angular size, or the angle subtended in the sky, by compact radio sources of different redshifts. (Redshift is a proxy for distance, as farther objects are more redshifted.) The data suggested that the angular size bottomed out at a redshift of between 1 and 2, instead of decreasing forever as one would expect from the ordinary laws of perspective. A milliarcsecond is one-thousandth of an arcsecond, which is itself one-3,600th of a degree: for comparison, the sun and the moon each subtend about half a degree in the sky, or 1,800 arcseconds. These estimates of angular sizes were later considered unreliable. Nature Vol. 361, pages 134 – 136; January 14, 1993.

Unfortunately, Kellermann’s methodology was later put into question and the radio sources he used are nowadays generally considered unreliable. That is, astronomers are not sure they can accurately estimate the sources’ true size.

But why should such a counter-intuitive effect be true at all? It has to do with non-Euclidean geometry–with the non-flatness of the universe.

“Hold on a second,” you say, “Didn’t NASA’s WMAP show that our universe is flat? I read countless articles saying that.” Sure, but it depends what you mean by “universe.” The term is often used sloppily without regard for the fact that it can mean different things. If by universe you mean space now–call it the nowverse–then it definitely looks uncannily close to being flat. If by universe you mean spacetime, then it certainly isn’t flat, if Albert Einstein’s general relativity is true: mass and energy produce curvature, so the only way that spacetime could be flat is if it were completely empty.

But what I mean here by universe is neither the nowverse nor spacetime, but yet another thing. What I am talking about is the observed universe–the stuff we actually see in the sky. In the next post, I will explain why the observed universe is curved–as well as why it’s supposed to act as a magnifying lens.

Read the follow-up post: A Step-by-Step Guide to Cosmology’s Best-Kept Secret

References and further readings:

The Relation of Radio Astronomy to Cosmology, by Fred Hoyle. Radio Astronomy, IAU Symposium No. 9, p. 529; 1959.

Observational Tests of World Models, by Allan Sandage. Annual Reviews of Astronomy and Astrophysics 1988. 26: 561-630.

The Cosmological Deceleration Parameter Estimated from the Angular-Size/Redshift Relation for Compact Radio Sources, by K. I. Kellermann. Nature 361, 134 – 136; January 14, 1993.

Testing the Angular-Size Versus Redshift Relation with Compact Radio Sources, by Youri Dabrowski, Anthony Lasenby and Richard Saunders. Monthly Notices of the Royal Astronomical Society, Volume 277, Issue 3, pages 753-757.

Poetry of the Universe, by Robert Osserman (RIP 1926-2011). Anchor Books, 1995.

An Introduction to the Science of Cosmology, by D. J. Raine and E. G. Thomas. Institute of Physics, 2001.

Cosmology, by Steven Weinberg. Oxford University Press, 2008.

What Do You Mean, The Universe Is Flat?, Part 1. Degrees of Freedom, July 25, 2011.

Another cool reverse perspective animation.

Scientific American is part of Nature Publishing Group.

On the Physics Nobels, The Atlantic Gets Dark Energy All Wrong

Davide Castelvecchi — Sun, 16 Oct 2011 15:04:01 +0000

Let's keep it within the galaxy, Jim

The piece run by The Atlantic last week on the Nobel Prizes for Physics, sadly, contained a number of misleading or inaccurate statements on physics and cosmology.

Gregg Easterbrook, the journalist who wrote it, has a storied past as a science writer. He was one of the clear-minded people who saw early on the nonsense behind the space shuttle. The full Rube Goldbergian magnificence and absurdity of it is well detailed in a masterful article by Easterbrook that is practically a history of the whole program, including its cost overruns and its deadly failures—and he wrote that in 1981.

That story makes for a chilly read. You can almost see, unfolding before your eyes, the disasters of Columbia (“The tiles are the most important system NASA has ever designed as ‘safe life.’ That means there is no back-up for them. If they fail, the shuttle burns on reentry”) and Challenger (“Here’s the plan. Suppose one of the solid-fueled boosters fails. The plan is, you die”).

More recently, his criticism of NASA’s priorities, seen for example in Wired, has been (mostly) spot on.

But Easterbrook has also periodically displayed creationist beliefs that are a bit disturbing for a science writer called on to write about the origins of life (also in Wired).

And occasionally he seems to overestimate his ability to understand science. Several years ago, Carl Zimmer took him to task for some nonsensical statements about string theory and other dimensions. Last week, Easterbrook ventured again into cosmology, on the web site od The Atlantic. Unfortunately his piece contains a number of bizarre or outright wrong statements. I don’t mean this blog to engage in character assassination, and certainly not of Easterbrook, as I like the guy, but I would just like to correct his article for the record.

His article’s summary gets it off to a bad start, by talking of “galactic expansion.” But that may be forgivable. Dark energy is often a source of confusion even for physicists. People often ask whether the expansion of space means that galaxies—or perhaps even the solar system, even Brooklyn—are expanding.

S’far as we can tell, they are not. The only thing dark energy seems able to do is make orbits imperceptibly larger than they would otherwise be. Dark energy is so dilute that it only has appreciable effects on larger scales, larger than the millions of light years of galaxy clusters.

But perhaps by “galactic expansion” the editors of The Atlantic meant the motion of galaxies with respect to one another. Let’s move on.

“Some theoreticians,” Easterbrook writes, “predicted the expansion, driven by the momentum of the Big Bang, should be slowing.” Ok.

“Eventually the galaxies would either stop their outward travel and the cosmos become static, or gravity would pull everything back together for a Big Crunch.”

Not really. As far as I know, no one thought that the universe could go from dynamic to static. In standard cosmological models that were prevalent until the end of last century, no matter how far the galaxies spread, they will still “feel” each other’s gravitational tug. The universe either expands for ever or recollapses.

“Other theoreticians felt cosmic expansion would continue at a steady pace essentially forever.”

Perhaps here Easterbrook was referring to the “steady state” universe model of Fred Hoyle. But Hoyle’s whole point was that he didn’t want to believe in a big bang, so his model was not a variant of the big bang models.

“Since the galaxies must long ago have overcome the gravity of the Big Bang in order to be rushing outward, this reasoning went, they’ll simply keep going.”

This is just so wrong I don’t even know how to unwrap it. There is no “gravity of the big bang.” If the galaxies keep going it is because the geometry of spacetime allows them to do so.

“Dark energy appears strong enough to push the entire universe - yet its source is unknown, its location is unknown and its physics are highly speculative.”

Here Easterbrook seems to picture scientists going around with a magnifying lens and saying, “where did I put the dark energy?” In reality, physicists believe that dark energy is everywhere.

“For a century, physicists have elaborately fine-tuned a concept of the natural world in which there are four fundamental forces: gravity, the ‘strong force’ that holds atoms together, the ‘weak force’ that keeps electrons in place around atoms…”

Wait, what?!?

First of all, the “elaborately fine-tuned concept of the natural world,” by which Easterbrook presumably means the Standard Model of particle physics, did not arise until the 1970s. Even wanting to be charitable, the idea that there was a fourth force was proposed 80 years ago at the most. But where Easterbrook goes stupendously wrong is in describing the weak force as holding atoms together. The weak (nuclear, to be precise) force is only involved in nuclear decay, and has nothing to do with keeping electrons in place around atoms. It is the electromagnetic force that does that.

Easterbrook goes on. “Entire academic careers have been made on work refining four-forces thinking.” Fair enough.

“Suddenly there’s a fifth force, dark energy. And although it appears to comprise three-quarters of the universe, nobody’s noticed it till now.”

Actually, although it is seductive to think that dark energy is a fifth force, it does not fairly represent mainstream physicists’ thinking, which is that dark energy is part of the stuff that fills the universe and that its effects on the expansion of the universe are gravitational–that is, entirely predictable within Albert Einstein theory of gravitation. (See Sean Carroll’s Dark Energy FAQ.)

Moreover, physicists had been conjecturing the existence of dark energy (in its incarnation as the “cosmological constant”) long before the accelerating expansion of the universe was discovered.

“It does not appear to be possible to make a vacuum in which there is nothing at all, so it is now assumed that intergalactic space is not a true void.”

But nobody ever assumed that. Space is crisscrossed by a multitude of photons—including those of the cosmic microwave background and those emitted by stars—as well as by neutrinos and by wandering cosmic rays particles such as protons.

And the fields of quantum field theory extend everywhere, so physicists did not really expect the vacuum to be totally empty. The point of the existence of dark energy is not about interstellar “true void.” Anyway dark energy, assuming it exists, would not just pervade the interstices between elementary particles, it would be truly everywhere.

Finally, Easterbrook’s concluding remark personally offended me as a Trekkie. “Intercourse between galaxies will become unimaginable,” he writes, “even if Captain Kirk’s warpdrive is invented.” But as far as I recall, Kirk never ventured much outside of the galaxy.

For reliable information about dark energy, I recommend Sean Carroll’s wonderfully clear and thorough Dark Energy FAQ.

“‘We Hate Math,’ Say 4 in 10 — a Majority of Americans”

Davide Castelvecchi — Sat, 15 Oct 2011 08:45:49 +0000
How did I miss this until now? This clip has apparently been making the rounds of the Interwebs for years, but I couldn’t resist posting it after I saw it on Facebook this morning. I have no idea where the article was published–nor whether it’s a joke–though the news may have originated from a 2005 [...]

The Periodic Table, and Why Batteries Don’t Work the Way You Think

Davide Castelvecchi — Thu, 13 Oct 2011 13:57:14 +0000

The chemical elements—the varieties of atoms existing in nature and even some that are manmade—are an endless source of fascination. But something about them remains mysterious to most people, perhaps even to a lot of chemists.

I had a chance to remind myself of that conundrum while I reading two terrific books on the subject–The Disappearing Spoon, by Sam Kean, and Periodic Tales, by Hugh Aldersey-Williams–I was doing research to write up the text for ScientificAmerican.com’s Interactive Periodic Table.

The periodic table neatly arranges the elements into columns. Those elements that share a column are supposed to possess (roughly) similar chemical properties. Most people who know the table well and use it every day—which includes virtually every chemist, biochemist, materials scientist, and lots of engineers—hardly give it a thought, but the predictions of the table are some of the oddest facts in nature. The laws that govern most of the phenomena before our very eyes—everything from cellular metabolism to a laptop’s batteries—are dictated by the chemistry of the elements, but we rarely realize how weird and wonderful the underlying forces are.

The significance of the table’s columns is most explicit in the elements on the leftmost column, called the alkali metals (which include lithium, sodium and potassium), and in those on the second column from the right, called the halogens (fluorine, chlorine and their pals). These two families comprise the most reactive of all elements. Atoms of halogens such as fluorine have an extreme tendency to rip an electron off of other atoms, while alkali atoms have an equally strong tendency to give an electron away. Thus, mix a halogen and an alkali metal and you get a perfect one-to-one match—a salt such as potassium chloride or sodium chloride, aka table salt.

More generally, the tendency is that of a progressive transition from electron-donation to electron-acceptance as you move from the left to the right on the periodic table. This gradient is quantitatively measured by the property called electronegativity, which (by and large) increases going from left to right. Once you reach the last column on the right, though, you reset the dial. The elements of that family are the noble gases which are virtually unreactive.

Every scientist will tell you that the reason why the families of chemicals that make up each column have more or less predictable behavior—in other words, the reason why there is a periodic table at all—is that all elements secretly “want to be noble gases.” In an atom of a noble gas such as neon (element 10), the orbits of the electrons around the nucleus are neatly and symmetrically arranged like the petals of a flower. The halogen fluorine (9), on the other hand, which has one electron fewer than neon, has a skewed orbital arrangement. It desperately “wants” that extra electron to make the arrangement symmetrical and happy. Meanwile, for the alkali metal sodium (11), the easiest thing to do to become like neon is to shed one electron.

It goes without saying that this narrative about atoms’ unfulfilled electronic desires is not the actual scientific explanation. The typical user of the periodic table doesn’t need to go much deeper: the true reasons have been figured out long time ago and the answer now lies buried in some difficult quantum physics textbook. But if we stop and think for a minute, we realize what an astoundingly bizarre phenomenon this is.

Take oxygen. The corroding—rusting, tarnishing, well, oxidating—chemical par excellence, oxygen reacts because it “wants to” complete its bouquet of outer electronic orbitals to a full set of eight, and thus mimic neon’s serene ikebana. It hardly matters if some of those orbitals also have to fly around other atoms: by sharing some of its electrons with two hydrogen atoms, for example, oxygen can form a molecule of water. As long as the outer orbitals form a full octet around its nucleus, chemical nirvana is within reach.

But here’s why this is so weird. If you take an oxygen atom in isolation and feed it an electron, it will capture it and become an oxygen ion O-. Now imagine that an extra electron flies by. The two objects, the electron and the oxygen ion, are both negatively charged, so they should repel each other. And yet, the oxygen craves that second electron so much that it will grab it and become a doubly ionized ion, O–. The reactivity of oxygen is so strong that it will win over the electrostatic (or Coulomb) repulsion, a force of notorious intensity. (The setting I am describing is, I admit, pretty abstract, as electrons and oxygen don’t really get a chance to interact in the vacuum, and probably the resulting ion would not be stable, but please bear with me.)

We often hear that everything that happens in nature—with the possible exception of dark energy, whose origin remains a complete mystery—is a result of one of four fundamental forces: gravity, the weak and strong nuclear forces, and electromagnetism. Chemical reactions and the formation of states of matter such as quasicrystals or people are entirely governed by the electromagnetic force. But electromagnetic interactions are varied and complex, and the electrostatic force is but one special case of them. Chemical reactions are electromagnetic, but most of the time they take place against, not following, electrostatic forces.

The mechanisms that power a battery, for example, have everything to do with the electromagnetic interactions we call chemistry; but contrary to what we often think, electrons do not move from the negative pole to the positive pole because of electrostatics. It’s not that the negative pole has a surplus of electrons—a negative charge—and the positive pole a depletion of them. Both electrodes in a battery are electrically neutral.

What really powers a battery is the difference in electronegativity between the materials its electrodes are made of. Take the voltaic pile, for example, the first battery in history, invented around 1800 by Alessandro Volta. The pile’s negative electrode is made of zinc (30) and the positive electrode is made of copper (29). Copper is slightly more electronegative than zinc*.

The electronegativity of copper is higher than that of zinc.

Thus, if you put the two metals next to each other (or if you connect them by a wire), some electrons will move from the zinc to the copper.

Connecting the two materials result in the transfer of some electrons.

We say that copper is the positive pole and zinc is the negative one, but in reality, the transition of electrons will happen against electrostatic forces, not following them: the positive electrode, copper, will become negatively charged from the extra electrons, at the expense of the negative electrode, zinc which will charge positively!

Given such state of affairs, just connecting two materials made of atoms with different electronegativity (in the case of materials, the corresponding term is electrochemical potential) would not give out much in terms of energy. The negative charges accumulating on the positive pole would quickly become too strong and they would repel further electrons; the negative electrode, meanwhile, would quickly become positively charged from the loss of electrons and thus it would hang on more strongly to its remaining electrons by electrostatic attraction. The transfer of electrons would quickly come to a halt.

The negative pole becomes positively charged, and vice versa; the flow of electrons stops.

That’s why a battery is not made just of two electrodes, but includes an electrolyte. The electrolyte permits the transfer of ions from the negative pole to the positive pole of the battery. Because the positive pole tends to accumulate negative charges from the electrons, it also tends to attract positive ions. The ions thus keep charges neutral on both sides and allow the transfer of electrons to go on—at least for a while.

The electrolyte enables charges to be neutralized so the current can proceed.

When too many ions have transferred, the battery’s performance begins to decline. Eventually, all the ions that could move have moved, and the battery is discharged. If your battery is rechargeable, you can apply a potential to its electrodes to moves the electrons back to the negative pole the ions will follow suit.

So what is the mysterious quantum physics that governs the flowery arrangements of electron orbitals? That, I am afraid, will have to be the subject of another post.

(*) Note: the attentive reader will have noticed that copper is actually to the left of zinc in the table. However, copper is the more electronegative of the two metals. The rule that electronegativity increases when you move from left to right does have a few exceptions.

While preparing this essay, I benefited from conversations with Piotr Zelenay.

Superluminal Neutrinos Would Wimp Out En Route

Davide Castelvecchi — Mon, 03 Oct 2011 01:23:41 +0000

The heat is on, too

[Note: October 5 update and clarification added at the bottom]

Neutrinos that go beyond light speed? Not so fast, say two theoretical physicists.

In a terse, peremptory-sounding paper posted online on September 29, Andrew Cohen and Sheldon Glashow of Boston University calculate that any neutrinos traveling faster than light would radiate energy away, leaving a wake of slower particles analogous to the sonic boom of a supersonic fighter jet. Their findings cast doubt on the veracity of measurements recently announced at CERN (and posted online here) that clocked neutrinos going a sliver faster than light.

For someone who may have just helped to save the edifice of modern physics (if it was ever really at risk of crumbling down), Cohen is not especially upbeat or relieved. “On the contrary, I am saddened and disappointed,” he says. After all, a lot physicists would love the shocking measurement to be correct. For the experimentalists who made it, it could mean that they had made the discovery of the century. For theorists, it could be the start of an exciting period of creative upheaval. “It gets boring if [nature] always works the same way you expected,” Cohen says.

The result announced at CERN on September 23 (although the news had leaked out ahead of time) was certainly unexpected. By now, if you haven’t heard of it, you must have been a straggler from the Imperial Japanese Army coming out of Iwo Jima’s tunnels. Anyway, to recap, the war in the Pacific is over, and a team of physicists has released data on neutrinos they beamed through the Earth’s crust, from Geneva to the Gran Sasso Massif, near Rome, in an experiment known as OPERA. According to the physicists’ estimates, the neutrinos arrived at destination around 60 nanoseconds too fast, violating the cosmic speed limit set by Albert Einstein’s theory of relativity.

Experts urged caution, especially because another measurement of neutrino velocity—one done in 1987 by detecting particles from a supernova that had gone off in the Magellanic Cloud, just outside our Milky Way—indicated to high precision and accuracy that neutrinos do respect the cosmic speed limit.

The neutrinos coming from that supernova, however, were relatively weak; by comparison, those shot from from CERN have more than 1,000 times the energy. What if supercharged neutrinos could be superluminal even as less-energetic ones were confined to our boring, relativistic world?

So, Cohen and Glashow (the latter a Nobel Prize winner) looked at precisely the high-energy kind of neutrinos that are detected at Gran Sasso. From basic principles such as the conservation of energy and momentum, they deduced that if superluminal particles indeed existed, they could decay into other particles that are bound to a lower speed limit. “When all particles have the same maximal attainable velocity, it is not possible for one particle to lose energy by emitting another,” Cohen explains. “But if the maximal velocities of the particles involved are not all the same,” then it can happen.

An effect of this type is well-known in the case in which electrons have the higher speed limit (light speed) and light itself has the lower one. This can happen because when light propagates in a medium, such as water, air or glass, its speed gets substantially reduced–a change that’s at the basis of the familiar refraction effect in which a pencil half-dipped in water looks as if it’s broken in two. (The universal speed limit of relativity is, to be precise, the speed of light in the vacuum.)

Electrons then, can move in a medium at a speed higher than the maximums speed of photons in that medium, and lose energy by emitting photons. This process is called Cherenkov radiation, and it makes the reactor pools of nuclear power stations (such as the one pictured here) glow with a bluish light. It is also used to detect electrons that shower down on Earth after a high-energy cosmic ray crashes on the upper atmosphere.

The possibility of a transfer of energy between particles with different speed limits was well known, Cohen says, and is a fact that he often gives to his undergraduate physics students as a homework problem. But in their paper, he and Glashow go further. They discuss the exact mechanisms by which such a conversion can happen, and make precise quantitative estimates of how often the neutrinos would decay into each type of particle.

The emission that is most likely is, by far, that of an electron paired with its antimatter twin, a positron, the authors conclude. (The high-energy neutrino would create them by interacting with one of the “virtual particles” that incessantly and fleetingly froth out of the vacuum—in this case, a Z boson, one of the carriers of the weak nuclear force; it was by understanding precisely that type of interaction that Glashow shared a Nobel Prize in Physics in 1979.)

Crucially, the rate of production of these electron-positron pairs is such that a typical superluminal neutrino emitted at CERN would lose most of its energy before reaching Gran Sasso. “The beam sent from CERN would be significantly depleted” of high-energy neutrinos, Cohen says. The neutrinos picked up at the Italian lab, however, do not seem to have lost any of their energy.

But then, perhaps they were not superluminal to begin with.

“I think this seals the case,” says Lawrence Krauss, a theoretical physicist and the director of the Origins Projet at Arizona State University. “It is a very good paper.” Krauss has been among the most critical of the OPERA team’s decision to go public with their findings, as he has written in an op-ed for the Los Angeles Times and told my former colleague John Matson.

The OPERA collaboration did not respond to a request for comments.

Carlo Rovelli, a theoretical physicist a the University of the Mediterranean in Marseille, says that Glashow and Cohen’s results are “plausible,” and did not seem particularly surprised. “It seems that the majority of physicists, including myself, strongly suspects that there is some mistake in OPERA’s measurements.”

Some physicists have suggested that neutrinos could be finding shortcuts in spacetime–for example, by moving in extra dimensions of space–that would allow them to get there faster while still respecting the speed limit. Such a possibility may not be ruled out by neutrinos’ Cherenkov radiation, but may begin to look increasingly contrived.

“Let’s put it this way: physicists who work on string theory for more than 20 years have assumed that there are additional dimensions, and yet none of them had ever consider the possibility that a particle could find shortcuts in other dimensions, and go faster than light,” Rovelli says.

As to what may or may not have gone wrong with the experiment, Cohen does not want to speculate (though others have: see for example the blog of theoretical physicist Lubos Motl). “I am not the right person to say what happened,” a task that he says is best left to other experimentalists.

Was Einstein right after all? Einstein’s relativity superseded Isaac Newton’s physics, and probably something else will some day supersede it. And physicists will still continue to use either one, when appropriate. “All of our scientific results have some domain of validity,” says Cohen; no scientific theory is “right” or “wrong” in an absolute sense–each just is in more or less accurate agreement with experiment. Meanwhile, others will no doubt keep trying to find glitches in Einstein’s theories. “We never stop testing our ideas,” says Cohen. “Even those that have been established well.”

October 5 Update and Clarification:

Since the post went up, there has been a very interesting exchange of viewpoints in the comments section: thanks to everyone who has been contributing.

First, the clarification: andrewgdotcom pointed out that was sloppy when I described the production of electron/positron pairs as a decay. Indeed, the neutrinos wouldn’t decay; they would proceed on their superluminal journey, but with less energy.

I disagree with the interpretation that some have given below of Cohen and Glashow’s result as an attempt at using theory to disprove facts; to me the point seems to be whether (something that for the authors amounts to) a back-of-the-envelope calculation can show that a certain experimental finding is in contradiction with scores of other experimental findings which also were done with high precision and accuracy.

But couldn’t there be could assumptions in the paper (such as basic facts in quantum field theory) that one could imagine failing to hold true here? After all, the paper deals wtih the weird and hypothetical realm of superluminal particles: who knows how much of the “old” theory we would have to throw away.

Rovelli says there do not seem to be any “hidden” assumptions in the paper that would invalidate it in a superluminal world.

“There are many things we don’t know,” Krauss says. “But there are many things we know. And one of these things involves the interactions of neutrinos. The process presented by Glashow and Cohen must occur, given all the existing measurements of neutrinos.”

In any event, it will be exciting to see what OPERA and other neutrino experiments will do in coming months and whether their incredible findings will hold up.

I will be doing my own experiment, too. Gran Sasso is just two hours away from where I live; I will go hiking just to the south of it to see if I can catch some of the neutrinos that bypass the OPERA detector and emerge overground. And I will keep you posted.

Paper: “New Constraints on Neutrino Velocities,” by Andrew G. Cohen and Sheldon L. Glashow.

Added October 11: Physicist Matt Strassler blogged about the Cohen-Glashow paper too.

Images courtesy of Istituto Nazionale di Fisica Nucleare, Australian Nuclear Science and Technology Organization and Wikimedia Commons

Archimedes and Euclid? Like String Theory versus Freshman Calculus

Davide Castelvecchi — Tue, 20 Sep 2011 15:25:01 +0000

Archimedes spiral imaged in UV rays, from the Archimedes Palimpsest, which will be showcased next month at the Walters Art Museum in Baltimore

The archetype of the science genius didn’t use to be Albert Einstein. For centuries, the quintessential irreverent, visionary scientist, immersed in a world of his own making to the point of forgetting to put on his clothes, was instead an ancient Greek mathematician. His name was Archimedes of Syracuse.

Archimedes was the stuff of legend around the Mediterranean world—what with the jumping out of his bath tub, the mirrors he used to set Roman ships on fire, the lever that he said he could have used to lift the world—even while he was alive. But the “Eureka!” incident may be a good indicator of the extent to which the lore failed to capture the true significance of his mind.

The story says that Archimedes had an epiphany while taking a bath, jumped out of the water and ran naked down the street screaming “Eureka!” which means “I’ve found it!” Supposedly, while contemplating the floating of his own body in the tub, Archimedes had realized that he could solve a riddle proposed by King Hiero II.

The king wanted to know whether his crown was made of pure gold, as stipulated, or whether the goldsmith had mixed some silver in. Archimedes’ answer: dip the crown in a tub and see how much water it displaces. That way you can measure the crown’s volume, and from that you can then calculate its density and thus guess at its composition.

But I think it is unlikely that a mind of Archimedes’ caliber would have gotten all worked up about such a triviality. If there is anything true to the legend, perhaps it’s that while in his bath tub Archimedes figured the law of buoyancy: the principle that still bears his name. Far from being a sideshow trick of Monty Pythonesque flavor, it was a true scientific law, one that applies whether it’s a scientist in his bath tub or a hot air balloon floating in the air.

In the October Scientific American I write about an exhibition that will open next month at the Walters Art Museum in Baltimore, showcasing the incredible vicissitudes of one of just three medieval copies of Archimedes’ works that survived through the Dark Ages “by the narrowest of threads,” as the manuscript’s curator, Will Noel, puts it. The book is called the Archimedes Palimpsest.

This 10th-century prayer book was made of recycled parchment. Before being washed out and reused, the pages contained the only surviving copies of two of Archimedes' works. It is now known as the Archimedes Palimpsest.

The story of the Palimpsest, as Noel said to me in an interview several years ago, is the “Jurassic Park of manuscripts.” It is a story that has been told on many occasions, nowhere more poignantly than in The Archimedes Codex, a book Noel co-authored in 2007 with Reviel Netz, a historian of mathematics at Stanford University. Theirs is a must-read book for anyone who has an interest in archeology or ancient history or ancient mathematics–or simply for anyone who likes a damn good story.

Noel assembled a team of some of the world’s best imaging experts to recover as much as possible of Archimedes’ text from the Palimpsest that no eyes had seen in modern times. One of them was physicist Uwe Bergmann at the Stanford Synchrotron Radiation Lab, who starting in 2006 scanned some of the pages with x-rays from a particle accelerator: during the scans, Noel watched ecstatically as the images slowly appeared on the computer screen, pixel by pixel, which was “like receiving a fax from the 3rd Century B.C.,” Noel told the BBC at the time.

Detail of an x-ray scan of a page of the Archimedes Palimpsest, showing the prayer text (vertical) and the older text of a 10th-century copy of Archimedes (horizontal), in red. The x-rays revealed iron contained in the ink that had seeped into the parchment.

One of the incredible facts I learned from Noel and Netz’s book is that to this day, few of Archimedes’ works have even been translated into English. T. L. Heath’s 1897 edition of Archimedes’ works—at least the ones available to him back then, before the Palimpsest was rediscovered—was admittedly more a paraphrase than a translation.

Netz made it his lifelong mission to transcribe and translate the 100,000-odd words of text that survive from Archimedes’s writings, including, for the first time, a critical edition of the figures, which older editions usually tended to leave aside or to interpret in their own way.

In fact, although Archimedes always had the reputation of being the greatest mathematician of the ancient world, very few people ever read much of his works because few could understand them, says Netz.

For two millennia Euclid’s Elements had its place as a geometry textbook and a paragon of rational thought. While Euclid (who may have been one of Archimedes’ mentors when the Syracusan spent time in Alexandria) was a great systematizer and a master of exposition, Archimedes wrote about his original findings, at too high a level for most people, Netz says.

As Netz writes in one of the chapters he authored in the Archimedes Codex (he and Noel took turns, each writing every other chapter), Archimedes did not hold Euclid’s Elements in much esteem. “Archimedes wouldn’t think very highly of them, as they consist mainly of basic mathematics. Archimedes was an advanced mathematician, writing for people who knew much more than the contents of Euclid’s Elements.”

Compared to reading Euclid, reading Archimedes may have been a bit like reading an abstruse string theory article versus reading a college physics textbook, or perhaps one of calculus for freshmen.

Most of Archimedes’ writings were in the form of letters written to people whose minds Archimedes considered worthy of his attention. It was in one such letter that Archimedes made use of the concept of infinity, according to Noel. That letter was addressed to Eratosthenes, one of the most eminent intellectuals of the time—the man who, with incredible ingenuity, had calculated the radius of the Earth to within a few percent points of its actual value (a story masterfully told by Carl Sagan in the first episode of Cosmos).

Among those few who later understood Archimedes were Galileo Galilei, Isaac Newton and Gottfried Wilhelm von Leibniz, and it is not a coincidence that these men were the founders of modern science, Netz says. In particular, Archimedes’ use of infinitesimals to calculate areas and volumes was the starting point for the invention of the calculus, he says. And the modern mathematicians explicitly credited Archimedes for their use of infinitesimals, says Netz. “It was not a rediscovery by any means.”

Further readings:

Lost and Found: The Secrets of Archimedes, upcoming exhibition at the Walters Art Museum in Baltimore

A Tale of Math Treasure: An exhibition traces the reconstruction of a long-missing collection of writings by Archimedes. Davide Castelvecchi in Scientific American; October 2011

The Archimedes Codex: How a Medieval Prayer Book is Revealing the True Genius of Antiquity’s Greatest Scientist. By Reviel Netz and William Noel.

Reading Between the Lines: Scientists with high-tech tools are deciphering lost writings of the ancient Greek mathematician Archimedes. Mary K. Miller in Smithsonian, March 2007

The Archimedes Palimpsest official website

Will Noel’s blog

NOVA episode on the Archimedes Palimpsest

sciencewriter.org/archie

Images courtesy of the anonymous owner of the Archimedes Palimpsest and the Walters Art Museum

Why There’s No Such Thing as North and South

Davide Castelvecchi — Mon, 12 Sep 2011 23:16:28 +0000

Spot the cultural bias

The human mind often confuses familiarity with understanding.

You’ve learned the basics of a field. You’ve memorized the rules and used them so many times they have become second nature, or “common sense”–which means that you have stopped asking yourself why they should be true. And now it’s often harder for you to learn a new concept than it would be if you were to start from tabula rasa.

That is why many of us who studied science or engineering or mathematics at university find it hard to convince ourselves that electromagnetism–one of the four fundamental forces of nature–does not have a preferred handedness. (which in particular implies that one cannot use the laws of electromagnetism to explain our concept of left and right to far away aliens, or explain it to Martians over the phone, as Richard Feynman put it).

The first time many of us had to face the formal concept of handedness was, in fact, precisely in electromagnetism class.

In EM class, students learn that an electric current generates a magnetic field. That field swirls around the space surrounding the wire similar to how the pattern of wind velocity in a hurricane wraps itself around the eye of the storm. To remember which way the field goes, students are taught something called the right-hand rule.

The association of the right hand rule with electromagnetism gets so ingrained that, in one’s mind, EM theory can become the mental picture of handedness itself–the quintessential example of a theory that has a specific handedness built in.

Then someone comes along and claims that electromagnetism has nothing to do with handedness after all. You listen to their words but all the while your brain keeps blocking them out and instead visualizing the picture of the magnetic field around a wire. How could it ever be, your inner voice keeps repeating, that the theory of the right hand rule cannot tell left from right?

The reason is simple: the idea that the magnetic field itself points in a well-defined direction–the idea that there is a north and a south–is purely a convention. To see why, it helps to look at what a magnetic field actually does. A static magnetic field enters in essentially two (not entirely unrelated) types of phenomena. The first is that it puts a torque on permanent magnets, for example, on the needle of a compass: more on this later.

The second is that it deflects moving electric charges: hence the curved trajectories you see in some of the tracks coming out of atom smashers such as the LHC. Particle physicists embed their detectors in powerful superconducting magnets because they can can glean lots of information just by looking at how those tracks are bent.

The first high-energy collision recorded by a detector at the LHC. Electrically charged particles (such as electrons) have curved trajectories because the detector is bathed in a strong magnetic field.

The magnetic field pushes the electron in a direction that’s at 90 degrees both to the elctron’s motion and to the magnetic field itself. This is called the Lorentz force, and its exact direction is described again by a right-hand rule.

Here is what happens in a very simple case: say you have a vertical wire in which current is running in the “up” direction. According to the right hand rule, the wire produces a magnetic field that looks more or less like this (pardon the extremely low-tech illustration):

Now an electron shows up and it’s moving vertically. The field then acts on the electron with a Lorentz force that’s at 90 degrees both to the field itself and to the motion of the electron. That force is directed away from the wire, and looks as follows:

To figure out which way the force pushes the electron, one applies the right hand rule once to get the direction of the magnetic field, and then once more to calculate the corresponding force. The end result is a force pointing in a direction that has nothing to do with any left or right hand: it just points towards or away from the wire.

“When we actually predict how matter moves due to magnetic fields, we use the right-hand rule twice, so it cancels out.” explains John Baez, a mathematical physicist at the University of California, Riverside. “We use the right-hand rule once when describing how a current or changing electric field produces a magnetic field, and again when describing how a magnetic field pushes on matter!”

If we had used the opposite convention (a left-hand rule) for defining the magnetic field, but also to calculate the resulting Lorentz force, “we’d get the same answer,” Baez points out.

But is the orientation of the magnetic field really aribitrary? After all, doesn’t a bar magnet point in a definite direction? In fact, one way to define the magnetic field is by observing its effects on bar magnets, in particular on a compass. You place the compass at a point in space and you take note of which way the “N” points. If you walk your compass around the electric wire the S->N direction is always that of the magnetic field, as defined by the right-hand rule.

There is one small problem, though. Our very definition of magnetic north is itself a convention. It would not be any easier to explain to an alien what we mean by north than it would be to explain our concept right-handed.

We are accustomed to looking at maps in which north is up and south is down (although the North Pole of maps does not quite coincide with the North Magnetic Pole, which complicates things a bit). Maps point north perhaps because they were invented by people in the Northern Hemisphere, who may have found it convenient because they used the North Star for navigation. If you look at the North Star while holding up a map in front of you, it helps to be able to read the labels on the map without having to tilt your head. According to some, the tradition of putting north up and south down dates back to Ptolemy.

But there is a perfect symmetry between the north and south magnetic pole of the Earth. Nothing moves preferentially from south to north–or from north to south–except in our imagination. Auroras don’t happen any differently at the South Magnetic Pole than they do at the North Magnetic Pole. An alien arriving at Earth would certainly be able to measure the geomagnetic field, but from that he could never guess which way we have conventionally decided to point the arrow on our compasses.

This post is part of a series on handedness. Here are the all the posts in the series:

A Galactic Challenge: How Would You Teach Left from Right to an Alien Civilization?

Galactic Challenge, Part II: The Richard Feynman Files

Galactic Challenge Part III: The “Easy” Solutions

Why There’s No Such Thing as North and South

Still to come: The “hard solutions” to the challenge

Suggested reading:
The New Ambidextrous Universe: Symmetry and Asymmetry from Mirror Reflections to Superstrings: Third Revised Edition. By Martin Gardner. 2005.
The Handedness of the Universe. Roger A. Hegstrom and Dilip K. Kondepudi in Scientific American, Vol. 262, pages 108-115; January 1990.
Alien Pizza, Anyone? Davide Castelvecchi in Science News, Vol. 172, No. 7, pages 107-; August 18, 2007

Image credits: Steele Hill/NASA; National High Magnetic Field Laboratory

Galactic Challenge Part III: The “Easy” Solutions

Davide Castelvecchi — Mon, 12 Sep 2011 17:36:39 +0000

Which hand is this?

Scores of readers responded to my Galactic Challenge (proposed in Part I of this series), with lots of cool ideas. The challenge was to explain our concept of left and right to far away aliens; or to explain it to Martians over the phone, as Richard Feynman put it and as I describe in Part II.

Here I will review the solutions that came up and I will discuss how one could implement them in practice. I will focus on the “easy” solutions, meaning the ones that appeal to the shared experience of a physical object, be it observing configurations of galaxies or interacting with the same electromagnetic waves. In a follow-up post I will talk about the tougher problem of explaining our concepts of left and right spiral motion to aliens with whom we share no such experience. All we can do, then, is refer to the laws of physics, which for all we know hold the same everywhere in our universe, throughout space and time.

Kimballk and others suggested using galaxies as reference points. To assign an orientation of space, we would need three galaxies in addition to our Milky Way. Together, the four galaxies should not lie on the same plane (which implies in particular that no three of them should be aligned). Given all these assumptions, we could define the center of our galaxy to be the origin, and the lines connecting it to the three galaxies to be our x, y and z axes. Once we have such a labeled reference system, it is easy to talk about left and right corkscrew motion, for example.

A variation on that theme was the one proposed by _jeremy, who said that an advanced civilization should be able to leave radio beacons scattered troughout the galaxy. By referring to those beacons, one could construct axes for an oriented system of coordinates.

In fact, it should not even be necessary to place the beacons too far apart from one another–just far enough that a good radio telescope such as Arecibo would be able to tell them apart.

Unfortunately the power required to broadcast signals in all directions throughout the galaxy would be enormous, so as @therealtinasky and others suggested, it might be cheaper for everyone to refer to beacons offered by nature free of charge: pulsars. The rotational frequency of pulsars can be measured with great accuracy and precision from enormous distances.

jtdwyer pointed out that our alien friends probably would be aware of the fact that our galaxy, the Milky Way, is rotating. Its rotation by itself does not define an orientation of 3-D space, but it does if paired with a notion of “up” and “down”: for that, we could choose the direction of another galaxy, for example we could say that the Andromeda Galaxy is “up.” (The Andromeda Constellation, or any other constellation for that matter, would not be very helpful because constellations are just arbitrary groupings of stars as seen from our vantage point: the aliens might not know what we are talking about.)

Another way to distinguish an “up” direction could be to point to the galaxy’s motion with respect to the cosmic microwave background, which could even be detected from other galaxies. (It was by detecting the relative motion of galaxies with respect to the CMB that astronomers discovered the strange and unexplained phenomenon called dark flow (story I wrote for Science News magazine).

Now comes one of my favorite solutions, which had been suggested to me by my friend David Harris and which several readers, beginning with KWillets, quickly thought of as well: the aliens could impose a circular polarization on the radio signal. Here’s how that works.

As the name suggests, electromagnetic waves propagating in space consist of oscillating electric and magnetic fields. Those oscillations are at 90 degrees to each other, and each of them is at 90 degrees from the direction of propagation of the wave. If the direction of the electric and magnetic oscillation is always the same instead of turning randomly–for example, if the electric fields always oscillate vertically–the wave is called linearly polarized.

Linearly polarized light

In a circularly polarized wave, the fields’ direction rotates continuously as the wave moves on, in a corkscrew motion. As I mentioned in Part I of this series, a corkscrew defines an orientation of 3-D space.

Circularly polarized light

Typically, radio antennas emit linearly polarized waves, but it is not difficult to build a circularly polarized radio antenna. So we could send right-handed corkscrew waves to our aliens and tell them, “this is what we mean by right-handed.”

To pick up the orientation of our radio waves in the correct way, the aliens would have to build a receiving antenna that discriminates between left and right circular polarization. An easy way to do so could be to place antenna rods at 90 degrees from each other but also on different planes, separated by one-fourth of the wavelength of the signal. When the wave’s electric field aligns with the first rod, the aliens’ apparatus would record a maximum electric field there, say, going “up.”

At the same instant, one-fourth of a wavelength ahead, the electric field would be rotated by 90 degrees either to the left or to the right. If it went right, the apparatus would record a maximum electric field going in that direction, and the aliens would know that we have transmitted waves with a right-handed spiral motion. If instead the electric field on that plane were going left, the motion would be in a left-handed spiral.

A skeptic might ask, How do the aliens know what we mean by electric field? On Earth, our convention is that the electric field points in the direction going from positive to negative charges; electrons are by convention called negative and they accelerate in the opposite direction to the electric field. An engineer on Earth would know which way the electric field points by measuring small electric currents induced on the antenna. So it’s easy! Just tell the aliens which way the electrons in their antennas are supposed to move.

There is one subtlety though, the skeptic says. What’s an electron? We could explain our notion of electrons to the aliens by saying that electrons are the things that orbit atoms, and they are about 2,000 times lighter than their positively charged counterparts, the protons. But what if the aliens were made entirely of antimatter? It is not entirely impossible that there could be antimatter galaxies far, far away. In an antimatter world, the small things that orbit atoms would be anti-electrons, also known as positrons, and they would accelerate in the direction of the electric field, not the opposite.

Fortunately, though, our instructions for building the antenna would give exactly the same result whether the aliens are made of matter or of antimatter. In the latter case, the aliens would have a notion of electric field that points in the direction opposite to ours. But while our electric field rotates to the right by 90 degrees, its evil antimatter twin also rotates the same way!

Read the next installment in this series: Why There’s No Such Thng as North and South

This post is part of a series on handedness. Here are the all the posts in the series:

A Galactic Challenge: How Would You Teach Left from Right to an Alien Civilization?

Galactic Challenge, Part II: The Richard Feynman Files

Galactic Challenge Part III: The “Easy” Solutions

Why There’s No Such Thing as North and South

Suggested reading:
The New Ambidextrous Universe: Symmetry and Asymmetry from Mirror Reflections to Superstrings: Third Revised Edition. By Martin Gardner. 2005.
The Handedness of the Universe. Roger A. Hegstrom and Dilip K. Kondepudi in Scientific American, Vol. 262, pages 108-115; January 1990.
Alien Pizza, Anyone? On other worlds, biochemistry could have taken a different turn. Davide Castelvecchi in Science News, Vol. 172, No. 7, pages 107-; August 18, 2007

Alien courtesy of lauren/Open Clip Art

Galactic Challenge, Part II: The Richard Feynman Files

Davide Castelvecchi — Sun, 04 Sep 2011 06:24:21 +0000

In a recent post, I proposed a riddle on handedness and how one could communicate one’s notions of left and right to faraway aliens. It should perhaps surprise no one that the way I formulated the riddle was just a more cumbersome and less elegant version of one that Richard Feynman presented to Cornell students in 1964, as I found out thanks to our Blog Network Czar, Bora Zivcovic.

“Suppose that we were in a telephone conversation with a Martian, or an Arcturian or something,” Feynman said in his lecture. “We don’t know where he is and we would like to describe things to him.” One way to establish a communication, Feynman points out, is to start from the basics, and there’s nothng more basic than integer numbers (the same idea that Carl Sagan later exploited in Contact).

At some point, though, we presumably have learned how to communicate, and the Martian is curious to learn about us. “Suppose that he says, ‘You fellas’–after we get familiar with him–’You’re very nice; now I’d like to know what you look like.’”

Describing features such as body size would be easy, Feynman points out, because we could appeal to facts about the world that are the same everywhere–for example the size of a hydrogen atom.

But the Martian wants to know more. “And he says, ‘That’s very interesting; what do you look on the inside?’ So we describe the heart and so on, and we say, ‘Now, put the heart on the left side.’ Now the question is, how can we tell him which side is the left side?”

One point of reference we might be tempted to use is that of biochemistry. “‘Aw, you take beet sugar, see, and you put it in water, and it turns.’ Only trouble is, he has no beets up there.” Here, Feynman was referring to the fact that when polarized light goes through a solution of water and sucrose its polarization twists.

That effect is due to the fact that sucrose comes in two varieties whose molecular structures are mirror images of each other, and which have opposite effects on the polarization of light. (An even mix of the two has no effect on light.) All sucrose of biological origin is of the same variety, called right-handed, but we have no way of knowing if the aliens’ sugars–assuming they have any–have the same handedness as ours do.

The same is true of proteins and DNA. “We have no way of knowing … whether the accidents of evolution would have started with maybe the wrong-headed threads: there’s no way to tell.” (Incidentally, that is one reason why it would be a bad idea to eat alien pizza before doing some chemical analysis.)

Feynman’s lecture, entitled “Symmetry in Physical Law,” was part of a cycle of lectures he gave at Cornell in 1964 called “The Character of Physical Law,” which can be watched in full on a Microsoft educational web site. You can jump to section 11 of the lecture to see the part about handedness. But I recommend watching the whole thing. The presence and wits and charisma of the man were just extraordinary.

Spoiler alert: after talking about sugar Feynman proceeds to give away the solution to the riddle, which was based on physics that at the time was very new, having been discovered in 1957. (More details on that in a follow-up post.) Had he given the same lecture ten years before, one can only wondered what he would have said–perhaps, simply that there was yet no known way of telling left from right using the laws of physics.

To be continued!

This post is part of a series on handedness. Here are the all the posts in the series:

A Galactic Challenge: How Would You Teach Left from Right to an Alien Civilization?

Galactic Challenge, Part II: The Richard Feynman Files

Galactic Challenge Part III: The “Easy” Solutions

Why There’s No Such Thing as North and South

Suggested reading:
The New Ambidextrous Universe: Symmetry and Asymmetry from Mirror Reflections to Superstrings: Third Revised Edition. By Martin Gardner. 2005.
The Handedness of the Universe. Roger A. Hegstrom and Dilip K. Kondepudi in Scientific American, Vol. 262, pages 108-115; January 1990.
Alien Pizza, Anyone? Davide Castelvecchi in Science News, Vol. 172, No. 7, pages 107-; August 18, 2007

The Lede Desk: Fighting the Scourge of Boring Writing

Davide Castelvecchi — Tue, 30 Aug 2011 09:41:21 +0000

It was a dark and stormy night in New York City, so why was I instead slouching on my couch in sunny Rome?

Because I was concocting a weather report-anecdote-question-postural opening for this blog post.

It is probably safe to say that no journalist is fully immune from cliches, especially in the openings of their articles, which many of us insist on calling ledes (in that cliquish, intentionally misspelled way, just like we write “graf” for paragraph, “hed” for headline, and so on).

To curb the plague (or fight the scourge, or buck the trend, or stem the tide) of the cliche lede, some time in the 1990s Steve Twomey, who at the time was ~~a writer~~ assistant national editor at the San Jose Mercury News, distributed a memorandum around the paper’s newsroom. The memo came from a fictional Lede Desk. Twomey, who had won a Pulitzer Prize for a fantastic feature article he had published in 1987 in the Philadelphia Inquirer, knows a thing or two about writing well, and the memo (to which, he says, other Merc writers also contributed) showed by example how not to write a lede.

When I studied science writing at the University of California, Santa Cruz, one of my teachers of newspaper news writing, Glennda Chui–who at the time was a science writer at the Mercury News–distributed copies of the Lede Desk Memo to her class, and I have religiously kept those pages with me all these years.

Glennda, who herself shared a Pulitzer Prize with other Mercury News staff for their coverage of the Loma Prieta earthquake of 1989, has graciously given me permission to post the memo here, and so has Twomey. I hope it will help future journalists to avoid falling into the same traps. (It’s really hard to say anything without using cliches, isn’t it?)

I certainly have violated many of these rules in my ledes over the years (including rule 2, rule 3, rule 6 and rule 10). I hope Glennda will forgive me.

So, what do Davide Castelvecchi and two Pulitzer Prize winners have in common? Not a lot, unfortunately, but we all do love the Lede Desk.

The San Jose Mercury News Lede Desk Memo

Before all future stories go belly-up, bringing the Mercury News to a crossroads and necessitating sweeping recommendations in the wake of diminishing sales, welcome to the lede desk. Or meet the lede desk. Or this is the story of the lede desk. You’ll catch on. What if all stories began like these:

1. First, the good news: On one occasion, many years ago, this kind of lede worked. Now the bad news: It doesn’t anymore.

2. What do you use when you can’t think of a lede?
A question.

3. “Whenever I feel stymied for an opening, I find a good quote and use that,” said Joe Reporter.
“Yeah,” said his assigning editor, “that’s always a cheap and dull-as-shit way to start a story that no one will read.”

4. Joe Reporter leaned back in his chair, put his feet up on his chair and admitted that describing how someone was sitting was a pretty stupid way to begin a story.

5. Outside, the snow lay deep and crisp and even. The sky was a deep, cloudless blue, the temperature hovered at zero, the wind howled out of the west.
Inside, a reporter had opted to give the weather rather than think of a better lede.

6. When Joe Reporter got back to the office one day not long ago, he plopped himself down in the newspaper morgue, hauled a couple of stacks of old papers and sifted through page after page, looking for a good idea for a lede.
He decided to use an anecdote.

7. Take one vague story idea and an 18-inch hole on the page, add a couple hours of mediocre interviews and two old clips. What do you get?
The desperation recipe lede.

8. Like the captain of the ship of state, piloting his country through the turbulent waters of international seas, a reporter often finds himself facing waves of doubt about his lede, and ultimately he turns to what he thinks is a safe harbor, the metaphor or simile lede.
There, his lede sinks.

9. What do a lazy reporter at the Mercury News, an unthinking editor at the San Francisco Chronicle and sleepy copyeditors at the San Francisco Examiner all have in common?
They all just love to pieces the “what do these things have in common” lede.

Real life example: (INSIGHT News Service) TORONTO — What do nuclear waste and retired people have in common?

10. You might think it’s great to set up a false premise in the lede, only to knock it down in the second graf before getting to what you really mean to say.
You’d be wrong.

11. When Joe Reporter left home that morning, little did he know that when he turned in his lede, his editor would spike it.
Joe had failed at predicting the future.

Real life examples:
Knight-Ridder Newspapers – When Robert Stevenson went out drinking last night, he didn’t expect to pay with his life.
OAKLAND, Calif., June 29 /PRNewswire/ – When Nancy Seymour went shopping for ice cream last week, little did she know the experience would save her life.

12. Do you often find yourself meeting someone in the lede of a story who you found to be pretty hackneyed in the introduction?
Meet the “Meet Joe Interesting” lede.

13. Consider the following; ledes that ask you to ‘consider the following’ are showing up with increasing frequency in this newspaper.

Many thanks to Steve Twomey and Glennda Chui for their permission to reproduce the Lede Desk Memo.
Image courtesy of ArtFavor/Open Clip Art Library

A Galactic Challenge: How Would You Teach Left from Right to an Alien Civilization?

Davide Castelvecchi — Sun, 28 Aug 2011 13:30:45 +0000

The concept of handedness—of left and right, say, or of clockwise and anti-clockwise—is deceptively simple. In fact, I think it is among the most subtle in all of science and mathematics. In this post I will pose a challenge that I hope intrigue my readers.

This will not be a test or a quiz: I have not yet completely worked out a solution myself. Rather, it is the opening salvo for what I hope will be an interesting discussion. For a follow-up post, I plan to interview some physicists to see what their take is. But first, some preliminaries.

Imagine that you had to explain the meaning of the words “left” and “right” to someone who had never heard those words before. And imagine, moreover, that you had to do so in a purely verbal manner, that is, without drawing pictures or pointing at things or otherwise making gestures.

After giving it some thought, you would perhaps start by appealing to some shared experience. For example, to an American you could say that if they were to drive cross country from New York City to San Francisco, their right side would be where Canada is, while their left side would be the side of Mexico.

But what if you were told to make no assumptions about where the person is coming from or how much geography he or she knows? You could hope that they knew something about the stars. You could explain, for example, that if one looks at the constellations of the Zodiac with their “up” side pointing north, then they would see the constellation of Gemini, say, to the left of Taurus and to the right of Cancer. (In the celestial sphere, the constellations of the Zodiac are those traversed by the sun in its apparent path in the sky during Earth’s yearly revolution.)

But constellations are purely conventional groupings of stars, and in fact the way they’re assembled is culture-dependent. Besides, how many of us can recognize them? In a dark, moonless sky I can perhaps spot the Big Dipper, Orion, and a couple more if I’m lucky.

Even if your friend had never learned about any constellations, though–or if they had never seen any because they spent their entire lives in L.A. or New York–you could still use astronomical references to explain left and right. Perhaps the simplest way to do so would be to tell them that if they’re facing north, “right” is where the sun will rise and “left” where it will set.

Of course, you’d first have to explain the word “north.” But that is easy to tell—at least if you live in the Northern Hemisphere—because the North Star is the only star that virtually doesn’t move during the Earth’s rotation. (There is no South Star.) In the long exposure below, where the stars form streaks in the sky over the Annapurna Range (Himalayas) as the Earth rotates, the North Star is the little dot in the middle.

Another way that you could introduce the concept of “left” and “right” could be by resorting to human anatomy. You could point out that that “left” is the side where the heart is, while the liver is on the right—and then you’d have to hope that your interlocutor is not among those rare people who have their entire bodies inverted, with their hearts on the right, their livers on the left and so on.

Or, you could take a biochemistry approach. Have your friend learn how to purify and crystallize DNA and analyze its structure. Ordinarily, the DNA’s double helix is twisted in such a way that it looks like a spiral staircase that goes up as it goes from left to right: think of a forward slash, “/”. It is what people call a right-handed screw. A left-handed screw, on the other hand, is like a spiral staircase that goes down, like a backward slash, “\”. (You would also have to make sure that your friend does the experiment properly, so that their DNA doesn’t curl up the wrong way, in the so-called Z-DNA conformation, instead of in the usual conformation, called B-DNA. The two conformations however look very different to a structural biologist.)

Perhaps you are beginning to see my point. To communicate or even establish a notion of left and right, you have to appeal to some common experience, some tangible object or phenomenon. Or, as a physicist might say, you have to define that notion operationally. Absent that, there is no a priori way to orient yourself. This, by the way, is reflected in the way mathematicians describe handedness, also known as chirality or orientation, in an abstract space: In geometry there is no a priori notion of left and right the way that there is an a priori notion of positive and negative numbers. It is purely a convention.

So here is my challenge to you, dear reader. How would you communicate the concept of left and right via radio signals to an alien civilization?

First, of course, the two civilizations would have to detect each other and decrypt each other’s languages, which could take some back and forth; and messages would take tens or hundreds of years to get from here to their star system and back, depending how far their star system is. But let’s say you’ve had a few centuries to practice interstellar communication.

To spice things up a bit, let’s revert the situation–so that it is the aliens who have to teach left and right to us–and let’s say that the future of humanity is at stake. We have discovered that in a few decades the sun will explode, and that the only way our species can survive is to abandon the solar system. Fortunately, the aliens possess the technology to build a sort of cosmic gate to cross wormholes. A specially-built spacecraft could take four men and four women on board, cross the cosmic gate machine and almost instantaneously travel across the galaxy. There, these pioneers could find a hospitable planet to settle. They could then go forth and multiply, ensuring the survival of the species.

There isn’t enough time for the aliens to send a cosmic gate and a wormhole spacecraft our way, so we need them to teach us how to build one. We need them to send us the blueprint. So they begin to beam information to us in the form of a 3-D technical drawing, encoded as a set of 3-D coordinates in space.

But there’s a snag. To work properly, wormhole traveling relies on a network of cosmic gate machines the aliens have placed around the galaxy. All of those machines are built in such a way that a ship must cross them in a corkscrew motion. That motion must be like what we on Earth would call a right-handed screw. Any attempt to cross the gates in a left-handed motion will result in disintegration of the gate machine and of the ship and everything inside it.

You see, we can reconstruct a detailed 3-D drawing from the coordinates–all those x’s, y‘s, and z‘s they sent us. We earthlings have a convention to set up coordinates in such a way that if you stand up in the positive z direction and look down to the xy plane, the positive-x axis will be to the right of the positive-y axis. But we have no way to tell if that is the same convention that the aliens use. Thus, we have no way to tell if model we build, and its corscrew motion, are the correct ones or their mirror images.

The aliens’ language does include words for “left” and “right” and for “left-handed screw” and “right-handed screw”. But in all our communications with them, we were never able to figure out which was which. We need them to explain to us which of their words corresponds to our word “left,” and which to our word “right.” To do so, they will need to appeal to some common point of reference or phenomenon. I shall restate the challenge as follows:

How can an alien civilization instruct us via radio signals on how to build a spaceship that flies with a right-handed twist?

I can think of at least a couple of “easy” solutions to this problem, one of which was suggested to me by my friend David Harris. I will describe those solutions in a subsequent post, but in the meantime I am curious however to see what ScientificAmerican.com readers—who are a smart bunch—will come up with. Remember, you have to save the human species!

Later, I will “cheat” and I will modify the problem a bit to make it harder, and also more interesting. At that point, some rather deep physics concepts should come into play.

Read the follow up to this post, Galactic Challenge, Part II: The Richard Feynman Files

This post is part of a series on handedness. Here are the all the posts in the series:

A Galactic Challenge: How Would You Teach Left from Right to an Alien Civilization?

Galactic Challenge, Part II: The Richard Feynman Files

Galactic Challenge Part III: The “Easy” Solutions

Why There’s No Such Thing as North and South

Suggested reading:
The New Ambidextrous Universe: Symmetry and Asymmetry from Mirror Reflections to Superstrings: Third Revised Edition. By Martin Gardner. 2005.
The Handedness of the Universe. Roger A. Hegstrom and Dilip K. Kondepudi in Scientific American, Vol. 262, pages 108-115; January 1990.
Alien Pizza, Anyone? On other worlds, biochemistry could have taken a different turn. Davide Castelvecchi in Science News, Vol. 172, No. 7, pages 107-; August 18, 2007

Fox Commentator Distorts Physics

Davide Castelvecchi — Thu, 11 Aug 2011 22:51:04 +0000

This is not a climate science blog, nor is it a political or media critique blog. But it does cover physics, so I’d like to get some physics facts straight.

On the August 6 edition of Fox and Friends Saturday, the hosts interviewed Joe Bastardi—whom they introduced as “chief meteorologist at WeatherBell”—on global warming.

Before introducing Bastardi the hosts said that the global warming debate was heating up “after a new NASA study seems to debunk whether it’s actually manmade.” No further details were provided. Instead, as evidence the hosts provided the results of a poll. But presumably the Fox presenters were referring to a study that has created a lot of controversy and media hype.

The most jarring part however came later, when Bastardi commented that he didn’t believe CO2 emissions could ever affect the climate. Unfortunately, Bastardi’s argument was based on what seemed to be poor understanding of basic physics, including thermodynamics and atmospheric physics.

“If you look at carbon dioxide, it increases by 1.5 parts per million a year,” Bastardi said. “We contribute 3 percent of that.”

According to the International Energy Agency, global CO2 emissions have reached a record of 30.6 billion tons during the year 2010.

Many natural sinks and sources also contribute to the global carbon cycle. The oceans absorb more CO2 than they release, and so do vegetation and the soil, while natural sources such as volcanoes contribute smaller amounts. In other words, natural sources and sinks, if anything, would reduce the amount of CO2 in the atmosphere. Therefore, if there is any increase in CO2 concentrations, it is entirely due to emissions caused by humans.

To make matters worse, Bastardi claimed that the idea of manmade global warming is incompatible with the laws of physics.

“[Saying that CO2 could affect the climate] contradicts what we call the first law of thermodynamics: energy can never be created nor destroyed,” Bastardi said. “So, to look for an input of energy into the atmosphere you have to come from a foreign source.” His prepared remarks were accompanied by screens that seemed to display an intent from the TV show to be pedagogical.

The first law of thermodynamics does indeed guarantee conservation of energy. And the CO2 injected into the atmosphere does not carry energy with it—or rather, it does, because matter always carries energy, but not in a way that would raise temperatures significantly, if at all. But no one has ever claimed that CO2 would raise temperature by itself. Putting it this way is a grotesque distortion of what climatologists say.

What climate science says is not that CO2 carries energy into the atmosphere or somehow magically generates it out of nowhere. Instead, it says that CO2 and other gases acts as a blanket, keeping heat from escaping into space. This, as Bastardi should know, is called the greenhouse effect.

The Earth radiates into space roughly the same amount of energy that it receives from the sun. But much of what it radiates is in the infrared spectrum, whereas most of the sun’s energy reaches us in the visible spectrum.

The greenhouse effect results from the fact that CO2 (and other greenhouse gases, chiefly water vapor) is more opaque to infrared radiation than it is to visible light. So it lets the sun’s rays in, but it won’t allow the Earth to cool down too much.

Bastardi proceeded to say that what global warming there is “is already out there, carbon dioxide being a part of it,” a statement that seems devoid of any meaning, and that “you can trace it to the sunspot cycles and you can trace it to the movement of the oceans.”

But if global warming was caused by sunspots, why would it be happening now, when the sun is has been in an unusually long period of low activity?

According to Washington Post blog Capital Weather Gang, WeatherBell, the company that employs Bastardi, is “funded entirely by angel investors.”

Update August 16: Bad Astronomy points out that Bastardi apparently has a long history of misunderstanding and misrepresenting science.

[Note added August 12: I recommend reading John Rennie's "Seven Answers to Climate Contrarian Nonsense"; I will not respond to comments that are already addressed therein.]

David Biello contributed some reporting for this story; many thanks to Robin Lloyd for pointing me to the Media Matters story.

Project Polymath: Collaborative Mathematics through Blogs

Davide Castelvecchi — Thu, 11 Aug 2011 03:57:45 +0000

[This article was originally posted on ScientificAmerican.com on March 17, 2010 and I am shamelessly recycling it here]

In the mid-20th century the encyclopedic works of French mathematician Nicolas Bourbaki traced every mathematical concept back to the subject’s foundations in the theory of sets—the stuff of Venn diagrams—and changed the face of his field. Like many of his notions, Bourbaki existed only in the abstract: he was the pseudonym for a tight-knit group of young Parisian researchers. The Internet-age version could be D.H.J. Polymath, another collective pseudonym who could define a new style of mathematics.

Polymath began life on the blog of Timothy Gowers, a University of Cambridge winner of the Fields Medal, mathematics’ most coveted prize. In a blog post in January 2009, Gowers asked whether spontaneous online collaborations could crack hard mathematical problems—and if they could do so in the open, laying the creative process out for the world to see. Web-based scientific collaborations and even “crowdsourcing” are now common, but this one would be different. In typical online collaborations, scientists each perform a small amount of research that contributes to a larger project, Gowers pointed out. In some cases, citizen-scientists such as bird-watchers or amateur astronomers collectively can make significant contributions. “What about the solving of a problem that does not naturally split up into a vast number of subtasks?” he asked. Could such a problem be solved by the readers of his blog—simply by posting comments?

For a first experiment, Gowers chose the so-called density Hales-Jewett theorem. This problem, Gowers says, is akin to “playing a sort of solitaire tic-tac-toe and trying to lose.” The theorem states that if your tic-tac-toe board is multidimensional and has sufficiently many dimensions, after a short while it is impossible to avoid arranging X’s into a line—you cannot avoid winning no matter how hard you try. Mathematicians have known since 1991 that the theorem was true, but the existing proof used sophisticated tools from other branches of math. Gowers challenged his blog’s readers to help him find a more elementary proof, a problem generally considered quite hard.

The project took off a lot faster than Gowers expected. Within six weeks, he announced a solution. Turning the proof into a conventional paper took longer, especially because the argument was scattered across hundreds of comments (blogs may not be the ideal platform, and ad-hoc collaboration tools may turn out to be better suited for math). But last October the group posted a paper on the online repository arxiv.org under the name of D.H.J. Polymath, where the initials are a reference to the problem itself.

In another way, however, the project was a bit of a disappointment. Just six people—all professional mathematicians and “usual suspects” in the field—did most of the work. Among them was another Fields medalist and prolific blogger, Terence Tao of the University of California, Los Angeles.

Pooling talent has its advantages, Gowers says. When trying to solve a problem, mathematicians usually make many failed attempts, in which they try lines of reasoning that can turn out to be “blind alleys,” after weeks or months of work. Often those lines of reasoning that seem promising to one expert look obviously fruitless to another. So when every attempt is exposed to public feedback, the process can become much faster.

Tao describes the experience as “chaotic” but a lot of fun and “more addictive than traditional research.” Gowers has since kicked off a few more online collaboration projects, and so has Tao—and nonprofessionals have begun to contribute in ways that are “genuinely useful,” Gowers says. These high-brow amateurs included a teacher, a priest (albeit one who as a kid took part in the Mathematical Olympiads) and a math Ph.D. who now works in computing. But how widely the approach will be adopted is unclear. A number of hard problems may be suitable, Tao says, such as devising an algorithm for playing chess that is not based on the brute-force calculation of possible future moves. Famous mathematical conjectures may not be as amenable, because those problems tend to have a long history—and experts already know all the blind alleys.

Rafael Núñez, a cognitive scientist at the University of California, San Diego, who has studied the mental and social process of doing mathematics, points out that problem solving is just another human activity. When mathematicians work together in front of a blackboard, they communicate in subtle ways with their voice and body language, clues that will be lost in online collaborations. But mathematicians will adjust to the new medium, just like people have adjusted to doing all kinds of other things in a connected world, Núñez notes: “Anything we do online is different, not just mathematics.”

In the end, the open nature of the project may have been its most important feature. As Gowers wrote on his blog, Polymath may be “the first fully documented account of how a serious [math] research problem was solved, complete with false starts, dead ends, etcetera.” Or, as Tao puts it, the project was valuable because it showed “an example of how the sausage is made.”

Plagiarism was not a concern: when everyone’s most minute contribution is on the public record, it is hard for others to copy ideas and claim to be original, Tao points out. Established online repositories such as arxiv.org, he adds, have also reduced the risk of plagiarism and at the same time they have made it easier to catch mistakes before a paper is formally published.

Image credit: Jeffrey Coolidge/Getty Images

What Do You Mean, the Universe Is Flat?, Part 2: In Which We Actually Answer the Question

Davide Castelvecchi — Mon, 01 Aug 2011 03:57:33 +0000

Stand up.
Walk 10 feet straight ahead.
Turn left by 90 degrees.
Walk another 10 feet.
Again, turn left by 90 degrees.
Do it for a third time: walk. then turn left.

Now the next time you walk 10 feet ahead, you’ll trace the fourth and last side of a square, and you’ll end up where you started. If you turn by 90 degrees for a fourth time, you’ll face in the original direction, too.

This seems intuitively obvious, even tautological—if you trace a square on the ground, well, you trace a square on the ground—but it is actually an empirical fact. And it’s important, so I’m gonna say it out loud:

There is no a priori reason why walking four equal sides and turning four right angles should take you exactly back to the same place. It is purely an empirical thing of our everyday experience.

As a matter of fact, it is not exactly true empirically, either. The failure to come back to the exact same spot—to precisely close a square—is not just true; it is one of the most important phenomena ever observed in the history of science. It is at the heart of everything. It is the way that gravity works the way that Einstein understood it. It tells us how black holes form and why they trap light. And it tells us if and how the universe should expand.

Our intuition tells us that every square should close. The world is far stranger than our intuition would have us believe.

In the previous part of this series, Part I, I promised that Part II would explain what it means for the universe to be flat. In this second part, I will talk about the concept—no, the phenomenon—of curved space, which is essentially when square paths fail to close, and about why flat space is where all square paths do close up.

Euclid Tried

So far I have intentionally emphasized the physical nature of this phenomenon called curvature of space. Most authors when they write about it follow a very different approach: they start with history.

You see, mathematicians came up with the idea of curvature—as a logically consistent but abstract concept—long time before anyone proved that it was relevant to reality. And measuring the curvature of space is actually very hard to do in practice, so it’s possible that no one would have tried if mathematicians had not told them that it was at least a possibility worth considering.

The mathematics required to fully make sense of curvature was invented in the mid-1800s by Georg Bernhard Riemann, and it is rather intricate. But curved space is a fact of life. In principle, you could discover it by walking around your room, without the need for mathematicians or physicists or philosophers to come up with abstract concepts first.

Euclid, the great geometer of Hellenistic Alexandria, was well aware of the fact that the closing of square paths is not a priori true. Euclid might have said it this way: the inner angles of a square (or of a rectangle or, for that matter, of a parallelogram) add up to 360 degrees. Going around a square means making four 90-degree turns.

Another way that Euclid might have put it is by stating a related fact: that the inner angles of a triangle always add up to 180 degrees. Cut any rectangle into two triangles along its diagonal, and you’ll see why: your four right angles get divided into 6 angles, but the sum is still the same.

But geometry does not have to work that way. When it does, it is called Euclidean. But in the vast majority of cases when it does not, it is called non-Euclidean geometry.

Oftentimes, the way that authors introduce the idea of non-Euclidean geometry is by giving examples of what happens when instead of tracing triangles on a plane you trace them on a curved surface—say, on the surface of the Earth.

So start at any point on the equator and head for the North Pole. Once you get there, you’ve covered one-fourth of the circumference of the globe, or about 10,000 kilometers. Now turn left by 90 degrees and start walking south. After 10,000 kilometers, you’ll reach the equator again. But you won’t be at the place where you started. Instead, you’ll be at a place 10,000 kilometers to the west of the starting point. Now turn left by 90 degrees so that you’re facing East, and walk another 10,000 kilometers: you’ll be back where you started.

You have traced a triangle on the surface of the Earth—and the inner angles are all right angles, so they add up to 270 degrees, not 180.

Notice that you have only done three legs of your trip. If you were to follow the instructions at the beginning of this post, you would still have another 90-degree turn and another full side to walk. In this case, the failure to close the square would be rather spectacular: instead of coming back to the original point on the equator, you would have ended up at the North Pole.

Tracing squares with sides that are 10,000 kilometers long is kind of extreme, of course. If you were to try a similar experiment with sides of, say, 1,000 kilometers instead, the error would be a lot smaller, but still conspicuous. And if you tried moving in 10-foot legs, you would notice nothing amiss: the world would look perfectly Euclidean to you. You could be forgiven for thinking that the Earth is flat.

In any event, the sphere a totally legit example of a non-Euclidean geometry, but can also be confusing. “Ok, the Earth is curved,” you say, “but what does that tell me about the curvature of space?”

“What if I had dug tunnels straight across the Earth, joining the two points on the equator and those two points with the North Pole? Together, the three tunnels would form an equilateral triangle. I could then imagine pointing lasers down the tunnels to join the three points with one another into a triangle of laser light. That triangle would surely have angles that add up to 180 degrees.”

Perhaps. But perhaps not.

Space in Outer Space

So here we come to the basic fact of life that I was referring to at the beginning of this post. The curvature of space itself.

To avoid any confusion caused by the Earth, take a trip to outer space. You could think of a spacecraft tracing a triangle or a square by traveling in space. That would not be ideal, though, because it raises all sort of thorny issues about what exactly it means for a spacecraft to fly straight ahead or to turn by 90 degrees to the left.

Instead, you and two buddies each have a spaceship, and each of the three travels to some place in the near universe. Once you’re there, you point lasers at one another and form a triangle of beams.

Now each of you can measure the angle between the two beams that go in or out of the respective spaceship.

Fact: Those three angles won’t always add up to 180 degrees.

You could do the appropriate calculations and realize that this fact is a consequence of Einstein’s general theory of relativity. Or you could distrust math and physics and just go out to space to see for yourself.

Regardless, this is what it means for space to be curved. Whenever you can find three points in space, and join them with laser beams, and find that the triangle doesn’t have the expected 180 degrees, that means that space is curved.

And when no matter where the spacecraft are the angles add up to 180 degrees–that is what it means for space to be flat.

The mathematical machinery of Riemannian geometry goes much further and actually gives you a way to define and calculate numerical measures of curvature—not to just say if there is some or none.

There are two important special types of curved space. If in a certain region of space, no matter where you place your three spaceships the three angles they form always add up to more than 180 degrees, then the curvature is positive throughout the region. When they always add up to less than 180 degrees, that means the region has negative curvature. In the flat case, it’s precisely zero.

This post is part of a series on cosmology. Here are the previous posts:

What Do You Mean, The Universe Is Flat? Part I
(On what I mean by “the universe”)

Being Mister Fantastic
(On visualizing a finite speed of light)

Under a Blood Red Sky
(On the afterglow of the big bang, and why the sky used to glow red)

Still to come: how do we know that the curvature of space is a fact of life; what would the world look like if space were very curved; what is the curvature (and the size) of the observable universe; and what the heck does the observable universe have to do with Dante.

Footprint icon courtesy of palomaironique/Open Clip Art Library.
Spacecraft image courtesy of NASA. The artist’s impression represents the planned Laser Interferometry Space Antenna, or LISA, international space mission, which would in fact be unmanned. Also, LISA is not designed to measure the angles of the triangle but temporary changes in the distances of the space probes from one another due to the passage of gravitational waves–which are themselves perturbations in the curvature of space.

Strings, Geometry, and the Ultimate Reality: The Debate

Davide Castelvecchi — Sat, 30 Jul 2011 16:29:25 +0000

Can strings be the ultimate constituents of the universe–more fundamental than matter or energy, and even than space or time? If they’re not made of matter or energy, what are they, then?

If you look for some light fare for your placid Saturday afternoon, here’s an idea: ponder these ultimate questions–on life, nature, the universe and everything–with my fellow SciAm network bloggers George Musser and John Horgan, by watching the debate they had last night at Bloggingheads.tv.

George and John make an especially compelling duo to watch because their personas are almost diametrically opposed. George’s is that of an unabashed optimist, and toward the end he states his belief that science will eventually discover the ultimate simple laws of everything that will make everyone smack their forehead and go, “why didn’t I think of it?”

John on the other hand has for decades fashioned himself as the curmudgeon of science journalism, poking fun at the cultural idiosyncrasies of science and essentially declaring game over in his 1997 book The End Of Science: Facing The Limits Of Knowledge In The Twilight Of The Scientific Age (as well as in numerous articles for Scientific American, where he used to be a senior writer).

Both of them however reason with much more nuance and subtlety than those simplistic descriptions would have you think, as they demonstrate in more than an hour of discussion intertwining the grand themes of fundamental physics: string theory, the multiverse, cosmic inflation and the anthropic principle–and even the issue of what science itself is.

The part I found most intriguing is toward the beginning, when John takes issue with the idea that strings, those infinitesimally thin and frustratingly enigmatic loops that many of our readers either hate to love or love to hate, aren’t made of matter or energy.

Instead, some physicists say, strings would somehow occupy a deeper layer of reality. It is matter and energy that are made of strings, not the other way around. Similarly, John laments, some physicists contend that strings do not exist in space or time, but instead that space and time themselves may be made of strings.

“My question was,” John says, “What is a string then? If it’s not something that can be situated in space and time and if it’s not constituted of matter or energy, what the hell is it? Is it some kind of pure mathematical form?”

(Mathematical? Now you’re talking, I said to myself.)

George’s answer: let’s not get ahead of ourselves. “It is perhaps premature to talk about what a string might be made of since it’s already a big jump to talk about strings.”

I suspect however that John’s objection is more of a philosophical nature. It strikes at heart the same dispute between realism and phenomenology that has divided physicists ever since Albert Einstein and Niels Bohr were arguing over the implications of quantum mechanics. Simplifying, one could trace that tension all the way back to the philosophers of ancient Greece, starting with Parmenides and Heraclitus.

Immanuel Kant on the other hand observed that science cannot access the ultimate nature of reality–the noumenon (or “thing in itself”). Our eyes and ears, or our finest scientific instruments for that matter, only detect phenomena, not noumena.

In that view, a scientific theory cannot say what the ultimate constituents are: only that they behave according to the predictions of certain mathematical rules. Thus, the question of what the string is made of is not relevant as long as we can experimentally verify that it acts the way that a theoretical string does.

And theoretical strings are geometrical objects; in modern geometry–and by modern I mean ever since Carl Friedrich Gauss, 1777-1855, and Georg Bernhard Riemann, 1826-1866–geometrical objects can be defined intrinsically, that is, it is not necessary to think of them as occupying a larger “space.”

But strings may forever be beyond the scope of science, as John points out. His objection is that strings are too small to detect with any conceivable experiment.

George (who is the author of The Complete Idiot’s Guide to String Theory) had a great answer: that smallness is not specific to strings. Any theory that unifies all forces of nature will have to include gravity. But gravity is extremely weak compared to the other forces, which implies that detecting its quantum behavior requires experimenting with energies that are completely outside of our reach. Any test of a quantum theory of gravity “will have to be indirect and none of them is going to be decisive.”

One thing that fascinates me about the focus on phenomena versus noumena is that in my view, on a very different philosophical level, it is beautifully paralleled in the formal structure of mathematics. Modern math is entirely rooted in the theory of sets, in the sense that any mathematical object and construction can be defined starting from sets. But in any description of set theory that I’ve seen, you never say anything about what the sets ultimately are made of. There’s never a set that contains anything except other sets.

The Information: James Gleick Chats with Robert Krulwich

Davide Castelvecchi — Fri, 29 Jul 2011 02:43:12 +0000

James Gleick is best known for his groundbreaking bestseller Chaos, and has also authored inspired biographies of Newton and Richard Feynman. His new book, The Information, came out earlier this year and has been on my list of books to blog about for a while. Tonight I saw him chat about it at the New York Public Library with Robert Krulwich, the co-host of the WNYC show Radiolab.

Much of his book deals with the idea of information being something that has a physical meaning. We are made out of the information contained in the 750 Megabytes of our DNA, Gleick said. “Information was always what it was even before we knew about it.”

Cool Math & Physics Blogs

Davide Castelvecchi — Thu, 28 Jul 2011 06:21:52 +0000

From time to time, I’ve done something that could be construed as blogging for years now (at my web site, sciencewriter.org), but I am still a blogosphere novice.

As far as I understand, it is good blogging etiquette, not to mention a service to your readers, to have a blogroll–links to blogs that one likes, or that one follows anyway, or that one recommends that others read even if he has no intention of doing so, sort of like Netflix’s “if you liked A, you’ll also like B.”

So while our blogging platform doesn’t have a “blogroll” feature yet (we just started!), I’ll just mention some of my favorite blogs in this brief post. Some of these are blogs I find invaluable and read as often as I can; others are just fun to check out once in a while.

Anyone has great math or physics blogs to recommend? Please feel free to do so by leaving a comment below.

Fun stuff:
Vi Hart, with her amazing mathematical scribblog videos
Krulwich Wonders, from Radiolab genius Robert Krulwich
13.7, NPR’s collective blog on science and philosophy
Physics Buzz, brought to you by Physics Central

Cosmology:
Cosmic Variance, with Sean Carroll among others

Math meets physics:
Not Even Wrong, by string theory skeptic Peter Woit
This week’s finds, John Baez’s protoblog on mathematical physics

Physics news:
Physics World Blog, from Physics World magazine
The Physics arXiv Blog, the anonymously written gold mine
Photonist, by my friend and mentor David Harris
Physics Today News Picks, a news aggregator from Physics Today magazine

Heavy-duty math:
The n-Category Cafe’, a collective blog by mathematicians
What’s new, by Fields medalist Terry Tao, also has very interesting links
Gowers’ Weblog, by Tim Gowers, Fields medalist and creator of Polymath

Image credit: warszawianka

What Do You Mean, The Universe Is Flat?, Part 1

Davide Castelvecchi — Tue, 26 Jul 2011 03:26:33 +0000

The universe is three-dimensional.
The universe is four-dimensional—three for space, one for time.
The universe has nine, or ten or eleven dimensions.
Matter curves spacetime.
The universe is flat.
The universe is infinite.
The universe is 84 billion light-years wide.
The universe is a bubble, or an onion.
Or a hall of mirrors, shaped like soccer ball.
Or a shape out of Dante’s Divine Comedy.

Statements like these appear quite frequently in popular science magazines–including Scientific American–and they seem to be in utter contradiction with one another. But all of them are true, or at least plausible. What gives?

The subtlety is that the word “universe” has different meanings in different contexts. In colloquial English, the word is often taken to mean “everything that exists.” So this intuitive notion of universe seems like a good place to start. If we follow this line of thought, the first thing we notice is that the present tense of the verb “to exist” implicitly assumes that we are referring to “everything that exists now.”

Leaving aside the issue of whether “now” can have a universal meaning–and the even subtler ontological question of what it means to exist–it makes sense to think of the totality of space and all of its contents at the present time, and to imagine this totality as a contiguous entity.

Space or spacetime?

If we take this route, we may first notice that space appears to us to be three-dimensional. Thus, we could make the assumption that we can locate anything in the universe using three Cartesian coordinates: at this frozen moment in time that we call the present, every object occupies a certain x, y and z in our three-dimensional continuum.

So here is one natural notion of the universe: all of three-dimensional space at the present time. Call it the nowverse.

But what about all those other dimensions?

Fanciful theoretical constructs such as string theory postulate that, in fact, there is more to space than we can see, but for now those theories have no experimental evidence to support them. So, for the time being we may as well just focus on our familiar three dimensions.

In this schematic of spacetime, the disk at the top represents space at the present time; the ones below represent space at earlier times

Time, on the other hand, is indeed an additional dimension, and together with space it forms a larger, four-dimensional entity called spacetime. It is natural to think of the nowverse as a 3-D slice in this 4-D space, just like horizontal planes are 2-D slices in our 3-D world. Because most people (including yours truly) have a hard time visualizing 4-D objects, a common way of thinking of spacetime is to pretend that space had only two dimensions. Spacetime, then, would have a more manageable total of three. In this way of looking at things, the nowverse is one of many parallel planes, each of which represent the universe at a particular time of its history.

Thus, the seeming inconsistency of

The universe is three-dimensional.
The universe is four-dimensional—three for space, one for time.
The universe has nine, or ten or eleven dimensions.

is just a matter of clarifying language. For all we know, space is 3-D, and spacetime is 4-D; but if string theory is true, then space turns out to be 9-D, and spacetime 10-D.

Incidentally, when cosmologists talk about the expansion of the universe, they mean that space has been expanding, not spacetime.

Flat or Curved?

A plane and the surface of a sphere are the prototype for flat and curved space

In the last decade—you may have read this news countless times—cosmologists have found what they say is rather convincing evidence that the universe (meaning 3-D space) is flat, or at least very close to being flat.

The exact meaning of flat, versus curved, space deserves a post of its own, and that is what Part II of this series will be about [update July 31: read What Do You Mean, The Universe is Flat? Part II: In Which We Actually Answer the Question]. For the time being, it is convenient to just visualize a plane as our archetype of flat object, and the surface of the Earth as our archetype of a curved one. Both are two-dimensional, but as I will describe in the next installment, flatness and curviness make sense in any number of dimensions.

What I do want to talk about here is what it is that is supposed to be flat.

When cosmologists say that the universe is flat they are referring to space—the nowverse and its parallel siblings of time past. Spacetime is not flat. It can’t be: Einstein’s general theory of relativity says that matter and energy curve spacetime, and there are enough matter and energy lying around to provide for curvature. Besides, if spacetime were flat I wouldn’t be sitting here because there would be no gravity to keep me on the chair. To put it succintly: space can be flat even if spacetime isn’t.

Moreover, when they talk about the flatness of space cosmologists are referring to the large-scale appearance of the universe. When you “zoom in” and look at something of less-than-cosmic scale, such as the solar system, space—not just spacetime—is definitely not flat. Remarkable fresh evidence for this fact was obtained recently by the longest-running experiment in NASA history, Gravity Probe B, which took a direct measurement of the curvature of space around Earth. (And the most extreme case of non-flatness of space is thought to occur inside the event horizon of a black hole, but that’s another story.)

On a cosmic scale, the curvature created in space by the countless stars, black holes, dust clouds, galaxies, and so on constitutes just a bunch of little bumps on a space that is, overall, boringly flat.

Thus the seeming contradiction:

Matter curves spacetime. The universe is flat

is easily explained, too: spacetime is curved, and so is space; but on a large scale, space is overall flat.

Finite or Infinite?

If everything in the nowverse has an x, a y and a z, it would be natural to assume that we can push these coordinates to take any value, no matter how large. A spaceship flying off “along the x axis” could then go on forever. After all, what could stop her? Space would need to have some kind of boundary; most cosmologists don’t think it does.

The fact that you can go on forever however does not mean that space is infinite. Think of the two-dimensional sphere on which we live, the surface of the Earth. If you board an airplane and fly over the equator, you can just keep flying—you’ll never run into the “end of the Earth.” But after a while (assuming you have enough fuel) you would come back to the same place. Something similar could, in principle, happen in our universe: a spaceship that flew off in one direction could, after a long time, reappear from the opposite direction.

Or perhaps it wouldn’t. Cosmologists seem to believe that the universe goes on forever without coming back—and in particular, that space has infinite extension. But when pressed, most cosmologists would also admit that, in fact, they have no clue whether it’s finite or infinite.

In principle, the universe could be finite and without a boundary—just like the surface of the Earth, but in three dimensions. In fact, when Einstein formulated his cosmological vision, based on his theory of gravitation, he postulated that the universe was finite. Einstein’s Weltanschauung was rooted in his deep, almost mystical sense of aesthetics; the most symmetric, aesthetically perfect three-dimensional shape is that of a three-dimensional sphere. (Some have suggested that the way Dante describes the universe in his Divine Comedy has something to do with a 3-D sphere, too: I guess that will have to wait for a future post, too.)

In more recent times, some cosmologists have taken this possibility quite seriously, and have tried to check whether space might be a 3-D sphere, or perhaps a more complicated 3-D space that is essentially a sphere wrapped around itself [see “Is Space Finite?” by Glenn D. Starkman, Jean-Pierre Luminet and Jeffrey R. Weeks; Scientific American, April 1999]. In a universe that has one of these shapes, one could observe trippy hall-0f-mirror type of effects.

The reason why we don’t know if space is finite or infinite is that we seem to have no way of observing beyond a limited horizon. The universe is 13.7 billion years old, and because nothing can travel faster than the speed of light, we don’t have any information about events that happen beyond a certain distance. (For reasons that would be too complicated to go into here, that maximum distance is actually not 13.7 billion light years.)

The observed universe

So one thing we know is what we cannot know: the universe we can observe has finite extension. Cosmologists often refer to it as the observable universe.

How large is the observable universe? That is a surprisingly difficult question, which will be the subject of yet another future post.

For now, let’s just notice that the most distant galaxies whose light we have detected emitted that light about 13.2 billion years ago. Because the universe (meaning space) has been expanding ever since, those galaxies are now at a much greater distance—some 26 billion light-years away.

Even farther away than the farthest galaxies, the most distant object we have been able to observe, the plasma that existed before the age of recombination [see Under a Blood Red Sky], existed about 13.7 billion years ago, a puny 400 millennia after the big bang. Light coming from it has taken 13.7 billion light years to reach us. The matter we “see” in that plasma has also moved farther away: that matter is now an estimated 42 billion light years away. So that’s what cosmologists talk about when they say that the observable universe has a radius of 42 billion light years. (Of course, the answer had to be 42.)

The bizarre fact about the observable universe, however, is that it is not part of the nowverse. Because light from distant galaxies took millions of years to reach us, what we see is in the past, not in the present, and the farther it is, the older it is. So if the observable universe is not part of the nowverse, how can we picture it? Where in spacetime should we place it? [to be continued]

Read Part II: In Which We Actually Answer the Question

This post is part of a series on cosmology. Here are the other posts:

What Do You Mean, the Universe Is Flat?, Part 2: In Which We Actually Answer the Question
(“Flat” means “not curved,” but what does “curved” mean?)

Being Mister Fantastic
(On visualizing a finite speed of light)

Under a Blood Red Sky
(On the afterglow of the big bang, and why the sky used to glow red)

Still to come: how do we know that the curvature of space is a fact of life; what would the world look like if space were very curved; what is the curvature (and the size) of the observable universe; and what the heck does the observable universe have to do with Dante.

Hubble Ultra Deep Field view courtesy of NASA. Sphere-and-plane image by Joe Doliner.

Many thanks to Scientific American cosmology guru George Musser.