Where Have We Tested Gravity?

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General relativity is a rich theory that makes a wide variety of experimental predictions. It’s been tested many ways, and always seems to pass with flying colors. But there’s always the possibility that a different test in a new regime will reveal some anomalous behavior, which would open the door to a revolution in our understanding of gravity. (I didn’t say it was a likely possibility, but you don’t know until you try.)

Not every experiment tests different things; sometimes one set of observations is done with a novel technique, but is actually just re-examining a physical regime that has already been well-explored. So it’s interesting to have a handle on what regimes we have already tested. For GR, that’s not such an easy question; it’s difficult to compare tests like gravitational redshift, the binary pulsar, and Big Bang nucleosynthesis.

So it’s good to see a new paper that at least takes a stab at putting it all together:

Linking Tests of Gravity On All Scales: from the Strong-Field Regime to Cosmology
Tessa Baker, Dimitrios Psaltis, Constantinos Skordis

The current effort to test General Relativity employs multiple disparate formalisms for different observables, obscuring the relations between laboratory, astrophysical and cosmological constraints. To remedy this situation, we develop a parameter space for comparing tests of gravity on all scales in the universe. In particular, we present new methods for linking cosmological large-scale structure, the Cosmic Microwave Background and gravitational waves with classic PPN tests of gravity. Diagrams of this gravitational parameter space reveal a noticeable untested regime. The untested window, which separates small-scale systems from the troubled cosmological regime, could potentially hide the onset of corrections to General Relativity.

The idea is to find a simple way of characterizing different tests of GR so that they can be directly compared. This will always be something of an art as well as a science — the metric tensor has ten independent parameters (six of which are physical, given four coordinates we can choose), and there are a lot of ways they can combine together, so there’s little hope of a parameterization that is both easy to grasp and covers all bases.

Still, you can make some reasonable assumptions and see whether you make progress. Baker et al. have defined two parameters: the “Potential” ε, which roughly tells you how deep the gravitational well is, and the “Curvature” ξ, which tells you how strongly the field is changing through space. Again — these are reasonable things to look at, but not really comprehensive. Nevertheless, you can make a nice plot that shows where different experimental constraints lie in your new parameter space.

baker-etal

The nice thing is that there’s a lot of parameter space that is unexplored! You can think of this plot as a finding chart for experimenters who want to dream up new ways to test our best understanding of gravity in new regimes.

One caveat: it would be extremely surprising indeed if gravity didn’t conform to GR in these regimes. The philosophy of effective field theory gives us a very definite expectation for where our theories should break down: on length scales shorter than where we have tested the theory. It would be weird, although certainly not impossible, for a theory of gravity to work with exquisite precision in our Solar System, but break down on the scales of galaxies or cosmology. It’s not impossible, but that fact should weigh heavily in one’s personal Bayesian priors for finding new physics in this kind of regime. Just another way that Nature makes life challenging for we poor human physicists.

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Einstein’s Papers Online

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If any scientist in recent memory deserves to have every one of their words captured and distributed widely, it’s Albert Einstein. Surprisingly, many of his writings have been hard to get a hold of, especially in English; he wrote an awful lot, and mostly in German. The Einstein Papers Project has been working heroically to correct that, and today marks a major step forward: the release of the Digital Einstein Papers, an open resource that puts the master’s words just a click away.

As Dennis Overbye reports in the NYT, the Einstein Papers Project has so far released 14 of a projected 30 volumes of thick, leather-bound collections of Einstein’s works, as well as companion English translations in paperback. That’s less than half, but it does cover the years 1903-1917 when Einstein was turning physics on its head. You can read On the Electrodynamics of Moving Bodies, where special relativity was introduced in full, or the very short (3 pages!) follow-up Does the Inertia of a Body Depend on Its Energy Content?, where he derived the relation that we would now write as E = mc2. Interestingly, most of Einstein’s earliest papers were on statistical mechanics and the foundations of thermodynamics.

Ten years later he is putting the final touches on general relativity, whose centennial we will be celebrating next year. This masterwork took longer to develop, and Einstein crept up on its final formulation gradually, so you see the development spread out over a number of papers, achieving its ultimate form in The Field Equations of Gravitation in 1915.

What a compelling writer Einstein was! (Not all great scientists are.) Here is the opening of one foundational paper from 1914, The Formal Foundation of the General Theory of Relativity:

In recent years I have worked, in part together with my friend Grossman, on a generalization of the theory of relativity. During these investigations, a kaleidoscopic mixture of postulates from physics and mathematics has been introduced and used as heuristical tools; as a consequence it is not easy to see through and characterize the theory from a formal mathematical point of view, that is, only based on these papers. The primary objective of the present paper is to close this gap. In particular, it has been possible to obtain the equations of the gravitational field in a purely covariance-theoretical manner (section D). I also tried to give simple derivations of the basic laws of absolute differential calculus — in part, they are probably new ones (section B) — in order to allow the reader to get a complete grasp of the theory without having to read other, purely mathematical tracts. As an illustration of the mathematical methods, I derived the (Eulerian) equations of hydrodynamics and the field equations of the electrodynamics of moving bodies (section C). Section E shows that Newton’s theory of gravitation follows from the general theory as an approximation. The most elementary features of the present theory are also derived inasfar as they are characteristic of a Newtonian (static) gravitational field (curvature of light rays, shift of spectral lines).

While Einstein certainly did have help from Grossman and others, to a large extent the theory of general relativity was all his own. It stands in stark contrast to quantum mechanics or almost all modern theories, which have grown up through the collaborative effort of many smart people. We may never again in physics see a paragraph of such sweep and majesty — “Here is my revolutionary theory of the dynamics of space and time, along with a helpful introduction to its mathematical underpinnings, as well as derivations of all the previous laws of physics within this powerful new framework.”

Thanks to everyone at the Einstein Papers project for undertaking this enormous task.

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Thanksgiving

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This year we give thanks for a technique that is central to both physics and mathematics: the Fourier transform. (We’ve previously given thanks for the Standard Model Lagrangian, Hubble’s Law, the Spin-Statistics Theorem, conservation of momentum, effective field theory, the error bar, gauge symmetry, and Landauer’s Principle.)

Let’s say you want to locate a point in space — for simplicity, on a two-dimensional plane. You could choose a coordinate system (x, y), and then specify the values of those coordinates to pick out your point: (x, y) = (1, 3).

axes-rotate

But someone else might want to locate the same point, but they want to use a different coordinate system. That’s fine; points are real, but coordinate systems are just convenient fictions. So your friend uses coordinates (u, v) instead of (x, y). Fortunately, you know the relationship between the two systems: in this case, it’s u = y+x, v = y-x. The new coordinates are rotated (and scaled) with respect to the old ones, and now the point is represented as (u, v) = (4, 2).

Fourier transforms are just a fancy version of changes of coordinates. The difference is that, instead of coordinates on a two-dimensional space, we’re talking about coordinates on an infinite-dimensional space: the space of all functions. (And for technical reasons, Fourier transforms naturally live in the world of complex functions, where the value of the function at any point is a complex number.)

Think of it this way. To specify some function f(x), we give the value of the function f for every value of the variable x. In principle, an infinite number of numbers. But deep down, it’s not that different from giving the location of our point in the plane, which was just two numbers. We can certainly imagine taking the information contained in f(x) and expressing it in a different way, by “rotating the axes.”

That’s what a Fourier transform is. It’s a way of specifying a function that, instead of telling you the value of the function at each point, tells you the amount of variation at each wavelength. Just as we have a formula for switching between (u, v) and (x, y), there are formulas for switching between a function f(x) and its Fourier transform f(ω):

f(\omega) = \frac{1}{\sqrt{2\pi}} \int dx f(x) e^{-i\omega x}
lf(x) = \frac{1}{\sqrt{2\pi}} \int d\omega f(\omega) e^{i\omega x}.

Absorbing those formulas isn’t necessary to get the basic idea. If the function itself looks like a sine wave, it has a specific wavelength, and the Fourier transform is just a delta function (infinity at that particular wavelength, zero everywhere else). If the function is periodic but a bit more complicated, it might have just a few Fourier components.

MIT researchers showing how sine waves can combine to make a square-ish wave.
MIT researchers showing how sine waves can combine to make a square-ish wave.

In general, the Fourier transform f(ω) gives you “the amount of the original function that is periodic with period 2πω.” This is sometimes called the “frequency domain,” since there are obvious applications to signal processing, where we might want to take a signal that has an intensity that varies with time and pick out the relative strength of different frequencies. (Your eyes and ears do this automatically, when they decompose light into colors and sound into pitches. They’re just taking Fourier transforms.) Frequency, of course, is the inverse of wavelength, so it’s equally good to think of the Fourier transform as describing the “length domain.” A cosmologist who studies the large-scale distribution of galaxies will naturally take the Fourier transform of their positions to construct the power spectrum, revealing how much structure there is at different scales.

microcontrollers_fft_example

To my (biased) way of thinking, where Fourier transforms really come into their own is in quantum field theory. QFT tells us that the world is fundamentally made of waves, not particles, and it is extremely convenient to think about those waves by taking their Fourier transforms. (It is literally one of the first things one is told to do in any introduction to QFT.)

But it’s not just convenient, it’s a worldview-changing move. One way of characterizing Ken Wilson’s momentous achievement is to say “physics is organized by length scale.” Phenomena at high masses or energies are associated with short wavelengths, where our low-energy long-wavelength instruments cannot probe. (We need giant machines like the Large Hadron Collider to create high energies, because what we are really curious about are short distances.) But we can construct a perfectly good effective theory of just the wavelengths longer than a certain size — whatever size it is that our theoretical picture can describe. As physics progresses, we bring smaller and smaller length scales under the umbrella of our understanding.

Without Fourier transforms, this entire way of thinking would be inaccessible. We should be very thankful for them — as long as we use them wisely.

Credit: xkcd.

Note that Joseph Fourier, inventor of the transform, is not the same as Charles Fourier, utopian philosopher. Joseph, in addition to his work in math and physics, invented the idea of the greenhouse effect. Sadly that’s not something we should be thankful for right now.

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Guest Post by Alessandra Buonanno: Nobel Laureates Call for Release of Iranian Student Omid Kokabee

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buonannoUsually I start guest posts by remarking on what a pleasure it is to host an article on the topic being discussed. Unfortunately this is a sadder occasion: protesting the unfair detention of Omid Kokabee, a physics graduate student at the University of Texas, who is being imprisoned by the government of Iran. Alessandra Buonanno, who wrote the post, is a distinguished gravitational theorist at the Max Planck Institute for Gravitational Physics and the University of Maryland, as well as a member of the Committee on International Freedom of Scientists of the American Physical Society. This case should be important to everyone, but it’s especially important for physicists to work to protect the rights of students who travel from abroad to study our subject.

Omid Kokabee was arrested at the airport of Teheran in January 2011, just before taking a flight back to the University of Texas at Austin, after spending the winter break with his family. He was accused of communicating with a hostile government and after a trial, in which he was denied contact with a lawyer, he was sentenced to 10 years in Teheran’s Evin prison.

According to a letter written by Omid Kokabee, he was asked to work on classified research, and his arrest and detention was a consequence of his refusal. Since his detention, Kokabee has continued to assert his innocence, claiming that several human rights violations affected his interrogation and trial.

Since 2011, we, the Committee on International Freedom of Scientists (CIFS) of the American Physical Society, have protested the imprisonment of Omid Kokabee. Although this case has received continuous support from several scientific and international human rights organizations, the government of Iran has refused to release Kokabee.

Omid Kokabee

Omid Kokabee has received two prestigious awards:

  • The American Physical Society awarded him Andrei Sakharov Prize “For his courage in refusing to use his physics knowledge to work on projects that he deemed harmful to humanity, in the face of extreme physical and psychological pressure.”
  • The American Association for the Advancement of Science awarded Kokabee the Scientific Freedom and Responsibility Prize.

Amnesty International (AI) considers Kokabee a prisoner of conscience and has requested his immediate release.

Recently, the Committee of Concerned Scientists (CCS), AI and CIFS, have prepared a letter addressed to the Iranian Supreme Leader Ali Khamenei asking that Omid Kokabee be released immediately. The letter was signed by 31 Nobel-prize laureates. (An additional 13 Nobel Laureates have signed this letter since the Nature blog post. See also this update from APS.)

Unfortunately, earlier last month, Kokabee’s health conditions have deteriorated and he has been denied proper medical care. In response, the President of APS, Malcolm Beasley, has written a letter to the Iranian President Rouhani calling for a medical furlough for Omid Kokabee so that he can receive proper medical treatment. AI has also made further steps and has requested urgent medical care for Kokabee.

Very recently, the Iran’s supreme court has nullified the original conviction of Omid Kokabee and has agreed to reconsider the case. Although this is positive news, it is not clear when the new trial will start. Considering Kokabee’s health conditions, it is very important that he is granted a medical furlough as soon as possible.

More public engagement and awareness is needed to solve this unacceptable case of violation of human rights and freedom of scientific research. You can help by tweeting/blogging about it and responding to this Urgent Action that AI has issued. Please note that the date on the Urgent Action is there to create an avalanche effect; it is not a deadline nor it is the end of action.

Alessandra Buonanno for the American Physical Society’s Committee on International Freedom of Scientists (CIFS).

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Unsolicited Advice: Becoming a Science Communicator

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Everyone who does science inevitably has “communicating” as part of their job description, even if they’re only communicating with their students and professional colleagues. But many people start down a trajectory of becoming a research scientist, only to discover that it’s the communicating that they are most passionate about. And some of those people might want to take the dramatic step of earning a living doing such communication, whether it’s traditional journalism or something more new-media focused.

So: how does one make the transition from researcher to professional science communicator? Heck if I know. I do a lot of communicating, but it’s not my primary job. You’d be better off looking at this thread from Ed Yong, where he coaxed an impressive number of science writers into telling their origin stories. But lack of expertise has never stopped me from offering advice!

First piece of advice: don’t make the tragic mistake of looking at science communication as a comfortable safety net if academia doesn’t work out. Not only is it an extremely demanding career, but it’s one that is at least as hard as research in terms of actually finding reliable employment — and the career trajectories are far more chancy and unpredictable. There is no tenure for science communicators, and there’s not even a structured path of the form student → postdoc → faculty. Academia’s “up or out” system can be soul-crushing, but so can the “not today, but who knows? Maybe tomorrow!” path to success of the professional writer. It’s great to aspire to being Neil deGrasse Tyson or Mary Roach, but most science communicators don’t reach that level of success, just as most scientists don’t become Marie Curie or Albert Einstein.

Having said all that, here are some tips that might be worth sharing. …

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Discovering Tesseracts

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I still haven’t seen Interstellar yet, but here’s a great interview with Kip Thorne about the movie-making process and what he thinks of the final product. (For a very different view, see Phil Plait [update: now partly recanted].)

tesseract One of the things Kip talks about is that the film refers to the concept of a tesseract, which he thought was fun. A tesseract is a four-dimensional version of a cube; you can’t draw it faithfully in two dimensions, but with a little imagination you can get the idea from the picture on the right. Kip mentions that he first heard of the concept of a tesseract in George Gamow’s classic book One, Two, Three… Infinity. Which made me feel momentarily proud, because I remember reading about it there, too — and only later did I find out that many (presumably less sophisticated) people heard of it in Madeleine L’Engle’s equally classic book, A Wrinkle in Time.

But then I caught myself, because (1) it’s stupid to think that reading about something for the first time in a science book rather than a science fantasy is anything to be proud of, and (2) in reality I suspect I first heard about it in Robert Heinlein’s (classic!) short story, “–And He Built a Crooked House.” Which is just as fantastical as L’Engle’s book.

So — where did you first hear the word “tesseract”? A great excuse for a poll! Feel free to elaborate in the comments.

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The Science of Interstellar

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The intersection — maybe the union! — of science and sci-fi geekdom is overcome with excitement about the upcoming movie Interstellar, which opens November 7. It’s a collaboration between director Christopher Nolan and physicist Kip Thorne, both heroes within their respective communities. I haven’t seen it yet myself, nor do I know any secret scoop, but there’s good reason to believe that this film will have some of the most realistic physics of any recent blockbuster we’ve seen. If it’s a success, perhaps other filmmakers will take the hint?

Kip, who is my colleague at Caltech (and a former guest-blogger), got into the science-fiction game quite a while back. He helped Carl Sagan with some science advice for his book Contact, later turned into a movie starring Jodie Foster. In particular, Sagan wanted to have some way for his characters to traverse great distances at speeds faster than light, by taking a shortcut through spacetime. Kip recognized that a wormhole was what was called for, but also realized that any form of faster-than-light travel had the possibility of leading to travel backwards in time. Thus was the entire field of wormhole time travel born.

As good as the movie version of Contact was, it still strayed from Sagan’s original vision, as his own complaints show. (“Ellie disgracefully waffles in the face of lightweight theological objections to rationalism…”) Making a big-budget Hollywood film is necessarily a highly collaborative endeavor, and generally turns into a long series of forced compromises. Kip has long been friends with Lynda Obst, an executive producer on Contact, and for years they batted around ideas for a movie that would really get the science right.

Long story short, Lynda and Kip teamed with screenwriter Jonathan Nolan (brother of Christopher), who wrote a draft of a screenplay, and Christopher eventually agreed to direct. I know that Kip has been very closely involved with the script as the film has developed, and he’s done his darnedest to make sure the science is right, or at least plausible. (We don’t actually whether wormholes are allowed by the laws of physics, but we don’t know that they’re not allowed.) But it’s a long journey, and making the best movie possible is the primary goal. Meanwhile, Adam Rogers at Wired has an in-depth look at the science behind the movie, including the (unsurprising, in retrospect) discovery that the super-accurate visualization software available to the Hollywood special-effects team enable the physicists to see things they hadn’t anticipated. Kip predicts that at least a couple of technical papers will come out of their work.

And that’s not all! Kip has a book coming out on the science behind the movie, which I’m sure will be fantastic. And there is also a documentary on “The Science of Interstellar” that will be shown on TV, in which I play a tiny part. Here is the broadcast schedule for that, as I understand it:

SCIENCE
Wednesday, October 29, at 10pm PDT/9c

AHC (American Heroes Channel)
Sunday, November, 2 at 4pm PST/3c (with a repeat on Monday, November 3 at 4am PST/3c)

DISCOVERY
Thursday, November 6, at 11pm PST/10c

Of course, all the accurate science in the world doesn’t help if you’re not telling an interesting story. But with such talented people working together, I think some optimism is justified. Let’s show the world that science and cinema are partners, not antagonists.

Interstellar Movie - Official Trailer 3

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How to Communicate on the Internet

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Let’s say you want to communicate an idea X.

You would do well to simply say “X.”

Also acceptable is “X. Really, just X.”

A slightly riskier strategy, in cases where miscomprehension is especially likely, would be something like “X. This sounds a bit like A, and B, and C, but I’m not saying those. Honestly, just X.” Many people will inevitably start arguing against A, B, and C.

Under no circumstances should you say “You might think Y, but actually X.”

Equally bad, perhaps worse: “Y. Which reminds me of X, which is what I really want to say.”

For examples see the comment sections of the last couple of posts, or indeed any comment section anywhere on the internet.

It is possible these ideas may be of wider applicability in communication situations other than the internet.

(You may think this is just grumping but actually it is science!)

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Does Santa Exist?

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There’s a claim out there — one that is about 95% true, as it turns out — that if you pick a Wikipedia article at random, then click on the first (non-trivial) link, and keep clicking on the first link of each subsequent article, you will end up at Philosophy. More specifically, you will end up at a loop that runs through Reality, Existence, Awareness, Consciousness, and Quality (philosophy), as well as Philosophy itself. It’s not hard to see why. These are the Big Issues, concerning the fundamental nature of the universe at a deep level. Almost any inquiry, when pressed to ever-greater levels of precision and abstraction, will get you there.

Does Santa Exist? Take, for example, the straightforward-sounding question “Does Santa Exist?” You might be tempted to say “No” and move on. (Or you might be tempted to say “Yes” and move on, I don’t know — a wide spectrum of folks seem to frequent this blog.) But even to give such a common-sensical answer is to presume some kind of theory of existence (ontology), not to mention a theory of knowledge (epistemology). So we’re allowed to ask “How do you know?” and “What do you really mean by exist?”

These are the questions that underlie an entertaining and thought-provoking new book by Eric Kaplan, called Does Santa Exist?: A Philosophical Investigation. Eric has a resume to be proud of: he is a writer on The Big Bang Theory, and has previously written for Futurama and other shows, but he is also a philosopher, currently finishing his Ph.D. from Berkeley. In the new book, he uses the Santa question as a launching point for a rewarding tour through some knotty philosophical issues. He considers not only a traditional attack on the question, using Logic and the beloved principles of reason, but sideways approaches based on Mysticism as well. (“The Buddha ought to be able to answer our questions about the universe for like ten minutes, and then tell us how to be free of suffering.”) His favorite, though, is the approach based on Comedy, which is able to embrace contradiction in a way that other approaches can’t quite bring themselves to do.

Most people tend to have a pre-existing take on the Santa question. Hence, the book trailer for Does Santa Exist? employs a uniquely appropriate method: Choose-Your-Own-Adventure. Watch and interact, and you will find the answers you seek.

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