The other day I mused on Twitter about three big origin questions: the origin of the universe, the origin of life, and the origin of consciousness. Which isn’t to say they are related, just that they’re all interesting and important (and currently nowhere near solved). Physicists have taken stabs at the life question, but (with a few dramatic exceptions) they’ve mostly stayed away from consciousness. Probably for the best.
Here’s Ed Witten giving his own personal — and characteristically sensible — opinion, which is that consciousness is a really knotty problem, although not so difficult that we should start contemplating changing the laws of physics in order to solve it. Though I am more optimistic than he is that we’ll understand it on a reasonable timescale. (Hat tip to Ash Jogalekar.)
[Video has been removed, sorry]
Anyone seriously interested in tackling these big questions would be well-served by acknowledging that much (most? almost all?) progress in science is incremental, sneaking up on major discoveries by a series of small steps rather than leaping right to a dramatic new paradigm. Even if you want to understand the origin of the universe, it might behoove you to think about some more specific and tractable problems, like the nature of quantum fluctuations in inflation, or the emergence of spacetime in string theory. If you want to understand the origin of consciousness, it’s a good strategy to think about something like our perception of color, with the idea of working your way up to the more challenging issues.
Conversely, it’s these big questions that attract crackpots like honey attracts flies. I get a lot of emails (and physical letters) from cranks, but they never have a new theory of the branching ratio of the Higgs boson into four leptons; it’s always about the nature of space and time and everything. It’s too easy for anyone to have an opinion about these big questions, whether or not those opinions are worth paying attention to.
All of which leads up to saying: it’s still worth tackling the big questions! Start small, but think big. Because they are so hard, it’s too easy to make fun of attempts to solve the biggest questions, or to imagine that they are irreducibly mysterious and will never be solved. I wouldn’t be at all surprised if we had quite compelling pictures of the origin of the universe, life, and consciousness within the next hundred years. But only if we’re willing to tackle the big problems seriously.
If you’re reading this you probably know about the BICEP2 experiment, a radio telescope at the South Pole that measured a particular polarization signal known as “B-modes” in the cosmic microwaves background radiation. Cosmologists were very excited at the prospect that the B-modes were the imprint of gravitational waves originating from a period of inflation in the primordial universe; now, with more data from the Planck satellite, it seems plausible that the signal is mostly due to dust in our own galaxy. The measurements that the team reported were completely on-target, but our interpretation of them has changed — we’re still looking for direct evidence for or against inflation.
Here I’m very happy to publish an interview that was carried out with Jamie Bock, a professor of physics at Caltech and a senior research scientist at JPL, who is one of the leaders of the BICEP2 collaboration. It’s a unique look inside the workings of an incredibly challenging scientific effort.
New Results from BICEP2: An Interview with Jamie Bock
What does the new data from Planck tell you? What do you know now?
A scientific race has been under way for more than a decade among a dozen or so experiments trying to measure B-mode polarization, a telltale signature of gravitational waves produced from the time of inflation. Last March, BICEP2 reported a B-mode polarization signal, a twisty polarization pattern measured in a small patch of sky. The amplitude of the signal we measured was surprisingly large, exceeding what we expected for galactic emission. This implied we were seeing a large gravitational wave signal from inflation.
We ruled out galactic synchrotron emission, which comes from electrons spiraling in the magnetic field of the galaxy, using low-frequency data from the WMAP [Wilkinson Microwave Anisotropy Probe] satellite. But there were no data available on polarized galactic dust emission, and we had to use models. These models weren’t starting from zero; they were built on well-known maps of unpolarized dust emission, and, by and large, they predicted that polarized dust emission was a minor constituent of the total signal.
Obviously, the answer here is of great importance for cosmology, and we have always wanted a direct test of galactic emission using data in the same piece of sky so that we can test how much of the BICEP2 signal is cosmological, representing gravitational waves from inflation, and how much is from galactic dust. We did exactly that with galactic synchrotron emission from WMAP because the data were public. But with galactic dust emission, we were stuck, so we initiated a collaboration with the Planck satellite team to estimate and subtract polarized dust emission. Planck has the world’s best data on polarized emission from galactic dust, measured over the entire sky in multiple spectral bands. However, the polarized dust maps were only recently released.
On the other side, BICEP2 gives us the highest-sensitivity data available at 150 GHz to measure the CMB. Interestingly, the two measurements are stronger in combination. We get a big boost in sensitivity by putting them together. Also, the detectors for both projects were designed, built, and tested at Caltech and JPL, so I had a personal interest in seeing that these projects worked together. I’m glad to say the teams worked efficiently and harmoniously together.
What we found is that when we subtract the galaxy, we just see noise; no signal from the CMB is detectable. Formally we can say at least 40 percent of the total BICEP2 signal is dust and less than 60 percent is from inflation.
How do these new data shape your next steps in exploring the earliest moments of the universe?
It is the best we can do right now, but unfortunately the result with Planck is not a very strong test of a possible gravitational wave signal. This is because the process of subtracting galactic emission effectively adds more noise into the analysis, and that noise limits our conclusions. While the inflationary signal is less than 60 percent of the total, that is not terribly informative, leaving many open questions. For example, it is quite possible that the noise prevents us from seeing part of the signal that is cosmological. It is also possible that all of the BICEP2 signal comes from the galaxy. Unfortunately, we cannot say more because the data are simply not precise enough. Our ability to measure polarized galactic dust emission in particular is frustratingly limited.
Figure 1: Maps of CMB polarization produced by BICEP2 and Keck Array. The maps show the ‘E-mode’ polarization pattern, a signal from density variations in the CMB, not gravitational waves. The polarization is given by the length and direction of the lines, with a coloring to better show the sign and amplitude of the E-mode signal. The tapering toward the edges of the map is a result of how the instruments observed this region of sky. While the E-mode pattern is about 6 times brighter than the B-mode signal, it is still quite faint. Tiny variations of only 1 millionth of a degree kelvin are faithfully reproduced across these multiple measurements at 150 GHz, and in new Keck data at 95 GHz still under analysis. The very slight color shift visible between 150 and 95 GHz is due to the change in the beam size.
However, there is good news to report. In this analysis, we added new data obtained in 2012–13 from the Keck Array, an instrument with five telescopes and the successor to BICEP2 (see Fig. 1). These data are at the same frequency band as BICEP2—150 GHz—so while they don’t help subtract the galaxy, they do increase the total sensitivity. The Keck Array clearly detects the same signal detected by BICEP2. In fact, every test we can do shows the two are quite consistent, which demonstrates that we are doing these difficult measurements correctly (see Fig. 2). The BICEP2/Keck maps are also the best ever made, with enough sensitivity to detect signals that are a tiny fraction of the total.
Figure 2: A power spectrum of the B-mode polarization signal that plots the strength of the signal as a function of angular frequency. The data show a signal significantly above what is expected for a universe without gravitational waves, given by the red line. The excess peaks at angular scales of about 2 degrees. The independent measurements of BICEP2 and Keck Array shown in red and blue are consistent within the errors, and their combination is shown in black. Note the sets of points are slightly shifted along the x-axis to avoid overlaps.
In addition, Planck’s measurements over the whole sky show the polarized dust is fairly well behaved. For example, the polarized dust has nearly the same spectrum across the sky, so there is every reason to expect we can measure and remove dust cleanly.
To better subtract the galaxy, we need better data. We aren’t going to get more data from Planck because the mission has finished. The best way is to measure the dust ourselves by adding new spectral bands to our own instruments. We are well along in this process already. We added a second band to the Keck Array last year at 95 GHz and a third band this year at 220 GHz. We just installed the new BICEP3 instrument at 95 GHz at the South Pole (see Fig. 3). BICEP3 is single telescope that will soon be as powerful as all five Keck Array telescopes put together. At 95 GHz, Keck and BICEP3 should surpass BICEP2’s 150 GHz sensitivity by the end of this year, and the two will be a very powerful combination indeed. If we switch the Keck Array entirely over to 220 GHz starting next year, we can get a third band to a similar depth.
Figure 3: BICEP3 installed and carrying out calibration measurements off a reflective mirror placed above the receiver. The instrument is housed within a conical reflective ground shield to minimize the brightness contrast between the warm earth and cold space. This picture was taken at the beginning of the winter season, with no physical access to the station for the next 8 months, when BICEP3 will conduct astronomical observations (Credit: Sam Harrison)
Finally, this January the SPIDER balloon experiment, which is also searching the CMB for evidence of inflation, completed its first flight, outfitted with comparable sensitivity at 95 and 150 GHz. Because SPIDER floats above the atmosphere (see Fig. 4), we can also measure the sky on larger spatial scales. This all adds up to make the coming years very exciting.
Figure 4: View of the earth and the edge of space, taken from an optical camera on the SPIDER gondola at float altitude shortly after launch. Clearly visible below is Ross Island, with volcanos Mt. Erebus and Mt. Terror and the McMurdo Antarctic base, the Royal Society mountain range to the left, and the edge of the Ross permanent ice shelf. (Credit: SPIDER team).
Why did you make the decision last March to release results? In retrospect, do you regret it?
We knew at the time that any news of a B-mode signal would cause a great stir. We started working on the BICEP2 data in 2010, and our standard for putting out the paper was that we were certain the measurements themselves were correct. It is important to point out that, throughout this episode, our measurements basically have not changed. As I said earlier, the initial BICEP2 measurement agrees with new data from the Keck Array, and both show the same signal. For all we know, the B-mode polarization signal measured by BICEP2 may contain a significant cosmological component—that’s what we need to find out.
The question really is, should we have waited until better data were available on galactic dust? Personally, I think we did the right thing. The field needed to be able to react to our data and test the results independently, as we did in our collaboration with Planck. This process hasn’t ended; it will continue with new data. Also, the searches for inflationary gravitational waves are influenced by these findings, and it is clear that all of the experiments in the field need to focus more resources on measuring the galaxy.
How confident are you that you will ultimately find conclusive evidence for primordial gravitational waves and the signature of cosmic inflation?
I don’t have an opinion about whether or not we will find a gravitational wave signal—that is why we are doing the measurement! But any result is so significant for cosmology that it has to be thoroughly tested by multiple groups. I am confident that the measurements we have made to date are robust, and the new data we need to subtract the galaxy more accurately are starting to pour forth. The immediate path forward is clear: we know how to make these measurements at 150 GHz, and we are already applying the same process to to the new frequencies. Doing the measurements ourselves also means they are uniform so we understand all of the errors, which, in the end, are just as important.
What will it mean for our understanding of the universe if you don’t find the signal?
The goal of this program is to learn how inflation happened. Inflation requires matter-energy with an unusual repulsive property in order to rapidly expand the universe. The physics are almost certainly new and exotic, at energies too high to be accessed with terrestrial particle accelerators. CMB measurements are one of the few ways to get at the inflationary physics, and we need to squeeze them for all they are worth. A gravitational wave signal is very interesting because it tells us about the physical process behind inflation. A detection of the polarization signal at a high level means that the certain models of inflation, perhaps along the lines of the models first developed, are a good explanation.
But here again is the real point: we also learn more about inflation if we can rule out polarization from gravitational waves. No detection at 5 percent or less of the total BICEP2 signal means that inflation is likely more complicated, perhaps involving multiple fields, although there are certainly other possibilities. Either way is a win, and we’ll find out more about what caused the birth of the universe 13.8 billion years ago.
Our team dedicated itself to the pursuit of inflationary polarization 15 years ago fully expecting a long and difficult journey. It is exciting, after all this work, to be at this stage where the polarization data are breaking into new ground, providing more information about gravitational waves than we learned before. The BICEP2 signal was a surprise, and its ultimate resolution is still a work in progress. The data we need to address these questions about inflation are within sight, and whatever the answers are, they are going to be interesting, so stay tuned.
Longtime readers know that I’ve made a bit of an effort to help people understand, and perhaps even grow to respect, the Everett or Many-Worlds Interpretation of Quantum Mechanics (MWI) . I’ve even written papers about it. It’s a controversial idea and far from firmly established, but it’s a serious one, and deserves serious discussion.
Which is why I become sad when people continue to misunderstand it. And even sadder when they misunderstand it for what are — let’s face it — obviously wrong reasons. The particular objection I’m thinking of is:
MWI is not a good theory because it’s not testable.
It has appeared recently in this article by Philip Ball — an essay whose snidely aggressive tone is matched only by the consistency with which it is off-base. Worst of all, the piece actually quotes me, explaining why the objection is wrong. So clearly I am either being too obscure, or too polite.
I suspect that almost everyone who makes this objection doesn’t understand MWI at all. This is me trying to be generous, because that’s the only reason I can think of why one would make it. In particular, if you were under the impression that MWI postulated a huge number of unobservable worlds, then you would be perfectly in your rights to make that objection. So I have to think that the objectors actually are under that impression.
An impression that is completely incorrect. The MWI does not postulate a huge number of unobservable worlds, misleading name notwithstanding. (One reason many of us like to call it “Everettian Quantum Mechanics” instead of “Many-Worlds.”)
Now, MWI certainly does predict the existence of a huge number of unobservable worlds. But it doesn’t postulate them. It derives them, from what it does postulate. And the actual postulates of the theory are quite simple indeed:
The world is described by a quantum state, which is an element of a kind of vector space known as Hilbert space.
The quantum state evolves through time in accordance with the Schrödinger equation, with some particular Hamiltonian.
That is, as they say, it. Notice you don’t see anything about worlds in there. The worlds are there whether you like it or not, sitting in Hilbert space, waiting to see whether they become actualized in the course of the evolution. Notice, also, that these postulates are eminently testable — indeed, even falsifiable! And once you make them (and you accept an appropriate “past hypothesis,” just as in statistical mechanics, and are considering a sufficiently richly-interacting system), the worlds happen automatically.
Given that, you can see why the objection is dispiritingly wrong-headed. You don’t hold it against a theory if it makes some predictions that can’t be tested. Every theory does that. You don’t object to general relativity because you can’t be absolutely sure that Einstein’s equation was holding true at some particular event a billion light years away. This distinction between what is postulated (which should be testable) and everything that is derived (which clearly need not be) seems pretty straightforward to me, but is a favorite thing for people to get confused about.
Ah, but the MWI-naysayers say (as Ball actually does say), but every version of quantum mechanics has those two postulates or something like them, so testing them doesn’t really test MWI. So what? If you have a different version of QM (perhaps what Ted Bunn has called a “disappearing-world” interpretation), it must somehow differ from MWI, presumably by either changing the above postulates or adding to them. And in that case, if your theory is well-posed, we can very readily test those proposed changes. In a dynamical-collapse theory, for example, the wave function does not simply evolve according to the Schrödinger equation; it occasionally collapses (duh) in a nonlinear and possibly stochastic fashion. And we can absolutely look for experimental signatures of that deviation, thereby testing the relative adequacy of MWI vs. your collapse theory. Likewise in hidden-variable theories, one could actually experimentally determine the existence of the new variables. Now, it’s true, any such competitor to MWI probably has a limit in which the deviations are very hard to discern — it had better, because so far every experiment is completely compatible with the above two axioms. But that’s hardly the MWI’s fault; just the opposite.
The people who object to MWI because of all those unobservable worlds aren’t really objecting to MWI at all; they just don’t like and/or understand quantum mechanics. Hilbert space is big, regardless of one’s personal feelings on the matter.
Which saddens me, as an MWI proponent, because I am very quick to admit that there are potentially quite good objections to MWI, and I would much rather spend my time discussing those, rather than the silly ones. Despite my efforts and those of others, it’s certainly possible that we don’t have the right understanding of probability in the theory, or why it’s a theory of probability at all. Similarly, despite the efforts of Zurek and others, we don’t have an absolutely airtight understanding of why we see apparent collapses into certain states and not others. Heck, you might be unconvinced that the above postulates really do lead to the existence of distinct worlds, despite the standard decoherence analysis; that would be great, I’d love to see the argument, it might lead to a productive scientific conversation. Should we be worried that decoherence is only an approximate process? How do we pick out quasi-classical realms and histories? Do we, in fact, need a bit more structure than the bare-bones axioms listed above, perhaps something that picks out a preferred set of observables?
All good questions to talk about! Maybe someday the public discourse about MWI will catch up with the discussion that experts have among themselves, evolve past self-congratulatory sneering about all those unobservable worlds, and share in the real pleasure of talking about the issues that matter.
If I were ever to publish a second edition of Spacetime and Geometry — unlikely, but check back in another ten years — one thing I would like to do would be to increase the number of problems at the end of each chapter. I like the problems that are there, but they certainly could be greater in number. And there is no solutions manual, to the chagrin of numerous professors over the last decade.
What I usually do, when people ask for solutions and/or more problems, is suggest that they dig up a copy of the Problem Book in Relativity and Gravitation by Lightman, Press, Price, and Teukolsky. It’s a wonderful resource, with twenty chapters chock-full of problems, all with complete solutions in the back. A great thing to have for self-study. The book is a bit venerable, dating from 1975, and the typesetting isn’t the most modern; but the basics of GR haven’t changed in that time, and the notation and level are a perfect fit for my book.
And now everyone can have it for free! Where by “now” I mean “for the last five years,” although somehow I never heard of this. Princeton University Press, the publisher, gave permission to put the book online, for which students everywhere should be grateful.
[Edit: apparently as of Sept 2017, PUP changed their mind, so the book is no longer available for free. You can still buy it from Amazon.]
If you’re learning (or teaching) general relativity, you owe yourself to check it out.
Polarization measurements from Planck superimposed on CMB temperature anisotropies. From the Planckoscope, h/t Bob McNees and Raquel Ribeiro.
The good news is: we understand the current universe pretty darn well! So much so, in fact, that even an amazingly high-precision instrument such as Planck has a hard time discovering truly new and surprising things about cosmology. Hence, the Planck press releases chose to highlight the finding that the earliest stars formed about 0.1 billion years later than had previously been thought. Which is an awesome piece of science, but doesn’t quite rise to the level of excitement that other possible discoveries might have reached.
Power spectrum of CMB temperature fluctuations, from Planck. Now that is some agreement between theory and experiment!
For example, the possibility that we had seen primordial gravitational waves from inflation, as the original announcement of the BICEP2 results suggested back in March. If you’ll remember, the polarization of the CMB can be mathematically decomposed into “E-modes,” which look like gradients and arise naturally from the perturbations in density that we all know and love, and “B-modes,” which look like curls and are not produced (in substantial amounts) from density perturbations. They could be produced by gravitational waves, which in turn could be generated during cosmic inflation — so finding them is a very big deal, indeed.
A big deal that apparently hasn’t happened. As has been suspected for a while now, while BICEP2 did detect B-modes, they seem to have been generated by dust in our galaxy, rather than by gravitational waves during inflation. That is the pretty definitive conclusion from the new Planck/BICEP2/Keck joint analysis.
And therefore, what we had hoped was a detection of primordial gravitational waves now turns into a less-thrilling (but equally scientifically crucial) upper limit. Here’s one way of looking at the situation now. On the horizontal axis we have ns, the “tilt” in the power spectrum of perturbations, i.e. the variation in the amplitude of those perturbations on different distances across space. And on the vertical axis we have r, the ratio of the gravitational waves to the ordinary density perturbations. The original BICEP2 interpretation was that we had discovered r = 0.2; now we see that r is less than 0.15, probably less than 0.10, depending on which pieces of information you combine to get your constraint. No sign that it’s anything other than zero.
Current constraints on the “tilt” of the primordial perturbations (horizontal axis) and the contribution from gravitational waves (vertical axis).
So what have we learned? Here are some take-away messages. …
If you’ve ever wondered about dark matter, or been asked puzzled questions about it by your friends, now you have something to point to: this charming video by 11-year-old Lucas Belz-Koeling. (Hat tip Sir Harry Kroto.)
Dark matter draw my life style
The title references “Draw My Life style,” which is (the internet informs me) a label given to this kind of fast-motion photography of someone drawing on a white board.
You go, Lucas. I doubt I would have been doing anything quite this good at that age.
Last October I was privileged to be awarded the Emperor Has No Clothes award from the Freedom From Religion Foundation. The physical trophy consists of the dashing statuette here on the right, presumably the titular Emperor. It’s made by the same company that makes the Academy Award trophies. (Whenever I run into Meryl Streep, she’s just won’t shut up about how her Oscars are produced by the same company that does the Emperor’s New Clothes award.)
Part of the award-winning is the presentation of a short speech, and I wasn’t sure what to talk about. There are only so many things I have to say, but it’s boring to talk about the same stuff over and over again. More importantly, I have no real interest in giving religion-bashing talks; I care a lot more about doing the hard and constructive work of exploring the consequences of naturalism.
So I decided on a cheerful topic: Death and Physics. I talked about modern science gives us very good reasons to believe (not a proof, never a proof) that there is no such thing as an afterlife. Life is a process, not a substance, and it’s a process that begins, proceeds along for a while, and comes to an end. Certainly something I’ve said before, e.g. in my article on Physics and the Immortality of the Soul, and in the recent Afterlife Debate, but I added a bit more here about entropy, complexity, and what we mean by the word “life.”
If you’re in a reflective mood, here it is. I begin at around 3:50. One of the points I tried to make is that the finitude of life has its upside. Every moment is precious, and what we should value is what is around us right now — because that’s all there is. It’s a scary but exhilarating view of the world.
I got to know Charles “Chip” Sebens back in 2012, when he emailed to ask if he could spend the summer at Caltech. Chip is a graduate student in the philosophy department at the University of Michigan, and like many philosophers of physics, knows the technical background behind relativity and quantum mechanics very well. Chip had funding from NSF, and I like talking to philosophers, so I said why not?
We had an extremely productive summer, focusing on our different stances toward quantum mechanics. At the time I was a casual adherent of the Everett (many-worlds) formulation, but had never thought about it carefully. Chip was skeptical, in particular because he thought there were good reasons to believe that EQM should predict equal probabilities for being on any branch of the wave function, rather than the amplitude-squared probabilities of the real-world Born Rule. Fortunately, I won, although the reason I won was mostly because Chip figured out what was going on. We ended up writing a paper explaining why the Born Rule naturally emerges from EQM under some simple assumptions. Now I have graduated from being a casual adherent to a slightly more serious one.
But that doesn’t mean Everett is right, and it’s worth looking at other formulations. Chip was good enough to accept my request that he write a guest blog post about another approach that’s been in the news lately: a “Newtonian” or “Many-Interacting-Worlds” formulation of quantum mechanics, which he has helped to pioneer.
In Newtonian physics objects always have definite locations. They are never in two places at once. To determine how an object will move one simply needs to add up the various forces acting on it and from these calculate the object’s acceleration. This framework is generally taken to be inadequate for explaining the quantum behavior of subatomic particles like electrons and protons. We are told that quantum theory requires us to revise this classical picture of the world, but what picture of reality is supposed to take its place is unclear. There is littleconsensus on many foundational questions: Is quantum randomness fundamental or a result of our ignorance? Do electrons have well-defined properties before measurement? Is the Schrödinger equation always obeyed? Are there parallel universes?
Some of us feel that the theory is understood well enough to be getting on with. Even though we might not know what electrons are up to when no one is looking, we know how to apply the theory to make predictions for the results of experiments. Much progress has been made―observe the wonder of the standard model―without answering these foundational questions. Perhaps one day with insight gained from new physics we can return to these basic questions. I will call those with such a mindset the doers. Richard Feynman was a doer:
“It will be difficult. But the difficulty really is psychological and exists in the perpetual torment that results from your saying to yourself, ‘But how can it be like that?’ which is a reflection of uncontrolled but utterly vain desire to see it in terms of something familiar. I will not describe it in terms of an analogy with something familiar; I will simply describe it. … I think I can safely say that nobody understands quantum mechanics. … Do not keep saying to yourself, if you can possibly avoid it, ‘But how can it be like that?’ because you will get ‘down the drain’, into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.”
In contrast to the doers, there are the dreamers. Dreamers, although they may often use the theory without worrying about its foundations, are unsatisfied with standard presentations of quantum mechanics. They want to know “how it can be like that” and have offered a variety of alternative ways of filling in the details. Doers denigrate the dreamers for being unproductive, getting lost “down the drain.” Dreamers criticize the doers for giving up on one of the central goals of physics, understanding nature, to focus exclusively on another, controlling it. But even by the lights of the doer’s primary mission―being able to make accurate predictions for a wide variety of experiments―there are reasons to dream:
“Suppose you have two theories, A and B, which look completely different psychologically, with different ideas in them and so on, but that all consequences that are computed from each are exactly the same, and both agree with experiment. … how are we going to decide which one is right? There is no way by science, because they both agree with experiment to the same extent. … However, for psychological reasons, in order to guess new theories, these two things may be very far from equivalent, because one gives a man different ideas from the other. By putting the theory in a certain kind of framework you get an idea of what to change. … Therefore psychologically we must keep all the theories in our heads, and every theoretical physicist who is any good knows six or seven different theoretical representations for exactly the same physics.”
In the spirit of finding alternative versions of quantum mechanics―whether they agree exactly or only approximately on experimental consequences―let me describe an exciting new option which has recently been proposed by Hall, Deckert, and Wiseman (in Physical Review X) and myself (forthcoming in Philosophy of Science), receiving media attention in: Nature, New Scientist, Cosmos, Huffington Post, Huffington Post Blog, FQXi podcast… Somewhat similar ideas have been put forward by Böstrom, Schiff and Poirier, and Tipler. The new approach seeks to take seriously quantum theory’s hydrodynamic formulation which was developed by Erwin Madelung in the 1920s. Although the proposal is distinct from the many-worlds interpretation, it also involves the postulation of parallel universes. The proposed multiverse picture is not the quantum mechanics of college textbooks, but just because the theory looks so “completely different psychologically” it might aid the development of new physics or new calculational techniques (even if this radical picture of reality ultimately turns out to be incorrect).
Let’s begin with an entirely reasonable question a dreamer might ask about quantum mechanics.
“I understand water waves and sound waves. These waves are made of particles. A sound wave is a compression wave that results from particles of air bunching up in certain regions and vacating other. Waves play a central role in quantum mechanics. Is it possible to understand these waves as being made of some things?”
There are a variety of reasons to think the answer is no, but they can be overcome. In quantum mechanics, the state of a system is described by a wave function Ψ. Consider a single particle in the famous double-slit experiment. In this experiment the one particle initially passes through both slits (in its quantum way) and then at the end is observed hitting somewhere on a screen. The state of the particle is described by a wave function which assigns a complex number to each point in space at each time. The wave function is initially centered on the two slits. Then, as the particle approaches the detection screen, an interference pattern emerges; the particle behaves like a wave.
Figure 1: The evolution of Ψ with the amount of color proportional to the amplitude (a.k.a. magnitude) and the hue indicating the phase of Ψ.
There’s a problem with thinking of the wave as made of something: the wave function assigns strange complex numbers to points in space instead of familiar real numbers. This can be resolved by focusing on |Ψ|2, the squared amplitude of the wave function, which is always a positive real number.
Figure 2: The evolution of |Ψ|2.
We normally think of |Ψ|2 as giving the probability of finding the particle somewhere. But, to entertain the dreamer’s idea about quantum waves, let’s instead think of |Ψ|2 as giving a density of particles. Whereas figure 2 is normally interpreted as showing the evolution of the probability distribution for a single particle, instead understand it as showing the distribution of a large number of particles: initially bunched up at the two slits and later spread out in bands at the detector (figure 3). Although I won’t go into the details here, we can actually understand the way that wave changes in time as resulting from interactions between these particles, from the particles pushing each other around. The Schrödinger equation, which is normally used to describe the way the wave function changes, is then viewed as consequence of this interaction.
Figure 3: The evolution of particles with |Ψ|2 as the density. This animation is meant to help visualize the idea, but don’t take the precise motions of the particles too seriously. Although we know how the particles move en masse, we don’t know precisely how individual particles move.
In solving the problem about complex numbers, we’ve created two new problems: How can there really be a large number of particles if we only ever see one show up on the detector at the end? If |Ψ|2 is now telling us about densities and not probabilities, what does it have to do with probabilities?
Removing a simplification in the standard story will help. Instead of focusing on the wave function of a single particle, let’s consider all particles at once. To describe the state of a collection of particles it turns out we can’t just give each particle its own wave function. This would miss out on an important feature of quantum mechanics: entanglement. The state of one particle may be inextricably linked to the state of another. Instead of having a wave function for each particle, a single universal wave function describes the collection of particles.
The universal wave function takes as input a position for each particle as well as the time. The position of a single particle is given by a point in familiar three dimensional space. The positions of all particles can be given by a single point in a very high dimensional space, configuration space: the first three dimensions of configuration space give the position of particle 1, the next three give the position of particle 2, etc. The universal wave function Ψ assigns a complex number to each point of configuration space at each time. |Ψ|2 then assigns a positive real number to each point of configuration space (at each time). Can we understand this as a density of some things?
A single point in configuration space specifies the locations of all particles, a way all things might be arranged, a way the world might be. If there is only one world, then only one point in configuration space is special: it accurately captures where all the particles are. If there are many worlds, then many points in configuration space are special: each accurately captures where the particles are in some world. We could describe how densely packed these special points are, which regions of configuration space contain many worlds and which regions contain few. We can understand |Ψ|2 as giving the density of worlds in configuration space. This might seem radical, but it is the natural extension of the answer to the dreamer’s question depicted in figure 3.
Now that we have moved to a theory with many worlds, the first problem above can be answered: The reason that we only see one particle hit the detector in the double-slit experiment is that only one of the particles in figure 3 is in our world. When the particles hit the detection screen at the end we only see our own. The rest of the particles, though not part of our world, do interact with ours. They are responsible for the swerves in our particle’s trajectory. (Because of this feature, Hall, Deckert, and Wiseman have coined the name “Many Interacting Worlds” for the approach.)
Figure 4: The evolution of particles in figure 3 with the particle that lives in our world highlighted.
No matter how knowledgeable and observant you are, you cannot know precisely where every single particle in the universe is located. Put another way, you don’t know where our world is located in configuration space. Since the regions of configuration space where |Ψ|2 is large have more worlds in them and more people like you wondering which world they’re in, you should expect to be in a region of configuration space where|Ψ|2 is large. (Aside: this strategy of counting each copy of oneself as equally likely is not so plausible in the old many-worlds interpretation.) Thus the connection between |Ψ|2 and probability is not a fundamental postulate of the theory, but a result of proper reasoning given this picture of reality.
There is of course much more to the story than what’s been said here. One particularly intriguing consequence of the new approach is that the three sentence characterization of Newtonian physics with which this post began is met. In that sense, this theory makes quantum mechanics look like classical physics. For this reason, in my paper I gave the theory the name “Newtonian Quantum Mechanics.”
Watch and savor this remarkable video by Daniel Stoupin. It shows tiny marine animals in motion — motions that are typically so slow that we would never notice, here enormously sped-up so that humans can appreciate them.
I found it at this blog post by Peter Godfrey-Smith, a philosopher of biology. He notes that some kinds of basic processes, like breathing, are likely common to creatures that live at all different timescales; but others, like reaching out and grasping things, might not be open to creatures in the slow domain. Which raises the question: what kinds of motion are available to slow life that we fast-movers can’t experience?
Not all timescales are created equal. In the real world, the size of atoms sets a fundamental length, and chemical reactions set fundamental times, out of which everything larger is composed. We will never find a naturally-occurring life form, here on Earth or elsewhere in the universe, whose heart beats once per zeptosecond. But who knows? Maybe there are beings whose “hearts” beat once per millennium.
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:
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.
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.
If you’re reading this you probably know about the 
