POWER OVER NATURE
What I’ve been thinking about today specifically is something of a potential breakthrough in understanding our fundamental theories of physics. We have something called a standard model, but its foundations are kind of scandalous. We have not known how to define an important part of it mathematically rigorously, but I think I have figured out how to do that, and it’s very pretty. I’m in the middle of calculations to check it out.
When we think about next steps in physics, we have to diagnose what’s wrong, first of all. Solving problems guides us into knowing what’s wrong and what is not wrong. Knowing that you can fix this problem is very important. It’s important because, in thinking about future theories, we want to build on our understanding of existing theories. The fact that there are theories whose statuses are questionable—we don’t know whether they’re respectable or not, whether they really satisfy the properties that we want them to have—is limiting. Now we’ll be able to assess them. Also, this technique that I’ve been developing not only shows that theories exist, it opens up new ways of calculating their properties so that it gives us a bigger toolbox of potential models to construct world theories.
Who does this falsify? It’s a funny situation where the theory of electroweak or weak interactions has been successful when you calculate up to a certain approximation, but if you try to push it too far, it falls apart. Some people have thought that would require fundamental changes in the theory, and have tried to modify the theory so as to remove the apparent difficulty. What I’ve shown is that the difficulty is only a surface difficulty. If you do the mathematics properly, organize it in a clever way, the problem goes away. It falsifies speculative theories that have been trying to cure a problem that doesn’t exist. It’s things like certain kinds of brane-world models, in which people set up parallel universes where that parallel universe's reason for being was to cancel off difficulties in our universe—we don’t need it. It's those kinds of speculations about how the foundations might be rotten, so you have to do something very radical. It’s still of course legitimate to consider radical improvements, but not to cure this particular problem. You want to do something that directs attention in other places.
What’s new in the universe? Well, the Large Hadron Collider—LHC—just announced its preliminary results from run two, which was the first time we’ve had results at their new higher energy. The statistics are not yet sufficient to draw any firm conclusion, but they have a suggestive new phenomenon, a heavier version of the Higgs particle that, if it holds up, would be very significant. It would mean probably a major expansion of the standard model, perhaps a whole new world of interactions. At present, it may very well go away; the statistical significance is unclear.
Things like this happen frequently in the sense that there are hints of new phenomena that don’t stand up to further investigation. For instance, almost two years ago in March, there were B-modes—the supposed gravity waves from the early universe—which would have been enormously significant as evidence for inflation and a window into extraordinarily high-energy physics and the first manifestation of quantum gravity we showed, but that went away. It turned out that what they were measuring had a much more mundane explanation in terms of cosmic dust scattering light and producing this effect. It doesn’t falsify the theories of course, it just means that different kinds of evidence will have to be gathered.
I had occasion recently to look at an old lecture by Sidney Coleman called “Quantum Mechanics in Your Face,” where he explained in great detail, and beautifully, a profound test of quantum mechanics. It’s a situation where you have three spins, or three polarized photons, and measure certain properties. A classical theory would always give one result plus one for this measurement, whereas the quantum mechanical theory gives minus one. It couldn’t be a more dramatic difference.
The experiment is done and quantum mechanics wins. When Sidney explained this in his inimitable style, it brought tears to my eyes and brought back a whole flood of memories. The reason I was watching this is that recently, with a brilliant student named Jordan Cotler, I had been working on a variant of that kind of experiment where instead of looking at three photons at the same time, you look at one photon at three different times. It turns out that some of the properties that are most peculiar in quantum mechanics of entanglement between different particles can also be a property of entangling histories of single particles.
I love the whole notion of entangling histories, where different possibilities for what things might have happened get to interfere with each other, and the whole notion of what the past is gets mixed up, gets the same weirdness that is characteristic of Einstein-Podolsky-Rosen effects and Bell's paradox. All these things not only affect particles in different places, but also can affect things as they develop in time.
At some level, the idea that physical reality is much richer than what we perceive is something that everybody knows. We know nowadays that we see much more in whole new worlds when we use microscopes or telescopes than we see when we use the naked eye.
There are many ways we can enhance our perception of the world using different kinds of gadgets. We can slow down motion by taking rapid pictures and slowing it down. We can also nowadays understand the microworld by calculating. We have a very precise, rigorous, and successful theory of how the world works based on very different ideas than are encountered in everyday life. We can present those ideas in visual form if we’re creative, using data visualization techniques to bring these other worlds into human perception that was built to do something quite different.
The particular thing that I got obsessed with recently is the mismatch between our perception of the most important way we interact with the external world, that is, our perception of light—our vision—and the underlying physical reality. We sample with our eyes a very narrow range of the electromagnetic spectrum—basically, one octave out of an infinite keyboard that, moreover, is not just discrete notes but a continuum. We have a reliable, well-tested theory of what light is: electromagnetic radiation. We can compare the reality of what light is to our perception of it. What we see is, as I said, a very narrow band of frequencies. But even within that narrow band, we do a paltry kind of sampling. We sample three different averages of the intensities. This is called trichromatic vision. The most common colorblindness is seeing only two averages.
There are many forms of electromagnetic radiation that are physically different yet look the same to us. There is information that we’re missing, which has two dramatic consequences. First of all, it means that there’s a lot of the visual world—the world we think we know—that we’re missing out on. Secondly, our ability to use that portal to convey information is relatively limited physically. There is much more bandwidth intrinsic to the visible portal than we exploit.
On the other hand, there are creatures that do a much better job of this. There is something called a mantis shrimp, which is a champion in the animal world. It’s a very successful species of underwater, shrimplike animal that exists in hundreds of varieties. All of them have this feature where instead of seeing three averages in the spectrum, they see a dozen or up to sixteen, depending on the variety. They also see down to the ultraviolet, they see some infrared. They have a much richer portal into color information than we do.
It occurred to me—and this may be one of the best ideas I ever had—that we can restore some of that information using modern technology and modern ideas about how information can be conveyed, namely, by encoding different aspects of the missing information as time-dependent modulation of the channels we have. So, open new channels by modulating in ways that are recognizable and that keep the image, the channels we have.
We can start to perhaps see like mantis shrimp, and that will both enrich our perception of the external world and also open up new possibilities for visualization. In quantum mechanics, we learn that the wave functions—the primary description of reality—live in high-dimensional spaces. If you have the wave function for two particles, it lives in a six-dimensional space. That is very hard to visualize.
Chemists could find it very useful if they were able to get a better visualization of things like that, or people dealing with complex datasets that depend on many factors; those naturally live in many dimensional spaces, and it would be very useful to be able to visualize those. Opening up extra channels, extra dimensions of color perception, could be a very good thing. I've been working on gadgets, tricks, software, and hardware to implement that.
It’s been fun. It’s a new direction for me. My father was a kind of engineer, and I’ve always had in the back of my mind that I’d love to do something useful. Finally, I had an idea that plausibly could be useful, so I’m going for it.
There are many practical applications of the information that’s in colors we don’t see, so to speak. We see three averages, but you can have a more fine-grained picture if you separate the different frequencies and have more channels of information. One very practical thing that people use this information for is sorting fruit that’s old and starting to go bad. Depending on the fruit, it shows different characteristics that are difficult to see with the resources our eyes give us naturally, but if you look at these extra pieces of information, it stands right out.
Another thing that’s, I don’t know if you call it practical, but it’s kind of cool, is that many insects and butterflies see four or five dimensions, and many flowers that want to make a good impression on butterflies or insects have displays in those extra dimensions. They have extra structure in the ultraviolet, extra structure that’s attuned to the particular capabilities of the insects that they want to attract that we don’t see. We can enhance our perception to see what they look like and see extra patterns. Gardens would look prettier, rainbows would look prettier, different aspects of art objects could leap out; it could be great fun.
The fact is we don’t know exactly what the mantis shrimps do with this information, and that’s a very active subject in biophysics. It's such a strange phenomenon, and striking, how capable in their own environment and successful these species are. They’re not that extraordinary: they’re not super creatures, they’re not superhuman, certainly. What do they do with this information? The most plausible idea is that they primarily use this information to make sexual displays to show their fitness and to communicate with other mantis shrimps. Part of the evidence for that is you just look at these mantis shrimps; they look extremely colorful even to us, so you can only imagine what they look like to each other.
Mantis shrimps have very small brains, so they don’t do the kind of sophisticated processing of the visual scene that we do. They don’t have as high a spatial resolution either, so they see more colors, but the picture is fuzzier.
A way of thinking of their experience as compared to ours is that we have a very fine-grained picture of a three-dimensional space of color, whereas they have a much coarser view of a twelve-dimensional space. We see lots of discrete points, so to speak. On a computer display, when you see millions of different colors, we can distinguish millions of different colors, but they’re all points in a three-dimensional space. They are all manufactured in the computer screen by combining red, green, and blue LEDs—or whatever the light source is—in different proportions. Millions of colors are really three colors in different proportions. The mantis shrimp has twelve base colors that you can put in different proportions, but they almost certainly can’t resolve the fine structure nearly as well. You could think of them as seeing big blobs in a high-dimensional space, whereas we see fine points in a low-dimensional space.
The surprise that I’m thinking about different things is no surprise. I have always had this style of thinking about something—trying to skim off the cream and then moving on to something else. I look for opportunities. I keep coming back to the subjects that I've visited before if I don’t feel that I’ve exhausted them. This thing that I mentioned before about what I was thinking about and am excited about is making the foundations of the standard model more secure. This problem that we’re addressing has been a worm in the rose for decades that has been worrying people. Most people don’t want to think about it; they think it’s somehow going to resolve itself.
It looks very technical, but it’s been there and it’s been annoying for those of us who care about logical consistency. That’s always been in the back of my mind. It’s one thing to have something in the back of your mind, it’s another thing to have a good idea about it.
I’m still interested in these possibilities for unusual quantum statistics—anyons, they’re called. Since I introduced them, they have been a very fertile source of theoretical work, and are firmly embedded in theories that have a lot of other success, but there is still no direct evidence for the primary concept. I keep coming back to that, thinking about how we can design experiments that will display these phenomena that are surely there, but subtle and hard to find. That leads me to think about new kinds of microscopy that are intrinsically sensitive to quantum effects, to the effects of entanglement. That’s how I came to think about those entangled histories.
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My research has mostly been in rather abstract, advanced quantum field theory, high-energy physics, cosmology, and low-temperature physics that is esoteric, if you like. For many years I've also kept a lively interest in artificial intelligence and what’s going on in neurobiology and computer science. I almost became a professional in that when I was a student. If things had been slightly different, I might have gone the other way. The work that I wound up concentrating on is the tip of the iceberg of a lot of other potentials.
What’s happening in physics depends on what you mean by physics. High-energy physics and fundamental physics, in the sense of finding new interactions, has been slow for quite a while. The standard model has held up much better than any of us thought it would. It’s been much more difficult to get beyond the standard model.
The LHC so far has just succeeded in verifying a standard model with unprecedented accuracy—dotting the i’s and crossing the t’s with the discovery of the Higgs particle. Maybe something new will show up. I hope so. There are very logical and compelling extensions of the standard model based on low-energy supersymmetry and unification that I've been fond of, which I pioneered thirty years ago. The experiments so far have not caught up with that.
There are beautiful ideas about extending the standard model using something called axions, which could very well be the dark matter. It's a very attractive theory that only gets more attractive as time goes on and the competition dies off. The experiments to test this theory are very difficult, but some heroic people have taken it on themselves to try to do this. Leslie Rosenberg is a brilliant experimental physicist who has devoted his whole career for thirty years now or more to developing the technology that’s needed to find axions, and he’s getting very close. There are other ideas that are very clever and that are relatively new, but also have a plausible chance. We’re getting there.
Dark matter is an unfortunate name, but the phenomenon is the following. We have (we think) very reliable laws for the gravitational force based on general relativity, which is a generalization of Newton’s theory of gravity; it’s famous—Einstein. There are many tests of it nowadays. It’s very successful, but hard to modify in a consistent way. People have tried to modify it, but that direction doesn’t seem very fruitful; however, if you apply the laws of gravity to the study of astronomy, you find a whole series of phenomena that all point in the same direction that are anomalous. You look at the way things are moving, like how one galaxy moves around another, or how the stars at the edge of a galaxy move around the center, and you find that they’re moving faster than they should be if the forces they’re responding to are due to the matter we see that they’re moving around. You can estimate the mass in stars and gas clouds and all kinds of matter that we understand, and figure out how fast particles or stars have to be moving in order to stay in orbit, and you compare with observations and you find that things are moving faster.
The explanation that stood the test of time is that there is another form of matter that contributes a lot of extra mass, but it’s a form of matter that resists detection, that our telescopes miss, that doesn’t emit cosmic rays, doesn’t absorb light; it’s very transparent, very inert as far as ordinary matter, including light, is concerned. That’s what’s called the dark matter—this extra stuff.
Basically every galaxy that’s been studied has turned out to have a dark matter halo around it. In fact, it would be better to call the galaxy an impurity within this dark matter cloud that surrounds it because, although it’s more diffuse than the visible matter when you add it all up, because it occupies a much bigger volume, it weighs about six times as much. It clumps, but not as much as ordinary matter.
As far as galaxy formation is concerned, ordinary matter looks to be an impurity within the dark matter. So what is it? The first thing to say is that it may seem outlandish to introduce as a hypothesis that there’s some new kind of matter just to solve this problem. Wouldn’t it be better to modify gravity? Maybe something profound is happening, not just another new particle, and that’s still possible, but that has not turned out to be a fruitful idea because no theory based on that has been mathematically consistent with observation. It just hasn’t worked.
Now that we understand fundamental interactions well—as far as ordinary matter is concerned in a standard model—and have profound principles of quantum mechanics and relativity, we think we know how things work. The possibility of the kinds of matter that interact very feebly with ordinary matter doesn’t seem outlandish at all. It’s easy for things like that to happen. In fact, we know of an example: neutrinos.
Neutrinos interact very feebly with ordinary matter. It was difficult to observe them at all. At one time, it was thought that they could be the dark matter, and if they had a slightly larger mass than they do, they would be the dark matter. Now we know enough about neutrinos to rule them out. It could be some neutrino-like particle, or it could be some other particle that doesn’t have any of the standard fundamental interactions. We know how to construct such consistent models that are even very attractive and solve problems that would lead to candidates for what this dark matter is.
To me, the most attractive of those ideas, partly because I had a lot to do with inventing it, is something called axions. It’s a long story why axions were introduced. Let me give you a very short version of it. It’s profound and entertaining to the people who are likely to listen to this.
It's been a remarkable thing since the earliest days of modern physics—you broadly consider since Newton’s day—that the fundamental laws have had the character that if you run them backwards in time, they don’t change, whereas if you look at a motion picture and run it backwards in time, it doesn’t look like the natural world. If you took a picture of things that are small—the microworld—and ran it backwards, it would be indistinguishable; the events would still satisfy the laws of physics, and you would have a hard time telling which way was forwards and which way was backwards.
The fundamental laws have this very different character from the world we ordinarily experience. Earlier, we talked about this theme that our perception of reality is quite different from deep reality, and this is one of the most outstanding examples.
The laws of physics had this property that seemed totally gratuitous, unnecessary to describe the world, in fact, kind of embarrassing. It’s a famous problem called the “arrow of time.” How can it be that the fundamental laws look the same forwards and backwards in time, and yet, the world doesn’t? Interesting problem, but an equally interesting problem is why the laws have that property.
It was only in the late 20th century in which that problem got a reasonable answer. It turns out that property where the fundamental laws look the same, to great accuracy, forwards and backwards in time, is an accidental consequence of deeper principles.
The principles of relativity, quantum mechanics, and gauge symmetry, which is necessary to make those work together properly, together greatly constrain the possible physical laws for the fundamental interactions. When you take all those constraints into account, you find that the only things that are allowed look almost the same forwards and backwards in time, and, in fact, there are subtle microphysical phenomena that people got Nobel Prizes for observing—obscure particle decays that don’t look the same forwards and backwards in time, but for the most part, the fundamental laws do look the same. It was a great triumph to understand that puzzle. The so-called time reversal symmetry of physical laws is a consequence of other deep principles.
There are certain interactions that are allowed by the fundamental principles that do look different run forwards and backwards in time. There are, for instance, some scattering processes where the probability that they happen in one direction: A plus B go to C plus D, is different from the probability of C plus D goes to A plus B; that’s the basic idea. It’s more complicated in detail, but that’s the basic idea. There are very slight asymmetries in certain reactions run backwards and forwards in time, but they’re very obscure and very small asymmetries. It was a great triumph to understand that.
This is a long shaggy-dog story, but it eventually does connect to the dark matter. This wonderful result has a loophole. It turns out there is one kind of interaction that would give a rather large asymmetry between forwards and backwards in time—one fundamental interaction that, if it existed, would. It’s not forbidden by any fundamental principles, so the puzzle has been narrowed but not solved. We still have this one loophole.
Two physicists named Helen Quinn and Roberto Peccei introduced an idea, a way of expanding the laws of physics, introducing more symmetry—a new profound principle in addition to relativity, quantum mechanics, and gauge symmetry—that would explain why that interaction doesn’t exist, either. What I noticed, and also Steve Weinberg noticed, is that that kind of theoretical proposal leads to the existence of a new kind of particle, which has very remarkable properties. It’s extremely light, extremely feebly interacting with matter, and it turns out that if you worked out how it gets produced in the Big Bang, it gets produced in about the right amount to make the observed dark matter that astronomers want.
That’s the axion. I named it after a laundry detergent. It wasn’t very long after I was an adolescent that I did this. There was a laundry detergent on the market called Axion, and I thought that sounds like a particle. I learned that there was no such particle, and I said to myself, "If I ever get the chance, I’m going to make such a particle." It turned out that this particle cleaned up—it cleans up a problem with an axial current—so I called it the axion, and that got through physical review letters and became the name which is now universally accepted. That was, gosh, almost forty years ago now.
First of all, I should say that I saved the world from the Higglet. Weinberg had been calling this thing the Higglet, so when we learned that we were both barking up the same tree and compared notes, he very wisely and graciously agreed to use axion, which became the standard name.
Just in the axion story itself, it wasn’t obvious at first what its cosmological consequences were. It was not introduced consciously to provide dark matter; it just turned out that the theory did provide dark matter. That’s pretty encouraging. I had a big role working that out and trying to think of experiments that would observe this stuff.
Another thing that I played with that has turned out to be very fruitful and connected to axions is a remarkable thing in physics. The basic equations that we use to describe particle physics interactions also turn out to describe things on a very different scale like superconductivity, behavior of matter at low temperatures, super fluidity. Various exotic quantum mechanical behaviors are common to the super duper microworld and the world of materials, especially at low temperatures. That’s a connection that I’ve been exploring for years, but is now commonly appreciated and has become a very big deal.
Axions, in particular, it turns out, are closely connected to the hottest subjects in condensed matter physics—something called topological insulators.
I wrote a paper for fun called "Two Applications of Axion Electrodynamics," where I wrote down the behavior that you would get if you had an axion-like field, which was an emergent consequence of condensed matter behavior. And by God, what’s been discovered is these topological insulators obey the equations of axion electrodynamics. That was like twenty-five years ago. Every once in a while something percolates.
The big development is like if you asked what causes an Ice Age. What causes an Ice Age is that there’s a little bit more snow every year that melts, so the ice accumulates over time. It’s very dramatic, but year by year you don’t necessarily know this. The big story of the 20th and the 21st century is that we’re learning to control the world better. With the development of quantum mechanics, we understand the fundamental principles of what matter is and how it behaves that’s adequate for all engineering purposes.
The limitation is just our imagination and our ability to calculate the consequences of the laws. We’re getting better at both of those as we gain experience. We have more imagination. As computing develops, we learn how to calculate the consequences of the laws better and better. There’s also a feedback cycle: when you understand matter better, you can design better computers, which will enable you to calculate better. It's kind of an ascending helix.
To me, that is the big story. We understand things better, and that gives us more and more power over nature.
Another important, interesting, and glamorous part of physics and fundamental science is finding essentially new things. In physics, which I know best, there are prospects from the Large Hadron Collider that’s opening up new ground. We will soon have gravitational wave detectors, we will soon have axion detectors, we will have perhaps surprises coming from sensitive experiments to detect rare events, rare decays, tiny asymmetries, and the behavior of laws so that there are lots of potential portals where we can have new phenomena that will change and enrich our understanding of fundamentals.
Of course, astronomy is another source. People are developing techniques that are ways of orchestrating much larger masses of data than we could handle before and instruments that are more sensitive. People, as they have also gotten a standard model of cosmology, have been able to ask more sophisticated questions, more profound questions about how it all began.
There are easy targets for this question of what theories will die, which are theories that have never had substantial backing in the scientific community—theories like creationism, theories like denial of global warming. I don’t even know if that’s a theory; it’s just crankiness.
A field where there’s lots of crap is the whole field around consciousness, where people have very woolly ideas about something they call consciousness. No one means exactly the same thing about what it is. There is something called the hard problem, which says that there’s something about consciousness that can’t be explained in terms of a physical substrate. Those ideas are doomed, and they’re very superficial to begin with.
It’s a profound fact and wonderful fact—and it’s only happened in the 20th century as far as I’m concerned—that the fundamental understanding of the world became very beautiful, that our ideas of symmetry and what I call exuberance, where you can get a lot more out than you put in, only became fully characteristic at the level they are now in the 20th century. Not all the laws we know are beautiful, either. There are a lot of loose ends. But what is quite remarkable to me is that the core of our understanding is based on beautiful equations.
One aspect of why the laws are beautiful is certainly that if they weren’t beautiful, we wouldn’t have discovered them.
In the case of the strong interactions, quantum chromodynamics (QCD) and the weak interactions, in particular, the phenomena are so difficult to study. The high-energy interactions, the short distances, the basic things that the theory is about are very difficult to study directly. You can’t in practice follow the model that people like Francis Bacon recommended and Newton, where you accumulate a lot of data but don’t make hypotheses, you just summarize the data in theories and try to make a simple explanation. That’s not practical when the information is so difficult to acquire.
The way we proceed now that’s been remarkably successful is to guess beautiful equations, derive their consequences, and compare crucial consequences with reality. That’s a different procedure. If we didn’t have beauty as a guide to what the plausible equations are, we would be lost; we wouldn’t find them. That’s how axions also arise—looking for a way to make the standard model more beautiful to clarify why certain interactions don’t occur.
If you want to explain something in this very unfamiliar world where there isn’t a lot of data and where everyday experience is not reliable, what have you got to go on other than aesthetic feeling for how things should fit together?
