Category Archives: Quantum Field Theory

If It Holds Up, What Might BICEP2’s Discovery Mean?

Well, yesterday was quite a day, and I’m still sifting through the consequences.

First things first.  As with all major claims of discovery, considerable caution is advised until the BICEP2 measurement has been verified by some other experiment.   Moreover, even if the measurement is correct, one should not assume that the interpretation in terms of gravitational waves and inflation is correct; this requires more study and further confirmation.

The media is assuming BICEP2’s measurement is correct, and that the interpretation in terms of inflation is correct, but leading scientists are not so quick to rush to judgment, and are thinking things through carefully.  Scientists are cautious not just because they’re trained to be thoughtful and careful but also because they’ve seen many claims of discovery withdrawn or discredited; discoveries are made when humans go where no one has previously gone, with technology that no one has previously used — and surprises, mistakes, and misinterpretations happen often.

But in this post, I’m going to assume assume assume that BICEP2’s results are correct, or essentially correct, and are being correctly interpreted.  Let’s assume that [here’s a primer on yesterday’s result that defines these terms]

  • they really have detected “B-mode polarization” in the “CMB” [Cosmic Microwave Background, the photons (particles of light) that are the ancient, cool glow leftover from the Hot Big Bang]
  • that this B-mode polarization really is a sign of gravitational waves generated during a brief but dramatic period of cosmic inflation that immediately preceded the Hot Big Bang,

Then — IF BICEP2’s results were basically right and were being correctly interpreted concerning inflation — what would be the implications?

Well… Wow…  They’d really be quite amazing. Continue reading

A Primer On Today’s Events

The obvious questions and their brief answers, for those wanting to know what’s going on today. If you already know roughly what’s going on and want the bottom line, read the answer to the last question.

You may want to start by reading my History of the Universe articles, or at least having them available for reference.

The expectation is that today we’re going to hear from the BICEP2 experiment.

  • What is BICEP2?

BICEP2, located at the South Pole, is an experiment that looks out into the sky to study the polarization of the electromagnetic waves that are the echo of the Hot Big Bang; these waves are called the “cosmic microwave background”.

  • What are electromagnetic waves?

Electromagnetic waves are waves in the electric and magnetic fields that are present everywhere in space.  Visible light is an electromagnetic wave, as are X-rays, radio waves, and microwaves; the only difference between these types of electromagnetic waves is how fast they wiggle and how long the distance is from one wave crest to the next.   Continue reading

What if the Large Hadron Collider Finds Nothing Else?

In my last post, I expressed the view that a particle accelerator with proton-proton collisions of (roughly) 100 TeV of energy, significantly more powerful than the currently operational Large Hadron Collider [LHC] that helped scientists discover the Higgs particle, is an obvious and important next steps in our process of learning about the elementary workings of nature. And I described how we don’t yet know whether it will be an exploratory machine or a machine with a clear scientific target; it will depend on what the LHC does or does not discover over the coming few years.

What will it mean, for the 100 TeV collider project and more generally, if the LHC, having made possible the discovery of the Higgs particle, provides us with no more clues?  Specifically, over the next few years, hundreds of tests of the Standard Model (the equations that govern the known particles and forces) will be carried out in measurements made by the ATLAS, CMS and LHCb experiments at the LHC. Suppose that, as it has so far, the Standard Model passes every test that the experiments carry out? In particular, suppose the Higgs particle discovered in 2012 appears, after a few more years of intensive study, to be, as far the LHC can reveal, a Standard Model Higgs — the simplest possible type of Higgs particle?

Before we go any further, let’s keep in mind that we already know that the Standard Model isn’t all there is to nature. The Standard Model does not provide a consistent theory of gravity, nor does it explain neutrino masses, dark matter or “dark energy” (also known as the cosmological constant). Moreover, many of its features are just things we have to accept without explanation, such as the strengths of the forces, the existence of “three generations” (i.e., that there are two heavier cousins of the electron, two for the up quark and two for the down quark), the values of the masses of the various particles, etc. However, even though the Standard Model has its limitations, it is possible that everything that can actually be measured at the LHC — which cannot measure neutrino masses or directly observe dark matter or dark energy — will be well-described by the Standard Model. What if this is the case?

Michelson and Morley, and What They Discovered

In science, giving strong evidence that something isn’t there can be as important as discovering something that is there — and it’s often harder to do, because you have to thoroughly exclude all possibilities. [It’s very hard to show that your lost keys are nowhere in the house — you have to convince yourself that you looked everywhere.] A famous example is the case of Albert Michelson, in his two experiments (one in 1881, a second with Edward Morley in 1887) trying to detect the “ether wind”.

Light had been shown to be a wave in the 1800s; and like all waves known at the time, it was assumed to be a wave in something material, just as sound waves are waves in air, and ocean waves are waves in water. This material was termed the “luminiferous ether”. As we can detect our motion through air or through water in various ways, it seemed that it should be possible to detect our motion through the ether, specifically by looking for the possibility that light traveling in different directions travels at slightly different speeds.  This is what Michelson and Morley were trying to do: detect the movement of the Earth through the luminiferous ether.

Both of Michelson’s measurements failed to detect any ether wind, and did so expertly and convincingly. And for the convincing method that he invented — an experimental device called an interferometer, which had many other uses too — Michelson won the Nobel Prize in 1907. Meanwhile the failure to detect the ether drove both FitzGerald and Lorentz to consider radical new ideas about how matter might be deformed as it moves through the ether. Although these ideas weren’t right, they were important steps that Einstein was able to re-purpose, even more radically, in his 1905 equations of special relativity.

In Michelson’s case, the failure to discover the ether was itself a discovery, recognized only in retrospect: a discovery that the ether did not exist. (Or, if you’d like to say that it does exist, which some people do, then what was discovered is that the ether is utterly unlike any normal material substance in which waves are observed; no matter how fast or in what direction you are moving relative to me, both of us are at rest relative to the ether.) So one must not be too quick to assume that a lack of discovery is actually a step backwards; it may actually be a huge step forward.

Epicycles or a Revolution?

There were various attempts to make sense of Michelson and Morley’s experiment.   Some interpretations involved  tweaks of the notion of the ether.  Tweaks of this type, in which some original idea (here, the ether) is retained, but adjusted somehow to explain the data, are often referred to as “epicycles” by scientists.   (This is analogous to the way an epicycle was used by Ptolemy to explain the complex motions of the planets in the sky, in order to retain an earth-centered universe; the sun-centered solar system requires no such epicycles.) A tweak of this sort could have been the right direction to explain Michelson and Morley’s data, but as it turned out, it was not. Instead, the non-detection of the ether wind required something more dramatic — for it turned out that waves of light, though at first glance very similar to other types of waves, were in fact extraordinarily different. There simply was no ether wind for Michelson and Morley to detect.

If the LHC discovers nothing beyond the Standard Model, we will face what I see as a similar mystery.  As I explained here, the Standard Model, with no other particles added to it, is a consistent but extraordinarily “unnatural” (i.e. extremely non-generic) example of a quantum field theory.  This is a big deal. Just as nineteenth-century physicists deeply understood both the theory of waves and many specific examples of waves in nature  and had excellent reasons to expect a detectable ether, twenty-first century physicists understand quantum field theory and naturalness both from the theoretical point of view and from many examples in nature, and have very good reasons to expect particle physics to be described by a natural theory.  (Our examples come both from condensed matter physics [e.g. metals, magnets, fluids, etc.] and from particle physics [e.g. the physics of hadrons].) Extremely unnatural systems — that is, physical systems described by quantum field theories that are highly non-generic — simply have not previously turned up in nature… which is just as we would expect from our theoretical understanding.

[Experts: As I emphasized in my Santa Barbara talk last week, appealing to anthropic arguments about the hierarchy between gravity and the other forces does not allow you to escape from the naturalness problem.]

So what might it mean if an unnatural quantum field theory describes all of the measurements at the LHC? It may mean that our understanding of particle physics requires an epicyclic change — a tweak.  The implications of a tweak would potentially be minor. A tweak might only require us to keep doing what we’re doing, exploring in the same direction but a little further, working a little harder — i.e. to keep colliding protons together, but go up in collision energy a bit more, from the LHC to the 100 TeV collider. For instance, perhaps the Standard Model is supplemented by additional particles that, rather than having masses that put them within reach of the LHC, as would inevitably be the case in a natural extension of the Standard Model (here’s an example), are just a little bit heavier than expected. In this case the world would be somewhat unnatural, but not too much, perhaps through some relatively minor accident of nature; and a 100 TeV collider would have enough energy per collision to discover and reveal the nature of these particles.

Or perhaps a tweak is entirely the wrong idea, and instead our understanding is fundamentally amiss. Perhaps another Einstein will be needed to radically reshape the way we think about what we know.  A dramatic rethink is both more exciting and more disturbing. It was an intellectual challenge for 19th century physicists to imagine, from the result of the Michelson-Morley experiment, that key clues to its explanation would be found in seeking violations of Newton’s equations for how energy and momentum depend on velocity. (The first experiments on this issue were carried out in 1901, but definitive experiments took another 15 years.) It was an even greater challenge to envision that the already-known unexplained shift in the orbit of Mercury would also be related to the Michelson-Morley (non)-discovery, as Einstein, in trying to adjust Newton’s gravity to make it consistent with the theory of special relativity, showed in 1913.

My point is that the experiments that were needed to properly interpret Michelson-Morley’s result

  • did not involve trying to detect motion through the ether,
  • did not involve building even more powerful and accurate interferometers,
  • and were not immediately obvious to the practitioners in 1888.

This should give us pause. We might, if we continue as we are, be heading in the wrong direction.

Difficult as it is to do, we have to take seriously the possibility that if (and remember this is still a very big “if”) the LHC finds only what is predicted by the Standard Model, the reason may involve a significant reorganization of our knowledge, perhaps even as great as relativity’s re-making of our concepts of space and time. Were that the case, it is possible that higher-energy colliders would tell us nothing, and give us no clues at all. An exploratory 100 TeV collider is not guaranteed to reveal secrets of nature, any more than a better version of Michelson-Morley’s interferometer would have been guaranteed to do so. It may be that a completely different direction of exploration, including directions that currently would seem silly or pointless, will be necessary.

This is not to say that a 100 TeV collider isn’t needed!  It might be that all we need is a tweak of our current understanding, and then such a machine is exactly what we need, and will be the only way to resolve the current mysteries.  Or it might be that the 100 TeV machine is just what we need to learn something revolutionary.  But we also need to be looking for other lines of investigation, perhaps ones that today would sound unrelated to particle physics, or even unrelated to any known fundamental question about nature.

Let me provide one example from recent history — one which did not lead to a discovery, but still illustrates that this is not all about 19th century history.

An Example

One of the great contributions to science of Nima Arkani-Hamed, Savas Dimopoulos and Gia Dvali was to observe (in a 1998 paper I’ll refer to as ADD, after the authors’ initials) that no one had ever excluded the possibility that we, and all the particles from which we’re made, can move around freely in three spatial dimensions, but are stuck (as it were) as though to the corner edge of a thin rod — a rod as much as one millimeter wide, into which only gravitational fields (but not, for example, electric fields or magnetic fields) may penetrate.  Moreover, they emphasized that the presence of these extra dimensions might explain why gravity is so much weaker than the other known forces.

Fig. 1: ADD's paper pointed out that no experiment as of 1998 could yet rule out the possibility that our familiar three dimensional world is a corner of a five-dimensional world, where the two extra dimensions are finite but perhaps as large as a millimeter.

Fig. 1: ADD’s paper pointed out that no experiment as of 1998 could yet rule out the possibility that our familiar three-dimensional world is a corner of a five-dimensional world, where the two extra dimensions are finite but perhaps as large as a millimeter.

Given the incredible number of experiments over the past two centuries that have probed distances vastly smaller than a millimeter, the claim that there could exist millimeter-sized unknown dimensions was amazing, and came as a tremendous shock — certainly to me. At first, I simply didn’t believe that the ADD paper could be right.  But it was.

One of the most important immediate effects of the ADD paper was to generate a strong motivation for a new class of experiments that could be done, rather inexpensively, on the top of a table. If the world were as they imagined it might be, then Newton’s (and Einstein’s) law for gravity, which states that the force between two stationary objects depends on the distance r between them as 1/r², would increase faster than this at distances shorter than the width of the rod in Figure 1.  This is illustrated in Figure 2.

Fig. 2: If the world were as sketched in Figure 1, then Newton/Einstein's law of gravity would be violated at distances shorter than the width of the rod in Figure 1.  The blue line shows Newton/Einstein's prediction; the red line shows what a universe like that in Figure 1 would predict instead.  Experiments done in the last few years agree with the blue curve down to a small fraction of a millimeter.

Fig. 2: If the world were as sketched in Figure 1, then Newton/Einstein’s law of gravity would be violated at distances shorter than the width of the rod in Figure 1. The blue line shows Newton/Einstein’s prediction; the red line shows what a universe like that in Figure 1 would predict instead. Experiments done in the last few years agree with the blue curve down to a small fraction of a millimeter.

These experiments are not easy — gravity is very, very weak compared to electrical forces, and lots of electrical effects can show up at very short distances and have to be cleverly avoided. But some of the best experimentalists in the world figured out how to do it (see here and here). After the experiments were done, Newton/Einstein’s law was verified down to a few hundredths of a millimeter.  If we live on the corner of a rod, as in Figure 1, it’s much, much smaller than a millimeter in width.

But it could have been true. And if it had, it might not have been discovered by a huge particle accelerator. It might have been discovered in these small inexpensive experiments that could have been performed years earlier. The experiments weren’t carried out earlier mainly because no one had pointed out quite how important they could be.

Ok Fine; What Other Experiments Should We Do?

So what are the non-obvious experiments we should be doing now or in the near future?  Well, if I had a really good suggestion for a new class of experiments, I would tell you — or rather, I would write about it in a scientific paper. (Actually, I do know of an important class of measurements, and I have written a scientific paper about them; but these are measurements to be done at the LHC, and don’t involve a entirely new experiment.)  Although I’m thinking about these things, I do not yet have any good ideas.  Until I do, or someone else does, this is all just talk — and talk does not impress physicists.

Indeed, you might object that my remarks in this post have been almost without content, and possibly without merit.  I agree with that objection.

Still, I have some reasons for making these points. In part, I want to highlight, for a wide audience, the possible historic importance of what might now be happening in particle physics. And I especially want to draw the attention of young people. There have been experts in my field who have written that non-discoveries at the LHC constitute a “nightmare scenario” for particle physics… that there might be nothing for particle physicists to do for a long time. But I want to point out that on the contrary, not only may it not be a nightmare, it might actually represent an extraordinary opportunity. Not discovering the ether opened people’s minds, and eventually opened the door for Einstein to walk through. And if the LHC shows us that particle physics is not described by a natural quantum field theory, it may, similarly, open the door for a young person to show us that our understanding of quantum field theory and naturalness, while as intelligent and sensible and precise as the 19th century understanding of waves, does not apply unaltered to particle physics, and must be significantly revised.

Of course the LHC is still a young machine, and it may still permit additional major discoveries, rendering everything I’ve said here moot. But young people entering the field, or soon to enter it, should not assume that the experts necessarily understand where the field’s future lies. Like FitzGerald and Lorentz, even the most brilliant and creative among us might be suffering from our own hard-won and well-established assumptions, and we might soon need the vision of a brilliant young genius — perhaps a theorist with a clever set of equations, or perhaps an experimentalist with a clever new question and a clever measurement to answer it — to set us straight, and put us onto the right path.

Brane Waves

The first day of the conference celebrating theoretical physicist Joe Polchinski (see also yesterday’s post) emphasized the broad impact of his research career.  Thursday’s talks, some on quantum gravity and others on quantum field theory, were given by

  • Juan Maldacena, on his latest thinking on the relation between gravity, geometry and the entropy of quantum entanglement;
  • Igor Klebanov, on some fascinating work in which new relations have been found between some simple quantum field theories and a very poorly understood and exotic theory, known as Vassiliev theory (a theory that has more fields than a field theory but fewer than a string theory);
  • Raphael Bousso, on his recent attempts to prove the so-called “covariant entropy bound”, another relation between entropy and geometry, that Bousso conjectured over a decade ago;
  • Henrietta Elvang, on the resolution of a puzzle involving the relation between a supersymmetric field theory and a gravitational description of that same theory;
  • Nima Arkani-Hamed, about his work on the amplituhedron, a set of geometric objects that allow for the computation of particle scattering in various quantum field theories (and who related how one of Polchinski’s papers on quantum field theory was crucial in convincing him to stay in the field of high-energy physics);
  • Yours truly, in which I quickly reviewed my papers with Polchinski relating string theory and quantum field theory, emphasizing what an amazing experience it is to work with him; then I spoke briefly about my most recent Large Hadron Collider [LHC] research (#1,#2), and concluded with some provocative remarks about what it would mean if the LHC, having found the last missing particle of the Standard Model (i.e. the Higgs particle), finds nothing more.

The lectures have been recorded, so you will soon be able to find them at the KITP site and listen to any that interest you.

There were also two panel discussions. One was about the tremendous impact of Polchinski’s 1995 work on D-branes on quantum field theory (including particle physics, nuclear physics and condensed matter physics), on quantum gravity (especially through black hole physics), on several branches of mathematics, and on string theory. It’s worth noting that every talk listed above was directly or indirectly affected by D-branes, a trend which will continue in most of Friday’s talks.  There was also a rather hilarious panel involving his former graduate students, who spoke about what it was like to have Polchinski as an advisor. (Sorry, but the very funny stories told at the evening banquet were not recorded. [And don’t ask me about them, because I’m not telling.])

Let me relate one thing that Eric Gimon, one of Polchinski’s former students, had to say during the student panel. Gimon, a former collaborator of mine, left academia some time ago and now works in the private sector. When it was his turn to speak, he asked, rhetorically, “So, how does calculating partition functions in K3 orientifolds” (which is part of what Gimon did as a graduate student) “prepare you for the real world?” How indeed, you may wonder. His answer: “A sense of pertinence.” In other words, an ability to recognize which aspects of a puzzle or problem are nothing but distracting details, and which ones really matter and deserve your attention. It struck me as an elegant expression of what it means to be a physicist.

Celebrating a Great Brane

Today and tomorrow I’m at the Kavli Institute for Theoretical Physics, on the campus of the University of California at Santa Barbara, attending a conference celebrating the career of one of the world’s great theoretical physicists, Joe Polchinski. Polchinski has shown up on this website a couple of times already (here, here and here).  And in yesterday’s post (on string/M theory) I mentioned him, because of his game-changing work from 1995 on “D-branes”, objects that arise in string theory. His paper on the subject has over 2000 citations! And now it’s such a classic that people rarely actually cite it anymore, just as they don’t cite Feynman’s paper on Feynman diagrams; its ideas have surely been used by at least double that number of papers.

Polchinski’s also very well-known for his work on quantum gravity, black holes, cosmic [i.e. astronomically large] strings, and quantum field theory.

Between 2000 and 2006, I had the extraordinary privilege to write four papers with Polchinski, all of them aimed at clarifying the relationship between string theory and quantum field theory. This was the longest collaboration of my career, and a very successful one. Because of this, I have the honor to give one of the talks today at the conference. So I’m going to cut my post short now, and tell you more about what’s happening at the conference when my duty is done.

But I will perhaps tease you with one cryptic remark. Although D-branes arise in string theory, that’s not the only place you’ll find them.  As we learned in 1998-2000, there’s a perspective from which protons and neutrons themselves are D-branes. From that point of view, we’re made out of these things.

Someday — not today — I’ll explain that comment. But it’s one of many reasons why Polchinski’s work on D-branes is so important.

Quantum Field Theory, String Theory and Predictions (Part 9)

Today I continue with my series of posts on fields, strings and predictions.

During the 1980s, as I discussed in the previous post in this series, string theorists learned that of all the possible string theories that one could imagine, there were only five that were mathematically consistent.

What they learned in the first half of the 1990s, culminating in early 1995, is that all five string theories are actually little corners of a single, more encompassing, and still somewhat mysterious theory. In other words, after 30 years of studying various types of theories with strings in them, they ended up with just one!

On the one hand, that sort of sounds like a flop — all that work, by all those people, over two decades, and all we got for our efforts was one new theory?

On the other hand, it’s very tempting to think that the reason that everyone ended up converging on the same theory is that maybe it’s the only consistent theory of quantum gravity! At this point there’s no way to know for sure, but so far there’s no evidence against that possibility.  Certainly its a popular idea among string theorists.

This unique theory is called “M theory” today; we don’t know a better name, because we don’t really know what it is. We don’t know what it describes in general. We don’t know a principle by which to define it. Sometimes it is called “string/M theory” to remind us that it is string theory in certain corners.

Fig. 1: M theory is a set of equations that, depending on how they are used, can describe all known consistent  string theories and 11-dimensional supergravity, as well as many more complex and harder to understand things.  Only at the corners does it give the relatively simple string theories described in my previous post.

Fig. 1: A famous but very schematic image of M theory, which is a set of equations that, depending on how they are used, can describe universes whose particles and forces are given by any one of the known consistent string theories or by 11-dimensional supergravity.   Only at the corners does it give the relatively simple string theories described in my previous post.  More generally, away from the corners, it describes much more complicated and poorly understood types of worlds.

Note that M theory is very different in one key respect from quantum field theory.  As I described in the second post in this series, “quantum field theory” is the term that describes the general case; “a quantum field theory” is a specific example within the infinite number of “quantum field theories”. But there’s no analogue of this distinction for M theory. M theory is (as far as anyone can discern) a unique theory; it is both the general and the specific case.  There is no category of “M theories”. However, this uniqueness, while remarkable, is not quite as profound as it might sound… for a reason I’ll return to in a future post.

Incidentally, the relationship between the five apparently very different string theories that appear in M theory is similar to the surprising relationships among various field theories that I described in this post. It’s not at all obvious that each string theory is related to the other four… which is why it took some time, and a very roundabout route involving the study of black holes and their generalizations to black strings and black branes, for this relationship to become clear.

But as it did become clear, it was realized that “M theory” (or “string/M theory”, as it is sometimes called) is not merely, or even mainly, a theory of strings; it’s much richer than that. In one corner it is actually a theory with 10 spatial (11 space-time) dimensions; this is a theory with membranes rather than strings, one which we understand poorly. And in all of its corners, the theory has more than just strings; it has generalizations of membranes, called “branes” in general. [Yes, the joke’s been made already; the experts in this subject had indeed been brane-less for years.] Particles are zero-dimensional points; strings are one-dimensional wiggly lines; membranes are two-dimensional surfaces. In the ordinary three spatial dimensions we can observe, that’s all we’ve got. But in superstring theory, with nine spatial dimensions, one doesn’t stop there. There are three-dimensional branes, called three-branes for short; there are four-branes, five-branes, and on up to eight-branes. [There are even nine-branes too, which are really just a way of changing all of space. The story is rich and fascinating both physically and mathematically.] The pattern of the various types of branes — specifically, which ones are found in which corners of M theory, and the phenomena that occur when they intersect one another — is a fantastically elegant story that was worked out in the early-to-mid 1990s.

A brane on which a fundamental string can end is called a “D-brane”. Joe Polchinski is famous for having not only co-discovered these objects in the 1980s but for having recognized, in mid-1995, the wide-ranging role they play in the way the five different string theories are related to each other. I still remember vividly the profound effect that his 1995 paper had on the field. A postdoctoral researcher at the time, I was attending bi-weekly lectures by Ed Witten on the new developments of that year. I recall that at the lecture following Polchinski’s paper, Witten said something to the effect that everything he’d said in his presentations so far needed to be rethought. And over the next few months, it was.


Fig. 2: In addition to fundamental strings (upper left), string theories can have D-branes, such as the D string (or D1-brane) shown at lower left, the D particle (or D0 brane) shown at lower right, or the D2-branes shown at right. There are also D3, D4, D5, D6, D7, D8 and D9 branes, along with NS5-branes, but since they have more than two spatial dimensions I can’t hope to draw them. There are no strings or D-branes, but there are M2-branes and M5- branes, in the 11-dimensional corner of M theory. A D-brane is an object where a fundamental string can end; therefore, in the presence of D-branes, a closed string can break into an open string with both ends on a D-brane (center and right).

The fact that string/M theory is more than just a theory of strings is strikingly similar to something known about quantum field theory for decades. Although quantum field theory was invented to understand particles in the context of Einstein’s special relativity, it turns out that it often describes more than particles. Field theory in three spatial dimensions can have string-like objects (often called “flux tubes”) and membrane-like objects (often called “domain walls”) and particle-like blobs (“magnetic monopoles”, “baryons”, and other structures). The simplest quantum field theories — those for which successive approximation works — are mainly theories of particles.  But flux tubes and domain walls and magnetic monopoles, which can’t be described in terms of particles, can show up even in those theories. So the complexities of M theory are perhaps not surprising. Yet it took physicists almost two decades to recognize that “branes” of various sorts are ubiquitous and essential in string/M theory. (We humans are pretty slow.)

Notably, there are contexts in which M theory exhibits no string-like objects at all. It’s the same with particles and fields; simple field theories have particles, but most field theories aren’t simple, and many complicated field theories don’t have particles. It can happen that the particles that would be observed in experiments may have nothing to do with the fields that appear in the equations of the theory; this was something I alluded to in this article. I also earlier described scale-invariant quantum field theories, which don’t have particles. Quantum field theories on curved space-time don’t have simple, straightforward notions of particles either. Quantum field theory is complex and rich and subtle, and we don’t fully understand it; I wrote seven posts about it in this series, and did little more than scratch the surface. String/M theory is even more complicated, so it will surely be quite a while before we understand it. But specifically, what this means is that what I told you in my last article about “simple superstring theories” is simply not always true. And that means that the first “vague prediction of string theory” that I described might not be reliable… no more than overall predictions of simple field theory, all of which are true in the context of simple field theories, but some of which are often false in more complex ones.

By the way, those of you who’ve read about string theory may wonder: where is supersymmetry in my discussion? Historically, in all these developments, the mathematics and physics of supersymmetry played an important role in making it easier to study and confirm the existence of these branes within string/M theory. However, the branes are present in the theory even when supersymmetry isn’t exact. One must not confuse the technically useful role of supersymmetry in clarifying how string/M theory works for a requirement that supersymmetry has to be an exact (or nearly-exact) symmetry for string/M theory to make sense at all. It’s just a lot harder to study string/M theory in the absence supersymmetry… something which is also true, though to a somewhat lesser extent, of quantum field theory.

To be continued… next, how are quantum field theory and M theory similar and different?

Quantum Field Theory, String Theory and Predictions (Part 8)

Last year, in a series of posts, I gave you a tour of quantum field theory, telling you some of what we understand and some of what we don’t. I still haven’t told you the role that string theory plays in quantum field theory today, but I am going to give you a brief tour of string theory before I do.

What IS String Theory? Well, what’s Particle Theory?

What is particle theory? It’s nothing other than a theory that describes how particles behave.  And in physics language, a theory is a set of equations, along with a set of rules for how the things in those equations are related to physical objects.  So a particle theory is a set of equations which can be used to make predictions for how particles will behave when they interact with one another.

Now there’s always space for confusion here, so let’s be precise about terminology.

  • “Particle theory” is the general category of the equations that can describe particles, of any type and in any combination.
  • A particle theory” is a specific example of such equations, describing a specific set of particles of specific types and interacting with each other in specific ways.

For example, there is a particle theory for electrons in atoms. But we’d need a different one for atoms with both electrons and muons, or for a bottom quark moving around a bottom anti-quark, even though the equations would be of a quite similar type.

Most particle theories that one can write down aren’t relevant (or at least don’t appear to be relevant) to the real world; they don’t describe the types of particles (electrons, quarks, etc.) that we find (so far) in our own universe.   Only certain particle theories are needed to describe aspects of our world.  The others describe imaginary particles in imaginary universes, which can be fun, or even informative, to think about.

Modern particle theory was invented in the early part of the 20th century in response to — guess what? — the discovery of particles in experiments. First the electron was discovered, in 1897; then atomic nuclei, then the proton, then the photon, then the neutrino and the neutron, and so on… Originally, the mathematics used in particle theory was called “quantum mechanics”, a set of equations that is still widely useful today. But it wasn’t complete enough to describe everything physicists knew about, even at the time. Specifically, it couldn’t describe particles that move at or near the speed of light… and so it wasn’t consistent with Einstein’s theory (i.e. his equations) of relativity.

What is Quantum Field Theory?

To fix this problem, physicists first tried to make a new version of particle theory that was consistent with relativity, but it didn’t entirely work.  However, it served as an essential building block in their gradual invention of what is called quantum field theory, described in much more detail in previous posts, starting here. (Again: the distinction between “quantum field theory” and “a quantum field theory” is that of the general versus the specific case; see this post for a more detailed discussion of the terminology.)

In quantum field theory, fields are the basic ingredients, not particles. Each field takes a value everywhere in space and time, in much the same way that the temperature of the air is something you can specify at all times and at all places in the atmosphere. And in quantum field theory, particles are ripples in these quantum fields.

More precisely, a particle is a ripple of smallest possible intensity (or “amplitude”, if you know what that means.)  For example, a photon is the dimmest possible flash of light, and we refer to it as a “particle” or “quantum” of light.

We call such a “smallest ripple” a “particle” because in some ways it behaves like a particle; it travels as a unit, and can’t be divided into pieces.  But really it is wave-like in many ways, and the word “quantum” is in some ways better, because it emphasizes that photons and electrons aren’t like particles of dust.

To sum up:

  • particles were discovered in experiments;
  • physicists invented the equations of particle theory to describe their behavior;
  • but to make those equations consistent with Einstein’s special relativity (needed to describe objects moving near or at the speed of light) they invented the equations of quantum field theory, in which particles are ripples in fields.
  • in this context the fields are more fundamental than the particles; and indeed it was eventually realized that one could (in principle) have fields without particles, while the reverse is not true in a world with Einstein’s relativity.
  • thus, quantum field theory is a more general and complete theory than particle theory; it has other features not seen in particle theory.

Now what about String Theory?

In some sense, strings also emerged from experiments — experiments on hadrons, back before we knew hadrons were made from quarks and gluons.  The details are a story I’ll tell soon and in another context. For now, suffice it to say that in the process of trying to explain some puzzling experiments, physicists were led to invent some new equations, which, after some study, were recognized to be equations describing the quantum mechanical behavior of strings, just as the equations of particle theory describe the quantum mechanical behavior of particles.  (One advantage of the string equations, however, is that they were, from the start, consistent with Einstein’s relativity.) Naturally, at that point, this class of equations was named “string theory”. Continue reading

Visiting the University of Maryland

Along with two senior postdocs (Andrey Katz of Harvard and Nathaniel Craig of Rutgers) I’ve been visiting the University of Maryland all week, taking advantage of end-of-academic-term slowdowns to spend a few days just thinking hard, with some very bright and creative colleagues, about the implications of what we have discovered (a Higgs particle of mass 125-126 GeV/c²) and have not discovered (any other new particles or unexpected high-energy phenomena) so far at the Large Hadron Collider [LHC].

The basic questions that face us most squarely are:

Is the naturalness puzzle

  1. resolved by a clever mechanism that adds new particles and forces to the ones we know?
  2. resolved by properly interpreting the history of the universe?
  3. nonexistent due to our somehow misreading the lessons of quantum field theory?
  4. altered dramatically by modifying the rules of quantum field theory and gravity altogether?

If (1) is true, it’s possible that a clever new “mechanism” is required.  (Old mechanisms that remove or ameliorate the naturalness puzzle include supersymmetry, little Higgs, warped extra dimensions, etc.; all of these are still possible, but if one of them is right, it’s mildly surprising we’ve seen no sign of it yet.)  Since the Maryland faculty I’m talking to (Raman Sundrum, Zakaria Chacko and Kaustubh Agashe) have all been involved in inventing clever new mechanisms in the past (with names like Randall-Sundrum [i.e. warped extra dimensions], Twin Higgs, Folded Supersymmetry, and various forms of Composite Higgs), it’s a good place to be thinking about this possibility.  There’s good reason to focus on mechanisms that, unlike most of the known ones, do not lead to new particles that are affected by the strong nuclear force. (The Twin Higgs idea that Chacko invented with Hock-Seng Goh and Roni Harnik is an example.)  The particles predicted by such scenarios could easily have escaped notice so far, and be hiding in LHC data.

Sundrum (some days anyway) thinks the most likely situation is that, just by chance, the universe has turned out to be a little bit unnatural — not a lot, but enough that the solution to the naturalness puzzle may lie at higher energies outside LHC reach.  That would be unfortunate for particle physicists who are impatient to know the answer… unless we’re lucky and a remnant from that higher-energy phenomenon accidentally has ended up at low-energy, low enough that the LHC can reach it.

But perhaps we just haven’t been creative enough yet to guess the right mechanism, or alter the ones we know of to fit the bill… and perhaps the clues are already in the LHC’s data, waiting for us to ask the right question.

I view option (2) as deeply problematic.  On the one hand, there’s a good argument that the universe might be immense, far larger than the part we can see, with different regions having very different laws of particle physics — and that the part we live in might appear very “unnatural” just because that very same unnatural appearance is required for stars, planets, and life to exist.  To be over-simplistic: if, in the parts of the universe that have no Higgs particle with mass below 700 GeV/c², the physical consequences prevent complex molecules from forming, then it’s not surprising we live in a place with a Higgs particle below that mass.   [It’s not so different from saying that the earth is a very unusual place from some points of view — rocks near stars make up a very small fraction of the universe — but that doesn’t mean it’s surprising that we find ourselves in such an unusual location, because a planet is one of the few places that life could evolve.]

Such an argument is compelling for the cosmological constant problem.  But it’s really hard to come up with an argument that a Higgs particle with a very low mass (and corresponding low non-zero masses for the other known particles) is required for life to exist.  Specifically, the mechanism of “technicolor” (in which the Higgs field is generated as a composite object through a new, strong force) seems to allow for a habitable universe, but with no naturalness puzzle — so why don’t we find ourselves in a part of the universe where it’s technicolor, not a Standard Model-like Higgs, that shows up at the LHC?  Sundrum, formerly a technicolor expert, has thought about this point (with David E. Kaplan), and he agrees this is a significant problem with option (2).

By the way, option (2) is sometimes called the “anthropic principle”.  But it’s neither a principle nor “anthro-” (human-) related… it’s simply a bias (not in the negative sense of the word, but simply in the sense of something that affects your view of a situation) from the fact that, heck, life can only evolve in places where life can evolve.

(3) is really hard for me to believe.  The naturalness argument boils down to this:

  • Quantum fields fluctuate;
  • Fluctuations carry energy, called “zero-point energy”, which can be calculated and is very large;
  • The energy of the fluctuations of a field depends on the corresponding particle’s mass;
  • The particle’s mass, for the known particles, depends on the Higgs field;
  • Therefore the energy of empty space depends strongly on the Higgs field

Unless one of these five statements is wrong (good luck finding a mistake — every one of them involves completely basic issues in quantum theory and in the Higgs mechanism for giving masses) then there’s a naturalness puzzle.  The solution may be simple from a certain point of view, but it won’t come from just waving the problem away.

(4) I’d love for this to be the real answer, and maybe it is.  If our understanding of quantum field theory and Einstein’s gravity leads us to a naturalness problem whose solution should presumably reveal itself at the LHC, and yet nature refuses to show us a solution, then maybe it’s a naive use of field theory and gravity that’s at fault. But it may take a very big leap of faith, and insight, to see how to jump off this cliff and yet land on one’s feet.  Sundrum is well-known as one of the most creative and fearless individuals in our field, especially when it comes to this kind of thing. I’ve been discussing some radical notions with him, but mostly I’ve been enjoying hearing his many past insights and ideas… and about the equations that go with them.   Anyone can speculate, but it’s the equations (and the predictions, testable at least in principle if not in practice, that you can derive from them) that transform pure speculations into something that deserves the name “theoretical physics”.