Category Archives: Quantum Field Theory

In Memory of Joe Polchinski, the Brane Master

This week, the community of high-energy physicists — of those of us fascinated by particles, fields, strings, black holes, and the universe at large — is mourning the loss of one of the great theoretical physicists of our time, Joe Polchinski. It pains me deeply to write these words.

Everyone who knew him personally will miss his special qualities — his boyish grin, his slightly wicked sense of humor, his charming way of stopping mid-sentence to think deeply, his athleticism and friendly competitiveness. Everyone who knew his research will feel the absence of his particular form of genius, his exceptional insight, his unique combination of abilities, which I’ll try to sketch for you below. Those of us who were lucky enough to know him both personally and scientifically — well, we lose twice.

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Polchinski — Joe, to all his colleagues — had one of those brains that works magic, and works magically. Scientific minds are as individual as personalities. Each physicist has a unique combination of talents and skills (and weaknesses); in modern lingo, each of us has a superpower or two. Rarely do you find two scientists who have the same ones.

Joe had several superpowers, and they were really strong. He had a tremendous knack for looking at old problems and seeing them in a new light, often overturning conventional wisdom or restating that wisdom in a new, clearer way. And he had prodigious technical ability, which allowed him to follow difficult calculations all the way to the end, on paths that would have deterred most of us.

One of the greatest privileges of my life was to work with Joe, not once but four times. I think I can best tell you a little about him, and about some of his greatest achievements, through the lens of that unforgettable experience.

[To my colleagues: this post was obviously written in trying circumstances, and it is certainly possible that my memory of distant events is foggy and in error.  I welcome any corrections that you might wish to suggest.]

Our papers between 1999 and 2006 were a sequence of sorts, aimed at understanding more fully the profound connection between quantum field theory — the language of particle physics — and string theory — best-known today as a candidate for a quantum theory of gravity. In each of those papers, as in many thousands of others written after 1995, Joe’s most influential contribution to physics played a central role. This was the discovery of objects known as “D-branes”, which he found in the context of string theory. (The term is a generalization of the word `membrane’.)

I can already hear the polemical haters of string theory screaming at me. ‘A discovery in string theory,’ some will shout, pounding the table, ‘an untested and untestable theory that’s not even wrong, should not be called a discovery in physics.’ Pay them no mind; they’re not even close, as you’ll see by the end of my remarks.

The Great D-scovery

In 1989, Joe, working with two young scientists, Jin Dai and Rob Leigh, was exploring some details of string theory, and carrying out a little mathematical exercise. Normally, in string theory, strings are little lines or loops that are free to move around anywhere they like, much like particles moving around in this room. But in some cases, particles aren’t in fact free to move around; you could, for instance, study particles that are trapped on the surface of a liquid, or trapped in a very thin whisker of metal. With strings, there can be a new type of trapping that particles can’t have — you could perhaps trap one end, or both ends, of the string within a surface, while allowing the middle of the string to move freely. The place where a string’s end may be trapped — whether a point, a line, a surface, or something more exotic in higher dimensions — is what we now call a “D-brane”.  [The `D’ arises for uninteresting technical reasons.]

Joe and his co-workers hit the jackpot, but they didn’t realize it yet. What they discovered, in retrospect, was that D-branes are an automatic feature of string theory. They’re not optional; you can’t choose to study string theories that don’t have them. And they aren’t just surfaces or lines that sit still. They’re physical objects that can roam the world. They have mass and create gravitational effects. They can move around and scatter off each other. They’re just as real, and just as important, as the strings themselves!


Fig. 1: D branes (in green) are physical objects on which a fundamental string (in red) can terminate.

It was as though Joe and his collaborators started off trying to understand why the chicken crossed the road, and ended up discovering the existence of bicycles, cars, trucks, buses, and jet aircraft.  It was that unexpected, and that rich.

And yet, nobody, not even Joe and his colleagues, quite realized what they’d done. Rob Leigh, Joe’s co-author, had the office next to mine for a couple of years, and we wrote five papers together between 1993 and 1995. Yet I think Rob mentioned his work on D-branes to me just once or twice, in passing, and never explained it to me in detail. Their paper had less than twenty citations as 1995 began.

In 1995 the understanding of string theory took a huge leap forward. That was the moment when it was realized that all five known types of string theory are different sides of the same die — that there’s really only one string theory.  A flood of papers appeared in which certain black holes, and generalizations of black holes — black strings, black surfaces, and the like — played a central role. The relations among these were fascinating, but often confusing.

And then, on October 5, 1995, a paper appeared that changed the whole discussion, forever. It was Joe, explaining D-branes to those of us who’d barely heard of his earlier work, and showing that many of these black holes, black strings and black surfaces were actually D-branes in disguise. His paper made everything clearer, simpler, and easier to calculate; it was an immediate hit. By the beginning of 1996 it had 50 citations; twelve months later, the citation count was approaching 300.

So what? Great for string theorists, but without any connection to experiment and the real world.  What good is it to the rest of us? Patience. I’m just getting to that.

What’s it Got to Do With Nature?

Our current understanding of the make-up and workings of the universe is in terms of particles. Material objects are made from atoms, themselves made from electrons orbiting a nucleus; and the nucleus is made from neutrons and protons. We learned in the 1970s that protons and neutrons are themselves made from particles called quarks and antiquarks and gluons — specifically, from a “sea” of gluons and a few quark/anti-quark pairs, within which sit three additional quarks with no anti-quark partner… often called the `valence quarks’.  We call protons and neutrons, and all other particles with three valence quarks, `baryons”.   (Note that there are no particles with just one valence quark, or two, or four — all you get is baryons, with three.)

In the 1950s and 1960s, physicists discovered short-lived particles much like protons and neutrons, with a similar sea, but which  contain one valence quark and one valence anti-quark. Particles of this type are referred to as “mesons”.  I’ve sketched a typical meson and a typical baryon in Figure 2.  (The simplest meson is called a “pion”; it’s the most common particle produced in the proton-proton collisions at the Large Hadron Collider.)



Fig. 2: Baryons (such as protons and neutrons) and mesons each contain a sea of gluons and quark-antiquark pairs; baryons have three unpaired “valence” quarks, while mesons have a valence quark and a valence anti-quark.  (What determines whether a quark is valence or sea involves subtle quantum effects, not discussed here.)

But the quark/gluon picture of mesons and baryons, back in the late 1960s, was just an idea, and it was in competition with a proposal that mesons are little strings. These are not, I hasten to add, the “theory of everything” strings that you learn about in Brian Greene’s books, which are a billion billion times smaller than a proton. In a “theory of everything” string theory, often all the types of particles of nature, including electrons, photons and Higgs bosons, are tiny tiny strings. What I’m talking about is a “theory of mesons” string theory, a much less ambitious idea, in which only the mesons are strings.  They’re much larger: just about as long as a proton is wide. That’s small by human standards, but immense compared to theory-of-everything strings.

Why did people think mesons were strings? Because there was experimental evidence for it! (Here’s another example.)  And that evidence didn’t go away after quarks were discovered. Instead, theoretical physicists gradually understood why quarks and gluons might produce mesons that behave a bit like strings. If you spin a meson fast enough (and this can happen by accident in experiments), its valence quark and anti-quark may separate, and the sea of objects between them forms what is called a “flux tube.” See Figure 3. [In certain superconductors, somewhat similar flux tubes can trap magnetic fields.] It’s kind of a thick string rather than a thin one, but still, it shares enough properties with a string in string theory that it can produce experimental results that are similar to string theory’s predictions.


Fig. 3: One reason mesons behave like strings in experiment is that a spinning meson acts like a thick string, with the valence quark and anti-quark at the two ends.

And so, from the mid-1970s onward, people were confident that quantum field theories like the one that describes quarks and gluons can create objects with stringy behavior. A number of physicists — including some of the most famous and respected ones — made a bolder, more ambitious claim: that quantum field theory and string theory are profoundly related, in some fundamental way. But they weren’t able to be precise about it; they had strong evidence, but it wasn’t ever entirely clear or convincing.

In particular, there was an important unresolved puzzle. If mesons are strings, then what are baryons? What are protons and neutrons, with their three valence quarks? What do they look like if you spin them quickly? The sketches people drew looked something like Figure 3. A baryon would perhaps become three joined flux tubes (with one possibly much longer than the other two), each with its own valence quark at the end.  In a stringy cartoon, that baryon would be three strings, each with a free end, with the strings attached to some sort of junction. This junction of three strings was called a “baryon vertex.”  If mesons are little strings, the fundamental objects in a string theory, what is the baryon vertex from the string theory point of view?!  Where is it hiding — what is it made of — in the mathematics of string theory?


Fig. 4: A fast-spinning baryon looks vaguely like the letter Y — three valence quarks connected by flux tubes to a “baryon vertex”.  A cartoon of how this would appear from a stringy viewpoint, analogous to Fig. 3, leads to a mystery: what, in string theory, is this vertex?!

[Experts: Notice that the vertex has nothing to do with the quarks. It’s a property of the sea — specifically, of the gluons. Thus, in a world with only gluons — a world whose strings naively form loops without ends — it must still be possible, with sufficient energy, to create a vertex-antivertex pair. Thus field theory predicts that these vertices must exist in closed string theories, though they are linearly confined.]


The baryon puzzle: what is a baryon from the string theory viewpoint?

No one knew. But isn’t it interesting that the most prominent feature of this vertex is that it is a location where a string’s end can be trapped?

Everything changed in the period 1997-2000. Following insights from many other physicists, and using D-branes as the essential tool, Juan Maldacena finally made the connection between quantum field theory and string theory precise. He was able to relate strings with gravity and extra dimensions, which you can read about in Brian Greene’s books, with the physics of particles in just three spatial dimensions, similar to those of the real world, with only non-gravitational forces.  It was soon clear that the most ambitious and radical thinking of the ’70s was correct — that almost every quantum field theory, with its particles and forces, can alternatively be viewed as a string theory. It’s a bit analogous to the way that a painting can be described in English or in Japanese — fields/particles and strings/gravity are, in this context, two very different languages for talking about exactly the same thing.

The saga of the baryon vertex took a turn in May 1998, when Ed Witten showed how a similar vertex appears in Maldacena’s examples. [Note added: I had forgotten that two days after Witten’s paper, David Gross and Hirosi Ooguri submitted a beautiful, wide-ranging paper, whose section on baryons contains many of the same ideas.] Not surprisingly, this vertex was a D-brane — specifically a D-particle, an object on which the strings extending from freely-moving quarks could end. It wasn’t yet quite satisfactory, because the gluons and quarks in Maldacena’s examples roam free and don’t form mesons or baryons. Correspondingly the baryon vertex isn’t really a physical object; if you make one, it quickly diffuses away into nothing. Nevertheless, Witten’s paper made it obvious what was going on. To the extent real-world mesons can be viewed as strings, real-world protons and neutrons can be viewed as strings attached to a D-brane.


The baryon puzzle, resolved.  A baryon is made from three strings and a point-like D-brane. [Note there is yet another viewpoint in which a baryon is something known as a skyrmion, a soliton made from meson fields — but that is an issue for another day.]

It didn’t take long for more realistic examples, with actual baryons, to be found by theorists. I don’t remember who found one first, but I do know that one of the earliest examples showed up in my first paper with Joe, in the year 2000.


Working with Joe

That project arose during my September 1999 visit to the KITP (Kavli Institute for Theoretical Physics) in Santa Barbara, where Joe was a faculty member. Some time before that I happened to have studied a field theory (called N=1*) that differed from Maldacena’s examples only slightly, but in which meson-like objects do form. One of the first talks I heard when I arrived at KITP was by Rob Myers, about a weird property of D-branes that he’d discovered. During that talk I made a connection between Myers’ observation and a feature of the N=1* field theory, and I had one of those “aha” moments that physicists live for. I suddenly knew what the string theory that describes the N=1*  field theory must look like.

But for me, the answer was bad news. To work out the details was clearly going to require a very difficult set of calculations, using aspects of string theory about which I knew almost nothing [non-holomorphic curved branes in high-dimensional curved geometry.] The best I could hope to do, if I worked alone, would be to write a conceptual paper with lots of pictures, and far more conjectures than demonstrable facts.

But I was at KITP.  Joe and I had had a good personal rapport for some years, and I knew that we found similar questions exciting. And Joe was the brane-master; he knew everything about D-branes. So I decided my best hope was to persuade Joe to join me. I engaged in a bit of persistent cajoling. Very fortunately for me, it paid off.

I went back to the east coast, and Joe and I went to work. Every week or two Joe would email some research notes with some preliminary calculations in string theory. They had such a high level of technical sophistication, and so few pedagogical details, that I felt like a child; I could barely understand anything he was doing. We made slow progress. Joe did an important warm-up calculation, but I found it really hard to follow. If the warm-up string theory calculation was so complex, had we any hope of solving the full problem?  Even Joe was a little concerned.

Image result for polchinski joeAnd then one day, I received a message that resounded with a triumphant cackle — a sort of “we got ’em!” that anyone who knew Joe will recognize. Through a spectacular trick, he’d figured out how use his warm-up example to make the full problem easy! Instead of months of work ahead of us, we were essentially done.

From then on, it was great fun! Almost every week had the same pattern. I’d be thinking about a quantum field theory phenomenon that I knew about, one that should be visible from the string viewpoint — such as the baryon vertex. I knew enough about D-branes to develop a heuristic argument about how it should show up. I’d call Joe and tell him about it, and maybe send him a sketch. A few days later, a set of notes would arrive by email, containing a complete calculation verifying the phenomenon. Each calculation was unique, a little gem, involving a distinctive investigation of exotically-shaped D-branes sitting in a curved space. It was breathtaking to witness the speed with which Joe worked, the breadth and depth of his mathematical talent, and his unmatched understanding of these branes.

[Experts: It’s not instantly obvious that the N=1* theory has physical baryons, but it does; you have to choose the right vacuum, where the theory is partially Higgsed and partially confining. Then to infer, from Witten’s work, what the baryon vertex is, you have to understand brane crossings (which I knew about from Hanany-Witten days): Witten’s D5-brane baryon vertex operator creates a  physical baryon vertex in the form of a D3-brane 3-ball, whose boundary is an NS 5-brane 2-sphere located at a point in the usual three dimensions. And finally, a physical baryon is a vertex with n strings that are connected to nearby D5-brane 2-spheres. See chapter VI, sections B, C, and E, of our paper from 2000.]

Throughout our years of collaboration, it was always that way when we needed to go head-first into the equations; Joe inevitably left me in the dust, shaking my head in disbelief. That’s partly my weakness… I’m pretty average (for a physicist) when it comes to calculation. But a lot of it was Joe being so incredibly good at it.

Fortunately for me, the collaboration was still enjoyable, because I was almost always able to keep pace with Joe on the conceptual issues, sometimes running ahead of him. Among my favorite memories as a scientist are moments when I taught Joe something he didn’t know; he’d be silent for a few seconds, nodding rapidly, with an intent look — his eyes narrow and his mouth slightly open — as he absorbed the point.  “Uh-huh… uh-huh…”, he’d say.

But another side of Joe came out in our second paper. As we stood chatting in the KITP hallway, before we’d even decided exactly which question we were going to work on, Joe suddenly guessed the answer! And I couldn’t get him to explain which problem he’d solved, much less the solution, for several days!! It was quite disorienting.

This was another classic feature of Joe. Often he knew he’d found the answer to a puzzle (and he was almost always right), but he couldn’t say anything comprehensible about it until he’d had a few days to think and to turn his ideas into equations. During our collaboration, this happened several times. (I never said “Use your words, Joe…”, but perhaps I should have.) Somehow his mind was working in places that language doesn’t go, in ways that none of us outside his brain will ever understand. In him, there was something of an oracle.

Looking Toward The Horizon

Our interests gradually diverged after 2006; I focused on the Large Hadron Collider [also known as the Large D-brane Collider], while Joe, after some other explorations, ended up thinking about black hole horizons and the information paradox. But I enjoyed his work from afar, especially when, in 2012, Joe and three colleagues (Ahmed Almheiri, Don Marolf, and James Sully) blew apart the idea of black hole complementarity, widely hoped to be the solution to the paradox. [I explained this subject here, and also mentioned a talk Joe gave about it here.]  The wreckage is still smoldering, and the paradox remains.

Then Joe fell ill, and we began to lose him, at far too young an age.  One of his last gifts to us was his memoirs, which taught each of us something about him that we didn’t know.  Finally, on Friday last, he crossed the horizon of no return.  If there’s no firewall there, he knows it now.

What, we may already wonder, will Joe’s scientific legacy be, decades from now?  It’s difficult to foresee how a theorist’s work will be viewed a century hence; science changes in unexpected ways, and what seems unimportant now may become central in future… as was the path for D-branes themselves in the course of the 1990s.  For those of us working today, D-branes in string theory are clearly Joe’s most important discovery — though his contributions to our understanding of black holes, cosmic strings, and aspects of field theory aren’t soon, if ever, to be forgotten.  But who knows? By the year 2100, string theory may be the accepted theory of quantum gravity, or it may just be a little-known tool for the study of quantum fields.

Yet even if the latter were to be string theory’s fate, I still suspect it will be D-branes that Joe is remembered for. Because — as I’ve tried to make clear — they’re real.  Really real.  There’s one in every proton, one in every neutron. Our bodies contain them by the billion billion billions. For that insight, that elemental contribution to human knowledge, our descendants can blame Joseph Polchinski.

Thanks for everything, Joe.  We’ll miss you terribly.  You so often taught us new ways to look at the world — and even at ourselves.

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Modern Physics: Increasingly Vacuous

One of the concepts that’s playing a big role in contemporary discussions of the laws of nature is the notion of “vacua”, the plural of the word “vacuum”. I’ve just completed an article about what vacua are, and what it means for a universe to have multiple vacua, or for a theory that purports to describe a universe to predict that it has multiple vacua. In case you don’t want to plunge right in to that article, here’s a brief summary of why this is interesting and important.

Outside of physics, most people think of a vacuum as being the absence of air. For physicists thinking about the laws of nature, “vacuum” means space that has been emptied of everything — at least, emptied of everything that can actually be removed. That certainly means removing all particles from it. But even though vacuum implies emptiness, it turns out that empty space isn’t really that empty. There are always fields in that space, fields like the electric and magnetic fields, the electron field, the quark field, the Higgs field. And those fields are always up to something.

First, all of the fields are subject to “quantum fluctuations” — a sort of unstoppable jitter that nothing in our quantum world can avoid.  [Sometimes these fluctuations are referred to as “virtual particles”; but despite the name, those aren’t particles.  Real particles are well-behaved, long-lived ripples in those fields; fluctuations are much more random.] These fluctuations are always present, in any form of empty space.

Second, and more important for our current discussion, some of the fields may have average values that aren’t zero. [In our own familiar form of empty space, the Higgs field has a non-zero average value, one that causes many of the known elementary particles to acquire a mass (i.e. a rest mass).] And it’s because of this that the notion of vacuum can have a plural: forms of empty space can differ, even for a single universe, if the fields of that universe can take different possible average values in empty space. If a given universe can have more than one form of empty space, we say that “it has more than one vacuum”.

There are reasons to think our own universe might have more than one form of vacuum — more than just the one we’re familiar with. It is possible that the Standard Model (the equations used to describe all of the known elementary particles, and all the known forces except gravity) is a good description of our world, even up to much higher energies than our current particle physics experiments can probe. Physicists can predict, using those equations, how many forms of empty space our world would have. And their calculations show that our world would have (at least) two vacua: the one we know, along with a second, exotic one, with a much larger average value for the Higgs field. (Remember, this prediction is based on the assumption that the Standard Model’s equations apply in the first place.)  An electron in empty space would have a much larger mass than the electrons we know and love (and need!)

The future of the universe, and our understanding of how the universe came to be, might crucially depend on this second, exotic vacuum. Today’s article sets the stage for future articles, which will provide an explanation of why the vacua of the universe play such a central role in our understanding of nature at its most elemental.

Which Parts of the Big Bang Theory are Reliable, and Why?

Familiar throughout our international culture, the “Big Bang” is well-known as the theory that scientists use to describe and explain the history of the universe. But the theory is not a single conceptual unit, and there are parts that are more reliable than others.

It’s important to understand that the theory — a set of equations describing how the universe (more precisely, the observable patch of our universe, which may be a tiny fraction of the universe) changes over time, and leading to sometimes precise predictions for what should, if the theory is right, be observed by humans in the sky — actually consists of different periods, some of which are far more speculative than others.  In the more speculative early periods, we must use equations in which we have limited confidence at best; moreover, data relevant to these periods, from observations of the cosmos and from particle physics experiments, is slim to none. In more recent periods, our confidence is very, very strong.

In my “History of the Universe” article [see also my related articles on cosmic inflation, on the Hot Big Bang, and on the pre-inflation period; also a comment that the Big Bang is an expansion, not an explosion!], the following figure appears, though without the colored zones, which I’ve added for this post. The colored zones emphasize what we know, what we suspect, and what we don’t know at all.

History of the Universe, taken from my article with the same title, with added color-coded measures of how confident we can be in its accuracy.  In each colored zone, the degree of confidence and the observational/experimental source of that confidence is indicated. Three different possible starting points for the "Big Bang" are noted at the bottom; different scientists may mean different things by the term.

History of the Universe, taken from my article with the same title, with added color-coded measures of how confident we can be in our understanding. In each colored zone, the degree of confidence and the observational/experimental source of that confidence is indicated. Three different possible starting points for the “Big Bang” are noted at the bottom; note that individual scientists may mean different things by the term.  (Caution: there is a subtlety in the use of the words “Extremely Cold”; there are subtle quantum effects that I haven’t yet written about that complicate this notion.)

Notice that in the figure, I don’t measure time from the start of the universe.  That’s because I don’t know how or when the universe started (and in particular, the notion that it started from a singularity, or worse, an exploding “cosmic egg”, is simply an over-extrapolation to the past and a misunderstanding of what the theory actually says.) Instead I measure time from the start of the Hot Big Bang in the observable patch of the universe.  I also don’t even know precisely when the Hot Big Bang started, but the uncertainty on that initial time (relative to other events) is less than one second — so all the times I’ll mention, which are much longer than that, aren’t affected by this uncertainty.

I’ll now take you through the different confidence zones of the Big Bang, from the latest to the earliest, as indicated in the figure above.

Continue reading

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.