Tag Archives: fields

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.

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

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.

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 7)

Appropriate for Advanced Non-Experts

[This is the seventh post in a series that begins here.]

In the last post in this series, I pointed out that there’s a lot about quantum field theory [the general case] that we don’t understand.  In particular there are many specific quantum field theories whose behavior we cannot calculate, and others whose existence we’re only partly sure of, since we can’t even write down equations for them. And I concluded with the remark that part of the reason we know about this last case is due to “supersymmetry”.

What’s the role of supersymmetry here? Most of the time you read about supersymmetry in the press, and on this website, it’s about the possible role of supersymmetry in addressing the naturalness problem of the Standard Model [which overlaps with and is almost identical to the hierarchy problem.] But actually (and I speak from personal experience here) one of the most powerful uses of supersymmetry has nothing to do with the naturalness problem at all.

The point is that quantum field theories that have supersymmetry are mathematically simpler than those that don’t. For certain physical questions — not all questions, by any means, but for some of the most interesting ones — it is sometimes possible to solve their equations exactly. And this makes it possible to learn far more about these quantum field theories than about their non-supersymmetric cousins.

Who cares? you might ask. Since supersymmetry isn’t part of the real world in our experiments, it seems of no use to study supersymmetric quantum field theories.

But that view would be deeply naive. It’s naive for three reasons. Continue reading

Quantum Field Theory, String Theory, and Predictions (Part 6)

For More Advanced Non-Experts

[This is part 6 of a series, which begins here.]

I’ve explained in earlier posts how we can calculate many things in the quantum field theory that is known as the “Standard Model” of particle physics, itself an amalgam of three, simpler quantum field theories.

When forces are “weak”, in the technical sense, calculations can generally be done by a method of successive approximation (called “perturbation theory”).  When forces are very “strong”, however, this method doesn’t work. Specifically, for processes involving the strong nuclear force, in which the distances involved are larger than a proton and the energies smaller than the mass-energy of a proton, some other method is needed.  (See Figure 1 of Part 5.)

One class of methods involves directly simulating, using a computer, the behavior of the quantum field theory equations for the strong nuclear force. More precisely, we simulate in a simplified version of the real world, the imaginary world shown in Figure 1 below, where

  • the weak nuclear force and the electromagnetic force are turned off,
  • the electron, muon, tau, neutrinos, W, Z and Higgs particles are ignored
  • the three heavier types of quarks are also ignored

(See Figure 4 of Part 4 for more details.)  This makes the calculations a lot simpler.  And their results allow us, for instance, to understand why quarks and anti-quarks and gluons form the more complex particles called hadrons, of which protons and neutrons are just a couple of examples. Unfortunately, computer simulations still are nowhere near powerful enough for the calculation of some of the most interesting processes in nature… and won’t be for a long time.

Fig 1:

Fig 1: The idealized, imaginary world whose quantum field theory is used to make computer simulations of the real-world strong-nuclear force.

Another method I mentioned involves the use of an effective quantum field theory which describes the “objects” that the original theory produces at low energy. But that only works if you know what those objects are; in the real world [and the similar imaginary world of Figure 1] we know from experiment that those objects are pions and other low-mass hadrons, but generally we don’t know what they are.

This brings us to today’s story.  Our success with the Standard Model might give you the impression that we basically understand quantum field theory and how to make predictions using it, with a few exceptions. But this would be far, far from the truth. As far as we can tell, much (if not most) of quantum field theory remains deeply mysterious. Continue reading

Quantum Field Theory, String Theory, and Predictions (Part 5)

[This is part 5 of a series, which begins here.]

In a previous post, I told you about how physicists use computers to study how the strong nuclear force combines certain elementary particles — specifically quarks and anti-quarks and gluons — into hadrons, such as protons and neutrons and pions.  Computers can also be used to study certain other phenomena that, because they involve the strong nuclear force where it is truly “strong” [in the technical sense described here], can’t be studied using simpler methods of successive approximation. While computers aren’t a panacea, they do allow some important and difficult questions about the strong nuclear force to be answered with precision.

To do these calculations, physicists study an imaginary world, as I described;

  • all forces except the strong nuclear force are ignored, and
  • all particles are forgotten except the gluons and the up, down and strange quarks (and their anti-quarks).
  • On top of this, the up, down and strange quark masses are typically changed. They are taken larger, which makes the calculations easier, and then gradually reduced towards their small values in the real world.

The Notion of “Effective” Quantum Field Theories

There’s one more interesting method for understanding the strong nuclear force that I haven’t mentioned yet, and it too involves changing the quark masses — making them smaller, rather than larger! And weirdly, this doesn’t involve the equations of the quantum field theory for the quarks, antiquarks and gluons at all. It involves a different quantum field theory altogether — one which says nothing about the quarks and gluons, but instead describes the physics of the hadrons themselves. More precisely, its equations are useful for making predictions about the hadrons of lowest masscalled pions, kaons and etas — and it works for processes

  • with rather low energy — too low to affect the behavior of the quarks and anti-quarks and gluons inside the pions — and
  • at rather long distance — too long to detect that the pions have a lot of internal structure.

This includes some of the phenomena involved in the physics of atomic nuclei, the next level up in the structure of matter (quarks/gluons → protons/neutrons → nuclei → atoms → molecules). Continue reading

The Twists and Turns of Hi(gg)story

In sports, as in science, there are two very different types of heroes.  There are the giants who lead the their teams and their sport, winning championships and accolades, for years, and whose fame lives on for decades: the Michael Jordans, the Peles, the Lou Gherigs, the Joe Montanas. And then there are the unlikely heroes, the ones who just happen to have a really good day at a really opportune time; the substitute player who comes on the field for an injured teammate and scores the winning goal in a championship; the fellow who never hits a home run except on the day it counts; the mediocre receiver who turns a short pass into a long touchdown during the Super Bowl.  We celebrate both types, in awe of the great ones, and in amused pleasure at the inspiring stories of the unlikely ones.

In science we have giants like Newton, Darwin, Boyle, Galileo… The last few decades of particle physics brought us a few, such as Richard Feynman and Ken Wilson, and others we’ll meet today.  Many of these giants received Nobel Prizes.   But then we have the gentlemen behind what is commonly known as the Higgs particle — the little ripple in the Higgs field, a special field whose presence and properties assure that many of the elementary particles of nature have mass, and without which ordinary matter, and we ourselves, could not exist.  Following discovery of this particle last year, and confirmation that it is indeed a Higgs particle, two of them, Francois Englert and Peter Higgs, have been awarded the 2013 Nobel Prize in physics.  Had he lived to see the day, Robert Brout would have been the third.

My articles Why The Higgs Particle Matters and The Higgs FAQ 2.0; the particles of nature and what they would be like if the Higgs field were turned off; link to video of my public talk entitled The Quest for the Higgs Boson; post about why Higgs et al. didn’t win the 2012 Nobel prize, and about how physicists became convinced since then that the newly discovered particle is really a Higgs particle;

The paper written by Brout and Englert; the two papers written by Higgs; the paper written by Gerald Guralnik, Tom Kibble and Carl Hagen; these tiny little documents, a grand total of five and one half printed pages — these were game-winning singles in the bottom of the 9th, soft goals scored with a minute to play, Hail-Mary passes by backup quarterbacks — crucial turning-point papers written by people you would not necessarily have expected to find at the center of things.  Brout, Englert, Higgs, Guralnik, Kibble and Hagen are (or rather, in Brout’s case, sadly, were) very fine scientists, intelligent and creative and clever, and their papers, written in 1964 when they were young men, are imperfect but pretty gems.  They were lucky: very smart but not extraordinary physicists who just happened to write the right paper at the right time. In each case, they did so

History in general, and history of science in particular, is always vastly more complex than the simple stories we tell ourselves and our descendants.  Making history understandable in a few pages always requires erasing complexities and subtleties that are crucial for making sense of the past.  Today, all across the press, there are articles explaining incorrectly what Higgs and the others did and why they did it and what it meant at the time and what it means now.  I am afraid I have a few over-simplified articles of my own. But today I’d like to give you a little sense of the complexities, to the extent that I, who wasn’t even alive at the time, can understand them.  And also, I want to convey a few important lessons that I think the Hi(gg)story can teach both experts and non-experts.  Here are a couple to think about as you read:

1. It is important for theoretical physicists, and others who make mathematical equations that might describe the world, to study and learn from imaginary worlds, especially simple ones.  That is because

  • 1a. one can often infer general lessons more easily from simple worlds than from the (often more complicated) real one, and
  • 1b. sometimes an aspect of an imaginary world will turn out to be more real than you expected!

2. One must not assume that research motivated by a particular goal depends upon the achievement of that goal; even if the original goal proves illusory, the results of the research may prove useful or even essential in a completely different arena.

My summary today is based on a reading of the papers themselves, on comments by John Iliopoulos, and on a conversation with Englert, and on reading and hearing Higgs’ own description of the episode.

The story is incompletely but perhaps usefully illustrated in the figure below, which shows a cartoon of how four important scientific stories of the late 1950s and early 1960s came together. They are:

  1. How do superconductors (materials that carry electricity without generating heat) really work?
  2. How does the proton get its mass, and why are pions (the lightest hadrons) so much lighter than protons?
  3. Why do hadrons behave the way they do; specifically, as suggested by J.J. Sakurai (who died rather young, and after whom a famous prize is named), why are there photon-like hadrons, called rho mesons, that have mass?
  4. How does the weak nuclear force work?  Specifically, as suggested by Schwinger and developed further by his student Glashow, might it involve photon-like particles (now called W and Z) with mass?

These four questions converged on a question of principle: “how can mass be given to particles?”, and the first, third and fourth were all related to the specific question of “how can mass be given to photon-like particles?’’  This is where the story really begins.  [Almost everyone in the story is a giant with a Nobel Prize, indicated with a parenthetic (NPyear).]

My best attempt at a cartoon history...

My best attempt at a cartoon history…

In 1962, Philip Anderson (NP1977), an expert on (among other things) superconductors, responded to suggestions and questions of Julian Schwinger (NP1965) on the topic of photon-like particles with mass, pointing out that a photon actually gets a mass inside a superconductor, due to what we today would identify as a sort of “Higgs-type’’ field made from pairs of electrons.  And he speculated, without showing it mathematically, that very similar ideas could apply to empty space, where Einstein’s relativity principles hold true, and that this could allow elementary photon-like particles in empty space to have mass, if in fact there were a kind of Higgs-type field in empty space.

In all its essential elements, he had the right idea.  But since he didn’t put math behind his speculation, not everyone believed him.  In fact, in 1964 Walter Gilbert (NP1980 for chemistry, due to work relevant in molecular biology — how’s that for a twist?) even gave a proof that Anderson’s idea couldn’t work in empty space!

But Higgs immediately responded, arguing that Gilbert’s proof had an important loophole, and that photon-like particles could indeed get a mass in empty space.

Meanwhile, about a month earlier than Higgs, and not specifically responding to Anderson and Gilbert, Brout and Englert wrote a paper showing how to get mass for photon-like particles in empty space. They showed this in several types of imaginary worlds, using techniques that were different from Higgs’ and were correct though perhaps not entirely complete.

A second paper by Higgs, written before he was aware of Brout and Englert’s work, gave a simple example, again in an imaginary world, that made all of this much easier to understand… though his example wasn’t perhaps entirely convincing, because he didn’t show much detail.  His paper was followed by important theoretical clarifications from Guralnik, Hagen and Kibble that assured that the Brout-Englert and Higgs papers were actually right.  The combination of these papers settled the issue, from our modern perspective.

And in the middle of this, as an afterthought added to his second paper only after it was rejected by a journal, Higgs was the first person to mention something that was, for him and the others, almost beside the point — that in the Anderson-Brout-Englert-Higgs-Guralnik-Hagen-Kibble story for how photon-like particles get a mass, there will also  generally be a spin-zero particle with a mass: a ripple in the Higgs-type field, which today we call a Higgs-type particle.  Not that he said very much!   He noted that spin-one (i.e. photon-like) and spin-zero particles would come in unusual combinations.  (You have to be an expert to even figure out why that counts as predicting a Higgs-type particle!)  Also he wrote the equation that describes how and why the Higgs-type particle arises, and noted how to calculate the particle’s mass from other quantities.  But that was it.  There was nothing about how the particle would behave, or how to discover it in the imaginary worlds that he was considering;  direct application to experiment, even in an imaginary world, wasn’t his priority in these papers.

Equation (2b) is the first time the Higgs particle explicitly appears in its modern form

In his second paper, Higgs considers a simple imaginary world with just a photon-like particle and a Higgs-type field.  Equation 2b is the first place the Higgs-type particle explicitly appears in the context of giving photon-like particles a mass (equation 2c).  From Physical Review Letters, Volume 13, page 508

About the “Higgs-type” particle, Anderson says nothing; Brout and Englert say nothing; Guralnik et al. say something very brief that’s irrelevant in any imaginable real-world application.  Why the silence?  Perhaps because it was too obvious to be worth mentioning?  When what you’re doing is pointing out something really “important’’ — that photon-like particles can have a mass after all — the spin-zero particle’s existence is so obvious but so irrelevant to your goal that it hardly deserves comment.  And that’s indeed why Higgs added it only as an afterthought, to make the paper a bit less abstract and a bit easier for  a journal to publish.  None of them could have imagined the hoopla and public excitement that, five decades later, would surround the attempt to discover a particle of this type, whose specific form in the real world none of them wrote down.

In the minds of these authors, any near-term application of their ideas would probably be to hadrons, perhaps specifically Sakurai’s theory of hadrons, which in 1960 predicted the “rho mesons”, which are photon-like hadrons with mass, and had been discovered in 1961.  Anderson, Brout-Englert and Higgs specifically mention hadrons at certain moments. But none of them actually considered the real hadrons of nature, as they were just trying to make points of principle; and in any case, the ideas that they developed did not apply to hadrons at all.  (Well, actually, that’s not quite true, but the connection is too roundabout to discuss here.)  Sakurai’s ideas had an element of truth, but fundamentally led to a dead end.  The rho mesons get their mass in another way.

Meanwhile, none of these people wrote down anything resembling the Higgs field which we know today — the one that is crucial for our very existence — so they certainly didn’t directly predict the Higgs particle that was discovered in 2012.   It was Steven Weinberg (NP1979) in 1967, and Abdus Salam (NP1979) in 1968, who did that.  (And it was Weinberg who stuck Higgs’ name on the field and particle, so that everyone else was forgotten.) These giants combined

  • the ideas of Higgs and the others about how to give mass to photon-like particles using a Higgs-type field, with its Higgs-type particle as a consequence…
  • …with the 1960 work of Sheldon Glashow (NP1979), Schwinger’s student, who like Schwinger proposed the weak nuclear force was due to photon-like particles with mass,…
  • …and with the 1960-1961 work of Murray Gell-Man (NP1969) and Maurice Levy and of Yoichiro Nambu (NP2008) and Giovanni Jona-Lasinio, who showed how proton-like or electron-like particles could get mass from what we’d now call Higgs-type fields.

This combination gave the first modern quantum field theory of particle physics: a set of equations that describe the weak nuclear and electromagnetic forces, and show how the Higgs field can give the W and Z particles and the electron their masses. It is the primitive core of what today we call the Standard Model of particle physics.  Not that anyone took this theory seriously, even Weinberg.  Most people thought quantum field theories of this type were mathematically inconsistent — until in 1971 Gerard ‘t Hooft (NP1999) proved they were consistent after all.

The Hi(gg)story is populated with giants.  I’m afraid my attempt to tell the story has giant holes to match.  But as far as the Higgs particle that was discovered last year at the Large Hadron Collider, the unlikely heroes of the story are the relatively ordinary scientists who slipped in between the giants and actually scored the goals.