Beyond the Standard Model


an incomplete theory

Where have we been?

We're not done yet.



It describes everything we see in the laboratory. Aside from leaving gravity out, it's a complete theory of what we see in nature. But it's not an entirely satisfactory theory, because it has a number of arbitrary elements. For example, there are a lot of numbers in this standard model that appear in the equations, and they just have to be put in to make the theory fit the observation. For example, the mass of the electron, the masses of the different quarks, the charge of the electron. If you ask, "Why are those numbers what they are? Why, for example, is the top quark, which is the heaviest known elementary particle, something like 300,000 times heavier than the electron?" The answer is, "We don't know. That's what fits experiment." That's not a very satisfactory picture.

Steven Weinberg, 2003

Unification as an ongoing theme in physics.

[slide, pdf]

Historical sequence

  1. Newton unifies the celestial gravitation of Kepler with the terrestrial gravitation of Galileo and universal gravitation is born.
  2. Faraday unifies electricity with magnetism through his observation of electromagnetic induction.
  3. Maxwell finishes Faraday's work and unifies electricity, magnetism, and optics. Classical electromagnetism is complete.
  4. Einstein completely overhauls electromagnetism with his special theory of relativity
  5. Einstein completely overhauls gravitation with his general theory of relativity.
  6. Feynman, Tomonaga, Schwinger, and Dyson overhaul electromagnetism creating quantum electrodynamics (QED). Unlike Einstein, their techniques do not work on gravity. No one has the slightest idea how to do this (or when they think they have it they are unable to complete it). To this day, there is no accepted theory of quantum gravity or quantum geometrodynamics (QGD).
  7. Gell-Mann and Zweig construct a modern theory of strong force interactions reminiscent of quantum electrodynamics (QED) called quantum chromodynamics (QCD).
  8. Glashow, Salam, and Weinberg unite the weak nuclear force with quantum electrodynamics resulting in the electroweak theory, which, for the sake of internal self-consistency, I like to call the theory of quantum flavordynamics (QFD).

Projecting into the future.

weak links in the standard model

What you see isn't what you get.

Frank Wilczek, 2006

complexity unifier elements
billions of proteins, carbohydrates, and fats polymerization 20 amino acids form all proteins
~10 monosaccharides form most carbohydrates
~10 fatty acids form most fats
trillions of unique, individual living things; billions of species dna 4 nucleotide bases on a double helix chain
billions of chemical compounds periodic
90 naturally ocurring chemical elements

(element families — metals, inert gases, etc. — hint at deeper layer of organization)
thousands of ions and isotopes atomic and
nuclear models
3 subatomic particles
electron, neutron, proton

(discovery of new "elementary" particles motivated the search for a model that could accomodate them all)
hundreds of subatomic particles standard
6 quarks, 6 leptons, 4 bosons
charge, color, flavor

(always recognized as incomplete since does not include gravitation)
all standard model particles plus new hypothetical particles superstrings?
m theory?
loop quantum gravity?
1 string in 10dimensions with multiple modes of vibration

(the theory of everything?)
Complex entities are built from elementary constituents.

a theory of everything

Once we decide to tackle gravity, the Standard Model as we know it transforms beyond recognition and an ultimate Theory of Everything becomes possible. We could then say that physics has reached its end. Superstring theory is an excellent candidate.


Stephen Hawking, 1988

All fundamental particles, formerly thought of as point-like entities, are now considered teeny, tiny one dimensional objects called strings. Just as a violin string can be made to vibrate in multiple modes (fundamental and overtones in a harmonic series) so too can these strings. But the modes available to a superstring are far richer and more complex than those of a simple violin string (which is itself pretty rich when you think about it). The reason for this is that superstrings live in a space quite unfamiliar to us all. A space beyond the familiar up-down, left-right, forward-backward, three-dimensional realm we're all so familiar with.

There were five or six different versions of string theory formulated in the 1980s, which turned out later in the 1990s to be facets of one, larger, overarching theory called M Theory.

M stands for "magic", "mystery","matrix", or "membrane", according to taste.

Edward Witten, 2003

I don't believe the "magic" or "mystery" stuff. Show me where it appears in the literature not written by Witten. The name M Theory most likely comes from the clever use of the word "membrane" to describe any object used to separate one part of a space from another. Think of your diaphragm for a moment. This is an obvious two-dimensional membrane that separates the three-dimensional abdominal cavity into two regions — the heart and lungs above; and the liver, spleen, and digestive tract below. What would you call the objects that divide a higher dimensional space in two? I have seen the terms "d-branes", "m-branes", and "p-branes" all used. "D-branes" do nothing for me, "m-branes" are a very clever alliteration to the biological term "membranes", but "p-branes" are probably too silly to gain much popularity for a potential Theory of Everything. (In North America, the term "pea brain" is slang for a stupid person. Somebody with a brain the size of a pea couldn't be very smart now could they? It makes for a somewhat clever joke, but a theory of "p branes" is likely to attract more chuckles than grant money.)

From symmetry (matter-antimatter) to supersymmetry (fermions-bosons). Say them as one word: "s-particles" and "particle-inos". Squarks, sleptons, selectrons, gluinos, photinos, winos, zinos. Try it. It's fun.

Is string theory right?

It's fine to discover new particles. But I don't think it's very good to believe ahead of time what you're going to discover.

Freeman Dyson, 2003


Peter Woit, 2002

I believe that there is a simple theory that governs everything — the four forces we know about, perhaps other forces as well. I'm not sure that's true. It may be that nature is irreducibly messy. I'm sure that we should assume it's not, because otherwise we're never going to find a fundamental theory. But even so, we're not guaranteed that we'll find it. We may not be smart enough. Dogs are not smart enough to understand quantum mechanics. I'm not sure that people are smart enough to understand the whatever-it-is that unifies everything. I think we probably are, because of our ability to link our minds through language, but I'm not certain.

There was a marvelous period from, I'd say, the mid-'60s until the late '70s when theoretical physicists actually had something to say that experimentalists were interested in. Experimentalists made discoveries that theoretical physicists were interested in. Everything was converging toward a simple picture of the known particles and forces, a picture that eventually became known as the standard model. I think I gave it that name. And it was a time when graduate students would run through the halls of a physics building saying they had discovered another particle and it fit the theories, and it was all so exciting.

Since the late '70s, I'd say, particle physics has been in somewhat of a doldrums. Partly it's just the price we're paying for the great success we had in that wonderful time then. I think cosmology now, for example, is much more exciting than particle physics. The string theorists are trying to push ahead without much support from relevant experiments, because there aren't any relevant experiments that can be done at the kind of scales that the string theorists are interested in.

They're trying to take the next big step by pure mathematical reasoning, and it's extraordinarily difficult. I hope they succeed. I think they're doing the right thing in pursuing this, because right now string theory offers the only hope of a really unified view of nature. They have to pursue it, but the progress is glacially slow. I'd rather study continental drift in real time than be a string theorist today. But I admire them for trying, because they are our best hope of making a great step toward the next big unified theory.

Steven Weinberg, 2003

Is string theory difficult?

Interviewer: Can we understand how these extra dimensions have curled themselves up into such a small size?

We can try to understand it and we can see that by making some simple assumptions about how the extra dimensions would curl up, we can get plausible and interesting rough models of particle physics. I don't think we can expect to understant definitively how the extra dimensions curl themselves up without understanding a little better what string theory is really all about, We are handicapped by having an extremely primitive and crude view of what the subject really is.

Einstein developed general relativity at a time when the basic ideas in geometry that he needed had already been devleoped in the nineteenth century. It's been said that string theory is part of the the physics of the twenty-first century that fell by chance into the twentieth century. That's a remark that was made by a leading physicist about fifteen years ago. What he meant was that humans on planet earth never had the conceptual framework that would lead them to invent string theory on purpose. String theory was invented essentially by accident in a long sequence of events, starting with the Veneziano model that was formulated in 1968. No one invented it on purpose, it was invented in a lucky accident.By rights, twentieth century physicists shouldn't have had the priviledge of studying this theory. By rights, string theory shouldn't have been invented until our knowledge of some of the areas that are prerequisite for string theory had developed to the point that it was possible for us to have the right concept of what it was all about.

Interviewer: We need twenty-first century mathematics?

Probably. What should have happened, by rights, is that the correct mathematical structures should have been developed in the twenty-first or tenty-second century, and then finally physicists should have invented string theory as a physical theory that is made possible by those structures. If that had happened, then the first physicicsts working with string theory would have known what they were doing perhaps., just like Einstein knew what he was doing when he invented general relativity. That would perhaps have been a normal way for things to happen but it wouldn't have given twentieth century physicists the chance to work on this fascinating theory. As it is we have had the stroke of good luck that string theory was invented in a sense without human beings on planet Earth really deserving it. But anyway we have this stroke of good luck and we are trying to make the best of it. But we are paying the price for the fact that we didn't come by this thing in the usual way.

Edward Witten, 1988

It seems immensely difficult because we haven't finished solving it yet. It's like the "Where's Waldo?" series of popular children's books. It'll take you hours and, in some cases, even days to find Waldo on a particular page — the first time — but once you know where to look for him, it's nearly effortless. The first time I "learned" calculus was in high school. I put "learned" in quotes because I just barely got through it. When I took it again in college, however, I was astounded at how easy it was. I couldn't understand how I could ever have been so ignorant.

Someone had to invent writing. Someone had to invent reading without speaking aloud. Someone had to discover electromagnetic induction. Someone had to discover zero. Someone had to be the first to look at the heavens through a telescope. Someone had to to be the first to eat with a fork!

Currently, no one has solved the mathematical problem of a complete "theory of everything". It hasn't been invented, it hasn't been discovered, it has never been seen or used. But it will be. This will be followed by a short period (two to two hundred years, say) when the theory will be discussed and tested and advanced and learned by tens then hundreds then thousands then millions of people. And then it won't seem like such a big deal anymore. And few will remember the time when it was considered unobtainable. And students learning it will find it a chore to learn for the first time and then be astounded at how easy it all was in retrospect.

Mastery, however, will always be left to the few.