Beyond the Standard Model

Discussion

an incomplete theory

Unification is an ongoing theme in physics.

Historical sequence

1687. Newton unifies the celestial gravitation of Kepler with the terrestrial gravitation of Galileo and universal gravitation is born.
1831. Faraday unifies electricity with magnetism through his observation of electromagnetic induction.
1865. Maxwell finishes Faraday's work and unifies electricity, magnetism, and optics. Classical electromagnetism is complete.
1905. Einstein completely overhauls electromagnetism with his special theory of relativity
1916. Einstein completely overhauls gravitation with his general theory of relativity.
1934. Yukawa comes up with the first decent explanation of alpha decay and other strong nuclear processes.
1934. Fermi comes up with the first decent explanation of beta decay and other weak nuclear processes.
1948. 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).
1964. Gell-Mann and Zweig construct a modern theory of strong force interactions reminiscent of quantum electrodynamics (QED) called quantum chromodynamics (QCD).
1967. Glashow, Salam, and Weinberg unite the weak nuclear force with quantum electrodynamics resulting in the electroweak theory (EWT), which, for the sake of internal self-consistency, I like to call the theory of quantum flavordynamics (QFD).

Weak links in the standard model

• Gravity
  Most important of all. Where the hell's gravity? A theory of quantum gravitation, or more formally quantum geometrodynamics (QGD), does not yet exist. Incorporating gravity into particle physics looks to be a horrendous challenge.
• Cosmology
  Dark matter and dark energy. What's up with that?
• Matter-antimatter asymmetry
  Why is everything made out of matter?
• Arbitrary parameters (like the mass of the electron)
  There are just too many (20?)
• Planck limits
  The standard model describes quite accurately physics near the electroweak symmetry breaking scale (246 GeV). But the standard model is only a low energy approximation to a more fundamental theory. The standard model cannot be valid at energies above the Planck scale (~10¹⁹ GeV), where gravity can no longer be ignored.

What you see isn't what you get.

Frank Wilczek, 2006

Projecting into the future

• Standard model theories hint that an extension of Salam and Weinberg's work should be possible. At higher energies QCD should unite with QFD in much the same way that the electromagnetism unites with the weak force to create QFD. Such a theory has been called the grand unified theory (GUT), but it is neither "grand" nor "unified" as many have said before me.
• What we really need is a theory of everything (TOE) — one that includes all four fundamental forces and unifies relativistic and quantum theories. I guess that makes the standard model a "theory of something" (TOS).

Possible steps beyond the standard model

• String theory
  • the standard model and quantum gravity
• Loop quantum gravity
  • general relativity and quantum mechanics, but mostly quantum mechanics
• Supersymmetry
  • new candidates particles for dark matter

the string's the thing

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. String theory has been proposed as a possible candidate.

There are grounds for cautious optimism that we may now be near the end of the search for the ultimate laws of nature.

Stephen Hawking, 1988 (paid link)

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 these string 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" does nothing for me, "m-branes" are a 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

The experimental situation is similarly bleak. It is best described by Wolfgang Pauli's famous phrase, "It's not even wrong." String theory not only makes no predictions about physical phenomena at experimentally accessible energies, it makes no precise predictions whatsoever. Even if someone were to figure out tomorrow how to build an accelerator capable of reaching the astronomically high energies at which particles are no longer supposed to appear as points, string theorists would be able to do no better than give qualitative guesses about what such a machine might show. At the moment string theory cannot be falsified by any conceivable experimental result.

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 understand 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 developed in the 19th century. It's been said that string theory is part of the the physics of the 21st century that fell by chance into the 20th 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, 20th century physicists shouldn't have had the privilege 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 21st century mathematics?

Probably. What should have happened, by rights, is that the correct mathematical structures should have been developed in the twenty-first or twenty-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 physicists 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 20th 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 (paid link)

String theory…

• only works with additional space dimensions that we have not seen. These dimensions could just be really, really small, which is why no experiments have ever seen them, or they might not exist at all because string theory is wrong.
• introduces supersymmetric particles that we have not seen. These particles might be really, really massive, which is why we haven't been able to produce with our current particle accelerators, or they might not exist at all because string theory is wrong.
• has on the order of 10⁵⁰⁰ different possible solutions, each with its own unique set of fundamental particles and values for the fundamental constants. These possible solutions may indicate that our universe is one of a large number of possible universes described by this amazing theory, or it may indicate that string theory is no more right than it is wrong — it is untestable.

S. James Gates

• String theory has done something I've never seen theoretical physics do. It has broken out into [the] consciousness of the general public before we're finished. You see, string theory doesn't actually exist, because when we use the word theory we mean a particular set of attributes. In particular it means that you have an overarching paradigm that explains what it is that you're doing. No such overarching paradigm exists for string theory. What string theory is currently is an enormously large, mutually reinforcing collection of mathematical facts — in which we can find no contradictions. We don't know why it's there, but we can certainly say that without challenge.
• Now, just because you find a piece of mathematics doesn't mean that this applies to nature. And, in fact, there has been a very heated debate about whether string theory is some sort of hysteria among the community of theoretical physicists or whether it has something fundamental to say about our universe. We don't yet know the answer to that question. What those of us who study string theory will tell you are things like "String theory has been extraordinarily productive in getting us to think more deeply, even about mathematics that's not string theory, but the kind of mathematics that we've use to describe elementary particles". There have been spinoffs in string theory (and this has been going on now for two decades almost) that have allowed us, for example, to more accurately calculate the force between electrons with the presence of quantum mechanics. This is not something you hear about in the public. There are other similar things….
• There are a number of direct mathematical effects that we learned in string theory but we take these ideas and look at math that we already know and we find suddenly we're more powerful. This is pretty good indication there's something interesting going on with string theory itself.

Interviewer

• So it's the early days of a powerful mathematical framework.

S. James Gates

• That's what we have right now.

froot loops

• The quest was launched by the Wheeler-DeWitt equation, which describes space at small scales as having something like the frothiness of quantum fields, with no arbitrarily small amounts of space. The economy and care with which Rovelli has prepared the reader now pays off, as he uses the vistas presented in the first half of the book to assemble a portrait of loop quantum gravity. Faraday and Maxwell's description of electric force in terms of lines that close or loop around resembles how the Wheeler-DeWitt equation describes gravitation. But whereas electromagnetic lines are infinitely fine and continuous, the gravitational lines of the Wheeler-DeWitt equation are quantized — patchy and distinct like a spiderweb. Finally, Einstein used gravitation to structure space in a similar way to how the Wheeler-DeWitt equation uses loops. In a nutshell: loop quantum gravity is Faraday's lines plus the granularity of quantum theory plus Einstein's idea that these lines are the structure of space. doi:10.1038/538032a
• Einstein pointed out that the existence of radiationless stable interatomic orbits is equally mysterious from the electromagnetic as from the gravitational point of view.
  • "Gleichwohl müßten die Atome zufolge der inneratomischen Elektronenbewegung night nur electromagnetische, sondern auch Gravitationsenergie ausstrahlen, wenn auch in winzigem Betrage. Da dies in Wahrheit in der Natur nicht zutreffen dürfte, so scheint es, daß die Quantentheorie nicht nur die Maxwellsche Elektrodynamik, sondern auch die neue Gravitationstheorie wird modifizieren müssen." Albert Einstein. Näherungsweise Integration der Feldgleichungen der Gravitation. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (Berlin), Seite 688–696 (1916). doi:10.1002/3527608958.ch7 also doi:10.1007/978-3-662-57411-9_13
    • "Nevertheless, because of the intra-atomic motion of electrons, atoms ought to emit not only electromagnetic but also gravitational energy, if only in tiny amounts. Since, in reality, this cannot be the case in nature, then it appears that quantum theory will have to modify not only Maxwell's electrodynamics but also the new theory of gravitation."
• He reiterated this stance two years later (Einstein 1918, p. 164).
• "Aus (27) ist ersichtlich, daß die Ausstrahlung in keiner Richtung negativ werden kann, also sicher auch nicht die totale Ausstrahlung. Bereits in der früheren Abhandlung ist betont geworden, daß das Endergebnis dieser Betrachtung, welches einen Energieverlust der Körper infolge der thermischen Agitation verlangen würde, Zweifel an der allgemeinen Gültigkeit der Theorie hervorrufen muß. Es scheint, daß eine vervollkommnete Quantentheorie eine Modifikation auch der Gravitationstheorie wird bringen müssen." Albert Einstein. Über Gravitationswellen. Königlich Preußische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1918): 154–167.
  • 'One sees from (27) that the emission cannot turn negative in any direction; consequently, the total emission certainly cannot turn negative, either. It has already been emphasized in a previous paper that the end result of this investigation — which would require a loss of energy of bodies due to the thermal agitation — must raise doubts as to the general validity of the theory. It seems that a more complete quantum theory would also have to bring about a modification of the theory of gravitation.'

supersymmetry

All particles in the standard model are either fermions (the particles of matter) or bosons (the particles of interactions. The fermions of ordinary matter are symmetric with their antimatter counterparts. There are quarks and antiquarks, electrons and antielectron, neutrinos and antineutrinos. Matter particles are identical to their antimatter counterparts with one exception — charge. Up quarks have a charge of +⅔ e, while antiup antiquarks have a charge of −⅔ e. Electrons have a charge of −1 e, while antielectrons (which are normally called positrons) have a charge of +1 e. Neutrinos are trickier since they have no charge. As a result, neutrinos may be their own antiparticles.

Supersymmetry is a candidate Theory of Everything that unifies all of particle physics by assuming a additional level of symmetry — one that switches fermions with bosons.

• The supersymmetric partners of the quarks are called squarks, the partner of the electron is called the selectron, and the partners of the neutrinos are called sneutrinos. The quarks, electron, and neutrinos are fermions. The squarks, selectron, and sneutrinos are bosons. This naming convention kind of makes sense. Add an "s" to the beginning of an ordinary particle to get its supersymmetric counterpart.
• The reverse naming convention is less logical. The fermion partners of the bosons have names that end with the suffix -ino. Gluons become gluinos. Photons, photinos. W and Z give us winos and zinos. Higgs bosons become higgsino fermions.

This crazy naming convention detracts from the usefulness of the supersymmetric standard model. Supersymmetric partners of the photon (photino), Higgs boson (higgsino), and Z boson (zino) can mix to form four different mass states of a particle known as the neutralino. In some theories, the neutralino is the lightest possible supersymmetric particle, making it an excellent candidate for a detectable form of dark matter.

Supersymmetry is great, but it's never been observed. It's popularity, like string theory's, is waning as a result. None of the current experiments designed to detect dark matter have detected any dark matter. The world's current largest particle accelerator, the Large Hadron Collider (LHC) in Switzerland and France, detected the Higgs boson in 2012 (the last confirmed particle of the standard model), but it has never detected a single particle of dark matter, supersymmetric or otherwise.

cosmological timeline

closing

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 incompetent.

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 person to cook a pancake.

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.