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

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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.

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

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[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 mass — called 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).

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The Twists and Turns of Hi(gg)story

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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 … Read more

Some Pre-Nobel Prizes

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This year’s Nobel Prize, presumably to be given for the prediction of the particle known today as the “Higgs boson”, will be awarded next week.  But in the meantime, the American Physical Society has made a large number of awards.  A few of them are to people whose work I know about, so I thought … Read more

Quantum Field Theory, String Theory and Predictions (Part 3)

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[This is the third post in a series; here’s #1 and #2.] The quantum field theory that we use to describe the known particles and forces is called the “Standard Model”, whose structure is shown schematically in Figure 1. It involves an interweaving of three quantum field theories — one for the electromagnetic force, one … Read more

Freeman Dyson, 90, Still Disturbing the Universe

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I spent the last two days at an extraordinary conference, “Dreams of Earth and Sky”, celebrating the life and career of an extraordinary man, one of the many fascinating scientists whom I have had the good fortune to meet. I am referring to Freeman Dyson, professor at the Institute for Advanced Study (IAS), whose career … Read more

Quantum Field Theory, String Theory, and Predictions (Part 2)

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[This post is a continuation of this one from Monday] Coming to Terms Before we continue, a little terminology — trivial, yet crucial and slightly subtle. Think about the distinction between the words “humanity” and “a human” and “humans”; or “higher education”, “university” and “universities”; or “royalty”, “king” and “kings”. In each case, the three … Read more

Quantum Field Theory, String Theory, and Predictions

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One of the important lessons of last Tuesday’s debate about string theory is that if I’m going to talk about theories that do or don’t predict things, I’d better be very clear about what’s a theory? what’s a scientific theory expected to do? what’s a prediction? On Thursday I asked my readers if they felt misled … Read more

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