A Unified Physics By 2050 Part III

 

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A Unified Physics by 2050?

Experiments at CERN and elsewhere should let us complete the Standard Model of particle physics, but a unified theory of all forces will probably require radically new ideas.

By: Prof. Steven Weinberg, Ph.D.

Suppressed Interactions 

What then? There is virtually no chance that we will be able to do experiments involving processes at particle energies like 10^16 GeV. With present technology the diameter of an accelerator is proportional to the energy given to the accelerated particles. To accelerate particles to an energy of 10^16 GeV would require an accelerator a few light-years across. Even if someone found some other way to concentrate macroscopic amounts of energy on a single particle, the rates of interesting processes at these energies would be too slow to yield useful information. 

But even though we cannot study processes at energies like 10^16 GeV directly, there is a very good chance that these processes produce effects at accessible energies that can be recognized experimentally because they go beyond anything allowed by the Standard Model. The Standard Model is a quantum field theory of a special kind, one that is "renormalizable." This term goes back to the 1940s, when physicists were learning how to use the first quantum field theories to calculate small shifts of atomic energy levels. 

They found that calculations using quantum field theory kept producing infinite quantities, a situation that usually means a theory is badly flawed or is being pushed beyond its limits of validity. In time, they found a way to deal with the infinite quantities by absorbing them into a redefinition, or "renormalization," of just a few physical constants, such as the charge and mass of the electron. (The minimum version of the Standard Model, with just one scalar particle, has 18 of these constants.) Theories in which this procedure worked were called renormalizable and had a simpler structure than nonrenormalizable theories.

Image: Johnny Johnson

THE HIERARCHY PROBLEM is a measure of our ignorance. Experiments (yellow band) have probed up to an energy of about 200 GeV and have revealed an assortment of particle masses (red) and interaction energy scales (green) that are remarkably well described by the Standard Model. The puzzle is the vast gap to two further energy scales, that of strong-electroweak unification near 10^16 GeV and the Planck scale, characteristic of quantum gravity, around 10^18 GeV.

It is this simple renormalizable structure of the Standard Model that has let us derive specific quantitative predictions for experimental results, predictions whose success has confirmed the validity of the theory. In particular, the principle of renormalizability, together with various symmetry principles of the Standard Model, rules out unobserved processes such as the decay of isolated protons and forbids the neutrinos from having masses. Physicists commonly used to believe that for a quantum field theory to have any validity, it had to be renormalizable. This requirement was a powerful guide to theorists in formulating the Standard Model. It was terribly disturbing that it seemed impossible, for fundamental reasons, to formulate a renormalizable quantum field theory of gravitation. 


Today our perspective has changed. Particle physics theories look different depending on the energy of the processes and reactions being considered. Forces produced by exchange of a very massive particle will typically be extremely weak at energies that are low compared with that mass. Other effects can be similarly suppressed, so that at low energies one has what is known as an effective field theory, in which these interactions are negligible. Theorists have realized that any fundamental quantum theory that is consistent with the special theory of relativity will look like a renormalizable quantum field theory at low energies. But although the infinities are still canceled, these effective theories do not have the simple structure of theories that are renormalizable in the classic sense. Additional complicated interactions are present; instead of being completely excluded, they are just highly suppressed below some characteristic energy scale.

Image: Slim Films

WHAT COMES NEXT? There are several possibilities for the unified physics that lies beyond the Standard Model. Technicolor models (a) introduce new interactions analogous to the "color" force that binds quarks. Accompanying the interactions are new generations of particles unlike the three known generations. Supersymmetry (b) relates fermions to bosons and adds the supersymmetric partners of each known particle to the model. M-theory and string theory (c) recast the entire model in terms of new entities such as tiny strings, loops and membranes that behave like particles at low energies.

Gravitation itself is just such a suppressed nonrenormalizable interaction. It is from its strength (or rather weakness) at low energies that we infer that its fundamental energy scale is roughly 10 ¹⁸ GeV. Another suppressed nonrenormalizable interaction would make the proton unstable, with a half-life in the range of 10 ³¹ to 10 ³⁴ years, which might be too slow to be observed even by 2050 [see my article "The Decay of the Proton"; Scientific American, June 1981]. Yet another suppressed nonrenormalizable interaction would give the neutrinos tiny masses, about 10^-11 GeV. There is already some evidence for neutrino masses of this order; this should be settled well before 2050. 

Observations of this kind will yield valuable clues to the unified theory of all forces, but the discovery of this theory will probably not be possible without radically new ideas. Some promising ones are already in circulation. There are five different theories of tiny one-dimensional entities known as strings, which in their different modes of vibration appear at low energy as various kinds of particles and apparently furnish perfectly finite theories of gravitation and other forces in 10 space-time dimensions. 

Of course, we do not live in 10 dimensions, but it is plausible that six of these dimensions could be rolled up so tightly that they could not be observed in processes at energies below 10 ¹⁶ GeV per particle. Evidence has appeared in the past few years that these five string theories (and also a quantum field theory in 11 dimensions) are all versions of a single fundamental theory (sometimes called M-theory) that apply under different approximations ["The Theory Formerly Known as Strings"]. But no one knows how to write down the equations of this theory.

Further Reading:

1. Unified Theories of Elementary-Particle Interaction. Steven Weinberg in Scientific American, Vol. 231, No. 1, pages 50-59; July 1974.

2. Dreams of a Final Theory. Steven Weinberg. Pantheon Books, 1992.

3. Reflections on the Fate of Spacetime. Edward Witten in Physics Today, Vol. 49, No. 4, pages 24-30; April 1996.

4. Duality, Spacetime and Quantum Mechanics. Edward Witten in Physics Today, Vol. 50, No. 5, pages 28-33; May 1997.

5. The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. Brian Greene. W. W. Norton,1999.

http://hera.ph1.uni-koeln.de/~heintzma/Weinberg/Weinberg.htm 

The Author
 

STEVEN WEINBERG is head of the Theory Group at the University of Texas at Austin and a member of its physics and astronomy departments. His work in elementary particle physics has been honored with numerous prizes and awards, including the Nobel Prize for Physics in 1979 and the National Medal of Science in 1991. 

The third volume (Supersymmetry) of his treatise The Quantum Theory of Fields is out from Cambridge University Press. The second volume (Modern Applications) was hailed as being "unmatched by any other book on quantum field theory for its depth, generality and definitive character."