June 01, 2007

A Unified Theory of Forces

Steven Weinberg, A Model of Leptons, 1967

As frequently happens in physics, the story of the unification of forces begins with Einstein. Pre-1905, the electric and magnetic forces were described by Maxwell's equations, which vary depending on how observers move relative to a postulated cosmic frame of rest, the ether. In the opening paragraph of his 1905 paper on special relativity, Einstein notes that this "leads to asymmetries which do not appear to be inherent in the phenomena", in particular that the pre-1905 interpretation brings two different forces into play (electric and magnetic) depending on whether a conductor or a magnet is at rest relative to the ether. He notes that the two forces have exactly the same effects if the relative motion between magnets and conductors is considered, rather than their motion relative to a cosmic frame of rest.

This "principle of motional symmetry" allowed Maxwell's equations to be considerably simplified. This is akin to the situation, frequently encountered in programming, where two sections of code are discovered to strongly resemble each other, and combined into a single subroutine. In this case, two sets of equations were found to produce identical results, and were combined into a single, unifying form. Physicists call this "discovering a principle of symmetry".

In 1967, Steven Weinberg discovered another principle of symmetry, this one noting a similarity in the way electrons, neutrinos, and their antiparticles (e-, e+, ν, and ν, collectively "leptons") interact with other particles. In the most familiar of these interactions (which isn't saying much) a neutron (n) changes to a proton (p+) and emits an e- and an ν. This is called "beta decay". Interestingly, physicists like to describe forces in terms of particle interactions. For example, a pair of electrons repelling each other can be described as one e- emitting a photon which carries some of its momentum to the other e-. Conversely, physicists will describe almost any particle interaction as the result of a force. In particular, beta decay is said to be the result of the weak force.

A whole family of additional interactions are also ascribed to the weak force, all of them involving leptons interacting with p+, p-, or n. By 1967, a way had been found to describe these interactions in terms of two intermediate "force carrier" particles (like the photon in the electron-electron example above), the W- and W+. In the case of beta decay, a n changes to a p+ and emits a W- particle, which travels a short distance and then decays into an e- and an ν.

Steven Weinberg noted that the W- particle can decay into an e- and an ν, and the W+ particle can decay into a e+ and a ν, and created a mathematical model that assumed the equivalence of electrons and neutrinos under the weak interaction. This led to the need for two more force carrying particles, one of which could decay into a ν and an ν, and another which could decay into an e- and a e+. The former he called a Z particle. The latter turns out to be well known: the photon, which acts as the force carrier for the electromagnetic force.

The symmetry here is obviously broken. The weak force and the electromagnetic force act quite differently. This is explained partly by the differences between the force carrying particles: the W and Z particles are quite massive, and thus travel slowly; and decay quickly, restricting their effects to a very short range. Photons, on the other hand, are massless, travel at c, and need not decay, giving electromagnetism its infinite range. To explain these differences, Weinberg invokes the Higgs mechanism, which I don't understand well enough to explain. The result, though, is a set of equations that predict the masses of the W, Z, and photon, the properties of the various leptons, and the probabilities of all the interactions between them. The theory also predicted several reactions involving the Z particle and neutrinos which hadn't yet been observed.

In short, Weinberg discovered a simple, yet powerful way to describe two previously distinct phenomena in a unified way.


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