| From: Chris (Avatar) | 31/07/2000
16:38:00 |
| Subject: re: Electro-Weak Theorum | post id:
108307 |
As Darth has pointed out, Salam, Weinberg and Glashow won the Nobel prize in 1979 for unifying the electromagnetic interaction with the weak nuclear interaction. Conceptually, unifying these two interactions involves theorising that they are simply two faces of the same interaction. The standard conc eptual model for unification (at the moment) is to suppose that at sufficiently high energies a symmetry exists between the two forces, and that this symmetry is naturally broken at everyday energies. An illustration I've seen Gribbon use might help here: Imagine you have a nice, smooth, rounded hill surrounded by two valleys (one either side). Now suppose you place a ball bearing at the top of the hill. When you let the ball bearing go it will roll down the hill into one of the valleys. Gribbon describes the ball at the top of the hill as a high energy symmetry - while you put energy into the system (holding the ball) it stays in the central position, the hill and ball system has symmetry. Let the ball go and the symmetry breaks naturally - the ball now resides in either the left or right valley and the whole system is no longer symmetrical. In electroweak theory, symmetry is assumed when the strength of the two forces is equal. The fine structure constant ( a = 1/137.036) measures the strength of the e/m interaction and the Fermi constant ( GF = 1.166*10-5GeV-2 ) the weak interaction. Equating these gives a mass for the W boson. Which is a problem. In QED the e/m interaction is carried by a single particle called a photon, and the photon is massless. Because of the extra degrees of freedom in the weak interaction three carrier particles are required - the charged W boson (W+ and W-) and the neutral Z boson. Both W and Z particles have mass. The electroweak theory explains this mass in terms of a hypothetical field called the Higgs field - particles gain their masses via the Higgs mechanism. At sufficiently high energies, when symmetry is restored between e/m and weak interaction, the four bosons which are required for the theory are designated W1, W2, W3 and Bo. The Higgs mechanism breaks the symmetry, and the W1 and W2 acquire mass to become W+ and W- bosons, whilst the photon and boson are "hybrids" (of a sort). The result is that the two interactions "appear" different at everyday scales and energies. The electroweak theory is embodied in a complete description called a Lagrangian function. The Langrangian of any system is just an equation which describes how the energy of the system evolves with time. The electroweak lagrangian function after spontaneous symmetry breaking includes the massless photon field, the massive charged boson fields (W+ and W-) and the neutral weak massive field (Z) as well as the Higgs field (the mass giving mechanism). In this Lagrangian the two interactions can be described as two faces of the same force. Hope this helps! Chris | |