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By Root 830 0

rule we have used throughout the book to this point does not include the effects of Special Relativity. Including these, as we always must if we are to describe photons, means that the clock-winding rules are different for the electron and photon.

4. g is related to the fine structure constant:

5. This is a technical point, to ensure that the electron feels roughly the same sized magnetic force as it moves around.

6. The one first anticipated by Bohr back in 1913.

1. An ‘event’ is a single proton–proton collision. Because fundamental physics is a counting game (it works with probabilities) it is necessary to keep colliding protons in order to accumulate a sufficient number of those very rare events in which a Higgs particle is produced. What constitutes a sufficient number depends on how skilful the experimenters are at confidently eliminating fake signals.

2. Our ability to think of a massive particle as a massless particle supplemented with a ‘kink’ rule comes from the fact that P(A,B) = L(A,B)+L(A,1)L(1,B)S+L(A,1)L(1,2)L(2,B)S2+L(A,1)L(1,2)L(2,3)L(3,B)S3 +…, where S is the shrinkage factor associated with a kink and it is understood that we should sum over all possible intermediate points 1, 2, 3 etc.

3. This is a subtle point and derives from the ‘gauge symmetry’, which underwrites the hopping and branching rules of the elementary particles.

4. He was far too modest to call them by that name.

1. Recall from Chapter 5 that particles of definite momentum are in fact described by infinitely long waves and that as we allow for some spread in the momentum so we can start to localize the particle. But this can only go so far and it makes no sense to talk about a particle of a certain wavelength if it is localized to a distance smaller than that wavelength.

2. We can generalize to the entire star because we are not being specific about where the cube actually is. If we can show that a cube located anywhere in the star does not move then that means all such cubes don’t move and the star is stable.

3. It is of course possible to compute more precisely how the electrons move around but at the price of introducing more mathematics.

4. Newton’s second law can be written as F = dp/dt. For constant mass this can be written in the more familiar form: F = mdv/dt = ma.

5. Here we have combined the exponents according to the general rule xaxb = xa+b.

6. For those of a mathematical bent, show that , i.e. that the function g (a) is actually determined once we know the function f (a).