When fundamental forces unify at high energy, what is this energy "of"?

Question

For example, they say at 100 GeV the electromagnetic force and weak force unify into an "electroweak force". My question is, what energy has to exceed 100 GeV for the electroweak force to come into play? 100 GeV is actually a tiny amount of energy, much less than 1 joule. There's more energy in an AA battery. But I guess what it means is energy in a single particle, or average energy of particles according to kT.

What if the temperature is close to the kT cutoff for the electroweak force, so that some particles have energy below 100 GeV and others above 100 GeV? Then are half the particles affected separately by weak and electromagnetic forces, and half by the combined electroweak force? Or is there some fuzzy region where the effect is a mix of both descriptions? Or is it the energy of the bosons that determines which set of rules apply, so that we will get some photons and some B0 bosons, but all the electrons will interact with both? Is it impossible to have a gamma ray photon with more than 100 GeV energy? What about the fact that energy is dependent on reference frame? Some gamma ray might have less than 100 GeV energy in our reference frame, but in a reference frame moving relativistically toward the source, it will be blueshifted and might have more than 100 GeV energy. In that reference frame will the identity of the particle be different, because now electroweak rules apply?

What about other high-energy cutoffs, like asymptotic freedom in the strong force?

neb · Accepted Answer

Really great questions.

I'll give you an example of what happens with the electroweak force which can be extended to at least the strong nuclear, and maybe gravity (but maybe not ..)

At energies greater than the thermal equivalent of 100GEV (where the average particle would have 100GEV of kinetic energy), the four electroweak bosons (photon, W+, W-, and Z) were massless and could be interchanged without having any measurable change in physics (gauge symmetry),  As they cooled below that point, the W+, W-, and Z began interacting with the Higgs field gaining a lot of mass and breaking the electroweak symmetry and differentiating into the weak and electromagnetic forces (the range of a force depends inversely on the mass of the force carrying boson).

Your question about whether there was a fuzzy transition region is a really interesting question.  Since I don't know for sure, I'll speculate.  When this symmetry breaking occurred, the universe was very small, probably pretty close to thermal equilibrium, and expanding (and thus cooling) at a very rapid rate.  So the transition probably happened very quickly but there probably was a small amount of time where some of the bosons were massless and some were not (did they have intermediate masses also or was the symmetry breaking instantaneous?). Probably didn't make much difference though since there wasn't much for bosons to interact with at that point.

Energy is not dependent on a reference frame.  Total energy is invariant E^2 = (mc^2)^2 + (pc)^2

I believe the cutoff off for grand unification energies (strong, weak, electromagnetic unification) is 10^14 GEV with a thermal equivalent of 10^27 K

Can't remember what it would be for gravity thrown into the unification mix.

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When fundamental forces unify at high energy, what is this energy "of"?

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