# Is the heat required to alter the Higgs field an 'absolute heat'?

I have read and heard that manipulating the Higgs field would require heating up a local geometry to ridiculous temperature. I am trying to understand if there are stars or places in the universe which have this level of heat.

Would this be the upper limit on heat, an 'absolute heat'?

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## 1 Answer

We need to be clear about what temperature means in this context. For gases the temperature is linked to the particle velocities by the Maxwell-Boltzmann distribution, so we can convert a temperature to an average particle velocity and hence average particle energy, and vice versa.

The electroweak transition happened when the average particle energy was in the range 100GeV to 1TeV. We could take this energy and use a Maxwell-Boltzmann distribution to convert it back to a temperature, and if you do this the temperature comes out at about 10$^{16}$K. However it's debatable how much sense it makes to apply the concept of temperature to the universe at these high energies, so don't take this number too seriously.

The temperature at the core of a star is in the range 10$^7$ to 10$^8$K (depending on the size of the star) so it's unlikely there is anywhere in the universe that gets anywhere near the electroweak transition temperature. Individual cosmic rays can have energies far above 1TeV, but you can't convert this to a temperature because by definition only an assemblage of particles can have a temperature.

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 "it's debatable how much sense it makes to apply the concept of temperature to the universe at these high energies" Why is that? I've always heard that quasi-equilibrium holds throughout the expansion (except for the odd phase transition), so temperature definitely applies. What is the argument against it? – Michael Brown Feb 8 at 0:25 Lots of things have temperature that aren't gases. It can be defined as $\partial U/\partial S$ or as energy per degree of freedom, the two being very close approximations of one another except at low temperatures. Without knowing much about particle physics, I would imagine that energy per degree of freedom is easy to calculate and relatively unproblematic as a definition. – Nathaniel Mar 9 at 14:49