# How and why do the fundamental forces depend on temperature?

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I was watching a documentary on the Theory of Everything with some lectures by Holger Bech Nielsen. In this documentary, he mentions that in the early universe, the four fundamental forces were not existing separately because of the very high temperature, but does not explain why.

How can this be? I would understand it, if it were because energy associated with temperature completely dominated the other forces, making their respective forces insignificant, but it seems like this is not the case (e.g. the Placnk epoch subtitle on http://en.wikipedia.org/wiki/Timeline_of_the_Big_Bang)

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The coupling constants in the standard are not really constant but change their value as you probe smaller and smaller distances, or equivalent higher and higher energies. They are "running coupling constants".

It turns out that within the standard model the coupling constants for the electromagnetic, the strong and weak forces almost take the same value in the region of $10^{16}$ GeV, the GUT scale. See the diagram on the left.

If you include supersymmetry you can get them to meet. See the diagram on the right. For details consult [1].

The upshot of this is at hight enough energies, in the region of $10^{16}$ GeV, the forces within the standard model will unify. We have a single grand unified theory, we call that force the GUT force.

Including gravity in this is problematic. We do not have a full quantum theory of gravity. However, it is expected that gravity would unite with the GUT force near the Planck energy, which is about $10^{19}$ GeV.

References

[1] U. Amaldi, W. de Boer, H. Furstenau, Phys. Lett. B260 447-455 (1991).

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This is a lot to take in. I did some research to be able to grasp the meaning.

I have a few follow up questions if you don't mind.

First. Why are smaller distances equivalent to higher energies?

Second. When I look a the fine structure constant, it appears to be made up of other constants that also seem independent of energy.

Third. Is it correct to say, then, that the (known) fundamental forces become of the same (or comparable) magnitude, but does not become the same force per say? Or what does "unify" mean in this context?

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First. Why are smaller distances equivalent to higher energies?

In natural units energy has the units of inverse length.

Second. When I look a the fine structure constant, it appears to be made up of other constants that also seem independent of energy.

The reason for the running of coupling constant is to do with renormalisation and in particular the remormalisation group. The beta function encodes how the couplings depend on the energy scales of the processes.

This is all going to get technical very quickly.

Third. Is it correct to say, then, that the (known) fundamental forces become of the same (or comparable) magnitude, but does not become the same force per say? Or what does "unify" mean in this context?

Usually this means that the forces are different aspects of the same thing and they cannot be distinguished at high enough energies. For example, the electromagnetic force and the weak are unified into the electroweak force at about 100 GeV.

This has a lot to do with symmetry breaking. Very loosely, at high energies the theory has a lot of symmetry and you cannot distinguish the electromagnetic and weak sectors of the theory. As the system cools the symmetry broken and the theory separates into the electromagnetic and weak.

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