# I Question about statistical mechanics

#### Xenosis17

Hello, first of sorry for asking what maybe a stupid question. I am teaching myself physics by watching lessons about QM, Classical Mechanics, EMT etc. I was watching Susskind's lectures about statistical mechanics lately and he derived equation of energy E= 3/2 x k x T. 3 in 3/2 came from number of spatial dimensions. Could it be possible that our universe began as having higher amount of dimensions ? I am sure they already thought about this. What is the reason they do not use this equation for explaining the energy universe had at the beginning and possibly for this scenario: If our universe is embedded in some sort of medium which only consist of dimensions it can be possible to explain multiverse scenarios since number of dimensions determine the energy of a system and there can be other singularities like our universe. I am sorry if this sounds naive I just wanted to see why a relation between dimension and energy cannot be established.

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#### DrClaude

Mentor
The equipartition theorem is only a statement about how the thermal energy is distributed among different degrees of freedom. And even then, it only works under some strict conditions (only for quadratic degrees of freedom, in the classical regime). You can't say that the "number of dimensions determine the energy of a system."

Note also that statements like
If our universe is embedded in some sort of medium which only consist of dimensions
are meaningless (aka "gobbledygook").

#### Xenosis17

DrClaude, thanks a lot for the explanation. I know that my phrasing of '' medium which only consists of dimensions'' was gibberish. Also, I know intuitively that it is sort of wrong to assume that if you have same system but add more dimensions it could mean more energy. Now I understand it is about degrees of freedom regarding thermal energy. Again, I am so sorry for this question. I just tried to imagine the equation with more dimensions then felt the need to ask.

#### Khashishi

For a point particle, the number of degrees of freedom is the number of spatial dimensions, since this determines the number of components to the momentum of the particle. But for more complicated particles, like diatomic molecules, you can have rotational modes as well as linear momentum modes, so the number of degrees of freedom is higher.

If there were extra dimensions in the early universe and the universe was close to thermal equilibrium, then some fraction of the total energy would be partitioned into motion through these extra dimensions.

#### Xenosis17

Khashishi, thanks a lot for the info and the explanation ! I totally get it now. Again, it was just a curiosity with regards to what could happen if I changed the number of dimensions. Thanks for the insight !

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