Question about statistical mechanics

In summary, the conversation discusses the idea of the number of dimensions affecting the energy of a system in the early universe. The equipartition theorem is mentioned as a means of distributing thermal energy among different degrees of freedom, but it does not determine the energy based on the number of dimensions. The concept of extra dimensions and their potential impact on the energy of the early universe is also explored. The conversation concludes with the understanding that the number of dimensions does not directly determine the energy, but rather the degrees of freedom within a system.
  • #1
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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  • #2
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
Xenosis17 said:
If our universe is embedded in some sort of medium which only consist of dimensions
are meaningless (aka "gobbledygook").
 
  • #3
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.
 
  • #4
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.
 
  • #5
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 !
 

What is statistical mechanics?

Statistical mechanics is a branch of physics that uses statistical methods to explain the behavior of a large number of particles in a system. It provides a framework for understanding how microscopic properties of individual particles translate into macroscopic properties of a system.

What are the fundamental principles of statistical mechanics?

The fundamental principles of statistical mechanics are the laws of thermodynamics, the concept of entropy, and the assumption of equal a priori probabilities for all microstates of a system. These principles are used to derive equations that describe the behavior of a system at the microscopic level.

How is statistical mechanics used in practical applications?

Statistical mechanics has numerous practical applications, including predicting the properties of materials, understanding the behavior of gases and liquids, and studying phase transitions. It is also used in fields such as chemistry, biology, and engineering to model and analyze complex systems.

What is the role of probability in statistical mechanics?

Probability plays a central role in statistical mechanics, as it is used to describe the likelihood of a system occupying a certain microstate. The laws of thermodynamics and the concept of entropy also rely on probability to explain the behavior of a system.

How does statistical mechanics relate to other branches of physics?

Statistical mechanics is closely related to other branches of physics, such as thermodynamics, quantum mechanics, and classical mechanics. It provides a bridge between the microscopic and macroscopic worlds, connecting the behavior of individual particles to the overall properties of a system.

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