How Can Fermi Pressure Be Explained in Relativistic Conditions?

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Discussion Overview

The discussion revolves around the explanation of Fermi pressure under relativistic conditions, particularly focusing on the assumptions made regarding temperature and particle velocities in a Fermi gas. Participants explore the implications of low temperatures on the occupancy of momentum states and the resulting relativistic behavior of particles.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions the compatibility of assuming both low temperature and very relativistic conditions, suggesting that low temperatures imply low velocities.
  • Another participant argues that at low temperatures, all low energy states are filled, leaving only high energy states available, which can lead to relativistic behavior despite the low temperature.
  • A follow-up response reiterates that a sufficient number of electrons can result in relativistic particles due to the occupancy of lower momentum states.
  • There is a clarification that temperature is related to the average speed of particles, acknowledging that not all particles will have the same speed.
  • A participant introduces the concept of a non-interactive Fermi gas and questions how the Pauli exclusion principle contributes to maintaining pressure in electron or fermion gases, seeking clarification on their understanding.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between low temperature and relativistic conditions, with some asserting that relativistic effects can arise even at low temperatures due to occupancy of high energy states. The discussion remains unresolved regarding the implications of these assumptions and the nature of Fermi pressure in such contexts.

Contextual Notes

There are limitations in the assumptions made regarding temperature and particle velocities, as well as the conditions under which the Pauli exclusion principle applies. The discussion does not resolve these complexities.

Silviu
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Hello! I am reading a derivation for Fermi pressure and the author assumes that the electrons in a box are cooled so much that they occupy all the states in the momentum space from p=0 up to a maximum value of p. Then after he obtains a formula for the pressure, he simplifies the formula further, by assuming a very relativistic gas. I am not sure I understand how can we make both assumptions. If we reduce it as much as we can (basically close to 0K), it means that the velocities are very small (the temperature is given by the speed of the particles, so small temperature means small speed). So if the velocities are small, how can one assume "very relativistic" conditions? Thank you!
 
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At low temperature, all of the low energy states are filled. The only states available for interaction are the high energy states, which have an energy near the Fermi energy. This can lead to the particles being relativistic, even at low temperature.
 
phyzguy said:
At low temperature, all of the low energy states are filled. The only states available for interaction are the high energy states, which have an energy near the Fermi energy. This can lead to the particles being relativistic, even at low temperature.
So you mean that if you have a big enough number of electrons in the volume, the ones with the highest momentum, will be relativistic, just because all the lower velocity states have been occupied?
 
Silviu said:
So you mean that if you have a big enough number of electrons in the volume, the ones with the highest momentum, will be relativistic, just because all the lower velocity states have been occupied?

Yes, exactly. At least, that is my understanding.
 
Silviu said:
the temperature is given by the speed of the particles

The temperature is given by the average speed of the particles. Not all particles will have the average speed.
 
Is there a non interactive fermi gas?
Pauli principle saves the fermi gas from collapsing even at zero kelvin.There is cobditioned degeneracy pressure.
So separatedness of energy levels is only upto the conditoon that star is not big enough to overcome degeneracy pressure .Energy levels of nuclei are enormously big in comparison to atomic energy levels.
Does Pauli principle similarly maintains pressure in electron gas or fermion gas? How?
Please correct if my understanding is inadequate.
 

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