Maxwell's Distribution: Integrating Over Velocity Spectrum

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SUMMARY

The discussion centers on the integration of Maxwell's distribution over the velocity spectrum, specifically addressing the challenge of incorporating a speed limit, such as the speed of light. Participants highlight the relevance of the Maxwell–Jüttner distribution as a solution for modeling particles with velocities less than the speed of light. This distribution provides a framework for integrating over a finite range of velocities, thus addressing the limitations of traditional Maxwell's distribution.

PREREQUISITES
  • Understanding of Maxwell's distribution
  • Familiarity with the concept of velocity in physics
  • Knowledge of relativistic effects on particle dynamics
  • Basic grasp of statistical mechanics
NEXT STEPS
  • Research the Maxwell–Jüttner distribution and its applications
  • Explore the implications of relativistic speeds on particle behavior
  • Study integration techniques in statistical mechanics
  • Investigate the role of speed limits in physical models
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Physicists, researchers in statistical mechanics, and students studying thermodynamics and particle physics will benefit from this discussion.

ChrisVer
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I have one question, I am sorry if it's stupid or something.

So, when we write down the Maxwell's distribution, we integrate over the spectrum of velocities... But that is from 0 to infinity.. (or minus infinitiy to infinity nevermind)
Is there any way someone can cut-off the above? Since we know that nothing can overcome EVER the speed of light?
 
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ChrisVer said:
I have one question, I am sorry if it's stupid or something.

So, when we write down the Maxwell's distribution, we integrate over the spectrum of velocities... But that is from 0 to infinity.. (or minus infinitiy to infinity nevermind)
Is there any way someone can cut-off the above? Since we know that nothing can overcome EVER the speed of light?

Good question. See Maxwell–Jüttner distribution.
 
If any thing is smaller than light particles then it is possible
 

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