Maxwell's Distribution: Integrating Over Velocity Spectrum

[ChrisVer]

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?

 

[dvf]

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.

 

[Varun Bhardwaj]

If any thing is smaller than light particles then it is possible