# B Way to check relativity with temperature?

1. Jun 22, 2017

### jk22

Do we know if experiments with plasma fusion could test relativity and its speed limit because of the maximal speed ? Like $$3/2kT=1/2mc^2$$ hence for example with hydrogen the maximal temperature should be around $$10^{12}K$$. I read that they achieved 8*10^7 in wendelstein. Or should it be considered the relativistic mass hence no upper limit for T even for little masses ?

2. Jun 22, 2017

### Staff: Mentor

Particle accelerators like the LHC can accelerate particles much closer to the speed of light than fusion plasma can. The protons circling in the LHC have kinetic energy in the TeV range, which is much, MUCH higher than the KeV to MeV range of fusion plasma. Even if we could contain the plasma, at the TeV energy scale particles in the plasma would be colliding with each other so hard that they literally form new particles, robbing energy from the plasma and reducing its temperature.

3. Jun 22, 2017

### Orodruin

Staff Emeritus
Also, $mv^2/2$ is not a valid expression for kinetic energy at relativistic speeds.

4. Jun 22, 2017

### Ibix

The kinetic energy of a moving body is $(\gamma-1) mc^2$. This grows without bound as velocity approaches c, so there is no upper bound to particle energy imposed by relativity.

We usually recommend against using relativistic mass for anything. You'll note that the formula I cited for kinetic energy is not simply the Newtonian formula with $\gamma m$ dropped in. Thinking that it might be is one of the problems with relativistic mass.