Temperature & Relativity: Can Plasma Fusion Test Limits?

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Discussion Overview

The discussion centers on the potential of plasma fusion experiments to test the limits of relativity, particularly regarding the speed of light and the implications of temperature on particle energy. It explores theoretical aspects of kinetic energy in relativistic contexts and the comparison of energy scales between plasma fusion and particle accelerators.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether plasma fusion experiments could test relativity and its speed limit, referencing a temperature equation and suggesting a maximal temperature for hydrogen.
  • Another participant argues that particle accelerators like the LHC can achieve much higher kinetic energies than those found in fusion plasma, suggesting that the energy scales involved in plasma fusion are insufficient for such tests.
  • A participant challenges the use of the classical kinetic energy expression at relativistic speeds, implying that it does not apply in this context.
  • Another participant provides the correct relativistic expression for kinetic energy, stating that it grows without bound as velocity approaches the speed of light, indicating no upper limit to particle energy due to relativity.
  • There is a caution against using the concept of relativistic mass, with a participant emphasizing the importance of using the correct kinetic energy formula in relativistic scenarios.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of plasma fusion for testing relativity, with some emphasizing the limitations of fusion energy compared to particle accelerators, while others focus on the theoretical implications of relativistic kinetic energy. The discussion remains unresolved regarding the potential of plasma fusion experiments in this context.

Contextual Notes

There are limitations in the assumptions made about the energy scales of plasma fusion versus particle accelerators, and the discussion reflects varying interpretations of relativistic mass and kinetic energy equations.

jk22
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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 ?
 
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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.
 
Also, ##mv^2/2## is not a valid expression for kinetic energy at relativistic speeds.
 
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.
 
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