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One way in which an object is affected by temperature rise is that the wavelength of the radiation it emits is gets smaller and smaller. Another way of looking at it is that as an object gets hotter, the electrons of the atoms orbit faster and faster. It seems that the maximum temperature and object could have is when:

A) The wavelength of the radiation reaches Planck length.

B) When the speed of the electrons nears the speed of light.

Do processes A and B occur at the same temperature? Is it possible to have a wavelength smaller than Planck length, but it would be immeasurable (Would that be in some sense "infinite" or "negative temperature")?

Please keep the answers in layman's terms.


marked as duplicate by ACuriousMind, Ali, BMS, Brandon Enright, Kyle Kanos Sep 10 '14 at 2:14

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    $\begingroup$ The electrons don't "orbit faster" when an object is hotter. Rather, the entire atoms move more quickly in their vibrations within the material. $\endgroup$ – johnpaton Sep 9 '14 at 20:26
  • $\begingroup$ The temperature of an object has nothing to do with how fast "electrons" orbit. Long before either a) or b) happens, there would be no object. In the case of a), the only imaginable configuration (except for the very early universe) is the final stage of an evaporating black hole, and the emitted particles in that case would be gravitons, but that's an extrapolation of physics we don't really understand, yet. In order for a plasma to emit relativistic electrons, it has to reach a temperature of approx. 10 billion K, which is high, but not nearly as high as the temperature of case a) would be. $\endgroup$ – CuriousOne Sep 9 '14 at 20:29
  • $\begingroup$ Related: physics.stackexchange.com/q/1775/2451 and links therein. $\endgroup$ – Qmechanic Sep 9 '14 at 20:31
  • $\begingroup$ I think pair production (electrons and positrons) would also be a practical limiting factor. $\endgroup$ – Brandon Enright Sep 10 '14 at 1:24

The entire premise of this question is false, neither do electrons orbit atoms with a well-defined speed, nor does this, in any way, correspond to the temperature, since that is a property of systems in thermal equilibrium, not of single particles.

Also, whether the Planck length signifies really a shortest achievable wavelength is...debatable.


I am going to address only your second point:

It seems that the maximum temperature an object could have is when:
B) When the speed of the electrons nears the speed of light.

In fact this does not impose any limit to temperature. When you add more and more heat to a body, its atoms and molecules move faster. At this stage, the electrons are not directly affected. Eventually, however, the electrons are broken off from the atoms to form a plasma, and then they do indeed move faster as the temperature rises.

If the plasma is hot enough the electrons will move at close to the speed of light. If the plasma is even hotter, even the ions are moving near the speed of light. However, particles can have arbitrarily large kinetic energy - there is no limit - they just get closer and closer to light speed. The speed of light cannot be attained as this would require infinite energy. This is why there is no limit to temperature.


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