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Was reading Kroemer on high temperature mechanics, infinite temperatures and their dependance on negative kelvin temperatures.

One question does that mean that its actually physically possible to measure something as having infinite heat or temperature? That seems paradoxical to me? Or is it just a theoretical limit of the calculus within which temperatures may exhibit finite temperatures.

A quick google turned up absolute hot, which is AKA the planck temperature or the temperature at the big bang, so this would seem to contradict an actual measurable infinity.

Am I getting unnecessarilly confused as I always assumed infinity was a purely mathematical concept, not a physical reality? For example in kind of the same way 0k is not achievable infinite k is not achievable in experiment.

One question does that mean that its actually physically possible to measure something as having infinite heat or temperature? That seems paradoxical to me? Or is it just a theoretical limit of the calculus within which temperatures may exhibit finite temperatures.

A quick google turned up absolute hot, which is AKA the planck temperature or the temperature at the big bang, so this would seem to contradict an actual measurable infinity.

Am I getting unnecessarilly confused as I always assumed infinity was a purely mathematical concept, not a physical reality? For example in kind of the same way 0k is not achievable infinite k is not achievable in experiment.

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