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So I'm quite confused about Boltzmann's constant $k_B$ being fundamental. From here:

... the Boltzmann constant. Its value is well known but even if its value were 10 times bigger or if it were exactly 1 , or 45.90 or 106 well... the Universe would remain the same as it is now. The Boltzmann constant is not really fundamental to the existence of the Universe.

This leaves me confused.

Let's assume I have $2$ different universes:

  1. Is it possible they can have different Boltzmann's constants $k_B$ and $k_B'$ ?
  2. If yes what happens if I open a wormhole (assume existence of some exotic matter) and connect both universes?
  3. Is point 2. identical to arguing that $\beta = 1/k_BT$ and $\beta' = 1/k_B'T$ should be the same for all systems?
Qmechanic
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More Anonymous
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    See this other question: Is the Boltzmann constant really that important?. – DanielSank Feb 08 '23 at 20:31
  • @DanielSank click on here that I link int the question. Though at this point I suspect I must be being thick – More Anonymous Feb 08 '23 at 20:35
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    A general point to make here is that no dimensionful constant can be on its own physically significant. Dimensionless constants absolutely are, however. The mass of an electron is not physically significant. The ratio of the mass of an electron to the mass of a proton is physically significant. So the question becomes what can we compare the Boltzmann constant to to obtain a dimensionless hence physically meaningful ratio? The answer is that there isn't really anything. It's an artifact of making a (spurious) distinction between temperature and energy. – Charles Hudgins Feb 08 '23 at 22:09

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Boltzmann constant is the coefficient for converting temperature units to energy units. There is nothing fundamental about it.

Roger V.
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  • Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on [meta], or in [chat]. Comments continuing discussion may be removed. – Buzz Feb 13 '23 at 21:36