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The $cGh$-cube is a way to visualise todays theoretical physics framework(s).

cGh cube

This representation gives the impression $c$, $G$, and $\hbar$ could be viewed as variables between $0$ and $1$. This is not the case. These are constants (supposedly).

In the case of special relativity it is obvious how this can be corrected. It is not $1/c$ that goes to $1$, but rather $v/c$ with $v$ the (typical) velocity of a particle or system.

Could the other axes be corrected in a similar manner?

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    $\begingroup$ variables between 0 and 1 This diagram is not intended to be taken literally as a cube with side length 1. $\endgroup$
    – G. Smith
    Commented Jul 10, 2020 at 17:14
  • $\begingroup$ Well, but with the right relations (such as v/c) it could be written as going from 0 to 1. And now I'm looking for those relations: what would make sense? $\endgroup$
    – kalle
    Commented Jul 11, 2020 at 19:58

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This cube is just a representation of what physicists think about when exploring different limits of the as yet unknown theory of everything.
So rather than thinking too closely about the details, it's best to just think of each plane $x_i =0$ in $\mathbb{R}^3$ as the limit where one of the 3 effects become negligeable: relativity, quantum mechanics, and gravity.

And btw I should also say that one point has historically been disregarded, than is the non-relativistic quantum gravity point. But recently, progress has been made in Newton-Cartan geometry which hopes to advance understanding in towards that point.

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    $\begingroup$ Isn't "non-relativistic quantum gravity" just Schrodinger quantum mechanics with a Newtonian gravitational potential? Is there something missing there? $\endgroup$ Commented Jul 10, 2020 at 19:48
  • $\begingroup$ So up until now, there wasn't an action principle for Newtonian gravity. This was done in arxiv.org/pdf/1807.04765.pdf , and now they are trying to quantise this. I believe this point of this exercise is to disantagle gravity effects from relativistic effects. $\endgroup$ Commented Jul 10, 2020 at 20:03
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    $\begingroup$ Why would there not have been one already? Doesn't the usual Lagrangian w/a Newtonian potential provide it? Or does something go wrong with it? $\endgroup$ Commented Jul 10, 2020 at 20:04
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    $\begingroup$ So it's not my area of research and I just went to one seminar. From what I understand, NC geometry is a way to geometries Poisson's equation on a foliated manifold, and only recently did they understand how to write an action for Poisson's equation in an analogous way to the Einstein-Hilbert action. $\endgroup$ Commented Jul 10, 2020 at 21:25

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