
Getting to the Bottom of Noether’s Theorem - _Microft
https://johncarlosbaez.wordpress.com/2020/06/29/noethers-theorem-2/
======
mikhailfranco
Baez always makes interesting reading.

At the end of the abstract there is the arxiv-bait _" inverse temperature is
imaginary time",_ which relates to Wick Rotation and his work on _quantropy_ a
few years ago:

[http://jakobschwichtenberg.com/wick-rotation-action-
formalis...](http://jakobschwichtenberg.com/wick-rotation-action-formalism/)

[https://johncarlosbaez.wordpress.com/2011/12/22/quantropy/](https://johncarlosbaez.wordpress.com/2011/12/22/quantropy/)

[https://arxiv.org/abs/1311.0813](https://arxiv.org/abs/1311.0813)

TL;DR if Boltzmann says thermodynamic states occur in proportion to
exp(-E/kT), Feynman says paths in the quantum state space occur with weight
exp(-S/i hbar), and action S ~ Et, then there is some analogy, ignoring
constants (k,hbar,c) that goes like:

    
    
        (1/T) ~ it
    

then we vaguely remember that the fourth dimension of spacetime is not time
itself, but ict:

[https://en.wikipedia.org/wiki/Wick_rotation](https://en.wikipedia.org/wiki/Wick_rotation)

