That paper looks somewhat similar to another paper co-authored by Reginatto —which is the arxiv paper cited above. Click on reginatto and his paper with M Hall will show up (QM from UP).

the vixra paper cites reginatto (ref 2) —-i like that . i’m not in shape to try to go through these but the idea has been around along time—and even quantropy has. but its not like its common knowledge . stat mech, and QM and CM were always taught as opposites.

also i’m more philosopher or generalist than physicist so math isn’t easiest. i just haven’t found anyone interested in what these mean, only math to them. t.

]]>It’s a sketchy introduction to Fourier transform pair of position-momentum and the use of maximum entropy is non-mathematical (if you compare to Ariel Caticha’s Entropic Dynamic that I have tried to read). But the treatment of the “inverse” Ehrenfest’s theorem is new to me. But apparently that watered-down entropy approach is not related to partition functions and quantropies.

Any way, the axiomatic framework of QM suggests that we are missing a fundamental principle that can be mixed with statistical mechanics. Maybe the concept of quantropy turns out to be fruitful.

]]>Is that essentially just applying MaxEnt to the variance uncertainty?

]]>I found a paper that claims to give seemingly simple information theoretical derivation of QM from the uncertainty principle, maximum entropy distribution and Ehrenfest theorem:

http://vixra.org/abs/1912.0063

If that is correct, it would be nice to have a Newtonian approach to QM, along with Hamiltonian and Lagrangian.

]]>If you take the equations of quantum mechanics and carefully take a limit where you get classical mechanics. If you take the equations of general relativity and take a limit where you get Newtonian gravity. If you take the equations of general relativity and take a limit where you get special relativity. So, limits of this sort are essential for understanding how more sophisticated theories of physics reduce to earlier theories.

It’s natural to ask what it means to take these limits, given that you can’t actually change the constants of nature. The answer lies in the fact that these aren’t dimensionless constants. It doesn’t make sense to ask what would happen as since is dimensionless. But has units of action, has units of velocity, and has units of force times distance squared per mass squared.

So, if we’re studying a physics problem where all the velocities involved are small compared to the speed of light— is very small for all velocities in your problem—you typically can get a good approximate answer by taking the limit where And by changing units in a clever way, this can be reinterpreted as taking a limit where is held constant but The latter approach is often more convenient, because you just need to let one thing go to infinity (namely ) instead of letting lots of things go to infinity (all the velocities in your problem).

Similarly, in a physics problem where all the actions involved are large compared to classical mechanics is typically a good approximation to quantum mechanics. And it’s often convenient to study this by holding the actions that apprear in your problem constant but letting

In short, it involves a clever use of dimensional analysis.

]]>Naive question: isn’t ‘h bar’ (reduced Planck constant) a constant by itself? What does limit of h bar tending to zero mean? What is the motivation?

]]>I’ve ended on this site pondering a similar analogy and problem. My starting point was the problem of “correlations” in the many-body wavefunction, which are a bane for DFT calculations. The gist of the problem is: you have two interacting electrons, say, in a potential. Their effective wavefunction will have a certain degree of correlation built in; namely, if I know the position of electron 1, I now have SOME more knowledge about electron 2, though not certainties, of course (it’s not full on entanglement after all). This lowers the Von Neumann entropy of the wavefunction, of course. What makes me think is how there really is a “tradeoff” at work here. If there is only ONE potential well, for example, the energy would be minimized by both electrons sitting into it. But of course there is repulsion among them, so in that situation the energy would be higher. So in order to lower it they sacrifice some of the entropy of the wavefunction. Of course no one says that if I were to express Schroedinger’s equation as a minimization principle analogous to the free energy one Von Neumann’s would be THE entropy that appears in it – it could just be a function which happens to be somewhat monotonous with the ‘true’ entropy. But looking at it, it should be possible to recast the time independent Schroedinger equation with your formalism if one performs a Wick rotation and calculates only the closed loops in the path integral.

Now of course I say all that but the thought of the math scares the hell out of me.

]]>Ooops, sorry, I just noticed that I replied out-of-context; John already provides more or less the same answer.

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