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plank | 1 year ago

Interesting to read this, 27 years after my PhD* (theoretical physics), in which I did compare the view WITH and the view WITHOUT ‘unknowns’ causing entropy as a driver.

* My PhD was about how to treat a (quantum mechanical) system inside a cavity: a cavity with one perfect mirror and one 99.999999% perfect mirror. The (one dimensional) universe was made whole by another perfect mirror at the other side of the non-perfect mirror (in ASCII art:

[100%] —l— [100-epsilon] ——L——— [100%]

With L >> l. The ‘whole universe’ solution was simple (using standard quantum mechanics techniques), the ‘lossy’ ‘small universe’ was not. But they needed to be the same (physically). Thus using the exact solution for the ‘complete’ (l+L) universe and comparing it to possible ‘small’ (l) universe models in which some non-linear term accounted for loss. The connection between how a lossy system (in which entropy exists/is a driving ‘force’) and a losless system (in which everything is conserved) is thus not a new insight;-0

discuss

order

mojomark|1 year ago

I read you're comment with interest, but ultimately I can't understand the point being made because I don't know what kind of mirror you're referring to (optical?), I don't know what 'l' or 'L' represent (lateral spacing of mirrors?, vacuum energy desnities?), and the last sentence I think maybe the word 'how' should be deleted?

IIAOPSW|1 year ago

The imperfect mirror means that epsilon% of the time the light goes through to a much larger "back room" whereas (1-epsilon)% of the time the light just reflects like normal. The point being made is that this is an extension of an ordinary ideal cavity to include unavoidable (but weak) interaction with the much larger system outside of it (aka the whole universe). It just so happens the much larger external system is also being modeled as a simple 1d cavity.

In other words, entropy is equivalent to bits of information needed to specify the complete state of the system leaking outside of the confines of where those bits are being observed by an experiment (eg tunneling through an imperfect mirror).

Entropy is an accounting tool to keep track of how many bits are missing, and how far this ignorance has percolated into what you can safely predict about the system.

plank|1 year ago

Answers to your questions: 1): all the way to the left, a mirror with a reflectivity|r| of 1 (or a 100%). In the middle an |r| of slightly below 1. Yes, optical, system with photons (a and a^dagger with [a,a^dagger]=1). 2) distance between mirrors 1 and 2: l. Distance mirror 2 and 3:L. (Later taking the limit L/l ==>> infinity) 3) the how is actually correct, I guess the word behaves is missing twice: .... how .... behaves and a .... behaves.