Are commutators physical?

  • Thread starter Jimster41
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  • #1
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just finished Susskind's QM. Definitely blew my mind. Can't stop wondering about commutators. Trying synthesize and remember with self quiz I can't self grade.

Super quiz: Could one in principle calculate the number of Planck flops (commutaor operations or bits) in a human lifetime?

My answer: Sure, the Planck unit is the quanta of action. If one were just to consider the position-momentum basis (to keep it simple), and assume a person is at all proper seconds "located" (because wherever you go there you are), and assume that a person is always a set number of massive quanta (surface area*kg) you could calculate how many non-commutative decisions were made to localize their position in space over some proper time interval - in other words how many [x,p] plank-sized commutator bits were left behind as "lost energy", or added as "einselections" (depending on your preference).
 
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  • #2
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I wasn't trying to make trouble. This was the really question I had after understanding (I thought) what commutators do. So I misunderstood completely?? I thought I understood that they are physical, and represent the bit of energy and information that comes out of, or must be supplied to the non-commuative congugate pair of degrees of freedom called position and momentum, if you want to say some real thing "is somewhere called x".

So that's just totally wrong, or not even understandable to anyone?

I thought the energy information relation was sort of settled by Shannon or somebody, but maybe I was wrong about that. This paper looks pretty recent.

http://arxiv.org/abs/1009.5287
Information heat engine: converting information to energy by feedback control
Authors:https://www.physicsforums.com/find/cond-mat/1/au:+Toyabe_S/0/1/0/all/0/1 [Broken], https://www.physicsforums.com/find/cond-mat/1/au:+Sagawa_T/0/1/0/all/0/1 [Broken], https://www.physicsforums.com/find/cond-mat/1/au:+Ueda_M/0/1/0/all/0/1 [Broken], https://www.physicsforums.com/find/cond-mat/1/au:+Muneyuki_E/0/1/0/all/0/1 [Broken], https://www.physicsforums.com/find/cond-mat/1/au:+Sano_M/0/1/0/all/0/1 [Broken]
(Submitted on 27 Sep 2010 (https://www.physicsforums.com/abs/1009.5287v1 [Broken]), last revised 29 Sep 2010 (this version, v2))
Abstract: In 1929, Leo Szilard invented a feedback protocol in which a hypothetical intelligence called Maxwell's demon pumps heat from an isothermal environment and transduces it to work. After an intense controversy that lasted over eighty years; it was finally clarified that the demon's role does not contradict the second law of thermodynamics, implying that we can convert information to free energy in principle. Nevertheless, experimental demonstration of this information-to-energy conversion has been elusive. Here, we demonstrate that a nonequilibrium feedback manipulation of a Brownian particle based on information about its location achieves a Szilard-type information-energy conversion. Under real-time feedback control, the particle climbs up a spiral-stairs-like potential exerted by an electric field and obtains free energy larger than the amount of work performed on it. This enables us to verify the generalized Jarzynski equality, or a new fundamental principle of "information-heat engine" which converts information to energy by feedback control.
 
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  • #3
atyy
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The commutator of position and momentum is not zero. This means the position and momentum of an arbitrary unknown state cannot be simultaneously accurately measured.
 
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  • #4
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Yes, thanks. (honestly, thanks for answering) That part I got from awesome Dr. Susskind.

And so to say a set of locations was identified over some history (just say you chose to claim that) requires that a set of choices were made specifying which one was measured. Each of those choices is a bit, which is of energy equal to the commutator (the quanta of action)?

Or no?

I just tried to engage you and Bhobba over on the long "What's surprising" thread. Sorry, these things are related to me.

If I don't make sense, that's fine, I understand. It's a problem. I can only try harder. If I do make sense but I'm wrong that's okay too. Either would be better than not knowing which it is.
 
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  • #5
atyy
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Plack's constant is the quantum of action, but it's an informal concept.
 
  • #6
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So I am clearly jumping to conclusions. At the end of Susskud there, I was thinking I finally understood the meaning and implications of Planck's constant better - as a component of evolution in time . But I guess not.

@bhobba. I don't believe you.
 
  • #7
atyy
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You could look up Reif's Fundamentals of Statistical and Thermal Physics
https://www.amazon.com/dp/1577666127/?tag=pfamazon01-20

I'm not sure I agree with Reif's presentation of statistical mechanics, but I think he does present Planck's constant as the volume of action. You can also find a description of this way of thinking in http://arxiv.org/abs/1501.04463 and http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/phase.html.

The idea that it describes a minimum "something" also shows up in the Planck length, Planck time etc in quantum gravity. However, whether this implies a fundamental discreteness is still unknown. http://backreaction.blogspot.com/2015/08/dear-dr-bee-why-do-some-people-assume.html
 
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