A simple QM experiment analysis question

[Mentz114]

In a thermodynamic ensemble, counting microstates is a valid procedure, but it's not meaningful in single quantum events like when a photon encounters a beam splitter.

The overlap between QM and thermodynamics seems to be important only when there's entanglement. See

http://arxiv.org/abs/0905.2562

H.Casini, M.Huerta

(Submitted on 15 May 2009 (v1), last revised 7 Oct 2009 (this version, v2))
Abstract: In this review we first introduce the general methods to calculate the
 entanglement entropy for free fields, within the Euclidean and the real time formalisms.
 Then we describe the particular examples which have been worked out explicitly in two,
 three and more dimensions.

 

[dmtr]

In a thermodynamic ensemble, counting microstates is a valid procedure, but it's not meaningful in single quantum events like when a photon encounters a beam splitter.

Unfortunately we don't have a single quantum event of a photon encountering a beam splitter. We have a single photon encountering a beam splitter and causing a lot of entropy in the environment (via the interactions with the photomultipliers, heater, etc).

The whole point of this thought experiment is to illustrate how the probabilities on the outcome of a single quantum event can be influenced by the future entropy considerations.

The fact that they are influenced is trivial. Simply consider the setup with the quantum harmonic oscillators from my message "Oct21-09 08:10 PM".

The overlap between QM and thermodynamics seems to be important only when there's entanglement. See http://arxiv.org/abs/0905.2562

Correct me if I wrong, but it sounds like that you are thinking that the entanglement is a small and unimportant factor. Some "spooky action at the distance". That disappear almost instantly in any noticeable environment temperature. Yes. Clean "EPR-paradox" entanglement in fact disappears very fast. But only because of the other entanglements with the environment. Decoherence is entanglement with the environment. See a Wikipedia article on the decoherence, or any other generic introduction on the subject i.e.: http://arxiv.org/abs/quant-ph/9803052. Theoretically the entangled states can stay at any temperatures at any distance for an unlimited period of time. This is trivial from the unitarity principle in the QM. There have been experiments (reported in the Nature/Nature Physics, I can locate you the articles), directly confirming that the entangled states can stay at large distances (miles) over the large periods of time.

So yes. I would very much agree that "the overlap between QM and thermodynamics seems to be important only when there's entanglement". Only I would say that the entanglement is very very important. And if the Second Law is simply the effect caused by the Decoherence with the time flow, the entanglement would be the only important factor in the thermodynamics.

-- Dmtr

 

[Mentz114]

The whole point of this thought experiment is to illustrate how the probabilities on the outcome of a single quantum event can be influenced by the future entropy considerations.

I'm unconvinced. A thought experiment proves nothing.

 

[dmtr]

I'm unconvinced. A thought experiment proves nothing.

Yep. Exactly my thinking. Proves nothing. A thought experiment is only useful to illuminate some aspects of a theory or hypothesis.

Unfortunately I can only do a very limited testing (with the equipment I have access to). Most likely, what I'll be able to do, is to place some boundaries on the S values, not to see the effect itself. I'm trying to realize the experiment on a very simple setup made out of a 10⁶ bits/sec optical QRNG device. In the current setup I have ~3 µW 'extra' free energy spending per single photon. (That would be roughly the equivalent if you shine a laser pointer on the beam splitter and drain 50 GigaWats extra on one path.)

-- Dmtr