# Copenhagen interpretation and entropy confusion?

I don't see how the Copenhagen interpretation and the second law of thermodynamics can be compatible.
In the Copenhagen interpretation, upon losing coherence the system chooses a single definite state and all other possible states are eradicated. This seems to be losing entropy to me, as it's losing all other possible states.

Thanks

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Demystifier
Gold Member
You are right that entropy decreases when the system chooses a single definite state. However, according to the Copenhagen interpretation, this happens when a measurement is performed. This means that the previous higher-entropy state has not been measured. The second law, in Copenhagen interpretation, refers only to the measured states, not to the intermediate non-measured states. In this sense, if you ignore the unmeasured states and pay attention only to the measured ones, the second law is still valid.

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bhobba

Although I'm not sure that I'm completely understanding it.
The second law, in Copenhagen interpretation, refers only to the measured states, not to the intermediate non-measured states. In this sense, if you ignore the unmeasured states and pay attention only to the measured ones, the second law is still valid.
Why does the second law only refer to the measured states?
It seems to me, based off of my own intuition, that the only manner in which the Coperhagen intepretation could explain this is if it says that the act of measurement increases entropy more than the decrease in entropy from the loss of coherence.

Demystifier
Gold Member
Why does the second law only refer to the measured states?
Because, according to the Copenhagen interpretation, only the measured states are physically real.

Although I'm not sure that I'm completely understanding it.

Why does the second law only refer to the measured states?
It seems to me, based off of my own intuition, that the only manner in which the Coperhagen intepretation could explain this is if it says that the act of measurement increases entropy more than the decrease in entropy from the loss of coherence.
Entropy is a classical concept, related to someting called "reality", whatever that might be.
Entropy is also connected with a concept of *time* and QM does not need *time* to function.
In Copenhagen interpretatation the very act of measurement is responsible for reality to exist.
So any value or change of entropy can be determined only for observed events, eg those where wave function have collapsed.

Why does the second law only refer to the measured states?
It seems to me, based off of my own intuition, that the only manner in which the Coperhagen intepretation could explain this is if it says that the act of measurement increases entropy more than the decrease in entropy from the loss of coherence.
I agree with you on this one, measuring has its entropic cost indeed(to prevent things like a Maxwell's demon to occur), this one might be interesting for example http://www.nature.com/nphys/journal/v11/n2/full/nphys3230.html.

Quantum systems do have a well-defined entropy notion when not observed: the von Neumann-entropy. Under unitary time-evolution as usual in quantum mechanics, this one remains conserved, but measuring brings the density matrix in an eigenstate thus lowering the entropy of the measured system (but meanwhile increasing entropy for the measurer and his memory).

In fact, this whole discussion is also valid for classical measurements: if you throw a coin without looking at it, it has a shannon/gibbs entropy of ln(2), when you look at it afterwards you will know if it is head or tail and the entropy of the coin is ln(1)=0.

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ecause, according to the Copenhagen interpretation, only the measured states are physically real.
Oh. So does the Copenhagen interpretation have things popping into existence from nothing after being observed?

Oh. So does the Copenhagen interpretation have things popping into existence from nothing after being observed?
Why to assume that wave function is "nothing"?
Wave function is wave function, nothing is nothing, reality is reality and (as per Copenhagen interpretation) measurement converts wave function into something what we call reality.

Demystifier
Perhaps this is turning into a philosophical question, but if something is not an element of reality I would assume that it is "nothing".

Reality = something

Not reality = not real = nothing

The wave function before observation, at least in the manner I'm perceiving these explanations, appears to be not apart of reality but still something. Is this correct?

jambaugh
Gold Member
This is actual a very profound aspect of the measurement process. Measurement is not thermodynamically trivial, you MUST dump entropy in order to measure a system.

vanhees71, Demystifier and thephystudent
Perhaps this is turning into a philosophical question, but if something is not an element of reality I would assume that it is "nothing".

Reality = something

Not reality = not real = nothing

The wave function before observation, at least in the manner I'm perceiving these explanations, appears to be not apart of reality but still something. Is this correct?
Yes, as per Copenhagen interpretation wave function is not a part of reality, but still something.
Measurement is *forcing it* to deliver reality.

In *many worlds interpretation* wave function *is* reality, hence measurements are simply splitting it into numerous, very real histories in zillions of worlds.

Key word in this discussion is "interpretation".
Both have pros and cons, choose one up to your liking.
Actually there is quite a horrible way to find out which interpretation is true and such experiment can be run with current tech.
You would learn a result *only for your private use* if multiple worlds interpretation is true.
If Copenhagen version is true, you would die while learning nothing.

I personally stick to Copenhagen version, even if alternative seems more sexy and currently is more trendy.

Anyway QM deals with many features/"creatures" which cannot be considered real in normal circumstances, but yet they are "there" and sometimes will find way to reality.
Ever thought in this context about "virtual particles"?
Cassimir effect is an example where they are becoming very real and causing measurable effects.
Electric charges know about each other despite being at distance thanks to such "unreal" particles, beta decay can proceed on, hadrons are kept together in nuclei etc.

Sorry for drift from subject.
It is worth to remember that entropy is dealt with (usually) by classical thermodynamics.
In this sense it deals with collapsed wave functions.
One member also pointed out already that in QM entropy like function can also be investigated and also pointed up that in such situation a measurement would in all probabilities increase an overall entropy of measurer-measured system.

Demystifier
Gold Member
Perhaps this is turning into a philosophical question, but if something is not an element of reality I would assume that it is "nothing".

Reality = something

Not reality = not real = nothing
How about unicorns? Are they real? Are they something?
The wave function before observation, at least in the manner I'm perceiving these explanations, appears to be not apart of reality but still something. Is this correct?
In some interpretations, yes.

In fact I would say the wavefunction (of a pure quantum state, which has already S_vn=0 from the beginning) is just a vector in the Hilbert-space of the system, just as the measured state is. The only difference is that the measured state happens to be an eigenstate of the measurement-operator and the one before measurement not. But the one before measurement in its turn is an eigenstate of another kind of possible measurement-operator.
For example, a spin-1/2 particle may be prepared as an eigenstate of x-polarisation, which means it is a superposition of spin-up and spin-down along the z-axis. Measuring along the z-axis makes the particle collapse along the z-axis, but now it will be a superposition along the x-axis.

Similarly, a wavefunction which is a superposition of position, can be an eigenstate of momentum and after measuring position it turns into in an eigenstate of position and a superposition of momentum.

In this way, it is even unnecessary to invoke entropy increase of the measurer(unlike for classical measurements) for the second law to hold, because the wavefunction has already a zero-entropy beforehands(if you really want to, there is a way to define diagonal entropy for the quantum system as well, which will in general not remain zero even for a pure state). Or is this interpretation beyond Copenhagen?

Anyway, for many notions of entropy your knowledge about the system is important, so I can agree with Demistifier and Martin that for a second law only measurements are important, but it seems to me this is rather because of statistical mechanics reasons than reasons within QM itself.