# Wavefunction collapse => increase in entropy?

## Main Question or Discussion Point

Wavefunction collapse ==> increase in entropy??

I just read an article in Scientific American by Sean Carroll, called something like Does Time Run Backward in Other Universes. In it, he says that the reason wavefunctions only collapse and never un-collapse is because collapsing represents an increase in entropy, and therefore by the 2nd law of thermodynamics, a wavefunction can never un-collapse. This is strange to me for two reasons:

(1) Why does the 2nd law even apply, unless there are "hidden variables"? If the wavefunction encodes all possible information that can be known about the system, then there is no microstate to have more possible configurations in a given macrostate.

(2) How can the collapse of a wavefunction cause an increase in entropy, anyway? It seems to me that, depending at how you look at it, the entropy either stays the same (since we are simply going from one state to another, maybe the first was a superposition of basis vectors but maybe we can change basis to correct that) or even decrease (since we are losing information on how the state was prepared).

Note: this is not the only thing I found strange in the article :)

Any help with my understanding would be much appreciated.

Related Quantum Physics News on Phys.org
Click on Time's Arrow FAQ's at the lower left, and this is one of the questions:

Doesn’t quantum mechanics have an arrow of time?
According to the standard interpretation of quantum mechanics, the measurement of a system causes its wave function to “collapse,” a process that is asymmetric in time. But the reason wave functions collapse yet never uncollapse is the same reason that eggs break yet never unbreak—namely, because collapse increases the entropy of the universe. Quantum mechanics does not help explain why the entropy was low in the first place

Related is the difference between a pure density matrix and a mixed density matrix. Going from the former to the latter is part of collapse, if you will, and represents going from a closed system to an open one.

You're referring to somewhere within a "[URL [Broken] page SciAm article by David Layzer
[/URL]

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Who is? I'm referring to the third question of:

http://www.sciam.com/article.cfm?id=times-arrow-faqs"

which is a supplement to the Carroll article:

http://www.sciam.com/article.cfm?id=the-cosmic-origins-of-times-arrow"

But regardless of where it came from, can anybody help me understand it?

I guess, to me, a wavefunction *can* "un-collapse", it just depends on what basis you're using. For example, I can have an eigenstate of position, which is not an eigenstate of momentum. If I measure its momentum, the momentum wavefunction collapses, but the position wavefunction "un-collapses", no?

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OK, so finally, this is the quote you are talking about:

"Doesn’t quantum mechanics have an arrow of time?

"According to the standard interpretation of quantum mechanics, the measurement of a system causes its wave function to “collapse,” a process that is asymmetric in time. But the reason wave functions collapse yet never uncollapse is the same reason that eggs break yet never unbreak—namely, because collapse increases the entropy of the universe. Quantum mechanics does not help explain why the entropy was low in the first place."

I just read an article in Scientific American by Sean Carroll, called something like Does Time Run Backward in Other Universes. In it, he says that the reason wavefunctions only collapse and never un-collapse is because collapsing represents an increase in entropy, and therefore by the 2nd law of thermodynamics, a wavefunction can never un-collapse. This is strange to me for two reasons:

This is currently being discussed in another QM thread.

(1) Why does the 2nd law even apply, unless there are "hidden variables"? If the wavefunction encodes all possible information that can be known about the system, then there is no microstate to have more possible configurations in a given macrostate.

(2) How can the collapse of a wavefunction cause an increase in entropy, anyway? It seems to me that, depending at how you look at it, the entropy either stays the same (since we are simply going from one state to another, maybe the first was a superposition of basis vectors but maybe we can change basis to correct that) or even decrease (since we are losing information on how the state was prepared).
In assuming a process of collapse, the wavefunction is going to become entangled with another system. With the other system in a mixed state, it seems that the energy enytropy must unavoidably increase, nevermind that it become entangled, simply that it has interacted.

On the face of it, it seemed odd to me to. They're talking about S, but you're talking about information entropy. I don't know how the two relate.

dkv
Wave function can uncollapse at the atomic level. I dont think that there is any reason for this to not happen. It is just that the chance of this happening is small.

What if the observer dies immediately after making the measurement?
If the observer and observed gets erased from the memory of Universe then there is no reason to believe that Observation ever actually took place.Therefore in such circumstances the Wave function can uncollapse.

Laws of Thermodynamics

Okay let me see if I can help from what I learned in my AP Physics course. First of all, there is nothing in either electromagnetism nor in quantum mechanics that says you "can't" reverse the flow of time. However there is something in the Laws of Thermodynamics that says you "can't" reverse the flow of time. Specifically, the second law, stating that heat on its own can only pass from hot to cold.....never the other way around. As heat enters a system, it basically causes an increase in "entropy" (a.k.a. chaos or disorder). Since things can only go in one direction (hot to cold), this sets the direction for the flow of time. Basically, time flows in the direction of increasing entropy.

This is why you never see a swimming pool suddenly freeze on a hot summer day releasing heat into the already hot summer air and suddenly turning the pool water to ice. This is also why people have to constantly keep cleaning their houses, because no matter what, your home gets more and more disorganized everyday and we have to spend a good many hours to reverse this unstoppable trend. Increasing entropy however, is inevitable.

dkv
I thought there is a distinction between classical physics and quantum physics...

I just read an article in Scientific American by Sean Carroll, called something like Does Time Run Backward in Other Universes. In it, he says that the reason wavefunctions only collapse and never un-collapse is because collapsing represents an increase in entropy, and therefore by the 2nd law of thermodynamics, a wavefunction can never un-collapse.
It looks like an argument used in quantum decoherence. The argument, in this frame, to somewhat explain collapsing of wave functions is that there is, when a measure is done, interaction with a very very big system called "environment" which has many degrees of freedom (or if you prefer whose space of states has a dimension much more greater than the quantum system under study). Using a heuristic argument similar to the statistic interpretation of the Boltzmann H theorem one finds that the quantum system must be (almost everywhere) entangled with that "environment". Depending on the initial condition (just before the interaction wih the big system) a state will be selected and probability of measuring the other states will decrease very rapidly with a power law ; this is the collapse of the wave function.

Note that there is no direct link (just analogy though) with the second law of thermodynamics.

Demystifier
(1) Why does the 2nd law even apply, unless there are "hidden variables"? If the wavefunction encodes all possible information that can be known about the system, then there is no microstate to have more possible configurations in a given macrostate.
Let us assume that there are no hidden variables. Then, as you say, the wave function encodes all possible information about the system. However, a typical system (including not only the measured particle but also the measuring apparatus) contains a very large number of particles. In practice, you cannot measure the state of all these particles. Instead, a given state of the measured particle can be realized in many different ways corresponding to different states of all other unmeasured particles. This is actually known as the phenomenon of decoherence and can be understood even without the (interpretationally problematic) notion of wave-function collapse.

Let's be a little more concrete, here. Say we're considering a single particle with momentum eigenvalues p1, p2, ...

Now, Carroll is talking about wavefunction collapse after a measurement, which means that the particle is interacting with another system. So, when he says that a wavefunction never un-collapses after a measurement, he seems to be saying that there is no way to interact with the particle that will send it from a pure eigenstate into a mixed state. But, of course there is. If it is in the eigenstate with momentum p1, all we have to do is measure its position. That will send it into a superposition of p1, p2, ... eigenstates, effectively un-collapsing the momentum wavefunction.

There is a second question, which is "does the particle ever un-collapse without interaction with another system?" The answer is, only rarely (as dkv mentions), and even then there is interaction with a field. But, so what, because it only rarely will *collapse* in isolation, either! So, there is no asymmetry there.

To sum up my current position (subject to change, as always): I think that wavefunctions collapse just as often as they un-collapse (it all depends on what basis you're working in--the one you're measuring in is not special!). I also think that the application of the 2nd law is inappropriate to this situation.

Demystifier: I agree, if we are talking about a many-particle system about which we have limited knowledge, then yes, the 2nd law applies. My assumption was that Carroll was talking about the collapse of a single-particle wavefunction. If not, then he left that case out :)

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I guess, to me, a wavefunction *can* "un-collapse", it just depends on what basis you're using. For example, I can have an eigenstate of position, which is not an eigenstate of momentum. If I measure its momentum, the momentum wavefunction collapses, but the position wavefunction "un-collapses", no?
I think collapse is related to which observation you are doing. So, the choice of basis is related at this observation (uniquely, if observable doesn't degenerate), and wavefunction, to respect this basis, collapses EVER.