Is information lost in wavefunction collapse?

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Main Question or Discussion Point

Having in mind the idea that "information is not lost" (referring to the black hole information paradox), is not the same rule violated in the wave function collapse? I.e. during the decoherence process information is not lost as this process of entanglement of some object with its environment is reversible (in theory), but, supposing, only one "classical" alternative exists in the end (Many worlds interpretation aside), this looks for me like a loss of information. Or in other words it looks like an absolutely non-reversible process.
 

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What information is lost...?
 
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is not the same rule violated in the wave function collapse?
Wave function collapse is an interpretation of QM. It doesn't make any predictions that are different from standard QM. So this question can't really be resolved in standard QM, since standard QM also admits no-collapse interpretations.

At some point someone might figure out how to actually test whether wave function collapse happens as a real physical process--i.e., someone might develop a different theory from standard QM that includes an actual physical wave function collapse (some attempts have already been made at this, such as the GRW stochastic collapse theory) and we'll be able to run an experiment to test the theory. But we haven't (yet) reached that point. If we ever do, then we'll be able to actually test whether collapse occurs, and if so, what it does to information.
 
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Wave function collapse is an interpretation of QM. It doesn't make any predictions that are different from standard QM.
Actually I thought that the collapse is still a part of the standard QM (which is still the Copenhagen interpretation). If not, how the "Standard QM" describes expected results of "measurement"?
 
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What information is lost...?
I am sorry I am a layman and not knowledgeable enough to answer this question. I am just relying on my intuition. In my understanding lost of information in physics is somehow equivalent to time non-reversibility. So my question may be reformulated as whether the wave collapse is considered reversible, at least "in theory".
 
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I thought that the collapse is still a part of the standard QM (which is still the Copenhagen interpretation).
No, standard QM is not the Copenhagen interpretation. Standard QM is QM without any interpretation at all: just the math and the predictions for observable results.

how the "Standard QM" describes expected results of "measurement"?
In standard QM the term "measurement" does not have a precise meaning; it's basically "whatever works for a particular experiment". One of the main reasons that there are multiple interpretations of QM is that there are multiple ways of making more precise what a "measurement" is and what is going on "behind the scenes" during a measurement.
 
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Then if I rephrase my question asking whether what is calculated in the Standard QM looks as related to reversible/irreversible process, what may be the answer?

Let's for instance consider a circularly polarized photon incident on a linear polariser. According to the Standard QM it has 50% probability to be absorbed and 50% probability to pass the polariser. For a passed photon, for instance, can we consider this process potentially reversible?
 
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Having in mind the idea that "information is not lost" (referring to the black hole information paradox), is not the same rule violated in the wave function collapse? I.e. during the decoherence process information is not lost as this process of entanglement of some object with its environment is reversible (in theory), but, supposing, only one "classical" alternative exists in the end (Many worlds interpretation aside), this looks for me like a loss of information. Or in other words it looks like an absolutely non-reversible process.
Yes, information is lost after a measurement (the new wavefunction is given by a projection of the original one, and all other eigenstate are lost) and no, this is not contraddicting any axiom of QM, in opposite to the black hole information paradox case. This is beacuse information must not be lost in the evolution of a closed quantum system, like the black hole+radiated environment, but a measurement and wave function collapse involves the interference of an external agent, that is, the observer: the system is not closed.
 
nrqed
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Yes, information is lost after a measurement (the new wavefunction is given by a projection of the original one, and all other eigenstate are lost) and no, this is not contraddicting any axiom of QM, in opposite to the black hole information paradox case. This is beacuse information must not be lost in the evolution of a closed quantum system, like the black hole+radiated environment, but a measurement and wave function collapse involves the interference of an external agent, that is, the observer: the system is not closed.
I will play the devil's advocate...

Now imagine I am inside a box with a Stern-Gerlach setup. Won't I observe a specific spin measurement, even if I am in a closed environment with the SG? I know that an interpretation is that I will exist in a superposition of states having observed the two possible results but I don't buy it. If I do observe one result, then what happened to the information?
 
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Let's for instance consider a circularly polarized photon incident on a linear polariser. According to the Standard QM it has 50% probability to be absorbed and 50% probability to pass the polariser. For a passed photon, for instance, can we consider this process potentially reversible?
Standard QM can't answer this question; both answers (reversible, not reversible) are consistent with the math and predictions of standard QM. Different interpretations will give different answers, but unless and until "different interpretations" turns into "different theories that make different predictions that can be tested by experiment", we have no way of resolving the issue.
 
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I know that an interpretation is that I will exist in a superposition of states having observed the two possible results but I don't buy it.
Then you've already answered the question: you believe in actual, physical, collapse, which is a non-reversible, non-unitary process and destroys information. But you have no way of showing by experiment that your belief is correct.
 
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I will play the devil's advocate...

Now imagine I am inside a box with a Stern-Gerlach setup. Won't I observe a specific spin measurement, even if I am in a closed environment with the SG? I know that an interpretation is that I will exist in a superposition of states having observed the two possible results but I don't buy it. If I do observe one result, then what happened to the information?
Measuring is considered an action where an external system affects the quantum one, and from this comes the projection or "collapse". Should both be quantum, either they are decoupled and so no information can be obtained from the ""observer"" (no way to see a collapse) or the observer will change sensibly beacuse of entanglement, which is not what happens in reality. You are not engangled with the spin particle.

Just to mention: I am thinking according to Copenhagen interpretation.
 
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Well, if we believe that information may be lost in the collapse (as an option), I wonder why we generally don't hear much about it. For instance, there exists an opinion (popularised by Sean Carroll currently) that the time arrow exists due to the low entropy of the Universe in the past, so that the time asymmetry may be just due to the observable growth of entropy. On the other side, nobody mentions that the wave collapse itself may be time-asymmetrical and so be somehow (hypothetically) a cause of the existence of the time arrow. If this option is not mentioned, then may be physicists do not consider collapse as irreversible at all?

Sorry for this kind of non-scientifical argument.
 
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if we believe that information may be lost in the collapse (as an option)
It's an option logically speaking, because we don't have any way of experimentally distinguishing different interpretations of QM. But that doesn't necessarily mean it's an option in the minds of physicists who work with QM. Many of them (Carroll is an example) appear to believe, for theoretical reasons, that the most fundamental dynamics of the universe is unitary and therefore no information is ever lost. This also implies that the dynamics is always, in principle, reversible (even if reversibility is not possible in practice because there are far too many degrees of freedom involved). That's why you don't see them talking about information loss as a realistic option.
 
stevendaryl
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Well, if we believe that information may be lost in the collapse (as an option), I wonder why we generally don't hear much about it.
Well, in a measurement, there are (at least) two systems involved: the system being measured, and the measuring device/observer/environment/rest-of-the-universe. Since there is an interaction between these two systems, you wouldn't expect information to be conserved when you just look at one of the two. The other system is usually not studied with the same rigor (since it's basically impractical to treat a macroscopic system completely quantum-mechanically). So there is no way to rigorously demonstrate that information is lost. It's lost for all practical purposes, but maybe that's due to our treating the measurement device non-rigorously. I am not claiming that that solves the problem you bring up, but I think it explains why it's not as pressing a problem as the black hole information loss problem.
 
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Many of them (Carroll is an example) appear to believe, for theoretical reasons, that the most fundamental dynamics of the universe is unitary
Carroll personally support MWI interpretation as far as I know. Are there any other (mainstream) options/interpretation except for MWI to expect that the dynamics is always unitary and still have a wave function collapse or whatever else which looks like a "measurement" which "selects" one component from a superposition? That is, Carroll and MWI aside, why others do not consider this option of the measurement irreversibility seriously?
 
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Carroll personally support MWI interpretation as far as I know.
So do the other physicists I referred to.

Carroll and MWI aside, why others do not consider this option of the measurement irreversibility seriously?
You can't put "MWI aside" because MWI is a main reason most physicists don't take the irreversibility/information loss option seriously. More precisely, most physicists find unitarity to be a very strong theoretical requirement, and treating unitarity as a universal principle of dynamics in QM implies the MWI.
 
atyy
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So do the other physicists I referred to.
Carroll does not teach MWI as correct. Who are the other physicists?

All the major textbooks use Copenhagen. Standard QM is the Copenhagen interpretation.
 
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Carroll does not teach MWI as correct.
He certainly seems to think it's "probably correct":

http://www.preposterousuniverse.com/blog/2014/06/30/why-the-many-worlds-formulation-of-quantum-mechanics-is-probably-correct/

Who are the other physicists?
Any physicist who takes the "information is not lost" side in the black hole information loss question. Which, as far as I can tell, is most physicists.

All the major textbooks use Copenhagen. Standard QM is the Copenhagen interpretation.
Let's please not get involved in an argument over what "Copenhagen interpretation" means. When I say "standard QM" I mean just the machinery that makes predictions, with no interpretation whatsoever over and above the predictions.
 
atyy
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Well, that is not the same as "correct", and shows that he still would not teach it as standard QM.

Any physicist who takes the "information is not lost" side in the black hole information loss question. Which, as far as I can tell, is most physicists.
Yes, but the reason is not that they support MWI. If that were correct, one would not be able to formulate the black hole information paradox in Copenhagen. However, the black hole information paradox can be formulated in Copenhagen.

Let's please not get involved in an argument over what "Copenhagen interpretation" means. When I say "standard QM" I mean just the machinery that makes predictions, with no interpretation whatsoever over and above the predictions.
I am taking Copenhagen to mean standard QM, as I believe the OP is also. What I am saying is:

1. MWI is not standard QM.
2. Standard QM does contain a postulate of non-unitary time evolution, which can be called state reduction or collapse.
3. The black hole information paradox is obtained in standard QM with state reduction, and it is a paradox because it appears that unitarity is lost before a measurement is made.

Here is an explanation of the information paradox showing why the mixed state in black hole evaporation is different from the mixed state in the usual thermal radiation from hot everday objects: http://qpt.physics.harvard.edu/simons/Polchinski.pdf
 
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Stephen Tashi
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I'm curious why knowing more about something would be called a "loss" of information.

If a experiment is performed involving a probabilistic phenomena and the experimenter learns the outcome, why isn't this a gain in information?
 
stevendaryl
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I'm curious why knowing more about something would be called a "loss" of information.

If a experiment is performed involving a probabilistic phenomena and the experimenter learns the outcome, why isn't this a gain in information?
But if you set up an electron in the spin state ##\alpha |u\rangle + \beta |d\rangle##, where ##|u\rangle## and ##|d\rangle## are spin-up and spin-down relative to the z-axis, respectively, there is a lot of information in those coefficients ##\alpha## and ##\beta##. When you measure the spin in the z-direction later, you get only a single bit of information. So it's a net loss of information.
 
Stephen Tashi
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there is a lot of information in those coefficients ##\alpha## and ##\beta##.
What definition of "information" is being used to make that statement?
 
stevendaryl
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What definition of "information" is being used to make that statement?
Well, you can quantify information in terms of the number of bits necessary to specify a situation, but I was just using it in the informal sense. I have information about something if I can deduce something about it.

In deterministic classical physics, information is never lost, because complete knowledge of the state of the universe now allows me to retrodict the state of the universe yesterday. This theoretical reversibility doesn't do a whole lot of good, practically, because there is no way to know the current state of the universe in enough detail to retrodict everything about the past. But theoretically, there is no limits to retrodiction.

But if an electron is initially in a superposition of two states, and then I perform a measurement, there is (as far as anybody knows) no way, even theoretically, to retrodict what the initial superposition was. That information is gone forever. Or at least, QM doesn't specify where it has gone.
 

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