I Is information lost in wavefunction collapse?

[Dr. Courtney]

All the major textbooks use Copenhagen. Standard QM is the Copenhagen interpretation.

Agreed, but standard here just means a standard presentation in Physics education.

Yes, except for Copenhagen or whatever one wishes to call what is in the textbooks.

Sure, but the presence in textbooks is a stronger case for a consensus regarding what to teach students, it may not represent a consensus regarding a preference for truth or correctness.

It's an imperfect analogy, but one might argue that Newtonian mechanics is the "right" version of mechanics, because it is found in many more introductory textbooks (and therefore more textbooks, since most texts are introductory.) However, it is completely equivalent to Lagrangian mechanics and Hamiltonian mechanics. The consensus to teach Newtonian mechanics first (which I believe is correct) is based more on its usefulness with the math skills of most students in these classes rather than some sense that it is more correct than Lagrangian or Hamiltonian.

I would not make any more from the lack of alternate QM interpretations in the textbooks than I'd make from the piles and piles of Physics texts that ignore Lagrangian and Hamiltonian mechanics.

 

[Demystifier]

Thanks. So that really is something new.

So the idea is that you create an EPR pair---an electron and positron with entangled anticorrelated spins. You throw the positron into a black hole, which then vanishes in a puff of Hawking radiation. Now, you still have the electron, but the electron by itself was not in a pure state, it was in an entangled state. So how do you describe it now that its entangled partner no longer exists? A mixed state.

Now that I say it out loud, it occurs to me that in the case of spin entanglement, you might still have the electron entangled, rather than in mixed state. When the positron falls into the black hole, it imparts a tiny bit of angular moment to the black hole. When the black hole evaporates, that angular momentum is distributed among the particles produced by the Hawking radiation. So in that particular case, it seems that the electron's spin would be entangled with the resulting Hawking radiation.

That's correct.

So I think to really illustrate the information loss, you would need some property of a pair of particles that is nonconserved?

No. Instead of angular momentum, consider e.g. lepton number which is supposed to be conserved. If you have electron with positive lepton number outside and positron with negative lepton number inside, the total lepton number is zero. However, the lepton number cannot be seen in the external properties of geometry of the black hole (this is the so called no-hair theorem). When the black hole finally evaporates, the negative lepton number in the inside disappears. Hence the black hole evaporation violates the lepton number conservation, which otherwise is conserved.

 

[stevendaryl]

No. Instead of angular momentum, consider e.g. lepton number which is supposed to be conserved

I would say that quantities such as lepton number or baryon number are not actually conserved. It just happens to be that there are no interactions that cause it to change.

I of course didn't understand it, but t'Hooft gave an argument a long time ago to the effect that baryon number is not conserved in the standard model. So proton decay, for example, is a prediction of the standard model, even though no finite number of Feynman diagrams can show it. It's a nonperturbative effect. I'm pretty sure that he didn't consider black holes. (This prediction does not contradict the experimental evidence that protons don't decay, because t'Hooft's mechanism is way too weak to produce a detectable number of proton decay events. It's many orders of magnitude smaller than the number of decays predicted by various GUT theories.)

 

[stevendaryl]

I would say that quantities such as lepton number or baryon number are not actually conserved. It just happens to be that there are no interactions that cause it to change.

I of course didn't understand it, but t'Hooft gave an argument a long time ago to the effect that baryon number is not conserved in the standard model. So proton decay, for example, is a prediction of the standard model, even though no finite number of Feynman diagrams can show it. It's a nonperturbative effect. I'm pretty sure that he didn't consider black holes. (This prediction does not contradict the experimental evidence that protons don't decay, because t'Hooft's mechanism is way too weak to produce a detectable number of proton decay events. It's many orders of magnitude smaller than the number of decays predicted by various GUT theories.)

It is stated here (http://inspirehep.net/record/16152/files/v16-n1-p23.pdf) that decays by t'Hooft's mechanism are $10^{-77}$ less common than predicted decays by GUT theories.

 

[Demystifier]

I would say that quantities such as lepton number or baryon number are not actually conserved. It just happens to be that there are no interactions that cause it to change.

I of course didn't understand it, but t'Hooft gave an argument a long time ago to the effect that baryon number is not conserved in the standard model. So proton decay, for example, is a prediction of the standard model, even though no finite number of Feynman diagrams can show it. It's a nonperturbative effect. I'm pretty sure that he didn't consider black holes. (This prediction does not contradict the experimental evidence that protons don't decay, because t'Hooft's mechanism is way too weak to produce a detectable number of proton decay events. It's many orders of magnitude smaller than the number of decays predicted by various GUT theories.)

Even in GUT theories one has a conservation of a difference between baryon and lepton number B-L, but black hole evaporation violates it too.

 

[atyy]

I agree with the point you and @Demystifier make that these two things (collapse vs. BH information paradox) are different. Are you saying that that, in itself, is a sufficient answer to the question in the OP? If so, I would like the OP to say whether he agrees with that.

Yes, I do mean that those two things are sufficient for answering the OP (or at least for correcting the use of the black hole information paradox as motivation for the question in the OP). There is no need to bring in interpretations of QM.

There is the additional question of whether information is lost in collapse. This needs to be defined a bit better (eg. as stevendaryl has discussed at various points in this thread, but one can use standard QM, which includes collapse).

 

[atyy]

But in "standard QM", the OP's question can't be answered, because standard QM allows both kinds of interpretations: interpretations in which information is not lost in "wave function collapse" (because "collapse" is not a real process but just a calculational rule, no real non-unitary processes ever happen--for example, the MWI), and interpretations in which information is lost in collapse, because collapse is a real, non-unitary process.

stevendaryl's post #25 frames and answers this question in a way that is independent of the subtleties you mentioned. (As a side point, it is not really common to take collapse to be physical in Copenhagen. Physical collapse usually refers to alternative theories like GRW or CSL).

 

[atyy]

Sure, but the presence in textbooks is a stronger case for a consensus regarding what to teach students, it may not represent a consensus regarding a preference for truth or correctness.

It's an imperfect analogy, but one might argue that Newtonian mechanics is the "right" version of mechanics, because it is found in many more introductory textbooks (and therefore more textbooks, since most texts are introductory.) However, it is completely equivalent to Lagrangian mechanics and Hamiltonian mechanics. The consensus to teach Newtonian mechanics first (which I believe is correct) is based more on its usefulness with the math skills of most students in these classes rather than some sense that it is more correct than Lagrangian or Hamiltonian.

I would not make any more from the lack of alternate QM interpretations in the textbooks than I'd make from the piles and piles of Physics texts that ignore Lagrangian and Hamiltonian mechanics.

Yes, but the difference is that there are many advanced textbooks teaching the Lagrangain and Hamiltonian formalisms and their equivalence to Newtonian mechanics, and there is consensus in the community about these issues.

In the case of MWI, there are no advanced textbooks stating that MWI is standard QM - Cohen-Tannoudji, Sakurai and Weinberg are senior undergraduate level textboks, about the same level at which the Lagrangian and Hamiltonian formalisms are usually discussed. In fact, the research level discussions state problems MWI, even by people who are proponents of the approach. Stating unresolved physics as if it is standard is bad for beginners, because it is misleading false advertising, Stating unresolved physics as if it is standard is also bad for people who support the approach, because it means that we should stop research into these open questions, which ultimately means that the questions will never pass from being unresolved to resolved.

 

[PeterDonis]

it is not really common to take collapse to be physical in Copenhagen

If that is the case, then I don't think it's correct to describe the standard QM collapse as non-unitary.

 

[PeterDonis]

stevendaryl's post #25 frames and answers this question

No, it doesn't. The last sentence of that post highlights the issue: standard QM does not specify where the information has gone. But that doesn't mean the information is lost, or that it's not lost. It just means standard QM can't tell you whether it's lost or not.

 

[Mentz114]

No, it doesn't. The last sentence of that post highlights the issue: standard QM does not specify where the information has gone. But that doesn't mean the information is lost, or that it's not lost. It just means standard QM can't tell you whether it's lost or not.

Is this the same as saying the there is no observable (self-adjoint operator) in standard QM that can be attributed to that which has/has not been lost ?

 

[atyy]

If that is the case, then I don't think it's correct to describe the standard QM collapse as non-unitary.

No, it doesn't. The last sentence of that post highlights the issue: standard QM does not specify where the information has gone. But that doesn't mean the information is lost, or that it's not lost. It just means standard QM can't tell you whether it's lost or not.

I understand where you are coming from, and the more general sense of "information" in plain English. However, "information loss" in the black hole information paradox is one of those physics jargon terms that can be misleading for the general public, like "work" in Newtonian Mechanics or "observer" in special relativity.

Th black hole information paradox is that reasonable postulates lead to a loss of unitarity incompatible with standard QM. The most common approaches (AdS/CFT) to solving the paradox have to do with quantum gravity, and nothing to do with the measurement problem, and aim to restore unitarity in the framework of standard QM.

 

[bhobba]

Standard QM has collapse - see the texts by Dirac, Landau and Lifshitz, Cohen-Tannoudji et al, Weinberg, Sakurai, Griffiths.

For many years THE standard text on QM was Dirac which I have a copy of. It has a few issues but not related to this. What standard QM is can be found on page 45 under the heading of - The General Physical Interpretation. His assumption is given an observable O and a state x the average of making the observation associated with O, E(O) is E(O) = <x|O|x> .

Now I did not go through the whole book to see if he uses the word collapse anywhere, but it is not in his general physical Interpretation. And the above is all you need to solve problems.

It is often thought Dirac was in the Copenhagen School of Neil's Bohr - but in actual fact he wasn't - although its hard to find evidence of it because for him math was the thing - interpretations were not much of an issue - and he was notoriously a man of few words. That said, from what he did write, he had a very subtle view of QM and physics in general - here he is arguing with Heisenberg about one of the tenants of Copenhagen - that the state is a complete description of the system and it has reached it's final form:
http://philsci-archive.pitt.edu/1614/1/Open_or_Closed-preprint.pdf
'Dirac criticized the Copenhagen theorists for claiming that quantum theory had attained its final form. In a 1929 letter to Bohr he writes 'I am afraid I do not completely agree with your views. Although I believe that quantum mechanics has its limitations and will ultimately be replaced by something better, . . . I cannot see any reason for thinking that quantum mechanics has already reached the limit of its development. I think it will undergo a number of small changes.'

Thanks
Bill

 

[atyy]

For many years THE standard text on QM was Dirac which I have a copy of. It has a few issues but not related to this. What standard QM is can be found on page 45 under the heading of - The General Physical Interpretation. His assumption is given an observable O and a state x the average of making the observation associated with O, E(O) is E(O) = <x|O|x> .

Now I did not go through the whole book to see if he uses the word collapse anywhere, but it is not in his general physical Interpretation. And the above is all you need to solve problems.

It is often thought Dirac was in the Copenhagen School of Neil's Bohr - but in actual fact he wasn't - although its hard to find evidence of it because for him math was the thing - interpretations were not much of an issue - and he was notoriously a man of few words. That said, from what he did write, he had a very subtle view of QM and physics in general - here he is arguing with Heisenberg about one of the tenants of Copenhagen - that the state is a complete description of the system and it has reached it's final form:
http://philsci-archive.pitt.edu/1614/1/Open_or_Closed-preprint.pdf
'Dirac criticized the Copenhagen theorists for claiming that quantum theory had attained its final form. In a 1929 letter to Bohr he writes 'I am afraid I do not completely agree with your views. Although I believe that quantum mechanics has its limitations and will ultimately be replaced by something better, . . . I cannot see any reason for thinking that quantum mechanics has already reached the limit of its development. I think it will undergo a number of small changes.'

Thanks
Bill

Dirac has collapse.

 

[bhobba]

Dirac has collapse.

I could be wrong - but I could not find it in his text - can you give the page number?

Thanks
Bill

 

[atyy]

I could be wrong - but I could not find it in his text - can you give the page number?

Thanks
Bill

In the 4th edition, it is on p36.

 

[bhobba]

In the 4th edition, it is on p36.

No - he says - the measurement causes the system to jump to an eigenstate after the measurement. And he also uses the physical continuity argument I have mentioned many times to derive it must jump ie be in that sate immediately AFTER the measurement. Nobody argues it is in the eigenstate immediately after the measurement - its the specific collapse postulate we are talking about. Collapse has a stronger meaning than this - it means unitary evolution is broken and it discontinuously changes the state - see page 330-331 of Schlosshauer's textbook I am always mentioning - Decoherence and the Quantum to Classical Transition. The fact is we do not know if it is discontinuous or not - we only know it is different AFTER the measurement. Whats going on during the measurement is unknown - it is an interpretation to say it's discontinuous.

In fact decoherence suggests it is not discontinuous - but we really do not know. MW would indeed say it is not discontinuous. In collapse theories like GRW is does indeed happen spontaneously and presumably discontinuously.

Thanks
Bill

 

[stevendaryl]

No - he says - the measurement causes the system to jump to an eigenstate after the measurement.

Those words are ambiguous---they could be given a "disturbance" interpretation, which doesn't seem like collapse:

• If you try to measure the energy of a bound electron, the interaction between measuring device and electron will result in the electron being forced into an energy eigenstate.

However, if you have an entangled pair of particles (as with EPR), then measuring a property of one particle can seemingly cause the other particle to collapse into an eigenstate of whatever is being measured. The collapse of the distant particle can't be given a disturbance interpretation (without FTL influences).

So I don't think that Dirac's nuanced distinction between "collapse" and "measurement causing the system to jump to an eigenstate" really helps. If the latter is true, it sure seems to me that the former is, also.

 

[atyy]

No - he says - the measurement causes the system to jump to an eigenstate after the measurement. And he also uses the physical continuity argument I have mentioned many times to derive it must jump ie be in that sate immediately AFTER the measurement. Nobody argues it is in the eigenstate immediately after the measurement - its the specific collapse postulate we are talking about. Collapse has a stronger meaning than this - it means unitary evolution is broken and it discontinuously changes the state - see page 330-331 of Schlosshauer's textbook I am always mentioning - Decoherence and the Quantum to Classical Transition. The fact is we do not know if it is discontinuous or not - we only know it is different AFTER the measurement. Whats going on during the measurement is unknown - it is an interpretation to say it's discontinuous.

In fact decoherence suggests it is not discontinuous - but we really do not know. MW would indeed say it is not discontinuous. In collapse theories like GRW is does indeed happen spontaneously and presumably discontinuously.

Thanks
Bill

I disagree. Dirac does mean collapse.

As if there were any ambiguity, p108 further shows that this is what he meant.

 

[bhobba]

Those words are ambiguous---they could be given a "disturbance" interpretation, which doesn't seem like collapse

You are falling for the same trap. What Dirac calls a jump is a simple deduction of the Born Rule. Collapse says more. In EPR we know its a correlation and like any 100% correlation as soon as you know one you know the other. In the classical envelope analogy does the other envelope suddenly collapse - of course not. The only difference in QM is it has different statistical properties - but something may or may not have discontinuously changed - we simply do not know. To be specific entanglement is broken - does that happen instantaneously - its the same as any observation - we do not know.

Thanks
Bill

 

[atyy]

You are falling for the same trap. What Dirac calls a jump is a simple deduction of the Born Rule. Collapse says more. In EPR we know its a correlation and like any 100% correlation as soon as you know one you know the other. In the classical envelope analogy does the other envelope suddenly collapse - of course not. The only difference in QM is it has different statistical properties - but something may or may not have discontinuously changed - we simply do not know. To be specific entanglement is broken - does that happen instantaneously - its the same as any observation - we do not know.

Thanks
Bill

In the classical case, there is a sudden "collapse" representing a change in your knowledge. So it is not true that there is no discontinuity in the classical case.

 

[bhobba]

In the classical case, there is a sudden "collapse" representing a change in your knowledge. So it is not true that there is no discontinuity in the classical case.

The issue is not that your knowledge changes - if course it does. The issue is it discontinuous. Imagine opening the envelope - you don't open it and notice its color instantaneously and discontinuously - it takes time to register for example. This is the precise issue - collapse says it happens non unitaryily and discontinuously - we don't know it does that - it may or may not.

Thanks
Bill

 

[stevendaryl]

You are falling for the same trap. What Dirac calls a jump is a simple deduction of the Born Rule. Collapse says more.

I don't see that it does say more.

[edit: added]

If you say that AFTER a measurement, a system is in such-and-such a state, then it seems to me that are two possibilities:

1. It was in that state before the measurement, and the measurement just informed you of this fact.
2. The measurement process put it into that state.

Number 1. is impossible by Bell's theorem. Number 2 is collapse.

MWI actually rejects the premise: The fact that I measure the system to be in a state doesn't imply that it is in that state (or at least not exclusively---in some other "world", it's in a different state).

In EPR we know its a correlation and like any 100% correlation as soon as you know one you know the other. In the classical envelope analogy does the other envelope suddenly collapse - of course not.

Yes, and Bell's proof shows that EPR correlations are nothing like that.

 

[bhobba]

Yes, and Bell's proof shows that EPR correlations are nothing like that.

It says if you want it like classical correlations you need non locality - it says nothing about if entanglement is broken instantaneously or not.

Thanks
Bill

 

[stevendaryl]

It says if you want it like classical correlations you need non locality - it says nothing about if entanglement is broken instantaneously or not.

I don't know what it means for entanglement to be broken instantaneously or not instantaneously.

 

[bhobba]

I don't know what it means for entanglement to be broken instantaneously or not instantaneously.

When you observe one part of an entangled pair at the end of the observation we know what we observed and the entanglement with what it is entangled with is broken. But what is going on during the observation to that entanglement - does it change instantaneously and discontinuously or is something else going on? We do not know.

Thanks
Bill

 

[stevendaryl]

When you observe one part of an entangled pair at the end of the observation we know what we observed and the entanglement with what it is entangled with is broken. But what is going on during the observation to that entanglement - does it change instantaneously and discontinuously or is something else going on? We do not know.

I don't quite understand what it is that you're saying might be changing continuously. Let's make it concrete: We have a source of anti-correlated spin-1/2 pairs. We have two distant experimenters, Alice and Bob. Alice measures spin-up along the z-axis at time $t$. Then she knows instantly the following fact about Bob: "If Bob measures the spin of his particle along the z-axis, he will measure spin-down." I don't see how continuous versus noncontinuous evolution is relevant. There definitely isn't a time window in which Bob might get a different answer, so the breaking of the entanglement doesn't propagate slowly in that sense.

 

[bhobba]

As if there were any ambiguity, p108 further shows that this is what he meant.

There is no ambiguity. He says the state changes unpredictably. Nobody disagrees with that. Its the other baggage associated with collapse that is the issue.

MW proves it does not have to happen using non-unitary changes and instantaneously, nor does the formalism require it to be. It may be like that or not - we do not know. It may be like GRW - again we do not know. The formalism is silent on it.

Thanks
Bill

 

[bhobba]

I don't quite understand what it is that you're saying might be changing continuously. Let's make it concrete: We have a source of anti-correlated spin-1/2 pairs. We have two distant experimenters, Alice and Bob. Alice measures spin-up along the z-axis at time $t$. Then she knows instantly the following fact about Bob: "If Bob measures the spin of his particle along the z-axis, he will measure spin-down." I don't see how continuous versus noncontinuous evolution is relevant. There definitely isn't a time window in which Bob might get a different answer, so the breaking of the entanglement doesn't propagate slowly in that sense.

Does the measuring process of Alice happen instantaneously? Or is it like decoherence would suggest - continuous but in a very short time. During that time what happens to the entanglement with the other particle?

Thanks
Bill

 

[stevendaryl]

Does the measuring process of Alice happen instantaneously? Or is it like decoherence would suggest - continuous but in a very short time. During that time what happens to the entanglement with the other particle?

Let's suppose that Alice's measurement starts at time $t_1$ and finishes at time $t_2$, and let's suppose that Bob's starts at $t_3$ and finishes at $t_4$. If Bob is far enough away from Alice so that there is no possibility of a light-speed or slower signal propagating from Alice at time $t_1$ to Bob at time $t_4$, then I don't see what difference it makes how long Alice's measurement took.

 

[bhobba]

Let's suppose that Alice's measurement starts at time $t_1$ and finishes at time $t_2$, and let's suppose that Bob's starts at $t_3$ and finishes at $t_4$. If Bob is far enough away from Alice so that there is no possibility of a light-speed or slower signal propagating from Alice at time $t_1$ to Bob at time $t_4$, then I don't see what difference it makes how long Alice's measurement took.

Well let's be more precise. Suppose via slow transport Bob and Alice have syced clocks. And they both at exactly the same time observe the system (remember until entanglement is broken it is a single system). What happens then? That may be interesting to both analyse and do. I wonder if @DrChinese knows anything about that or has some papers to post.

My guess is its an entirely different setup - the observable will be a compound observable of observing both 'parts' of the entangled system which is different than what goes on in EPR.

Thanks
Bil

 

[stevendaryl]

Well let's be more precise. Suppose via slow transport Bob and Alice have syced clocks. And they both at exactly the same time observe the system (remember until entanglement is broken it is a single system). What happens then? That may be interesting to both analyse and do. I wonder if @DrChinese knows anything about that or has some papers to post.

I don't know what tests have been done along those lines, but I'm willing to bet that it doesn't make any difference whether Bob's measurement is at the same time as Alice's, or slightly earlier, or slightly later.

 

[Mentz114]

I don't know what tests have been done along those lines, but I'm willing to bet that it doesn't make any difference whether Bob's measurement is at the same time as Alice's, or slightly earlier, or slightly later.

That is correct because the singlet state tells us nothing about times or time-ordering, so we can say nothing about those times.

The singlet state is also silent on states before the measurement, so nothing is ruled out. Even the pair having a fixed value. It is irrelevant because of the imminent re-projection.

 

[atyy]

There is no ambiguity. He says the state changes unpredictably. Nobody disagrees with that. Its the other baggage associated with collapse that is the issue.

MW proves it does not have to happen using non-unitary changes and instantaneously, nor does the formalism require it to be. It may be like that or not - we do not know. It may be like GRW - again we do not know. The formalism is silent on it.

Thanks
Bill

That is not correct. MWI and GRW are research directions on which consensus has not been reached in the community. Even supporters of MWI like Carroll and Wallace state that it has open problems. It is misleading false advertising to place them on the same level as textbook physics. This false advertising also does not benefit those research programmes, since if the issues are settled, we should now stop research into MWI and GRW.

 

[atyy]

Does the measuring process of Alice happen instantaneously? Or is it like decoherence would suggest - continuous but in a very short time. During that time what happens to the entanglement with the other particle?

Thanks
Bill

That is not correct. Decoherence does not solve the measurement problem. Within the standard formalism, if one includes decoherence, the appearance of the measurement result still needs an instantaneous "measurement" on the measurement apparatus. One has to go to something like MWI for decoherence to remove collapse, but MWI is not yet textbook physics.

 

[StevieTNZ]

That is not correct. Decoherence does not solve the measurement problem. Within the standard formalism, if one includes decoherence, the appearance of the measurement result still needs an instantaneous "measurement" on the measurement apparatus. One has to go to something like MWI for decoherence to remove collapse, but MWI is not yet textbook physics.

Is there not an observable of the composite system, system + apparatus + rest of the universe, that, if measured, would indicate whether system + apparatus + rest of universe is in a superposition or not?

 

[atyy]

Is there not an observable of the composite system, system + apparatus + rest of the universe, that, if measured, would indicate whether system + apparatus + rest of universe is in a superposition or not?

Basically, there is no rest of the universe, because the rest of the universe excludes the final measurement apparatus. So if we include a measuring apparatus in the quantum state, we need another measuring apparatus to measure the first apparatus, otherwise no measurement outcome is obtained.

This is, as you know, the measurement problem, which remains unsolved. I think it is an important problem, but approaches to the measurement problem should not be brought up (as Peter Donis and bhobba did) in a thread which only refers to and makes sense within standard QM.

 

[PeterDonis]

a thread which only refers to and makes sense within standard QM.

I don't think we have agreement on this point. Your position appears to be that simply saying "wave function collapse isn't the same as black hole information loss" is enough to answer the OP's question. But the OP's question was whether information is lost in wave function collapse; the fact that the OP also brought in a mistaken analogy with black hole information loss does not mean his question was only about whether wave function collapse and black hole information loss are the same.

As I've already said, I don't think the question of whether information is lost in wave function collapse is answerable within standard QM. The question of whether wave function collapse is the same as BH information loss is answerable within standard QM (the answer is that the two are not the same), but, as above, that's not a complete answer to the OP's question.

 

[atyy]

I don't think we have agreement on this point. Your position appears to be that simply saying "wave function collapse isn't the same as black hole information loss" is enough to answer the OP's question. But the OP's question was whether information is lost in wave function collapse; the fact that the OP also brought in a mistaken analogy with black hole information loss does not mean his question was only about whether wave function collapse and black hole information loss are the same.

As I've already said, I don't think the question of whether information is lost in wave function collapse is answerable within standard QM. The question of whether wave function collapse is the same as BH information loss is answerable within standard QM (the answer is that the two are not the same), but, as above, that's not a complete answer to the OP's question.

If you read the OP and his clarifications in subsequent posts, you can see that he is asking for an answer within standard QM. He is aware of still speculative approaches beyond standard QM.

 

[atyy]

@PeterDonis, just to clarify - I am not objecting to the discussion of interpretations as one part of the answer to this thread. I am objecting in interpretations being brought up as a primary answer, and as if MWI is part of standard QM or that MWI has anything to do with the most common attempts (like AdS/CFT) to restore unitarity in the black hole information paradox.

If after those points have been discussed in standard QM, I do think it is perfectly fine to mention that more generally there is the measurement problem etc. Personally, I would not bring it up, since I prefer to have fewer discussion on interpretations in QM forum, and I don't like that every time collapse is brought up in the colloquial, innocuous sense of the word referring to standard QM, that interpretations are brought into the discussion. However, if no physics errors are made, I usually try (I confess, not always successfully ) to shut up. Here I entered the discussion to clarify that MWI is not part of standard QM and that MWI has nothing to do with the most common attempts (like AdS/CFT) to restore unitarity in the black hole information paradox.

[I think you agree, but bhobba entered the discussion on a post in which I was replying to you, and reintroduced the erroneous idea that MWI is part of standard QM].

 

[PeterDonis]

If you read the OP and his clarifications in subsequent posts, you can see that he is asking for an answer within standard QM.

An answer to what question? I am saying the question he wants an answer to is the title question of this thread. And that question cannot be answered within standard QM, for reasons I've already explained. So if you're right that the OP is only interested in an answer within standard QM, then all we can tell him is that there isn't one.

I am not objecting to the discussion of interpretations as one part of the answer to this thread. I am objecting in interpretations being brought up as a primary answer

I am fine with that. I agree that the MWI is an interpretation, not standard QM, and can't be an answer to any question that asks what standard QM says.

 

[rrogers]

Apparently disagreeing with others (perhaps more knowledgeable); I think information is gained after a measurement. We are going from uncertainty to certainty. I don't know how others define "information" but I would take that as an increase in information. I think any form of Shannon's formula would agree, but I will write it out if requested. I view "measurement" as a "filter" that selects some particular future effects; i.e. determines the future.

 

[Stephen Tashi]

I think any form of Shannon's formula would agree, but I will write it out if requested.

Within the thread, no one has yet offered a technical definition of information. What I get from the focus on unitary evolution (or a violation of it) is that a physical law specifying how the "state" of system changes from time t to time t+dt is considered to lose information if that law is a many-to-one-mapping. That definition defines "looses information" without specifying a quantitative measure of information. There's nothing wrong with such a definition from a logical point of view, but it would help to know explicitly if that's the definition that most participants have in mind.

The Shannon definition of information applies to a probability distribution, so it raises the question of what random variable you wish to look at. Various properties of a physical system can be measured. Measuring one property may increase the dispersion in a subsequent measurement of a different property. Applying the Shannon definition of information to a physical system is not straightforward.

The Shannon definition is related to the entropy of a probability distribution. Just stringing words together, there is such a thing as the "von Neumann entropy" in quantum statistical mechanics. There are also controversies about whether it is the best way to define entropy. Perhaps someone can comment on a relation between "information" as discussed in this thread and the various definitions of "entropy".

 

[.Scott]

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?

I totally agree.

Let me state the other (ie, wrong) logic explicitly and as I understand it:
They are saying that before the measurement or collapse, there are many possible outcomes. But once the measurement is made, there is only one. They believe this could indicate a loss of information.

Before I attack that logic, let me say that I do not believe there is a change in the amount of information.

That said: Going from many possibilities to one is an increase in information. If I tell you that the killer has 012 as the first 3 digits of his social security number, that is some information - but there are still hundreds of thousands of possibilities. If I then said the first 5 digits are 012-34, then I have given you more information and thus left you with fewer possibilities.

I suspect that MWI is not an "interpretation" since, in its simplest form, it requires a continuous increase in the amount of information in the universe. Without it, an event can be identified by initial conditions (for example, Big Bang), three spatial coordinates and a time coordinate. With it, the event also requires a "which world" parameter.

The way to avoid this increase in information is to presume that, although it was theoretically impossible to know what the outcome would be, that it was never-the-less predestined - and that it was entirely determined from information that existed before the measurement was made.

The only alternative I see is to allow the amount of information to increase steadily. Then, to avoid "coin flipping", we would need to invoke either an "external" information source or MWI.

 

[rrogers]

Within the thread, no one has yet offered a technical definition of information. What I get from the focus on unitary evolution (or a violation of it) is that a physical law specifying how the "state" of system changes from time t to time t+dt is considered to lose information if that law is a many-to-one-mapping. That definition defines "loses information" without specifying a quantitative measure of information. There's nothing wrong with such a definition from a logical point of view, but it would help to know explicitly if that's the definition that most participants have in mind.

The Shannon definition of information applies to a probability distribution, so it raises the question of what random variable you wish to look at. Various properties of a physical system can be measured. Measuring one property may increase the dispersion in a subsequent measurement of a different property. Applying the Shannon definition of information to a physical system is not straightforward.

The Shannon definition is related to the entropy of a probability distribution. Just stringing words together, there is such a thing as the "von Neumann entropy" in quantum statistical mechanics. There are also controversies about whether it is the best way to define entropy. Perhaps someone can comment on a relation between "information" as discussed in this thread and the various definitions of "entropy".

Well, my model is simple, if I use a fluorescent screen and see an electron light up a spot I can then determine where the electron was at that moment and with careful measurement probably the energy. So I have gained information that affects all my future calculations; i.e. I have filtered my future. There may be other "universes" but they don't affect my future. Of course I might not look for a while and the delayed choice experiments come into play. But for my future, I have greater certainty (and probably increased my entropy some way) thus more information. A sort of Bayesian attitude if you will.

 

[PeterDonis]

I have gained information that affects all my future calculations; i.e. I have filtered my future.

But you have lost information about your past; that is, if there are many possible past states that all could have led to your current state, the one you are using for your future calculations, then you have lost information. When physicists talk about non-unitary transformations (such as an actual physical wave function collapse) leading to loss of information in quantum mechanics, that is what they are talking about.

 

[rrogers]

But you have lost information about your past; that is, if there are many possible past states that all could have led to your current state, the one you are using for your future calculations, then you have lost information. When physicists talk about non-unitary transformations (such as an actual physical wave function collapse) leading to loss of information in quantum mechanics, that is what they are talking about.

Yes, I have always said the past is as uncertain as the future in QM; a radical oversimplification. But taking a Bayesian attitude, information allows future certainty. Otherwise, when we take measurements we are destroying knowledge of the past; sort of a squishy conserved thing that disturbs me. But let's think about this; you/that implies that my ignorance in the past has more "information" than after I take the measurement. I suppose that's possible but it seems that "information" now has two different meanings/measures. Which is reasonable if it's given two names with a conservation law linking them. Like "Potential Energy" and "Kinetic Energy" I guess?

 

[zdcyclops]

An interesting thread. I have no math skills and am an avid fan. In my opinion many of the posts describing information were wide of the OP. The information the OP asks about exists only in the system to be measured. It has nothing to do with knowledge that an experimenter will gain, or probable outcomes, or what state the particle is in. There is an assumption that the system being measured contains information. Although this is reasonable, it is still only an assumption.

 

[PeterDonis]

information allows future certainty

Not in general in QM, since QM only makes probabilistic predictions about the results of measurements. But if you know the result of a measurement you just made, using the state corresponding to that measurement result will give you better predictions about future measurements you can make than using the state before you made the measurement.

that implies that my ignorance in the past has more "information" than after I take the measurement

You have more information about the past state before your current measurement, and less information about future measurements.

 

[Fooality]

Within the thread, no one has yet offered a technical definition of information. What I get from the focus on unitary evolution (or a violation of it) is that a physical law specifying how the "state" of system changes from time t to time t+dt is considered to lose information if that law is a many-to-one-mapping. That definition defines "looses information" without specifying a quantitative measure of information. There's nothing wrong with such a definition from a logical point of view, but it would help to know explicitly if that's the definition that most participants have in mind.

The Shannon definition of information applies to a probability distribution, so it raises the question of what random variable you wish to look at. Various properties of a physical system can be measured. Measuring one property may increase the dispersion in a subsequent measurement of a different property. Applying the Shannon definition of information to a physical system is not straightforward.

Thanks!

I've been reading this thread, wishing people would take your question on. What I would say, having played with quantum computer simulators, is that the information relayed to an *observer* in bits is something like the base 2 logarithm of the reciprocal of the probability of *observing* the event.

So a qubit "in" some prepared state doesn't actually carry the information needed to specify the prepared state, because that can't be observed from the qubit alone. So no information is lost on measurement.

But where does the probability space come from in physical systems? If I give you a full gigabit removable drive, it's a gigabit of information *to the drive* in that it treats all 2 to the billion possible states as equally likely, allocates equal resources to each one. But if you already knew the info on the drive, I've given you personally zero bits of information with the same drive, in that your internal model, unlike the drive, remains unchanged. How can this be mapped to physical systems I wonder? I feel it has something to do with changes.