A Interpretations of the No Communication Theorem

[PeterDonis]

Moderator's note: Spin-off from previous thread due to topic change.

communication is an anthropocentric notion

Not in the sense in which it is used in the no communication theorem. That sense is basically the information theoretic sense, which in no way requires humans to process or even be aware of the information.

 

[Nullstein]

Not in the sense in which it is used in the no communication theorem. That sense is basically the information theoretic sense, which in no way requires humans to process or even be aware of the information.

It's not about information theory at all. The no communication theorem is about measurement, which is an anthropocentric notion. It says that no local operation at Bob's distant system (in the sense of separation by tensor products) can cause any disturbance of measurement results at Alice's local system, or more succintly: The Born rule obeys locality. So if there was non-locality, then there would be non-local effects everywhere, but the theory would prohibit them from being observable even in principle (not just due to insufficient equipment).

 

[PeterDonis]

The no communication theorem is about measurement, which is an anthropocentric notion.

I think that is a matter of interpretation. In decoherence theory, for example, "measurement" can be defined as any situation in which decoherence occurs. For example, the Moon is constantly measuring itself by this definition, whether or not a human being looks at it. And the no communication theorem would therefore apply to the Moon (and would say, for example, that the Moon's orbit cannot be affected by what is happening on Pluto at a spacelike separated event, even if particles in the Moon and particles in Pluto are quantum entangled).

 

[Nullstein]

I think that is a matter of interpretation. In decoherence theory, for example, "measurement" can be defined as any situation in which decoherence occurs. For example, the Moon is constantly measuring itself by this definition, whether or not a human being looks at it. And the no communication theorem would therefore apply to the Moon (and would say, for example, that the Moon's orbit cannot be affected by what is happening on Pluto at a spacelike separated event, even if particles in the Moon and particles in Pluto are quantum entangled).

But the no communication theorem doesn't consider a vague definition of measurement. It's stated clearly in terms of the Born rule. It says that the probability (given by the Born rule) to measure an observable of system 1 to yield a specific value is independent of what local quantum operations are performed on system 2. And that makes it anthropocentric, because the Born rule captures everything that is in principle accessible to humans while it hides everything that is inaccessible to humans in principle (such as details about hidden variables).

 

[PeterDonis]

the Born rule captures everything that is in principle accessible to humans

Again, this is a matter of interpretation. According to decoherence theory, the Moon had a perfectly well-defined orbit 4 billion years ago, when there were no humans around. In terms of the Born rule, the probabilities for the Moon to be at various positions were perfectly well-defined 4 billion years ago, and the no communication theorem would apply to them.

Whereas on the viewpoint you are taking here, the Born rule was meaningless until humans started doing QM experiments.

 

[Nullstein]

Again, this is a matter of interpretation. According to decoherence theory, the Moon had a perfectly well-defined orbit 4 billion years ago, when there were no humans around. In terms of the Born rule, the probabilities for the Moon to be at various positions were perfectly well-defined 4 billion years ago, and the no communication theorem would apply to them.

Things like well-defined positions and well-defined momenta don't exist in quantum mechanics. Decoherence just ensures that the probability distributions given by the wave function have always been peaked on one or more trajectories, rather than being spread across the universe. So if someone had measured the moon 4 billion years ago, he would have found it orbiting earth. It doesn't matter whether sombody was there though. The wave function evolves independent of whether someone is there or not and may also decohere in that process. You don't need the Born rule for that.

Whereas on the viewpoint you are taking here, the Born rule was meaningless until humans started doing QM experiments.

The Born rule is just a recipe for how to read off information about relative frequencies from the wave function. That doesn't make the Born rule meaningless though. The information is contained in the wave function even if you don't read it off.

 

[PeterDonis]

Things like well-defined positions and well-defined momenta don't exist in quantum mechanics.

Objects with a huge number of quantum degrees of freedom, like the Moon, can have center of mass positions and momenta that, while not delta functions, will both have widths that are much, much narrower than the corresponding widths for a single quantum particle (narrower by roughly the same order of magnitude as the number of particles in the object). That is what I mean by "well-defined" in this connection.

Decoherence just ensures that the probability distributions given by the wave function have always been peaked on one or more trajectories, rather than being spread across the universe.

But the Moon doesn't have "one or more" trajectories. It has one. And that was true 4 billion years ago. The Moon didn't have to wait for humans to start observing it to have one trajectory. Or at least, if you are taking the position that it did--that the Moon literally had multiple trajectories (each decohered, but still multiple ones) until the first human looked at it and collapsed them into one, then please make that argument explicitly.

So if someone had measured the moon 4 billion years ago, he would have found it orbiting earth. It doesn't matter whether sombody was there though.

"It doesn't matter whether someone was there" in the sense that the Moon had one single trajectory back then?

The wave function evolves independent of whether someone is there or not and may also decohere in that process. You don't need the Born rule for that.

You do in order for the Moon to have just one trajectory instead of multiple ones. More precisely, you need the Born rule to tell you what the probabilities were for various possible trajectories 4 billion years ago. And then you need to realize that, because the Moon is constantly measuring itself, it will have picked just one of those trajectories 4 billion years ago. And then you need the Born rule to tell you what the probabilities were for various possible trajectories 4 billion years minus one second (let's say--I think the decoherence time for the Moon is actually much shorter than that, but let's say one second for this discussion) ago--and then the Moon picks one of those. And then you're at 4 billion years minus two seconds ago...etc., etc.

 

[Nullstein]

But the Moon doesn't have "one or more" trajectories. It has one. And that was true 4 billion years ago. The Moon didn't have to wait for humans to start observing it to have one trajectory. Or at least, if you are taking the position that it did--that the Moon literally had multiple trajectories (each decohered, but still multiple ones) until the first human looked at it and collapsed them into one, then please make that argument explicitly.

We don't know whether the position probability distribution of the moon was always unimodal. Decoherence itself doesn't collapse the wave function into a single branch, so apart from the heavily debated collapse of the wave function, we don't know a mechanism that would make the distribution unimodal. We just don't know at the moment under what circumstances something like collapse occurs and how it occurs. The axioms of QM are operational in this regard.

"It doesn't matter whether someone was there" in the sense that the Moon had one single trajectory back then?

I don't know if there was a single trajectory, because we don't understand this part of QM very well at the moment. Maybe there even are multiple trajectories right now and we have just become entangled with one of them. We don't know for sure and everyone his their own favorite interpretation when it comes to this.

You do in order for the Moon to have just one trajectory instead of multiple ones. More precisely, you need the Born rule to tell you what the probabilities were for various possible trajectories 4 billion years ago. And then you need to realize that, because the Moon is constantly measuring itself, it will have picked just one of those trajectories 4 billion years ago.

No, that's not what decoherence tells us. Decoherence makes sure that there is no interference between the potential multiple trajectories of the moon. It doesn't collapse its wave function to a single trajectory. What you propose here seems to be something like GRW spontaneous collapse theory.

And then you need the Born rule to tell you what the probabilities were for various possible trajectories 4 billion years minus one second (let's say--I think the decoherence time for the Moon is actually much shorter than that, but let's say one second for this discussion) ago--and then the Moon picks one of those. And then you're at 4 billion years minus two seconds ago...etc., etc.

Decoherence doesn't eleminate the other branches. It just entangles them with the measurement apparatus. And that's just unitary evolution, no Born rule or collapse is involved there. We don't know when and how the collapse of the wave function occurs (or whether it occurs at all, i.e. many worlds). We know that at least something like collapse must occur when we as humans perform a measurement (unless we believe in many worlds), but even in that case, we don't understand the details very well. That's the measurement problem.

 

[PeroK]

It's not about information theory at all. The no communication theorem is about measurement, which is an anthropocentric notion. It says that no local operation at Bob's distant system (in the sense of separation by tensor products) can cause any disturbance of measurement results at Alice's local system, or more succintly:

Alice and Bob are anthropocentric notions, I'll give you that!

 

[Nullstein]

Alice and Bob are anthropocentric notions, I'll give you that!

Okay, let me try differently: Are there any entities in the universe, other than humans, that make use of the Born rule? The role of the Born rule is to extract relative frequencies from the state of the system. Relative frequencies are something that humans have ascribed meaning to. The system would evolve just fine if we didn't ascribe meaning to the relative frequencies. They play no role in the evolution laws of the system. All the universe needs is the wave function and the Hamilton operator. We could also decide to ascribe meaning to the value $\xi:=\psi(3)+\psi(8)$, but we don't because we are not interested in it, because it never appears as a result on any of our measurement devices. It is inaccessible to us. What we find interesting is the value $P([1,2]) := \int_1^2 |\psi(x)|^2\mathrm d x$. That's just a definition made by humans, just like my definition of $\xi$ earlier. But it is accessible to us by clever measurement setups.

As an analogy, think of temperature in classical statistical mechanics. The system is made of particles that evolve just fine according to Hamiltons equations of motion. There is no fundamental need for a quantity like temperature. It's invented by humans to quantify an aggregate property of the system. We could also define the variable $\eta:=x_{29} + x_{10^{23}+8}$, but it is of no interest to us, so we don't.

 

[gentzen]

All the universe needs is the wave function and the Hamilton operator.

No, that is not enough, see Nothing happens in the Universe of the Everett Interpretation by Jan-Markus Schwindt. MWI proponents like Lev Vaidman agree with that assessment, and Dieter Zeh independently already remarked much earlier that "a little bit more" is needed, even so I never found out what "little addition" exactly he had in mind when he made that remark. (I read his remark in his "Physik ohne Realität: Tiefsinn oder Wahnsinn?")

 

[PeterDonis]

Decoherence itself doesn't collapse the wave function into a single branch

I know that. That's why I said that what we are discussing is ultimately a matter of interpretation. You are free to adopt an interpretation like the MWI, in which there is no collapse at all, and in such an interpretation it would not be true that the Moon has a single position.

However, in such an interpretation your claim that the no communication theorem is anthropocentric is still not true, because in an interpretation like the MWI it makes no sense to even talk about whether Bob can do something to affect Alice's measurement results and thus send Alice a signal, since measurements don't even have single outcomes to begin with. This is just an aspect of the issue that it's not clear how the Born rule even makes sense in the MWI.

In any case, as I said before, if you are using an interpretation like the MWI, then you should say so explicitly. Then we can simply drop this whole subthread since we have been talking past each other: I was assuming we were using an interpretation in which measurements have single outcomes, so the Born rule makes sense and it makes sense to talk about whether or not Bob can send Alice a signal using measurement results on entangled particles.

(Note also that this thread is about superdeterminism, which also makes no sense in an interpretation like the MWI, since the whole point of superdeterminism is to try to reconcile violations of the Bell inequalities with an underlying local hidden variable theory in which measurements have single outcomes determined by the hidden variables, by violating the statistical independence assumption of Bell's theorem instead of the locality assumption. So the MWI as an interpretation is really off topic for this thread.)

If you are not using the MWI, and you are using an interpretation in which measurements do have single outcomes, then your statement quoted above, while true, is pointless. Yes, decoherence by itself does not make measurements have single outcomes, but in any interpretation where we are assuming that measurements do have single outcomes anyway, decoherence is an excellent way of defining what counts as a "measurement". That is the only use I am making of decoherence in my arguments, and you have not responded to that at all.

 

[PeterDonis]

Are there any entities in the universe, other than humans, that make use of the Born rule?

Any time Nature has to decide what single outcome a measurement has when there are two or more quantum possibilities, it is making use of the Born rule.

(For why I am assuming that measurements have single outcomes, see my post #79 just now.)

 

[PeterDonis]

The system would evolve just fine if we didn't ascribe meaning to the relative frequencies. They play no role in the evolution laws of the system. All the universe needs is the wave function and the Hamilton operator.

This is basically assuming the MWI. Again, see my post #79 above.

On any interpretation where measurements have single outcomes, no, just the wave function and the Hamiltonian are not enough.

 

[Nullstein]

No, that is not enough, see Nothing happens in the Universe of the Everett Interpretation by Jan-Markus Schwindt. MWI proponents like Lev Vaidman agree with that assessment, and Dieter Zeh independently already remarked much earlier that "a little bit more" is needed, even so I never found out what "little addition" exactly he had in mind when he made that remark. (I read his remark in his "Physik ohne Realität: Tiefsinn oder Wahnsinn?")

That is not even a peer reviewed paper and I'm not talking about the Everett interpretation in the first place.

I know that. That's why I said that what we are discussing is ultimately a matter of interpretation. You are free to adopt an interpretation like the MWI, in which there is no collapse at all, and in such an interpretation it would not be true that the Moon has a single position.

I don't adopt MWI. I was just explaining that decoherence doesn't cause the collapse.

I was assuming we were using an interpretation in which measurements have single outcomes, so the Born rule makes sense and it makes sense to talk about whether or not Bob can send Alice a signal using measurement results on entangled particles.

We are, I wasn't talking about MWI, except mentioning as an edge case to avoid questions about it. The Born rule is not the collapse postulate. You get single outcomes from the collapse postulate, but collapse, according to standard theory, only occurs after measurements. Decoherence doesn't induce a collapse. It just entangles the system with the measurement apparatus and the environment.

If you are not using the MWI, and you are using an interpretation in which measurements do have single outcomes, then your statement quoted above, while true, is pointless. Yes, decoherence by itself does not make measurements have single outcomes, but in any interpretation where we are assuming that measurements do have single outcomes anyway, decoherence is an excellent way of defining what counts as a "measurement". That is the only use I am making of decoherence in my arguments, and you have not responded to that at all.

But it's wrong, you can't just define what counts as a measurement this way. First of all, it is ambiguous, because there is no unique decomposition of the universe into a system, a measurement apparatus and the environment. Different decompositions will lead to different moments of decoherence. In one decomposition the off-diagonal terms may decay faster than in another or maybe they don't decay at all. Moreover, it is impossible to say when decoherence has finished and the collapse postulate should be invoked. Do the off-diagonal elements have to drop to $e^{-100}$ or to $e^{-10000}$? Also, a system can also recohere after it has decohered (see the quantum eraser), although this becomes more improbable as the size of the system grows. And finally, one can reduce the number of invokations of the collapse postulate to exactly $1$ by including enough enough systems that act as an ancilla. (To avoid confusion: Again, I'm not talking about MWI in any of this)

Any time Nature has to decide what single outcome a measurement has when there are two or more quantum possibilities, it is making use of the Born rule.

No, it's not. It's making use of the collapse postulate. If you start with a state $\Psi$, its time evolution is given by $U_4 P_3 U_3 P_2 U_2 P_1 U_1\Psi$ and so on, where you alternate between projections and unitary evolutions. At no point do you need to compute $|\Psi(t)|^2$. And as I said, using ancilla systems, you can reduce the whole formula to just $PU\Psi$.

This is basically assuming the MWI. Again, see my post #79 above.

Again, you never need the Born rule $\rho(x)=\left|\Psi\right|^2$ for time evolution. It has nothing to do with MWI.

On any interpretation where measurements have single outcomes, no, just the wave function and the Hamiltonian are not enough.

If you insist, you may insert projection operators in between, but the time of insertion is irrelevant, you can always shift it to the very end by considering ancillas. And decoherence doesn't tell you when a collapse occurs. My point is: You never need the Born rule. You only need unitary evolution and possibly one projection, or, if you prefer, several.

 

[PeterDonis]

you can't just define what counts as a measurement this way.

Basically, you seem to be expounding a "consciousness causes collapse" interpretation. In such an interpretation, yes, you could call the no communication theorem anthropomorphic, because anything to do with measurement at all is anthropomorphic. But once again, you are then saying that no measurements at all took place anywhere in the universe until the first conscious human looked at something.

If that is your position, once again, we are talking past each other and can just drop this subthread.

If it is not your position, then pretty much everything you are saying looks irrelevant to me as far as the discussion in this thread is concerned. Yes, I get that decoherence doesn't cause collapse, and collapse can't be proven to occur in a collapse interpretation whenever decoherence occurs, but once you've adopted a collapse interpretation, and once you've adopted an interpretation that says collapse doesn't require consciousness to occur, so a macroscopic object like the Moon can be continually collapsing itself, you are going to end up having measurements and decoherence events be pretty much the same thing. And neither decoherence nor measurements nor anything associated with them will be anthropomorphic.

 

[Nullstein]

Basically, you seem to be expounding a "consciousness causes collapse" interpretation.

No, I'm talking about bona fide Copenhagen. The axioms say that after a measurement, we have to collapse the wave function. It's just an inconvenient truth that we don't really understand how and why collapse happens. The axioms of quantum mechanics are silent on this issue. However, it's just not true that collapse always happens after decoherence as you indicate.

In such an interpretation, yes, you could call the no communication theorem anthropomorphic, because anything to do with measurement at all is anthropomorphic. But once again, you are then saying that no measurements at all took place anywhere in the universe until the first conscious human looked at something.

This is relative, because as I said, by shifting the split between system and environment, you can shift the collapse almost arbitrarily in time. And again, I'm not talking about consciousness causes collapse. I'm talking about measurement causes collapse, just as bona fide Copenhagen tells us. The biggest problem of quantum mechanics is that the axioms are not precise about what constitutes a measurement. This is the measurement problem. Your claim that collapse happens after decoherence is in direct contradiction to the first line of that Wikipedia article.

If it is not your position, then pretty much everything you are saying looks irrelevant to me as far as the discussion in this thread is concerned.

I was just claiming that the Born rule $\rho=|\Psi|^2$ is not needed for time evolution and this is just true. Time evolution is a concatenation of projections and unitary evolutions. At no point do you need the Born rule.

 

[Nullstein]

Yes, I get that decoherence doesn't cause collapse, and collapse can't be proven to occur in a collapse interpretation whenever decoherence occurs, but once you've adopted a collapse interpretation, and once you've adopted an interpretation that says collapse doesn't require consciousness to occur, so a macroscopic object like the Moon can be continually collapsing itself

That's not true. Can you give a citation that says that in bona fide Copenhagen, an object can collapse itself? Copenhagen says that collapse happens after a measurement. It is silent on what a measurement is, so we don't understand when collapse happens. But if a system would just continuously collapse, it would be frozen in time, as per the quantum Zeno effect, so we can also exclude this possibility.

you are going to end up having measurements and decoherence events be pretty much the same thing. And neither decoherence nor measurements nor anything associated with them will be anthropomorphic.

But this is not even relevant, even if it were true. You are still confusing the Born rule with the collapse postulate. Even if I don't agree that Copenhagen tells us that collapse happens regularly without human intervention (in fact I think you are rather talking about something like spontaneous collapse theories, such as GRW), I'll just for the sake of getting to the point, concede this to you.

But again, my point is not that the collapse postulate is athropocentric, but that the Born rule is anthropocentric, as argued in post #77. This is what is relevant to arguing that the no communication theorem is anthropocentric. Whether the collapse is only invoked by humans doesn't play a role for the argument.

Just to make it more clear: Let's take the standard mathematical formulation of QM as given in this link. You have been arguing that postulate II.c is not anthropocentric. I don't necessarily agree, but I'm willing to concede. I have been arguing that postulate II.b is anthropocentric. (Moreover you made me argue that postulate II.b is irrelevant for time evolution, because only postulates II.c and III are involved in time evolution. But that's not actually relevant to my argument.) So far, we have been talking past each other, because we were talking about different axioms.

 

[PeterDonis]

as I said, by shifting the split between system and environment, you can shift the collapse almost arbitrarily in time.

But within a pretty narrow window of time in any actual case. Unless, as I said, you're going to take a position that, for example, the Moon only has a single trajectory when humans are looking at it. If we limit ourselves to reasonable places to put the collapse for macroscopic objects, so that they behave classically regardless of whether they are being looked at, any place you put the collapse is going to be pretty close to a decoherence event, because macroscopic objects are always decohering themselves.

I was just claiming that the Born rule is not needed for time evolution and this is just true.

You're quibbling. Collapse is needed for time evolution on any collapse interpretation. You agree with that in your very next sentence:

Time evolution is a concatenation of projections and unitary evolutions.

And this being the case is already sufficient to disprove your claim, which originally started this subthread, that the no communication theorem is anthropomorphic. The theorem applies to any collapse, not just one triggered by a human looking.

my point is not that the collapse postulate is athropocentric, but that the Born rule is anthropocentric

The Born rule can't be anthropocentric if collapse isn't. Except in the (irrelevant for this discussion) sense that humans are the ones who invented the term "Born rule" and so that term can only be applied to human discussions of QM, not QM itself. And if you are going to take that position, then your claim that the no communication theorem has to do with the Born rule is false: the theorem has to do with QM itself, not human discussions of QM. And, as I said above, the theorem applies to any collapse events, not just ones that humans are looking at.

I have been arguing that postulate II.b is anthropocentric.

See above.

 

[PeterDonis]

Can you give a citation that says that in bona fide Copenhagen, an object can collapse itself?

Do you consider the literature on decoherence, when it is applied in the context of a collapse interpretation, to be "bona fide Copenhagen"? Because the fact that macroscopic objects are continually decohering themselves is an obvious consequence of decoherence theory in general. And, as I have argued in prior posts, unless you are going to say that collapse only happens when a human is looking, any collapse event in a macroscopic object is going to be close to a decoherence event.

Copenhagen says that collapse happens after a measurement. It is silent on what a measurement is, so we don't understand when collapse happens.

We can't prove when collapse happens. But that doesn't mean we can't say anything at all about when it happens.

But if a system would just continuously collapse, it would be frozen in time, as per the quantum Zeno effect, so we can also exclude this possibility.

No, the quantum Zeno effect does not say the system is "frozen in time". It only says that the probability of a quantum system making "quantum jumps" from one eigenstate of an observable to another can be driven to zero by measuring that observable at shorter and shorter time intervals. But there is nothing that says that the eigenstate it is being "held" in by continuous measurement has to be "frozen in time." If the system is a macroscopic object, then the "eigenstate" it starts out it is just a set of classical initial conditions, and being "held" in that eigenstate by continuous collapse just means it executes the classical motion that starts from those initial conditions.

To put it another way, a macroscopic object behaving classically does not have to make quantum jumps. It just behaves classically. If it is collapsing continuously, that just means it's following the classical trajectory that was picked out by its initial classical state.

 

[Nullstein]

But within a pretty narrow window of time in any actual case. Unless, as I said, you're going to take a position that, for example, the Moon only has a single trajectory when humans are looking at it. If we limit ourselves to reasonable places to put the collapse for macroscopic objects, so that they behave classically regardless of whether they are being looked at, any place you put the collapse is going to be pretty close to a decoherence event, because macroscopic objects are always decohering themselves.

Again, collapse has nothing to do with decoherence, I don't see why you bring it up. If you are proposing that collapse is an objective event, then you are arguing for an objective collapse model such as GRW. You can do that, but you should be explicit about it.

You're quibbling. Collapse is needed for time evolution on any collapse interpretation. You agree with that in your very next sentence:

Time evolution is a concatenation of projections and unitary evolutions.

And this being the case is already sufficient to disprove your claim, which originally started this subthread, that the no communication theorem is anthropomorphic. The theorem applies to any collapse, not just one triggered by a human looking.

This is not in contradiction with what I said, because there is a difference between collapse and the Born rule. Moreover, the moment of collapse is arbitrary, it can be shifted to the very end by the deferred measurement principle. It's not an objective, observer independent event in most interpretations.

The no communication theorem applies to collapse as well as to unitary evolution. But what's relevant is that it computes probabilities! Here, the Born rule comes into play and this is where it becomes anthropocentric.

The Born rule can't be anthropocentric if collapse isn't.

Why do you think so? You just claim it, but provide no argument.

Except in the (irrelevant for this discussion) sense that humans are the ones who invented the term "Born rule" and so that term can only be applied to human discussions of QM, not QM itself. And if you are going to take that position, then your claim that the no communication theorem has to do with the Born rule is false: the theorem has to do with QM itself, not human discussions of QM. And, as I said above, the theorem applies to any collapse events, not just ones that humans are looking at.

That's a misrepresentation of what I wrote. The point is that the Born rule extracts separates the humanly interesting facts about the quantum system from the non-interesting ones, such as the physically irrelevant phase of the wave function. The wave function contains e.g. an arbitrary phase $e^{i\phi}$, but it is both inaccessible and irrelevant to humans. And if there were hidden variables, the Born rule knew nothing about them either, they were forever hidden from human access, even if they may feel non-local effects.

Do you consider the literature on decoherence, when it is applied in the context of a collapse interpretation, to be "bona fide Copenhagen"? Because the fact that macroscopic objects are continually decohering themselves is an obvious consequence of decoherence theory in general. And, as I have argued in prior posts, unless you are going to say that collapse only happens when a human is looking, any collapse event in a macroscopic object is going to be close to a decoherence event.

So where in the literature does it say so? I asked for a specific reference. In all standard literature about QM, collapse happens after measurements unless you are defending an objective collapse model. And the moment of collapse is even arbitrary, it can be deferred to the very end of time evolution.

We can't prove when collapse happens. But that doesn't mean we can't say anything at all about when it happens.

No, we really have no idea, when it happens, because due to the deferred measurement principle, it can be shited arbitrarily close to the present. The actual moment of collapse is totally subjective and observer dependend unless you are defending an objective collapse model.

No, the quantum Zeno effect does not say the system is "frozen in time". It only says that the probability of a quantum system making "quantum jumps" from one eigenstate of an observable to another can be driven to zero by measuring that observable at shorter and shorter time intervals.

So if you claim that the system continuously collapses itself, then it is frozen in time.--
But again, all of this discussion is irrelevant, because we are only arguing about collapse again. Even if we were accepting an objective collapse model, the Born rule would still be irrelevant to time evolution. The very point is that the Born rule separates the humanly accessible information about a quantum system from the humanly inaccessible information, so it is anthropocentric. If you disagree, you should point to a humanly inaccessible fact about a quantum system, which is captured by the Born rule or a humanly accessible fact, which is not captured by the Born rule.

 

[PeterDonis]

collapse has nothing to do with decoherence

I have already agreed multiple times that they are not the same thing.

I don't see why you bring it up.

This whole subthread started because you claimed that the no communication theorem was anthropomorphic. I am trying to get you to either drop that claim or be explicit about exactly what kind of QM interpretation you are using to make it. I have repeatedly stated what kind of interpretation I think is necessary to make that claim: a "consciousness causes collapse" interpretation. I have brought up other interpretations, such as "decoherence and collapse go together" only in order to show that, under those interpretations, the no communication theorem is not anthropomorphic, because measurement itself is not. Instead of addressing that point, which is the only one that's relevant to the subthread, you keep complaining about irrelevancies like whether or not collapse and decoherence are the same thing (of course they're not, and I never said they were).

At this point I'm not going to respond further since you seem incapable of addressing the actual point of the subthread we are having. I've already corrected other misstatements of yours and I'm not going to keep correcting the same ones despite the fact that you keep making them.

 

[PeterDonis]

due to the deferred measurement principle, it can be shited arbitrarily close to the present.

Well, this, at least, is a new misstatement you hadn't made before. The reference you give does not say you can shift collapse "arbitrarily close to the present". It only says you can shift it "to the end of the quantum computation" (and if you actually read the details it doesn't even quite say that--it's talking about a particular result regarding equivalence of quantum computing circuits, not a general result about measurement and collapse). That's a much weaker claim (and is also irrelevant to this discussion). If a quantum computation happened in someone else's lab yesterday, I can't shift any collapses resulting from measurements made in that computation "arbitrarily close to the present".

 

[Nullstein]

OK, so why do you not agree that Valentini's version fixes this?

Because it doesn't work. Bohmian time evolution doesn't involve the coarse graining steps that are used in his calculation. A delta distribution remains a delta distribution at all times and does not decay into $|\Psi|^2$.

This whole subthread started because you claimed that the no communication theorem was anthropomorphic. I am trying to get you to either drop that claim or be explicit about exactly what kind of QM interpretation you are using to make it.

I am fully explicit about it. I am using standard textbook quantum mechanics as described e.g. in Landau. You can find the list of axioms I'm using here.

On the other hand, you are apparently not using standard QM. Instead you seem to be arguing with respect to an objective collapse model.

I have repeatedly stated what kind of interpretation I think is necessary to make that claim: a "consciousness causes collapse" interpretation.

And I have repeatedly stated that it is irrelevant for my argument. It does not require a "conscious causes collapse" interpretation. The argument is fully independent on the details of collapse. It may be an objective collapse model or a consciousness causes collapse model or even MWI with no collapse at all. That's because my argument does not reference collapse at all!

My argument depends only on the Born rule, which is a completely independent axiom, unrelated to the collapse axiom. (From what I can tell, you seem to have mixed up these independent axioms, which might cause the confusion, but I also have tried to make you aware of this multiple times.)

The argument goes as follows:
1. All humanly accessible facts about a quantum system are given by the Born rule.
2. Any fact about a quantum system that is not accessible to humans is not given by the Born rule.

The humanly accessible facts about a quantum system are in 1 to 1 correspondence with the facts about a quantum system that can be computed using the Born rule. Therefore the Born rule is anthropocentric if there are any facts about a quantum system that are inaccessible to humans. Such facts could be e.g. details about hypothetical hidden variables.

The no communication theorem depends on the Born rule, therefore it is anthropocentric as well.

At no point did I make any reference to the collapse of the wave function in this argument. It is fully independent of whatever collapse model you choose.

Well, this, at least, is a new misstatement you hadn't made before. The reference you give does not say you can shift collapse "arbitrarily close to the present".

You can read up on this e.g. in Nielsen, Chuang and convince yourself that what I wrote is true. But my argument doesn't even depend on that, so I have no interest in discussing it further and thereby causing further distraction from the main argument.

 

[PeterDonis]

I am using standard textbook quantum mechanics as described e.g. in Landau.

And where does that say the no communication theorem is anthropomorphic?

you are apparently not using standard QM. Instead you seem to be arguing with respect to an objective collapse model.

You apparently have a misunderstanding as to what "standard QM" is. "Standard QM" is not any particular interpretation. It is just the "shut up and calculate" math.

I have mentioned collapse interpretations, but not "objective collapse" ones specifically. Nothing I have said requires objective collapse. The only interpretation I have mentioned in this thread that I do not think is relevant to the discussion (because in it, measurements don't have single outcomes, and measurements having single outcomes seems to me to be a requirement for the discussion we are having) is the MWI.

My argument depends only on the Born rule

No, it also depends on the no communication theorem. I know you claim that the no communication theorem is only about the Born rule, and that the Born rule is anthropomorphic. I just disagree with those claims. I have already explained why multiple times. You haven't addressed anything I've actually said. You just keep repeating the same claims over and over.

You can read up on this e.g. in Nielsen, Chuang

Do you mean this?

https://www.amazon.com/dp/1107002176/?tag=pfamazon01-20

 

[Nullstein]

And where does that say the no communication theorem is anthropomorphic?

I don't know if it does, I cited the book just to tell you which version of QM the argument is based on. You keep insinuating that I use any non-standard interpretation, which isn't true.

You apparently have a misunderstanding as to what "standard QM" is. "Standard QM" is not any particular interpretation. It is just the "shut up and calculate" math.

No, I don't have that misunderstanding. I agree with that and I explained multiple times that my argument applies to all theories based on the axioms of QM, which you refer to as "shut up and calculate."

I have mentioned collapse interpretations, but not "objective collapse" ones specifically. Nothing I have said requires objective collapse.

You claim that collapse happens all the time, independent of measurement. That's not what the collapse axiom says. It says the collapse happens at measurement. However, my argument doesn't require any assumptions about the time of collapse, it works even in an objective collapse model, because it is not based on the collapse axiom at all. I'll happily concede that the collapse happens at your favorite time, it this helps drawing attention to the actual argument and not having to discuss collapse any further.

No, it also depends on the no communication theorem. I know you claim that the no communication theorem is only about the Born rule, and that the Born rule is anthropomorphic.

No my argument is not that the no communication is only about the Born rule, that's a misrepresentation of what I said. My argument is that the no communication theorem requires the Born rule. The no communication theorem involves many other things, but the crucial ingredient that makes it anthropocentric is the Born rule. Any prediction that requires the Born rule becomes just as anthropocentric as the Born rule itself, irrespective of what other input is needed.

I just disagree with those claims. I have already explained why multiple times. You haven't addressed anything I've actually said. You just keep repeating the same claims over and over.

You haven't explained that, because you keep on arguing about collapse, which isn't relevant to my argument at all. Perhaps because you think that anthropocentricity of a prediction can be lifted by adding additional non-anthropocentric ingredients. But that's not true. Once a prediction is tainted, it remains tainted even if you add other ingredients.

You just keep ommitting the relevant part of my posts that contains the actual argument:

The argument goes as follows:
1. All humanly accessible facts about a quantum system are given by the Born rule.
2. Any fact about a quantum system that is not accessible to humans is not given by the Born rule.

The humanly accessible facts about a quantum system are in 1 to 1 correspondence with the facts about a quantum system that can be computed using the Born rule. Therefore the Born rule is anthropocentric if there are any facts about a quantum system that are inaccessible to humans. Such facts could be e.g. details about hypothetical hidden variables.

The no communication theorem depends on the Born rule, therefore it is anthropocentric as well.

Do you mean this?

https://www.amazon.com/dp/1107002176/?tag=pfamazon01-20

Yes.

 

[gentzen]

The argument goes as follows:
1. All humanly accessible facts about a quantum system are given by the Born rule.
2. Any fact about a quantum system that is not accessible to humans is not given by the Born rule.
...
The no communication theorem depends on the Born rule, therefore it is anthropocentric as well.

You seem to define "fact accessible to humans" in a very special way, otherwise you would not claim that 2. is true. The Born rule itself has no problem to be used with observables whose actual measurement would be beyond the current technical abilities of humans.

From my point of view, both the Born rule and the no communication theorem contain multiple ingrediends, some more anthropocentric, some less. So trying to transfer information by making a specific measurement first sounds quite anthropocentric, but in the end it is not overly important for the theorem "why" a specific measurement took place. The observables occurring in the Born rule seem to be quite anthropocentric, but that may be a misinterpretation. It might instead be the case that both the Hamiltonian and the relevant observables are required to define a specific quantum model. For me personally, I find it easier to disentangle the anthropocentric elements from the non-anthropocentric elements for the no communication theorem, than for the Born rule.

 

[CoolMint]

Pointless discussion. To know whether anything is anthropocentric is akin to knowing whether when a tree falls in a forest and no one is around to hear it it makes a sound.

 

[Nullstein]

You seem to define "fact accessible to humans" in a very special way, otherwise you would not claim that 2. is true. The Born rule itself has no problem to be used with observables whose actual measurement would be beyond the current technical abilities of humans.

Right, but I'm talking about facts that are in principle accessible to humans. Facts that are in principle accessible to humans are in 1 to 1 correspondence with facts that can be calculated by the Born rule, hence it is anthropocentric.

 

[gentzen]

Pointless discussion. To know whether anything is anthropocentric is akin to knowing whether when a tree falls in a forest and no one is around to hear it it makes a sound.

But that was the point of the discussion. The randomness in the no communication theorem seems to have specific anthropocentric requirements, which would be satisfied by "absolute true randomness", but it is unclear whether non-relative randomness can really exist. Now in addition to this "interesting riddle", there are also many other elements where one could discuss whether they are anthropocentric or not, but that just leads to pointless discussions which distract from the "interesting riddle".

Because communication is an anthropocentric notion. If the theory needs to be fine tuned to make communication impossible, this is thus a very anthropocentric requirement.

That is an impressively nice thought. Much nicer and deeper than your later elaboration:
...
The nice thing about your thought is that quantum randomness should better not be anthropocentric and relative. Or maybe it should, because "true randomness" is.

 

[PeterDonis]

I don't know if it does

In other words, your claim is not "standard QM". It's your opinion.

You claim that collapse happens all the time, independent of measurement.

No, that's not what I have been claiming. I have been claiming that "measurement" is not limited to experiments run by humans; an object like the Moon is "measuring" itself constantly, whether a human looks at it or not.

The no communication theorem involves many other things, but the crucial ingredient that makes it anthropocentric is the Born rule.

This doesn't change anything I have said.

I don't think we're going to make any further progress in this discussion.

 

[PeroK]

Pointless discussion. To know whether anything is anthropocentric is akin to knowing whether when a tree falls in a forest and no one is around to hear it it makes a sound.

That would be more arboreocentric!

 

[Nullstein]

In other words, your claim is not "standard QM". It's your opinion.

No, that doesn't follow. Standard QM books don't waste time on hidden variable theories, so they are not explicit about all this stuff. But every standard QM book will state that the measurable facts about a quantum system are calculated by the Born rule. And measurable means measurable in principle by humans here.

No, that's not what I have been claiming. I have been claiming that "measurement" is not limited to experiments run by humans; an object like the Moon is "measuring" itself constantly, whether a human looks at it or not.

I don't think that we currently know under what circumstances a measurement happens, but anyway. I told you, I will happily concede whatever you want me to about the time of collapse, because it's not relevant to my argument.

This doesn't change anything I have said.

That is in fact correct, but only because you haven't said anything about the actual argument.

If the facts about a quantum system that can in principle be measured by humans are in 1 to 1 correspondence with the facts that are predicted by the Born rule (which they are), then the predictions of the Born rule are anthropocentric. Humans can only communicate using those facts which are accessible to them. The no communication theorem shows that those facts that are in principle accessible to humans can't be used for communication.

 

[PeterDonis]

If the facts about a quantum system that can in principle be measured by humans are in 1 to 1 correspondence with the facts that are predicted by the Born rule (which they are)

No, they're not. This seems to be a fundamental disagreement we have. I don't think we're going to resolve it.

 

[Nullstein]

No, they're not. This seems to be a fundamental disagreement we have. I don't think we're going to resolve it.

I don't see how you can defend this position. In order to disagree, you must be able to name one fact about a quantum system that that is accessible for humans but not predicted by the Born rule. I honestly think there isn't. The axioms of QM just don't offer any other method to extract information from a quantum state other than the Born rule.

 

[PeterDonis]

In order to disagree, you must be able to name one fact about a quantum system that that is accessible for humans but not predicted by the Born rule.

You have it backwards. My point is that there are many situations (like the orbit of the Moon 4 billion years ago) to which the Born rule can perfectly well be applied but which don't involve human measurements or observations.

 

[Nullstein]

Wikipedia is not a valid reference. You need to reference a textbook or peer-reviewed paper. (You do that for Boltzmann so that part is fine, although I don't have those books so I can't personally check the references.)

Fine, check Tolman (The Principles of Statistical Mechanics). Can you now explain what point in the last paragraph of post #125 you disagree with?

You have it backwards. My point is that there are many situations (like the orbit of the Moon 4 billion years ago) to which the Born rule can perfectly well be applied but which don't involve human measurements or observations.

But so what? The orbit of the moon is in principle measurable by humans, so it's not a counterexample. If nobody measured it 4 billion years ago, it's only because there were no humans at that time, not because it's not in principle measurable.

 

[PeterDonis]

The orbit of the moon is in principle measurable by humans

Then what isn't in principle measurable by humans? Your basic rule seems to be that anything to which the Born rule applies is "in principle measurable by humans" by definition, which is arguing in a circle.

 

[Fra]

in principle measurable by humans

Are you literally talking about humans(=physicists?) Or do you by human metaphor for any "observer/agent/meausurement device" ?

If the former do you refer to single human, or humans as in the whole scientific community? (ie intercommunication presumed? This would imply that invidivual observations by single human/physicists would not count, unless consensus is attained)

/Fredrik

 

[CoolMint]

Then what isn't in principle measurable by humans?

Systems isolated from the environment.

 

[Fra]

The no communication theorem is about measurement, which is an anthropocentric notion.

Reflecting again on this, my reaction is here, why the reference to humans. This is IMO introducing some fog, as was always the case in QM since the days of Heisenberg. If we can rephrase this to measurement beeing defined relative to a material observer/agent, then I would agree with this. The "external" view of the measurement process would rather be a normal interaction (following the laws of physics). It's only the inside observer that talks about it's own "measurement" of course. Other observers "measurements" are denoted as normal interactions.

From my perspective, the no communication theorem tells us something about the nature of causality in the laws of physics (that we do not yet understand btw). But I do not see why we need to bring "humans" into discussion? It gets confusing. Unless one actually refers to it as the "scientific consensus", it what is the communityes current "state of knowledge" of the laws of physics. But I do not think that is what is beeing discussed here?

/Fredrik

 

[jbergman]

Okay, let me try differently: Are there any entities in the universe, other than humans, that make use of the Born rule? The role of the Born rule is to extract relative frequencies from the state of the system. Relative frequencies are something that humans have ascribed meaning to. The system would evolve just fine if we didn't ascribe meaning to the relative frequencies. They play no role in the evolution laws of the system. All the universe needs is the wave function and the Hamilton operator. We could also decide to ascribe meaning to the value $\xi:=\psi(3)+\psi(8)$, but we don't because we are not interested in it, because it never appears as a result on any of our measurement devices. It is inaccessible to us. What we find interesting is the value $P([1,2]) := \int_1^2 |\psi(x)|^2\mathrm d x$. That's just a definition made by humans, just like my definition of $\xi$ earlier. But it is accessible to us by clever measurement setups.

As an analogy, think of temperature in classical statistical mechanics. The system is made of particles that evolve just fine according to Hamiltons equations of motion. There is no fundamental need for a quantity like temperature. It's invented by humans to quantify an aggregate property of the system. We could also define the variable $\eta:=x_{29} + x_{10^{23}+8}$, but it is of no interest to us, so we don't.

Thought experiment. Imagine instead of the Schrodinger's cat experiment, we set up a similar setup but the two outcomes are to either fill a bowl with dog food or water.

Then if a dog goes in there it will either eat the food or drink the water. You seem to be suggesting that without human observation, the dog is in a superposition of doing both.

Somehow this bothers me.

 

[DrChinese]

1. [The no communication theorem] says that no local operation at Bob's distant system (in the sense of separation by tensor products) can cause any disturbance of measurement results at Alice's local system...

2. The Born rule obeys locality. So if there was non-locality, then there would be non-local effects everywhere, but the theory would prohibit them from being observable even in principle (not just due to insufficient equipment).

3. If the facts about a quantum system that can in principle be measured by humans are in 1 to 1 correspondence with the facts that are predicted by the Born rule (which they are), then the predictions of the Born rule are anthropocentric.

1. This leaves out a critical component of the theorem: it's not that there can't be a change in the measurement results for Alice, because there might be... we don't currently know if that is the case or not (since that is an interpretational issue). I can always assert that the choice of measurement basis by Bob "causes" Alice's state to a very specific one (obviously randomly, at least as it appears to human observers). For the theorem itself: it's that Alice alone cannot detect a disturbance of those results - which is not an interpretational issue.2. To the extent that there is a question about locality or non-locality related to the Born rule: the Born Rule should not be considered local. Obviously, once Bob knows his measurement result, if he knows what distant Alice is measuring, he knows information about Alice's result - according to the Born rule. I don't see locality really applying one way or the other, but there is certainly nothing (random) limited here to c. But maybe someone has a good reference that says exactly otherwise. (Again, it is easy to fall into interpretational issues.) 3. But more importantly: I don't believe it is fair to say that there is some special connection between the Born Rule and human observers (anthropocentric). For example, Zurek (2002) derives the Born Rule from other quantum principles, and skips the idea of measurement:

"This is Born’s rule. We have derived it from the most fundamental properties of quantum physics, including in particular these embodied in envariance. In contrast with the other derivations, it relies on the most quantum of foundations – the incompatibility of the knowledge about the whole and about the parts, mandated by entanglement. It explains how Born’s rule arises in a purely quantum setting, i.e., without appeals to “collapse”, “measurement”, or any other such deus ex machina imposition of the symptoms of classicality that violate the unitary spirit of quantum theory."

From (14) of: https://arxiv.org/abs/quant-ph/0211037

 

[Nullstein]

Then what isn't in principle measurable by humans? Your basic rule seems to be that anything to which the Born rule applies is "in principle measurable by humans" by definition, which is arguing in a circle.

In standard QM, this would e.g. be the phase of the wave function. Humans cannot measure it. But this really becomes relevant as soon as you introduce any additional entities such as hidden variables. No facts about the hidden variables are accessible to humans. The facts that are accessible to humans is still in 1 to 1 correspondence with the facts that are predicted by the Born rule.

 

[Nullstein]

Reflecting again on this, my reaction is here, why the reference to humans. This is IMO introducing some fog, as was always the case in QM since the days of Heisenberg. If we can rephrase this to measurement beeing defined relative to a material observer/agent, then I would agree with this. The "external" view of the measurement process would rather be a normal interaction (following the laws of physics). It's only the inside observer that talks about it's own "measurement" of course. Other observers "measurements" are denoted as normal interactions.

From my perspective, the no communication theorem tells us something about the nature of causality in the laws of physics (that we do not yet understand btw). But I do not see why we need to bring "humans" into discussion? It gets confusing. Unless one actually refers to it as the "scientific consensus", it what is the communityes current "state of knowledge" of the laws of physics. But I do not think that is what is beeing discussed here?

/Fredrik

You are right, a better word would be agentocentric if there is such a thing. It's not solely about humans, but about agents.

 

[Nullstein]

Thought experiment. Imagine instead of the Schrodinger's cat experiment, we set up a similar setup but the two outcomes are to either fill a bowl with dog food or water.

Then if a dog goes in there it will either eat the food or drink the water. You seem to be suggesting that without human observation, the dog is in a superposition of doing both.

Somehow this bothers me.

This is in fact observer dependent. There is such a scenario was Wigner's friend and you don't even need to replace humans by dogs in order to arrive at it.

 

[Nullstein]

1. This leaves out a critical component of the theorem: it's not that there can't be a change in the measurement results for Alice, because there might be... we don't currently know if that is the case or not (since that is an interpretational issue). I can always assert that the choice of measurement basis by Bob "causes" Alice's state to a very specific one (obviously randomly, at least as it appears to human observers). For the theorem itself: it's that Alice alone cannot detect a disturbance of those results - which is not an interpretational issue.

Well, yes, this is basically the point I'm making. If there were non-local cause and effect relationships, the no communication theorem shows that they cannot even in principle be detected or exploited by humans (agents). This makes any non-local theory that reproduces QM anthropocentric (agentocentric).

2. To the extent that there is a question about locality or non-locality related to the Born rule: the Born Rule should not be considered local. Obviously, once Bob knows his measurement result, if he knows what distant Alice is measuring, he knows information about Alice's result - according to the Born rule. I don't see locality really applying one way or the other, but there is certainly nothing (random) limited here to c. But maybe someone has a good reference that says exactly otherwise. (Again, it is easy to fall into interpretational issues.)

I think this is just a terminology issue. When we say something is local, we usually mean that all cause and effect relationships obey the speed of light limit. The Born rule just predicts probabilities, it can't be local or non-local. The underlying theory can be. In the same sense, the classical probability assignment e.g. in the Bertelmann's socks scenario isn't local or non-local either, just because it predicts correlations between spacelike separated events. Correlations between spacelike separated events don't necessarily require non-local cause and effect relationships. Whether there are such non-local effects can only be decided by looking at the concrete underlying theory, not just at the predicted probabilities.

3. But more importantly: I don't believe it is fair to say that there is some special connection between the Born Rule and human observers (anthropocentric). For example, Zurek (2002) derives the Born Rule from other quantum principles, and skips the idea of measurement:

"This is Born’s rule. We have derived it from the most fundamental properties of quantum physics, including in particular these embodied in envariance. In contrast with the other derivations, it relies on the most quantum of foundations – the incompatibility of the knowledge about the whole and about the parts, mandated by entanglement. It explains how Born’s rule arises in a purely quantum setting, i.e., without appeals to “collapse”, “measurement”, or any other such deus ex machina imposition of the symptoms of classicality that violate the unitary spirit of quantum theory."

From (14) of: https://arxiv.org/abs/quant-ph/0211037

Zurek's derivation of the Born rule is universally acknowledged to be flawed though.

 

[PeterDonis]

Zurek's derivation of the Born rule is universally acknowledged to be flawed though.

Enough is enough. This kind of claim is one you cannot possibly substantiate with references. You've had more than enough opportunity to state your views and you seem unable to consider different viewpoints.

Thread closed.