What is the current perspective on quantum interpretation?

[Sunil]

Again: Local relativistic QFTs are a QT (afaik the only type we have) which is consistent with Einstein causality by implementing the microcausality constraints between any local observable with the Hamiltonian density. As a QT it's of course not a local deterministic theory but implies, as any QT, the probabilistic (and only probabilistic) meaning of quantum states, and thus there is no contradiction between long-ranged correlations described by entanglement and Einstein causality though of course it is incompatible with the predictions of local deterministic HV theories, as shown by Bell.

The disagreement remains to be one about causality but now shifts toward "Einstein causality".

I insist that to name something "causality" which does not have a principle of common cause is misleading.

Signal "causality" is that weaker notion of causality which is compatible with QFT, but it is not a variant of causality, it is something much weaker, it is only about correlations between what can be produced at some "source" and what can be measured at some "receiver". Instead, a notion of full causality, including a common cause principle, would be sufficient to prove the BI. Thus, to be compatible with QT/QFT, one needs a preferred frame with return to classical causality.

 

[vanhees71]

I don't understand what you mean by causality then. We are talking about relativistic causality, where causal connections cannot be between spacelike separated events. In non-relativistic physics there's no such constraint, and you have usually actions at a distance anyway. So here's also no tension between the collapse postulate and causality.

A causal connection is not the same as correlations of course. Causal connections are always due to a signal in relativistic physics (at least in our standard realizations as local (classical or quantum) field theories). There can be correlations between local observables measured at space-like separated spacetime points due to the state of the system (particularly in the case where a quantum system has entangled far-distantly measured subsystems).

 

[Demystifier]

the probabilistic (and only probabilistic) meaning of quantum states

If the interpretation was probabilistic and only probabilistic, then collapse would be interpreted as update and only update. Denying collapse (by the argument that it violates locality or Schrodinger equation) makes sense only if quantum state is not probabilistic and only probabilistic.

 

[vanhees71]

I think we argue in circles again...

I don't understand, for what I'd need a collapse assumption, which cannot be made in the fundamental formulation of the theory, because what happens with the system in the measurement process depends on the used measurment apparatus and if you need to determine a state after a measurement you have to think about how to get this new state case by case.

The "collapse" is a FAPP description for a very limited type of "measurements", namely von Neumann filter measurements.

 

[Demystifier]

The "collapse" is a FAPP description for a very limited type of "measurements", namely von Neumann filter measurements.

No. Even for general POVM measurements there is a generalized collapse rule
$$|\psi\rangle\to\frac{M_k|\psi\rangle}{|M_k|\psi\rangle|}$$
where $M_k$ are Kraus operators for the POVM
$$\sum_k M_k^{\dagger}M_k=1$$
Recall https://www.physicsforums.com/threads/difference-between-collapse-and-projection.998545/post-6445457 for photon measurement.

The projective "filter" measurements are a special case in which $M_k$ are projectors satisfying $M_k M_{k'}=M_k\delta_{kk'}$.

 

[atyy]

I think we argue in circles again...

I don't understand, for what I'd need a collapse assumption, which cannot be made in the fundamental formulation of the theory, because what happens with the system in the measurement process depends on the used measurment apparatus and if you need to determine a state after a measurement you have to think about how to get this new state case by case.

The "collapse" is a FAPP description for a very limited type of "measurements", namely von Neumann filter measurements.

It's a useful tool to understand what you mean by Einstein causality, ie. to understand whether you mean "classical relativistic causality" or "no superluminal signaling". Quantum theory is not consistent with classical relativistic causality, but it is consistent with no superluminal signaling.

It seems that although you reject classical relativistic causality because of the Bell inequality violations, it seems that you also accept it because of your rejection of physical collapse.

It doesn't make sense to reject collapse as inconsistent with no superluminal signaling, since interpreting the state update as physical collapse is consistent with no superluminal signaling.

 

[martinbn]

It's a useful tool to understand what you mean by Einstein causality, ie. to understand whether you mean "classical relativistic causality" or "no superluminal signaling". Quantum theory is not consistent with classical relativistic causality, but it is consistent with no superluminal signaling.

It seems that although you reject classical relativistic causality because of the Bell inequality violations, it seems that you also accept it because of your rejection of physical collapse.

It doesn't make sense to reject collapse as inconsistent with no superluminal signaling, since interpreting the state update as physical collapse is consistent with no superluminal signaling.

Can you tell us what "classical relativistic causality" is?

 

[Sunil]

I don't understand what you mean by causality then. We are talking about relativistic causality, where causal connections cannot be between spacelike separated events.

Of course, causality was part of physics even before 1905, so that it makes no sense to incorporate relativity into the very definition of causality. My understanding of classical causality necessarily includes a principle of common cause: Observed correlations require a causal explanation. Which can be a direct causal connection as well as a correlation caused by some common cause.
In non-relativistic physics there's no such constraint, and you have usually actions at a distance anyway. So here's also no tension between the collapse postulate and causality.

A causal connection is not the same as correlations of course. Causal connections are always due to a signal in relativistic physics (at least in our standard realizations as local (classical or quantum) field theories). There can be correlations between local observables measured at space-like separated spacetime points due to the state of the system (particularly in the case where a quantum system has entangled far-distantly measured subsystems).

So, your "there can be correlations ..." is followed by a "due to", showing that in your notion of causality a correlation also requires some causal explanation. A notion of causality which would say "some correlations can happen without any causal connection" is simply not worth to be named causality.

But if something is sufficient as an explanation of a correlation has a well-defined mathematical meaning. It means that if we control for the common cause C, then A and B become independent again: $P(A\land B|C) = P(A|C)P(B|C)$. And this is enough to prove the Bell inequalities. And therefore a theory with relativistic causality cannot make the predictions of QT. You have to give up Einstein causality, to replace it by some non-causality misnamed "signal causality".

 

[vanhees71]

It's a useful tool to understand what you mean by Einstein causality, ie. to understand whether you mean "classical relativistic causality" or "no superluminal signaling". Quantum theory is not consistent with classical relativistic causality, but it is consistent with no superluminal signaling.

It seems that although you reject classical relativistic causality because of the Bell inequality violations, it seems that you also accept it because of your rejection of physical collapse.

It doesn't make sense to reject collapse as inconsistent with no superluminal signaling, since interpreting the state update as physical collapse is consistent with no superluminal signaling.

What do you mean by "classical relativistic causality" then? For me causality simply means that two space-like separated events cannot be causally connected and that implies that signals can propagate maximally at the speed of light (i.e., such signals that are mediated by a massless field as the em. field).

Bell inequalities describe however constraints on correlations, and correlations can exist across spacelike separated parts of a system, e.g., the entangled photon pairs used in Bell experiments. Here measurements on far-distant parts show correlations violating Bell's inequalities showing that QT is incompatible with any local determinstic HV theory. The correlations are found also when the registration events of the two photons are spacelike separated. As you admit that local relativistic QFTs exclude faster-than light signalling this implies that within these QFTs it's impossible that the correlations are due to causal effects of one measurement on the other, and this excludes at least a naive collapse assumption: All that changes causally when A registers her photon can only be within the future light cone of this measurment event and thus there cannot be any causal influence on B's measurement result from A's measurement. So there cannot be any collapse in the sense of a dynamical causal physical process.

Note that there arise no contradictions when you assume a kind of "local collapse", i.e., if you just interpret "collapse" as an update of the state description by one of the observers. Say A has measured the polarization of her photon (prepared as one of the usual Bell states of a photon pair) being $H$. Then she knows that with certainty B must find his photon to be $V$ polarized (i.e., no matter when B measures his photon, i.e., before A's measurement or after A's measurement or even simultaneously or if his measurement event is space-like separated). Of course then $A$ may update her description of the pair to $|HV \rangle$ without changing any of her predictions what B has measured/will measure as compared to the predictions by using the original entangled state. So indeed, within local relativistic QFTs, there's no way to use entanglement for faster-than-light signalling.

 

[vanhees71]

Of course, causality was part of physics even before 1905, so that it makes no sense to incorporate relativity into the very definition of causality. My understanding of classical causality necessarily includes a principle of common cause: Observed correlations require a causal explanation. Which can be a direct causal connection as well as a correlation caused by some common cause.
In non-relativistic physics there's no such constraint, and you have usually actions at a distance anyway. So here's also no tension between the collapse postulate and causality.

So, your "there can be correlations ..." is followed by a "due to", showing that in your notion of causality a correlation also requires some causal explanation. A notion of causality which would say "some correlations can happen without any causal connection" is simply not worth to be named causality.

But if something is sufficient as an explanation of a correlation has a well-defined mathematical meaning. It means that if we control for the common cause C, then A and B become independent again: $P(A\land B|C) = P(A|C)P(B|C)$. And this is enough to prove the Bell inequalities. And therefore a theory with relativistic causality cannot make the predictions of QT. You have to give up Einstein causality, to replace it by some non-causality misnamed "signal causality".

The point to argue within relativistic physics is of course that there is no tension between causality and the collapse postulate within non-relativistic physics. In Galilean spacetime instantaneous actions at a distance are not excluded but rather usually what's used (e.g., in Newton's theory of the gravitational interaction). So there's simply nothing to argue about within non-relativistic QM.

The correlations described by entangled states are of course due to the fact that the system is prepared in such a state in the beginning. In that sense the correlations have a cause, but the cause is the preparation in an entangled state at the very beginning and not due to the measurement at part A of the system which may be very far distant from part B.

I don't understand your last paragraph: Most of the Bell tests are done with photon pairs, which are correctly described within standard QED, which is a local relativistic QFT leading to the very prediction of the violation of Bell's inequality. For me Einstein causality simply is that there are no causal connections between space-like separated events, and that's what's implied by the very construnction of local relativistic QFTs (microcausality condition).

 

[atyy]

What do you mean by "classical relativistic causality" then? For me causality simply means that two space-like separated events cannot be causally connected and that implies that signals can propagate maximally at the speed of light (i.e., such signals that are mediated by a massless field as the em. field).

Bell inequalities describe however constraints on correlations, and correlations can exist across spacelike separated parts of a system, e.g., the entangled photon pairs used in Bell experiments. Here measurements on far-distant parts show correlations violating Bell's inequalities showing that QT is incompatible with any local determinstic HV theory. The correlations are found also when the registration events of the two photons are spacelike separated. As you admit that local relativistic QFTs exclude faster-than light signalling this implies that within these QFTs it's impossible that the correlations are due to causal effects of one measurement on the other, and this excludes at least a naive collapse assumption: All that changes causally when A registers her photon can only be within the future light cone of this measurment event and thus there cannot be any causal influence on B's measurement result from A's measurement. So there cannot be any collapse in the sense of a dynamical causal physical process.

Note that there arise no contradictions when you assume a kind of "local collapse", i.e., if you just interpret "collapse" as an update of the state description by one of the observers. Say A has measured the polarization of her photon (prepared as one of the usual Bell states of a photon pair) being H. Then she knows that with certainty B must find his photon to be V polarized (i.e., no matter when B measures his photon, i.e., before A's measurement or after A's measurement or even simultaneously or if his measurement event is space-like separated). Of course then A may update her description of the pair to |HV⟩ without changing any of her predictions what B has measured/will measure as compared to the predictions by using the original entangled state. So indeed, within local relativistic QFTs, there's no way to use entanglement for faster-than-light signalling.

The problem with your argument is that no prediction is changed by physical collapse. So whether the collapse is physical or just a state update, all predictions of the theory are the same.

 

[martinbn]

The problem with your argument is that no prediction is changed by physical collapse. So whether the collapse is physical or just a state update, all predictions of the theory are the same.

To me this is an argument against physical collapse. If all the experiments, even in principle, cannot tell the difference, then what does it mean to say that it was physical!

ps What is "classical relativistic causality" and what is its relation to "no faster than light signalling"?

 

[vanhees71]

The problem with your argument is that no prediction is changed by physical collapse. So whether the collapse is physical or just a state update, all predictions of the theory are the same.

The important difference is that the interpretation as state update is not in contradiction with the mathematical foundation, but the collapse is!

 

[stevendaryl]

In my opinion, as I said in another thread about interpretations, the interpretation of collapse as state update is nonsensical, while the interpretation of collapse as physical is wrong.

Why do I say it's nonsensical to interpret collapse as state update? State update makes sense in classical probability, because the probability distribution is assumed to reflect the observer's lack of information about the actual state of affairs. When you learn something new, then you update the probability distribution to reflect that new information. That's sensible, but the underlying assumption is that probabilities are subjective. But in QM, the probabilities that come from the wave function cannot be interpreted as subjective. That would be a hidden-variables theory, not pure QM.

Let's consider the case of an anti-correlated twin-pair EPR experiment. For now, let's assume that it's agreed that Alice and Bob will measure the spin of their particle along the z-axis. Then when Alice measures her particle to have spin-up, she knows immediately that Bob will measure spin-down. To interpret this as just a "state update" means that the result of Bob's measurement was determined before Alice performed her measurement, and her measurement simply revealed this pre-existing value. That's a hidden variable theory.

 

[atyy]

The important difference is that the interpretation as state update is not in contradiction with the mathematical foundation, but the collapse is!

But no equation changes between state update and physical collapse, so how can physical collapse be in contradiction to the mathematical foundation?

 

[stevendaryl]

But no equation changes between state update and physical collapse, so how can physical collapse be in contradiction to the mathematical foundation?

I think you're right, that collapse or no collapse makes no difference to the mathematical foundation. However, I think the distinction is this: A collapse interpretation (along with other interpretations such as Bohmian mechanics) would mean that relativity is wrong. Relativity would still be recoverable as an effective, approximate theory, valid in certain circumstances.

 

[vanhees71]

But no equation changes between state update and physical collapse, so how can physical collapse be in contradiction to the mathematical foundation?

Well collapse means that instantaneously to a measurement the entire state changes to an eigenstate of the measured observable with the corresponding eigenstate, namely to the projection of the state before measurement to that corresponding eigenspace. If you take this as a physical process there's a contradiction in the case of relativistic microcausal QFTs, because the measurement is local and thus all interactions cannot leads to causal changes over space-like separated space-time points. So there's nothing in the formalism that allows for a collapse as a dynamical physical process.

On the other hand, why are you then so keen to keep the collapse in the interpretation, if it doesn't make any difference anyway? I agree with that, and because of these contradictions with the formalism I just don't use the collapse assumption without loosing anything in the application of the formalism to the description of experiments in the lab.

 

[atyy]

Well collapse means that instantaneously to a measurement the entire state changes to an eigenstate of the measured observable with the corresponding eigenstate, namely to the projection of the state before measurement to that corresponding eigenspace. If you take this as a physical process there's a contradiction in the case of relativistic microcausal QFTs, because the measurement is local and thus all interactions cannot leads to causal changes over space-like separated space-time points. So there's nothing in the formalism that allows for a collapse as a dynamical physical process.

But this argument is not correct. Microcausality imposes no superluminal signaling, Collapse interpreted as physical is also consistent with no superluminal signaling. So it doesn't make sense to say that collapse is inconsistent with microcausality.

On the other hand, why are you then so keen to keep the collapse in the interpretation, if it doesn't make any difference anyway? I agree with that, and because of these contradictions with the formalism I just don't use the collapse assumption without loosing anything in the application of the formalism to the description of experiments in the lab.

I prefer the state update interpretation, but I think it's important to get the understanding of microcausality correct. Microcausality is about there being no superluminal signaling, so it is consistent with collapse interpreted physically. By rejecting physical collapse on the basis of "microcausality", you are using a different intuition that is like classical relativistic causality to apply to microcausality. But it isn't correct to think of "microcausality" like classical relativistic causality.

 

[Sunil]

The point to argue within relativistic physics is of course that there is no tension between causality and the collapse postulate within non-relativistic physics.

Ok, but that does not mean that you can simply invent some new notion of "relativistic causality" which has nothing to do with the original notion of causality which becomes even stronger once we restrict the allowed causal connections to the lightcone.

The correlations described by entangled states are of course due to the fact that the system is prepared in such a state in the beginning. In that sense the correlations have a cause, but the cause is the preparation in an entangled state at the very beginning and not due to the measurement at part A of the system which may be very far distant from part B.

And once you identify the common cause with this preparation, you can apply $P(AB|C) = P(A|C)P(B|C)$. Apply it to the measurement in the same direction, with 100% correlation, and you get that the preparation gives either P(A|C)=1 or P(A|C)=0, thus, the measurement result is predefined by the state. With this assumption, the remaining proof of the BI becomes trivial.

I don't understand your last paragraph: Most of the Bell tests are done with photon pairs, which are correctly described within standard QED, which is a local relativistic QFT leading to the very prediction of the violation of Bell's inequality. For me Einstein causality simply is that there are no causal connections between space-like separated events, and that's what's implied by the very construnction of local relativistic QFTs (microcausality condition).

For me, Einstein causality is classical causality strengthened by the additional restriction that causal connections are allowed only inside the light cones. That means, if we have Einstein causality, we can prove the BI. Once the BI are violated, QED is not an Einstein-causal theory.

You have only that "signal causality", which follows from that "microcausality", both being essentially weaker than real causality with common cause principle.

 

[vanhees71]

But this argument is not correct. Microcausality imposes no superluminal signaling, Collapse interpreted as physical is also consistent with no superluminal signaling. So it doesn't make sense to say that collapse is inconsistent with microcausality.
I prefer the state update interpretation, but I think it's important to get the understanding of microcausality correct. Microcausality is about there being no superluminal signaling, so it is consistent with collapse interpreted physically. By rejecting physical collapse on the basis of "microcausality", you are using a different intuition that is like classical relativistic causality to apply to microcausality. But it isn't correct to think of "microcausality" like classical relativistic causality.

How can microcausality (implying the impossibility of superluminal signaling) be consistent with collapse as a physical process since the collapse clearly predicts superluminal signaling. Take the standard entangled photon pair. If you consider collapse a physical process, then when A finds her photon being H-polarized, the state instantaneously collapses to $|HV \rangle \langle HV|$, i.e., instaneously Bob's photon gets into the state $|V \rangle \langle V|$, while before its state clearly was different, namely $\hat{1}/2$ even Bob may be light-years away from Alice. That's clearly inconsistent with the impossibility of superluminal signaling.

The way out is also clear: You interpret the quantum state simply as what it is, namely providing probabilities for the outcome of measurements, including the correlations described by entanglement. Then you don't need any collapse to understand the 100% correlation between the polarizations of the photons, because it's already there from the very beginning when the photon pairs are prepared in this entangled state. It's not A's measurement causing a collapse, including B's photon that is registered maybe lightyears away at the same time as A's (in their common rest frame, for simplicity of the argument), that causes the correlation but the preparation of the photons in the very beginning before any measurment has been performed, and in this way everything is consistent with the impossibility of faster-than-light signalling and thus the microcausality property of QED.

I still don't get what you mean by "classical relativistic causality" in contradistinction to "microcausality". For me microcausality simply is a way to guarantee that the oucome of measurements must obey "relativistic causility". I don't know what you mean by "classical causality". Causality has the same meaning in all of physics.

 

[vanhees71]

You have only that "signal causality", which follows from that "microcausality", both being essentially weaker than real causality with common cause principle.

This makes no sense since QED IS a theory obeying Einstein causality by the imposing the microcausality constraint on local observables. I don't understand what you mean by "real causality with common cause principle" and why you think "signal causality" is in some sense weaker.

 

[martinbn]

I am still waiting for someone to explain the terms "Einstein causality", "classical relativistic causality", and "no faster than light signaling". Aren't they the same?

 

[Sunil]

This makes no sense since QED IS a theory obeying Einstein causality by the imposing the microcausality constraint on local observables.

No, it is not. What you can derive using that misnamed "microcausality" condition is only that (also misnamed) "signal causality", that you cannot send signals FTL. That's all. You don't have a common cause principle for that "microcausality".

I don't understand what you mean by "real causality with common cause principle" and why you think "signal causality" is in some sense weaker.

For the common cause principle, see https://plato.stanford.edu/entries/physics-Rpcc/. Some people are critical of it, in particular Arntzenius, but I have not found that criticism impressing. For example, one can formulate stochastic theories in such a way that the common cause does not appear in the theoretical formalism. So what? The principle is simple, if there is a correlation between A and B, it requires an explanation, which may be a direct causal influence $A\to B$ or $B\to A$ or some common cause $C\to A, C\to B$. The common cause is sufficient as an explanation if after controlling it the correlation disappears, $P(AB|C)=P(A|C)P(B|C)$, else the remaining correlation requires more explanation.

Once "signal causality" does not contain the common cause principle, it is much weaker and misnamed.

I am still waiting for someone to explain the terms "Einstein causality", "classical relativistic causality", and "no faster than light signaling". Aren't they the same?

Einstein causality is classical causality, inclusive the common cause principle, with the additional restriction that causal influences can exist only inside the light cone. "Signal causality" is the impossibility to send signals with FTL. It follows from Einstein causality but does not contain the common cause principle. That means, there may be arbitrary correlations between space-like separated events, but a request to explain them somehow will be ignored - correlations do not require causal explanations in signal causality.

So, assume you have two dices. If thrown at approximately the same time in the CMBR frame, they give always the same number. You obviously cannot use them to send signals. So, signal causality is not violated. It holds, and those dices give no reason to doubt that it holds.

Instead, in Einstein causality, these dices are surprising, and create an open scientific problem: To explain in a causal way why they give always the same number when thrown at the same time, even if that is done space-like separated.

 

[martinbn]

So when you say Einstein causality, you mean causality plus common cause principle. Who came up with this name? And what about all the objections to the common cause princple? Last time i asked you, you shruged it off. But why do you elevate it to a univarsal principle?

 

[vanhees71]

I am still waiting for someone to explain the terms "Einstein causality", "classical relativistic causality", and "no faster than light signaling". Aren't they the same?

I'm waiting too. For me they are all the same. I don't know what "classical" has to do with it. A theory is causal or not, no matter whether it's a classical (field) or a quantum (field) theory.

 

[atyy]

How can microcausality (implying the impossibility of superluminal signaling) be consistent with collapse as a physical process since the collapse clearly predicts superluminal signaling. Take the standard entangled photon pair. If you consider collapse a physical process, then when A finds her photon being H-polarized, the state instantaneously collapses to $|HV \rangle \langle HV|$, i.e., instaneously Bob's photon gets into the state $|V \rangle \langle V|$, while before its state clearly was different, namely $\hat{1}/2$ even Bob may be light-years away from Alice. That's clearly inconsistent with the impossibility of superluminal signaling.

Since collapse interpeted as a physical process doesn't change any predictions from state update, which you say is consistent with microcausality, the "superluminal signaling" you mention above for physical collapse is not observable.

Hence in quantum theory there are two definitions of "no superluminal signaling" - the unobservable definition and the observable definition. Collapse interpreted as a physical process is not consistent with the unobservable definition that you are using, but it is consistent with the observable definition.

 

[vanhees71]

Ok, "collapse" is so unsharply defined that you always can find some intepretation of this phrase that's consistent with the formalism. ;-)).

I don't know, what you mean by "unobservable definition".

 

[Fra]

I don't know, what you mean by "unobservable definition".

If we are thinking alike, it means the observable definition means that two observers can communicate at superluminal speeds. Alice and Bob can not do so.

In the case of statistical correlations, no one ever observers a FTL influence.

/Fredrik

 

[Sunil]

So when you say Einstein causality, you mean causality plus common cause principle. Who came up with this name?

I'm not a historian, I would naively guess that Reichenbach once it is named after him, but this is something one would have to check.

And what about all the objections to the common cause princple? Last time i asked you, you shruged it off. But why do you elevate it to a univarsal principle?

I did not found the objections impressive, as I said. If you feel differently for one of the many of those arguments, feel free to present it here and we will see. A forum is certainly not the place to write a complete refutation of all those arguments.

I elevate this to a universal principle because thinking about it I have recognized the central role of it in the scientific method. It is the very point of causality that, one the one hand, causality is something quite restricted, and, on the other hand, an arbitrary correlation requires a causal explanation.

If you give up to think that correlations require causal explanations, you can stop doing science and start astrology instead. Statistical experiments would not make sense. You have observed a correlation, so what?

Last but not least, there are correlations between the positions of stars and human behavior, quite in line with the predictions of astrology. Those who care about causal explanations explain them away mentioning that many people believe in astrology, so that one has to expect a lot of self-fulfilling prophecies. But once you don't think that such causal explanations are necessary, astrology itself will be fine too. Not?

 

[stevendaryl]

So when you say Einstein causality, you mean causality plus common cause principle. Who came up with this name? And what about all the objections to the common cause princple? Last time i asked you, you shruged it off. But why do you elevate it to a univarsal principle?

I don't think it's a matter of it being a universal principle, it's a matter of saying in what sense quantum mechanics is nonlocal. Before quantum mechanics, it was presumed that it was possible within a "patch" of spacetime, if not within the whole universe, to set up an inertial cartesian coordinate system $x, y, z, t$ such that the most complete description of that patch could be given by a state of the patch evolving over time: $S(t)$. The state would include facts about particles and fields. In terms of such a picture of the world, we can define locality in the following way:

Divide up the world (or the patch we're interested in) into boxes of size $\Delta x, \Delta y, \Delta z$. Label the boxes so that box $(i,j,k)$ is the region defined by the set of all points $(x,y,z)$ such that $i \Delta x \leq x \leq (i+1) \Delta x$, $j \Delta y \leq y \leq (j+1) \Delta y$, $k \Delta z \leq z \leq (k+1) \Delta x$.

The state $S(t)$ is said to be separable if it is possible to come up with "local states" $S_{ijk}(t)$ such that $S(t)$ is deducible from the values of all the $S_{ijk}(t)$, and vice-versa.

If the state of the world (or patch) is separable, then we can define locality in terms of the local states. If $\Delta t$ is an interval of time that is short enough that $c \Delta t \leq \Delta x$, $c \Delta t \leq \Delta y$, $c \Delta t \leq \Delta z$, then the evolution of local state $S_{ijk}(t)$ over the time from $t$ to $t + \Delta t$ can depend only on the states of neighboring boxes, (Box $(i,j,k)$ is a neighbor to Box $(i',j',k')$ is $|i - i'| \leq 1$, $|j - j'| \leq 1$, $|k - k'| \leq 1$).

 

[stevendaryl]

Quantum mechanics violates either locality or separability in the above sense. This is shown by the EPR experiment. If Alice and Bob are in regions that are far removed from each other spatially, the evolution of the state of Alice's region depends on what happens in Bob's region.

 

[Lord Jestocost]

Ok, "collapse" is so unsharply defined that you always can find some intepretation...

I don’t think that the terms “collapse” or “state reduction” are unsharply defined; maybe for those who got stuck in their classical world view and believe in some kind of ensemble interpretation. As Cord Friebe et al. put it in “The Philosophy of Quantum Physics”:

“Going one step further, we come to the ensemble interpretation: Here, the mathematical symbols indeed refer to microscopic objects, but only to a very large number of such systems. According to this view, quantum mechanics is a kind of statistical theory whose laws are those of large numbers. In regard to a particular system, this interpretation remains agnostic. This is not true of the ‘Copenhagen interpretation’: The physicists Niels Bohr and Werner Heisenberg were the first to presume that the formalism refers to particular quantum systems. This, however, caused a serious problem, since the question arose as to what would happen to such a system during a measurement. While Bohr remained reticent on this point and avoided discussing the details of the measurement process, Heisenberg emphasized the embedding of the measurement apparatus within an environment containing the observer as an essential element. At this point, the infamous collapse of the wavefunction comes into play; however, according to the Copenhagen interpretation, it is either merely methodological, or explicitly epistemological, but in any case not to be understood as ontological.”
[bold by LJ]

 

[martinbn]

I don't think it's a matter of it being a universal principle, it's a matter of saying in what sense quantum mechanics is nonlocal. Before quantum mechanics, it was presumed that it was possible within a "patch" of spacetime, if not within the whole universe, to set up an inertial cartesian coordinate system $x, y, z, t$ such that the most complete description of that patch could be given by a state of the patch evolving over time: $S(t)$. The state would include facts about particles and fields. In terms of such a picture of the world, we can define locality in the following way:

Divide up the world (or the patch we're interested in) into boxes of size $\Delta x, \Delta y, \Delta z$. Label the boxes so that box $(i,j,k)$ is the region defined by the set of all points $(x,y,z)$ such that $i \Delta x \leq x \leq (i+1) \Delta x$, $j \Delta y \leq y \leq (j+1) \Delta y$, $k \Delta z \leq z \leq (k+1) \Delta x$.

The state $S(t)$ is said to be separable if it is possible to come up with "local states" $S_{ijk}(t)$ such that $S(t)$ is deducible from the values of all the $S_{ijk}(t)$, and vice-versa.

If the state of the world (or patch) is separable, then we can define locality in terms of the local states. If $\Delta t$ is an interval of time that is short enough that $c \Delta t \leq \Delta x$, $c \Delta t \leq \Delta y$, $c \Delta t \leq \Delta z$, then the evolution of local state $S_{ijk}(t)$ over the time from $t$ to $t + \Delta t$ can depend only on the states of neighboring boxes, (Box $(i,j,k)$ is a neighbor to Box $(i',j',k')$ is $|i - i'| \leq 1$, $|j - j'| \leq 1$, $|k - k'| \leq 1$).

Ok, that is what locality means. But how is it related to "nonlocality" in QM?

 

[martinbn]

Quantum mechanics violates either locality or separability in the above sense. This is shown by the EPR experiment. If Alice and Bob are in regions that are far removed from each other spatially, the evolution of the state of Alice's region depends on what happens in Bob's region.

This is what is not clear to me. What is the state of Alice's region and how does it depend on what happens in Bob's region?

 

[stevendaryl]

This is what is not clear to me. What is the state of Alice's region and how does it depend on what happens in Bob's region?

Well, I don't need to say precisely what the state is, other than Alice and Bob's measurement results are part of the state. (That is, different measurement results correspond to different states.)

Suppose we have an anti-correlated twin pair, and Alice and Bob are each measuring particle spin along the z-axis. Let's suppose that Bob performed his measurement before Alice (but close enough that there is no possibility for light to travel from Bob to Alice before Alice performs her measurement). Then whether Alice gets spin-up depends on whether Bob got spin-up or spin-down.