Undergrad What is the current perspective on quantum interpretation?

[stevendaryl]

You appear to be using a different definition than the "appropriate" one I just referred to; your apparent definition seems to be saying that, since knowing B's measurement result gives us additional information about the probabilities for A's measurement result, we need to "check on the state" of B in order to make a prediction about the state of A. However, by this definition, it is equally true that we need to check on the state of A in order to make a prediction about the state of B. But those two claims, combined, would put us into a never-ending circle of checking on B to check on A to check on B to check on A to...

No, it just means that the evolution of the global state does not "factor" into evolution of local states. Or, maybe the global state is more than the sum of all the local states.

Let me illustrate with a very simple discrete-time cellular automaton analogy

Suppose you have a cellular automaton with 4 cells labeled $A, AN, C, BN, B$.

• Cell $A$ has $AN$ as a neighbor.
• Cell $AN$ has both $A$ and $C$ as neighbors.
• Cell $C$ has both $AN$ and $BN$ as neighbors.
• Cell $BN$ has both $C$ and $B$ as neighbors.
• Cell $B$ has only $BN$ as a neighbor.

Let $V$ be the set of possible states of any cell. A state of the whole automaton is a 5-tuple of values $a, an, c, bn, b$, each value an element of $V$. If $s$ is a state of the whole automaton, then I will use $s[a]$ to mean the state of cell $A$, $s[an]$ is the state of cell $AN$, etc.

Then there is a transition relation $T(s, s')$ that describes the evolution of the cellular automaton. The meaning is that if the global state at time $t$ is $s$, then $s'$ is a possible global state at time $t+1$. (We could make this model more sophisticated by using probabilities, instead of possibilities, but this is just a toy model for the purpose of illustrating the concept of separability.)

We say that the transition relation $T$ obeys locality if it factors into 5 local transition relations

1. $T_1(a, an, a', an')$ governing cell $A$
2. $T_2(a, an, c, a', an', c')$ governing cell $AN$
3. $T_3(an, c, bn, an', c', bn')$ governing cell $C$
4. $T_4(c, bn, b, c', bn', b')$ governing cell $BN$
5. $T_5(bn, b, bn', b')$ governing cell $B$.

$T$ factors into these local transition relations in case

$T(s,s') \Leftrightarrow$
$T_1(s[a], s[an], s'[a], s'[an]) \wedge$
$T_2(s[a], s[an], s[c], s'[a], s'[an], s'[c]) \wedge$
$T_3(s[an], s[c], s[bn], s'[an], s'[c], s'[bn]) \wedge$
$T_4(s[c], s[bn], s[ b], s'[c], s'[bn], s'[ b]) \wedge$
$T_5(s[bn], s[ b], s'[bn], s'[ b])$

With Alice and Bob both measuring spins along the z-axis, the global transition relation does not factor into local transition relations.

 

[Anixx]

I trust in the consciousness causes 'collapse' (regardless if its physical or not) interpretation.

This is not an interpretation.

 

[PeterDonis]

it just means that the evolution of the global state does not "factor" into evolution of local states

This only makes sense if there is a "global state". It is not clear that there is one consistent with relativistic invariance.

a very simple discrete-time cellular automaton analogy

This is not a valid analogy because the corresponding things in the QM case are regions of spacetime. Regions of spacetime don't "update" from one "time" to the "next". They just are. And the "neighbor" connections between them are one-way causal relations, not two-way "neighbor" relations.

 

[stevendaryl]

This only makes sense if there is a "global state". It is not clear that there is one consistent with relativistic invariance.

Relativistic invariance doesn't prevent there from being a global state. The state would be frame-dependent, but I don't think that's a problem.

This is not a valid analogy because the corresponding things in the QM case are regions of spacetime. Regions of spacetime don't "update" from one "time" to the "next". They just are. And the "neighbor" connections between them are one-way causal relations, not two-way "neighbor" relations.

I think the analogy is very close. As I said earlier: Pick a "patch" of spacetime for which we can set up an inertial cartesian coordinate system $(x,y,z,t)$. You split space up into boxes with dimensions $\Delta x, \Delta y, \Delta z$. The state of one box at time $t+\Delta t$ depends on the state of that box and neighboring boxes at time $t$ (where "neighboring" means that some points in the neighboring box is less than or equal to $c \Delta t$).

 

[stevendaryl]

Relativistic invariance doesn't prevent there from being a global state. The state would be frame-dependent, but I don't think that's a problem.

For example, in flat spacetime, the classical (relativistic, but non-quantum) global state at time $t$ according to a Cartesian coordinate system $(x,y,z,t)$ would be provided by giving the values of $\vec{E}$ and $\vec{B}$ at each point $(x,y,z)$ at time $t$, and the positions and locations of each particle at time $t$.

 

[PeterDonis]

The state would be frame-dependent, but I don't think that's a problem.

I don't see how it wouldn't be a problem, since "frame-dependent" is inconsistent with "relativistically invariant".

For example, in flat spacetime, the classical (relativistic, but non-quantum) global state at time $t$ according to a Cartesian coordinate system $(x,y,z,t)$ would be provided by giving the values of $\vec{E}$ and $\vec{B}$ at each point $(x,y,z)$ at time $t$, and the positions and locations of each particle at time $t$.

This state is, as you say, frame-dependent, and therefore not relativistically invariant. So I am totally confused as to how you can say this isn't a problem for consistency with relativistic invariance.

 

[PeterDonis]

Pick a "patch" of spacetime for which we can set up an inertial cartesian coordinate system $(x,y,z,t)$. You split space up into boxes with dimensions $\Delta x, \Delta y, \Delta z$. The state of one box at time $t+\Delta t$ depends on the state of that box and neighboring boxes at time $t$ (where "neighboring" means that some points in the neighboring box is less than or equal to $c \Delta t$).

Again, this is not a valid analogy because your $A$, $AN$, $C$, $BN$, $B$ are not "boxes" in space, they are regions of spacetime. It makes no sense to talk about "updating the state" of a region of spacetime from one time to the next.

 

[stevendaryl]

Again, this is not a valid analogy because your $A$, $AN$, $C$, $BN$, $B$ are not "boxes" in space, they are regions of spacetime. It makes no sense to talk about "updating the state" of a region of spacetime from one time to the next.

I'm sorry if I gave the wrong impression. The cells correspond to regions in SPACE, not regions in SPACETIME.

 

[stevendaryl]

I don't see how it wouldn't be a problem, since "frame-dependent" is inconsistent with "relativistically invariant".

Why does it matter if the notion of "state" is relativistically invariant, or not?

As I said, we can pick an inertial cartesian coordinate system, and with respect to this coordinate system, we can (pre-quantum mechanics) define the "state of the universe (or the patch of interest)" at time $t$ by giving the values of the electric and magnetic fields at every point in space, and by giving the locations and positions of every particle.

For my purposes, I don't care about relativistic invariance. The point is simply that the "state" of any small region of space at time $t + \Delta t$ depends only the state of neighboring regions at time $t$ (where "neighboring" means the distance is less than $c \Delta t$).

Relativistic invariance doesn't prevent me from doing this. It says, instead, that it's true for ANY choice of an inertial cartesian coordinate system.

 

[PeterDonis]

The cells correspond to regions in SPACE, not regions in SPACETIME.

Ah, I see.

Why does it matter if the notion of "state" is relativistically invariant, or not?

Because if your theory, or interpretation, or whatever, isn't consistent with relativistic invariance, it can't be fundamental, and I thought the whole point of QM interpretations was to try to come up with a fundamental account of what is going on. And a fundamental account of what is going on that uses a concept of "state" where "state" is frame-dependent doesn't seem to me to be consistent with relativistic invariance.

The point is simply that the "state" of any small region of space at time $t + \Delta t$ depends only the state of neighboring regions at time $t$ (where "neighboring" means the distance is less than $c \Delta t$).

The notion of "state of any small region of space at some particular time" is relativistically invariant--strictly speaking "small region" should be "point", but nobody is that strict when actually using relativity. I have no problem with considering, say, A's measurement of the spin of their qubit to be an "event" in the relativistic sense even though it occupies a finite region of spacetime, not a point.

I thought you were making use of a global concept of "state", where we have to assign a "state" to the whole universe at some time. That's not relativistically invariant. But it doesn't seem like you actually need that notion of "state". Your "states" are really just "events" in spacetime (where "event" has the non-strict interpretation described in my previous paragraph), and you are simply saying that some states don't depend only on other states in their past light cones. This is a purely local notion of "state", not a global one, and all of the relationships involved can be described as invariant spacetime relationships between local "states".

 

[PeterDonis]

it doesn't seem like you actually need that notion of "state". Your "states" are really just "events" in spacetime (where "event" has the non-strict interpretation described in my previous paragraph), and you are simply saying that some states don't depend only on other states in their past light cones.

Having said this, I now have a different issue to raise, with the word "depends". In Bell's Theorem, "depends" means statistical dependence--there is no way to factorize the function that describes the statistical correlation between the A and B measurement results. But then:

to understand what's going on in a small region, we need only consider that region and neighboring regions. QFT is not local in that sense.

This seems to be using a different notion of "dependence", one in which understanding the A and B measurement results requires knowing about things that aren't in the past light cones of those measurements. Or perhaps you have some sort of notion of "causal dependence" in mind.

Also, what, exactly, is supposed to "depend" on states not in the past light cone? It can't be just the A and B measurement results by themselves; the probabilities for each of those are dependent only on states in their past light cones. Only the statistical correlation between them can't be factorized, as above.

Perhaps the correlations between the results are what leads you to require some global notion of "state"; but then it makes no sense to talk about the "state" of either A or B by themselves; only their joint state is meaningful. That notion of "joint state" is not relativistically invariant, but it's also not the state of any individual "cell" in your scenario, so again the analogy with a cellular automaton breaks down.

 

[stevendaryl]

Also, what, exactly, is supposed to "depend" on states not in the past light cone? It can't be just the A and B measurement results by themselves; the probabilities for each of those are dependent only on states in their past light cones. Only the statistical correlation between them can't be factorized, as above.

I think I answered this already. Given an inertial coordinate system, there is a notion of global state that changes with time. If the laws of physics are "separable" in the sense that I'm talking about, then the laws for the evolution of the global state factors into laws for how each small region evolves. If it's not separable, then it means that the laws governing the evolution of the local states are not sufficient to determine the evolution of the global state.

An extremely simplified example might be this: Suppose there is a pair of coins, and no matter how far apart the coins are from each other, it's always the case that the $n^{th}$ flip of one coin produces the opposite result from the $n^{th}$ flip of the other coin. This is a nonlocal law of physics. A local law governing the coin would specify how the result of a coin flip depends on conditions near that coin.

Now, unlike EPR, there is a "hidden variables" explanation for this apparently nonlocal law. If somehow the coin has a "program" telling it what result to give on the $n^{th}$ flip, then that would account for the nonlocal correlation. So an apparently nonlocal evolution law can be explained in terms of a local hidden variable theory. EPR correlations, in contrast, provably cannot be explained in terms of the type of separable laws that I'm talking about.

 

[PeterDonis]

laws for the evolution of the global state

If the laws of physics are relativistically invariant, then there can't be any such "laws for evolution of the global state", since the global state is not relativistically invariant.

This is the same problem that I said in post #120 that nobody knows how to solve, and if nobody knows how to solve it, you can't just help yourself to assumptions and models that require that it be solved. Unless you know how to solve it and can point us to a reference that contains the solution?

 

[stevendaryl]

If the laws of physics are relativistically invariant, then there can't be any such "laws for evolution of the global state", since the global state is not relativistically invariant.

That is not true. I gave you a counterexample. If we define the "global state" to be the values of $\vec{E}$ and $\vec{B}$ at every point in space, together with the locations and positions of all particles, then classical relativistic theory gives you the evolution law for such a global state. So I don't know what you're talking about.

 

[PeterDonis]

That is not true. I gave you a counterexample. If we define the "global state" to be the values of $\vec{E}$ and $\vec{B}$ at every point in space, together with the locations and positions of all particles, then classical relativistic theory gives you the evolution law for such a global state.

The evolution law you refer to, Maxwell's Equations, is not global, it's local. The evolution of $\vec{E}$ and $\vec{B}$ at any particular point in space depends only on the values of $\vec{E}$ and $\vec{B}$, their derivatives, and the source (charge-current density) at that point in space. So calling this an evolution law for "the global state" is meaningless as physics; you might consider it a useful choice of words, but I don't, I think it just obfuscates things.

 

[stevendaryl]

The evolution law you refer to, Maxwell's Equations, is not global, it's local.

Yes. That's exactly my point! Classical electrodynamics is local in the sense that I'm talking about. You can define a global state, and you can define how the global state at one time depends on the global state at previous times. But, classical electrodynamics is local. The evolution of the global state factors into evolution equations in which the evolution of the local state only depends on nearby conditions.

 

[PeterDonis]

The evolution of the global state factors into evolution equations in which the evolution of the local state only depends on nearby conditions.

I see what you are saying, and I don't think we disagree on the physics. I just don't think this way of describing it in ordinary language is useful; I think it's likely to cause more confusion than it solves.

 

[stevendaryl]

I see what you are saying, and I don't think we disagree on the physics. I just don't think this way of describing it in ordinary language is useful; I think it's likely to cause more confusion than it solves.

The whole point is to say the sense in which classical electrodynamics is a local theory, but QM with entangled particles is NOT.

 

[stevendaryl]

The whole point is to say the sense in which classical electrodynamics is a local theory, but QM with entangled particles is NOT.

Some people say that we should interpret "local" to mean the impossibility of FTL communication. I don't think that captures the notion of "local" very well. I gave the counter-example of a hypothetical pair of coins such that the $n^{th}$ flip of one coin always returns the opposite result of the $n^{th}$ flip of the other coin, no matter how far away they are from each other (but are otherwise random--there is no way to predict which will be "heads" and which will be "tails"). Such a pair of coins could not be used for FTL communication, but such a correlation is certainly non-local, intuitively.

 

[PeterDonis]

The whole point is to say the sense in which classical electrodynamics is a local theory, but QM with entangled particles is NOT.

That's easy: a local theory can't make predictions that violate the Bell inequalities. Classical electrodynamics is local in this sense; QM is not.

Some people say that we should interpret "local" to mean the impossibility of FTL communication.

But of course this definition of locality does not distinguish classical electrodynamics from QM. So it's not the one you're looking for.

 

[vanhees71]

That's what I just did: The state of the universe factors into the state of local regions, and the state of local regions evolves in a way that depends only on neighboring regions.

The state does not factor into the state of local regions (whatever you mean by this) as the possibility of entanglement for far distant parts (i.e., parts measured at far distant places) of a quantum system shows. Within relativistic local QFT the interactions are local though. There's no faster-than light signal propagation and the linked-cluster principle holds (see Weinberg, Quantum theory of fields vol. 1).

 

[vanhees71]

I don't see how it wouldn't be a problem, since "frame-dependent" is inconsistent with "relativistically invariant".
This state is, as you say, frame-dependent, and therefore not relativistically invariant. So I am totally confused as to how you can say this isn't a problem for consistency with relativistic invariance.

The electromagnetic field is not frame dependent. It's a 2nd-rank antisymmetric tensor field!

 

[martinbn]

Ok, I am late for the discussion but I am still confused. Following @stevendaryl by locality we mean that to understand what is going on in a small region we only need the information from near by. But how is the usual Alice and Bob scenario any different? The results are probabilistic, and the predictions can only be probabilistic. Alice doesn't need anything from Bob in order to make her predictions. So how is there anything that is not local? Let me put it this way. If they make repeated predictions and measurements on an equally prepared pair of entangled particles. And if Alice measures hers a moment later than Bob, and Bob can decide whether to measure or not, she cannot tell if he did it or not. For me this is convincing that Bob's actions have no causal effect on Alice's particle.

 

[martinbn]

I think I answered this already. Given an inertial coordinate system, there is a notion of global state that changes with time. If the laws of physics are "separable" in the sense that I'm talking about, then the laws for the evolution of the global state factors into laws for how each small region evolves. If it's not separable, then it means that the laws governing the evolution of the local states are not sufficient to determine the evolution of the global state.

Unless I misunderstood you, then GR is nonseparable, but I wouldn't call it nonlocal.

Some people say that we should interpret "local" to mean the impossibility of FTL communication. I don't think that captures the notion of "local" very well. I gave the counter-example of a hypothetical pair of coins such that the $n^{th}$ flip of one coin always returns the opposite result of the $n^{th}$ flip of the other coin, no matter how far away they are from each other (but are otherwise random--there is no way to predict which will be "heads" and which will be "tails"). Such a pair of coins could not be used for FTL communication, but such a correlation is certainly non-local, intuitively.

I agree with this, but there is nothing in nature that behaves that way. For entangled pairs you can make only one measurement. If you did $n$ on the same pair it wouldn't be like that. But I object more to the insistance (not by you) to say that all this (the EPR case) implies action at a distance i.e. Bob causes something to happen at Alice's.

 

[vanhees71]

Entanglement does not imply action at a distance, because local relativistic QFT is an example for a QT, which of course allows entanglement but is at the same time a theory where you have only local interactions by construction.

 

[martinbn]

Entanglement does not imply action at a distance, because local relativistic QFT is an example for a QT, which of course allows entanglement but is at the same time a theory where you have only local interactions by construction.

Yes, but the question is should one still say that space-like events can be cause/effect related? I am not convinced that EPR, Bell and all that implies that one should.

 

[Tendex]

The electromagnetic field is not frame dependent. It's a 2nd-rank antisymmetric tensor field!

Sure, the tensor is local, what I think they mean by frame-dependent state is a supposed "global" state. But I'm not clear if this is trivial mathematical fact or something else.

 

[Tendex]

I think going back to the local vs nonlocal debates leads nowhere, it is much better going by Bell's distinction between classic correlations versus quantum correlations and their probabilities(although ironically it also helped introduce following the EPR article all this word salad philosophical debates about locality, causality, realism, determinism, action at a distance, ftl influence, etc).
It is also not very useful to still be going about the causal vs ftl influence(in whatever form) debate. By definition any theory that makes "predictions" is causal and doesn't allow ftl signaling or whatever one may like to call it, otherwise it couldn't claim to make "predictions", or to be a scientific theory for that matter and I find it a bit silly to still be using classically unexplained quantum correlations to speculate about spookiness, and ftl.
On the other hand, regardless of its making precise and accurate predictions a theory might be doubted in its mathematical completeness or rigor and correction, and in that sense the theory that is worse off is the generalization of nonrelativistic QM: QFT.

 

[atyy]

Entanglement does not imply action at a distance, because local relativistic QFT is an example for a QT, which of course allows entanglement but is at the same time a theory where you have only local interactions by construction.

Since you have used the unobservable definition of no superluminal signaling, QT is not local since it allows superluminal signaling in the form of collapse intrpreted physically. By using the unobservable definition, you promote quantum nonlocality.

 

[stevendaryl]

Unless I misunderstood you, then GR is nonseparable, but I wouldn't call it nonlocal.

Well, I am a little bit uncertain about that, but I specifically restricted my discussion to flat spacetime because I wasn't prepared to discuss GR in these terms.