I What is the current perspective on quantum interpretation?

[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.

 

[ShayanJ]

The Everett interpretation. But I think the current language in which we talk about it is a little misleading.

 

[Fra]

Still got headache, why make it complicated, try some QBism?

“Quantum nonlocality is an artifact of inappropriate interpretations of quantum mechanics."
-- https://arxiv.org/abs/1311.5253


/Fredrik

 

[vanhees71]

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.

The state evolves with a unitary transformation $\hat{C}(t)$ obeying
$$\mathrm{i} \dot{\hat{C}}=\hat{H}_1 \hat{C},$$
and the operators describing observables by one obeying
$$\mathrm{i} \dot{\hat{A}}=-\hat{H}_2 \hat{A},$$
where $\hat{H}_1+\hat{H}_2=\hat{H}$ is the Hamiltonian of the system. The split of $\hat{H}$ in two arbitrary self-adjoint operators $\hat{H}_1$ and $\hat{H}_2$ doesn't change anything in the physical predictions (probabilties for the outcome of measurements). It just defines the "picture of time evolution".

Can you specify what you mean by the last sentence? Are you referring to the partial traces, defining the states of the part of the system measured by Alice or Bob, respectively?

If yes, then of course you are right in a specific sense, and it also immediately follows that what's violated is separability and not locality (in the case of local relativistic QFTs) since the time evolution by construction (Hamilton density depends only on one space-time point and the microcausality property is fulilled for all local observables).

 

[stevendaryl]

The state evolves with a unitary transformation $\hat{C}(t)$ obeying
$$\mathrm{i} \dot{\hat{C}}=\hat{H}_1 \hat{C},$$
and the operators describing observables by one obeying
$$\mathrm{i} \dot{\hat{A}}=-\hat{H}_2 \hat{A},$$
where $\hat{H}_1+\hat{H}_2=\hat{H}$ is the Hamiltonian of the system. The split of $\hat{H}$ in two arbitrary self-adjoint operators $\hat{H}_1$ and $\hat{H}_2$ doesn't change anything in the physical predictions (probabilties for the outcome of measurements). It just defines the "picture of time evolution".

Can you specify what you mean by the last sentence? Are you referring to the partial traces, defining the states of the part of the system measured by Alice or Bob, respectively?

If yes, then of course you are right in a specific sense, and it also immediately follows that what's violated is separability and not locality (in the case of local relativistic QFTs) since the time evolution by construction (Hamilton density depends only on one space-time point and the microcausality property is fulilled for all local observables).

The quantum state is not separable in the sense that I am talking about. You can't talk about the quantum state of a single region of space.

 

[stevendaryl]

If yes, then of course you are right in a specific sense, and it also immediately follows that what's violated is separability and not locality.

I think that locality is sort of meaningless without separability. With separability + locality, physics is local, in the sense that to figure out what's going to happen in the near future, I don't need any more information than knowing what's happening nearby right now.

 

[vanhees71]

That's what I was asking! You said above "

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.

(emphasis mine). Now you say yourself that this makes no sense

You can't talk about the quantum state of a single region of space.

You are right as long as you don't specify what you mean by that, and it makes some sense, when you consider the standard example with an entangled photon pair, where A and B measure one of the two photons each, and the single-photon states are given by partial tracing the state over the other photon.

For a local relavistic QFT you have locality of the interactions (as defined above) but inseparability due to entanglement.

 

[stevendaryl]

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.

Let me expand on separabilty + locality: Let $\Delta t$ be some time interval.

Suppose we divide the universe (or the patch that we are interested in) into 4 regions:

1. Region $A$, where Alice is performing measurements.
2. Region $AN$, which is the neighborhood of $A$, the set of points that are less than $c \Delta t$ away from Region $A$.
3. Region $B$, where Bob is performing measurements.
4. Region $BN$, which is the neighborhood of $B$.
5. Region $C$, which is everything else.

Assume that regions $A, AN, B, BN$ have no overlap (but $C$ touches both $AN$ and $BN$).

Now, we're trying to predict the state of $A$ at time $t+\Delta t$. If the world is separable and local, then we don't need to check on the state of $B, BN$ or $C$ to make a prediction about the state of $A$.

 

[stevendaryl]

For a local relavistic QFT you have locality of the interactions (as defined above) but inseparability due to entanglement.

Yes, and in that sense, QFT is not local.

 

[Fra]

Now, we're trying to predict the state of $A$ at time $t+\Delta t$. If the world is separable and local, then we don't need to check on the state of $B, BN$ or $C$ to make a prediction about the state of $A$.

Are you making a distinction between prediction and expectation?

In the Qbist and similar perspectives, the local agent (Alice) does not have any other choice but to form the expectation from available information.
/Fredrik

 

[stevendaryl]

Are you making a distinction between prediction and expectation?

In the Qbist and similar perspectives, the local agent (Alice) does not have any other choice but to form the expectation from available information.
/Fredrik

I don't completely understand what the Qbist perspective is, but I don't think that there is any objective state of the universe in a Qbist interpretation. So it's not clear what locality means without a notion of state.

 

[vanhees71]

Yes, and in that sense, QFT is not local.

You have to specify what you mean by local, and a local relativistic QFT is local in a specific sense (Hamilton density a polynomial of the field operators and their derviatives at one space-time point and microcausality property for all local observables) and "non-local" in the same sense as any QT, and I think it's a good solution of the problem to specify the different sense of locality used here by calling the latter type "inseparability". Einstein made very clear that his quibbles with QT refer to "inseparability" and not so much on "non-locality".

 

[stevendaryl]

You have to specify what you mean by local

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.

 

[Fra]

I don't completely understand what the Qbist perspective is, but I don't think that there is any objective state of the universe in a Qbist interpretation. So it's not clear what locality means without a notion of state.

Yes, there is no objective state in Qbism. Also there locality follows from the construction, since any comparasions or is made on the information at hand of the local agent . This means any "external information", such as a phone call from Bob, has to be communicated to Alice first. And this communication is treated just like any other "measurement".

Also a distinction is that in the Qbism view I think most consider the purpose of expectations, is not to determined what will happen, but to decide howto place the bets. Ie. the expectation of Alice, determines first of all Alices own action - not the backreaction of the environment.

From my perspective, what you describe are various correlations (while mixing information from different agents, without considering the communication channel), that has no "function" in a Qbist interpretation I think.

/Fredrik

 

[stevendaryl]

Einstein made very clear that his quibbles with QT refer to "inseparability" and not so much on "non-locality".

I would say, rather, that you're using a narrower meaning of "locality" than Einstein. The point of locality is Einstein's belief that all physics is local, that 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.

 

[PeterDonis]

Now, we're trying to predict the state of $A$ at time $t+\Delta t$. If the world is separable and local, then we don't need to check on the state of $B, BN$ or $C$ to make a prediction about the state of $A$.

For an appropriate definition of "state" and "prediction", QFT meets this requirement.

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...

The fundamental conflict here is really between relativistic invariance and the implicit claim of QM, on which all discussions of "nonlocality" and "nonseparability" rely, that it makes sense to assign a "state" to the whole universe as a function of "time". The real point is that, at present, nobody knows how to resolve this conflict--nobody has a theory that has both properties, relativistic invariance and a "state of the universe" as a function of time.