I Who is Ballentine and why is he important in the world of quantum mechanics?

[A. Neumaier]

Of course. If you measure the intensity of the em. field prepared in single- or few-photon Fock states, it's also a very noisy observation.

But too noisy to extract any useful information, hence it cannot be called a measurement of the intensity of the field, which would produce numerical values for the intensity.

 

[vanhees71]

Of course, it's very useful information to register a photon with a photon detector. It's the only useful information you can get about a single photon. "Intensity" for a single photon has of course the meaning of a probability (density) for detecting a photon at a given region in space at a given time.

 

[physika]

Of course, it's very useful information to register a photon with a photon detector. It's the only useful information you can get about a single photon. "Intensity" for a single photon has of course the meaning of a probability (density) for detecting a photon at a given region in space at a given time.

Casually

https://www.azooptics.com/News.aspx?newsID=28527
.....

 

[A. Neumaier]

Of course, it's very useful information to register a photon with a photon detector. It's the only useful information you can get about a single photon. "Intensity" for a single photon has of course the meaning of a probability (density) for detecting a photon at a given region in space at a given time.

No. For a single photon, probability is operationally meaningless.

 

[vanhees71]

So you say all quantum-optics experiments with single photons are meaningless? That doesn't make sense. What you can know about a single photon operationally is the detection probability at a given time and place, given its state.

 

[gentzen]

So you say all quantum-optics experiments with single photons are meaningless? That doesn't make sense. What you can know about a single photon operationally is the detection probability at a given time and place, given its state.

He takes "single photon" literally. What makes no sense is his cryptic way of restarting that old discussion just now. No idea what he wants to achieve. Yes, you use words and concepts too much in the "you know what I mean" way, but this cryptic way of taking words literally won't change your mind either.

(We can have that discussion another time, but not today, or tomorrow, or ...)

 

[vanhees71]

Nowadays we indeed can take "single photon" literally since the quantum opticians can prepare true single-photon states (e.g., using parametric down conversion and using one of the entangled photons to herald the other one used for experiments). I don't know, what he means by the claim that probabilities for single photons were meaningless. The only thing, however, we have in QT for single quanta are probabilities. These are also not meaningless in an operational sense, because it simply means that when repeating the experiment with many equally prepared photons (operationally defining the "state" as the corresponding preparation procedure) you get in the limit of infinitely many such experiments the probability distribution for registering the photon at the place of the detector.

 

[PeterDonis]

So you say all quantum-optics experiments with single photons are meaningless?

No, he's saying that you can't use a single instance to test a statistical prediction, and QM's predictions are statistical.

 

[vanhees71]

Ok, but that's self-evident and not specific to photons.

 

[kurt101]

Nonlocal contextuality has been demonstrated in so many recent experiments, and that seems to fly in the face of traditional concepts of causality. Ordering just doesn't matter, and in a deterministic universe, you'd think it would.

And yet there is always a simple causal explanation for these experiments where order does not matter that you seem to ignore.

For instance, in the entanglement swapping experiment that you often cite as evidence for violating causality there is a simple explanation as to why photons 2 & 3 can tell you whether photons 1 & 4 were entangled. When photon 1 is measured, through the mechanism of entanglement it can provide all the information about the measurement angle to photon 2. When photon 4 is measured, through the mechanism of entanglement it can provide all of the information about the measurement angle to photon 3. So when photons 2 & 3 come together they have all the information about the measurements being used in the experiment to decide whether photons 1 & 4 were entangled or not.

 

[PeterDonis]

there is always a simple causal explanation

The problem with this view is that your so-called "simple causal explanation" is stated assuming a particular time ordering of the measurements. But the actual correlations in the experiments are the same regardless of the time ordering of the measurements.

In other words, for it to be the case (as it in fact is) that "order does matter", your "simple causal explanation" would have to allow "causes" that happen either spacelike separated from their "effects", or after their "effects" (i.e., future timelike or null separated), or that two events can be causally connected without there being any fact of the matter about which is the "cause" and which is the "effect". There are no other choices, and all of them are unpalatable. Strictly speaking, they aren't logically impossible (although they do imply a concept of "causation" which is highly at variance with all such concepts currently in the literature), but their unpalatability means you can't get away with calling your claimed explanation "simple". It's not.

 

[vanhees71]

It's true that the "time ordering" of the measurements on the far distant parts of entangled systems doesn't make a difference, which clearly shows that there is no causal influence of one of the measurements on the other. This is the more clear if the "measurement events" (i.e., the events when the measurement results are stored to the measurement protocols at the far distant places) are space-like separated.

Of course there's a cause for the observed correlations between these outcomes, which is of course the preparation of the system in the entangled state, and this preparation process is clearly time-like (or light-like for photons) separated to both measurements. There's no violation of causality by construction in standard relativistic QFTs due to the imposed microcausality constraints on all operators that represent local observables. Particularly the Hamilton density commutes with any local observable-operator at space-like separated arguments.

 

[kurt101]

The problem with this view is that your so-called "simple causal explanation" is stated assuming a particular time ordering of the measurements. But the actual correlations in the experiments are the same regardless of the time ordering of the measurements.

In other words, for it to be the case (as it in fact is) that "order does matter", your "simple causal explanation" would have to allow "causes" that happen either spacelike separated from their "effects", or after their "effects" (i.e., future timelike or null separated), or that two events can be causally connected without there being any fact of the matter about which is the "cause" and which is the "effect". There are no other choices, and all of them are unpalatable. Strictly speaking, they aren't logically impossible (although they do imply a concept of "causation" which is highly at variance with all such concepts currently in the literature), but their unpalatability means you can't get away with calling your claimed explanation "simple". It's not.

Fair enough. In retrospect I would have used the word "plausible" instead of "simple".

My point is that all orderings of the entanglement swapping experiment have plausible causal explanations.

So what is more likely?
That a causal explanation is not possible.
Or we have not figured out why the order doesn't matter.

 

[vanhees71]

The order doesn't matter, because there's no need for a causal effect of one measurement on the other. This should be clear from the fact that the temporal order of these measurements is irrelevant, and correlations do not necessarily imply causal connections.

In fact, at least within the minimal statistical interpretation, the correlations are present because of the preparation of the photons in an entangled state before any measurement has been done on these photons. E.g., if you take two entangled photons from parametric down conversion (e.g., type II, where the polarization state is in the singlet, antisymmetric state and thus so must also be the momentum state to get a symmetric state under exchange of the photons as it must be), the single-photon polarizations are maximally uncertain, i.e., each of the photons is ideally unpolarized, neverthereless when measuring the polarization in the same direction for each photon you get a 100% (anti-)correlation: if you find photon 1 as H-polarized, then you find photon 2 as V-polarized and vice versa. It is completely irrelevant in which temporal order you measure the single-photon polarizations, i.e., photon 2 doesn't get V-polarized because of the measurement on photon 1 (which you can ensure by registering the photons at spacelike separated events) but the correlation was there due to the preparation in the entangled state.

 

[jtbell]

Actress Sally Field once said of her brother, physicist Rick Field, "He invented something called Field theory."

There's a paper that examines the imperturbability of an elevator operator in a Marshall field.

 

[PeterDonis]

all orderings of the entanglement swapping experiment have plausible causal explanations

No, they don't; the case where all the measurements are spacelike separated cannot be explained using your method.

Even for the other cases, where the measurements are timelike or null separated, the "plausible causal explanation" is different for different orderings of the measurements. Which seems highly implausible given that the correlations are exactly the same regardless of the ordering.

 

[vanhees71]

The very fact that the order of measurements in the entanglement-swapping protocol shows that there is no mutual causal influence of these measurements on each other. By definition the cause is always and observer-independently before the effect. That's the fundamental definition of the "arrow of time" underlying all physics (the "causal arrow of time").

In relativistic physics this implies that cause-effect relations can only be between events that are time-like or light-like separated, and that's why in relativsitic QFT local observable-operators must obey the microcausality constraint, i.e., any such operators must commute if their spacetime arguments are space-like separated. That's fulfilled for QED and thus particularly for photon-detection probability-rate densities (the correlation function of the energy density of the em. field). This ensures that QED is a causal theory and thus there cannot be faster-than-light causal influences of one of the measurements on the other, if the measurement events are space-like separated, and thus if the observed correlations are independent of any time-order of the corresponding measurement events there cannot be by definition such a causal influence.

The correlations are due to the preparation of the initial photon state, i.e., the entanglement swapping is possible, because in the beginning, before any measurements are done (and each detector can the earliest register a photon when the wave front has reached this detector, i.e., the earliest after the propagation time of an electromagnetic wave from the source (BBO) to the detector), the photon pairs 1&2 as well as 3&4 are prepared in a maximally entangled Bell state.

 

[Morbert]

@vanhees71 I agree with your position: relativistic quantum theories can be consistently interpreted as local in the sense of events not affecting other spacelike-separated events, but your argument doesn't quite get us there. E.g. Bell would say that your statements do no imply locality in the above sense. They only imply that operations on a system will not affect the statistics of spacelike-separated systems. Relativistic quantum theories still fail Bell's local causality condition. We would need to go further and argue that Bell's local causality condition is not appropriate for determining whether or not, in quantum theories, events can affect spacelike-separated events.

 

[vanhees71]

I avoided this locality discussion, because then I run into danger of a thread ban. I don't know, what Bell means by "locality". For me locality is the assumption of QFT that we describe everything with a Hamilton density consisting of field operators at the same space-time point, have the usual local realization of the Poincare group on the field operators, and that self-adjoint operators representing local observables (like the em. energy-momentum tensor, which contains the description of photon detection, using the usual dipole approximation) obey the microcausality constraints.

Also for me the only consistent interpretation is the minimal statistical interpretation, and there is nothing else than the probabilities. Particularly it does not make sense to ask for a cause of a specific outcome of a measurment on a single system since within this interpretation there is none, but Nature behaves inherently random. Then there are obviously indeed no faster-than-light propagating causal effects, but the strong correlations of measurment results at far distant places when a quantum system is prepared in an entangled state are there due to the preparation of this state, i.e., the "cause" of the correlations is the preparation in the very beginning before any measurements are done. It should also be clear that it doesn't make sense to say a state were local or non-local. What's local are interactions due to the mathematical construction of relativistic, microcausal (in that sense local) QFTs, not states.

I think the big confusion about all this is because of the idea that there should be a cause for each single outcome of a measurement on a quantum system, and then the nebulous meaning of terms like locality or non-locality in the quantum-foundation literature. It seems to be still very hard to accept for some philosophically inclined physicists to accept the "objective randomness" of Nature (or to formulate it more care ful of our observations of Nature), and that after nearly 100 years of quantum theory and Born's break-through with the probability interpretation of the quantum state! On the other hand, I don't see any hint that this assumption is wrong. Particularly all the Bell tests in all kinds of variations, including the space-like separation of measursment/detection events with entangled photons, seem to me only to be consistently interpretible with this assumption of the statistical interpretation.

 

[kurt101]

No, they don't; the case where all the measurements are spacelike separated cannot be explained using your method.

No, they do. I am not sure why you are saying they don't, maybe you are using a different definition of causal than I am.

Where the measurements are done first:
Measurement at 1 causes 2 to receive information of the measurement via entanglement. Measurement 4 causes 3 to receive information of the measurement via entanglement. 2 & 3 have all the information available to decide if 1 & 4 were entangled.

Where measurements are done last:
2 & 3 come together at the BSM (Bell state measurement apparatus) where through the swap 4 gets entangled with 2's partner 1 and likewise 1 gets entangled with 3's partner 4.

Both cases and any mix of the cases can all be considered causal in nature.

 

[kurt101]

I don't know, what Bell means by "locality".

FWIW, I don't know if you are just saying this to make a point, but Bell is using the definition of locality used by everyone else outside of QFT (at least your version of QFT). If I read a QM paper and it used locality in the way you are using it and did not explicitly tell me, I would be extremely confused. It would at least be helpful to give it some extra context so we knew when you are talking about your versions of QFT locality versus the common definition. Is there such a term you use to avoid confusion?

 

[PeterDonis]

maybe you are using a different definition of causal than I am

The standard definition of "causal", as @vanhees71 has pointed out, requires an invariant time ordering of cause before effect. The time ordering of spacelike separated events is not invariant, so they cannot be causally connected using that definition.

If you are using a different definition of "causal", please give a reference to back it up.

 

[PeterDonis]

Where the measurements are done first:

Where measurements are done last:

If the events are spacelike separated, neither of these are true; the time ordering is frame dependent, and standard relativity says that no physical effect can depend on something that is frame dependent; all the physics must be contained in invariants.

 

[kurt101]

The standard definition of "causal", as @vanhees71 has pointed out, requires an invariant time ordering of cause before effect. The time ordering of spacelike separated events is not invariant, so they cannot be causally connected using that definition.

If you are using a different definition of "causal", please give a reference to back it up.

What would you call the dependency between two entangled photons? Using the definition of "casual" from the Oxford dictionary I would consider this dependency causal. Measuring one photon affects the measurement of the other photon.

 

[PeterDonis]

What would you call the dependency between two entangled photons?

Entanglement. Whether that counts as a "causal" connection is one of the key unresolved issues in QM interpretation.

Measuring one photon affects the measurement of the other photon.

If the measurements are spacelike separated, their time ordering is frame dependent, which means their cause and effect ordering is frame dependent. It is of course logically possible to extend one's definition of "causality" to include this case: but whether or not that is justified, and whether or not one is willing to accept all the consequences of that choices, is a matter of opinion. There is no generally accepted resolution to these issues.

 

[vanhees71]

I think there's nothing unsolved, and of course QM, which is non-relativistic, is not the right theory to discuss the issue, because for that you need a relativistic model, and the only successful relstivistic quantum theory is relativistic QFT.

What entanglement describes are correlations between the outcome of measurements. They are "caused" by the preparation of the measured system in the state. In general the operational definition of quantum state is that it describes a preparation procedure, e.g., the emission of an entangled photon pair from a BBO crystal due to parametric down conversion.

All observed facts about entanglement, including all the predicted effects like teleportation, entanglement swapping, delayed-choice erasing, etc. etc. are confirmed by highly accurate experiments (Nobel Prize of 2022). There's nothing unsolved here! It's now in the realm of engineering. Universities of Applied Sciences now develop curricula for quantum informatics!

 

[Fra]

The order doesn't matter, because there's no need for a causal effect of one measurement on the other.

This fact does not mean that nature itself has no causal internal relationships at all. I think THAT is somerhing many will not accept.

My opinion is that its the nature of causality that QM challenges. In Classical mechanics we tend to have a "mechanical view" of causal chains and something in 3D need to basically "poke" something to provide a mechanism.

In QM it seems to me that causation is more easily understood as a game of expectations. Any players behaviour is ultimately governed by its own expectations. The "poking" going on as in the space of expectations of a player(could be a detector)
This is IMO an intuitive way to understand HOW the hidden variable provides a mechanism for CORRELATIONS of outcomes but NOT for the actual outcome!

/Fredrik

 

[Fra]

I think there's nothing unsolved,

....

What entanglement describes are correlations between the outcome of measurements. They are "caused" by the preparation of the measured system in the state. In general the operational definition of quantum state is that it describes a preparation procedure,

I agree with all, but what I think is missing is a deeper understanding of what we describe well but does not understand well. This is what i label nature of causality.

/Fredrik

 

[vanhees71]

Then the question is, what you define as "understanding (Nature?) well". We have a pretty well formulated theory, Q(F)T, that describes almost all (everything except gravitation as far as we know) phenomena in accordance with all empirical evidence. What do you think is "lacking in understanding" then?

 

[Fra]

What do you think is "lacking in understanding" then?

Conceptually: The theoretical perspective of an "inside observer" AND how that would comply to the "external observer" perspective. Worth noting that any real observer is always and inside observer. Current perspective is an abstraction and a limiting case.

A bonus I expect from such insight, is that we will be able to reduce the number of "free" or "fine tuned" parameters in our current description.

/Fredrik