Is the moment of the measurement well defined?

[entropy1]

Suppose Alice and Bob do an experiment with an entangled pair of particles, for instance electron spin with SG magnets.

Now suppose Alice her SGM is stationary while Bob his SGM is switching fast between parallel to Alice and perpendicular to Alice.

So there are two possibilities: correlation or anticorrelation between Alice's and Bob's outcomes on each run.

The correlation per run depends on when, in particular, Bob's measurement occurs (for the outcome on that run depends on it).

My question is whether that moment of measurement is well-defined (specifically when spacelike separated).

Thanks.

UPDATE: Perhaps the example makes more sense with photon polarisation.

 

[PeterDonis]

The correlation per run depends on when, in particular, Bob's measurement occurs (for the outcome on that run depends on it).

Yes, but not in the way you are thinking. The correlation depends on what setting Bob's measurement device is at when Bob's particle passes through it. That is an invariant and has nothing to do with when Alice's particle passes through Alice's measurement device.

 

[entropy1]

Yes, but not in the way you are thinking. The correlation depends on what setting Bob's measurement device is at when Bob's particle passes through it. That is an invariant and has nothing to do with when Alice's particle passes through Alice's measurement device.

Ok. But if Alice and Bob only yield for 50% outcome 0 and for 50% outcome 1 (if we assume 0 and 1 are the possible outcomes for both), so totally random, and Alice and Bob don't inform each other's outcomes (they are not communicating/are independent), then the correlation could only be 0.5 right?

So this is probably an enormous open door, but if Alice's and Bob's outcomes correlate significantly different from 0.5, would that not mean that some informing is going on?

You probably want to remind me of the joint wave function?

 

[PeterDonis]

Ok. But

But you are concerned about a feature of the experiment that you put there. If you allow the relative orientation of Alice's and Bob's measuring devices to vary uncontrollably, then of course the correlations are going to vary uncontrollably and you might not be able to tell from those correlations whether Alice's and Bob's particles are entangled. That's not a problem with QM; it just means that you made a poor choice of experimental setup if your goal was to find out whether the particles were entangled. The best way to do that is to ensure that the relative orientations are controlled by the experimenter, not allowed to vary uncontrollably.

 

[PeterDonis]

this is probably an enormous open door

No, it isn't, it's just a poor choice of experimental setup on your part. See post #2.

 

[entropy1]

No, it isn't, it's just a poor choice of experimental setup on your part. See post #2.

In my setup, if there is a correlation different from 0.5, there must be a distinct moment for the outcome of Alice and the outcome of Bob to be produced, that form the pair of outcomes for that run. That pair of outcomes is part of the value of the correlation formed over multiple runs.

But I now realize that Bob's (and Alice's) outcome is unambiguously delivered by his measurement. So if I understand you correctly, that moment is well defined in QM? (The collapse or decoherence?)

 

[PeterDonis]

In my setup, if there is a correlation different from 0.5, there must be a distinct moment for the outcome of Alice and the outcome of Bob to be produced, that form the pair of outcomes for that run.

I have no idea what you mean by this or why you think it. The outcomes of the two measurements, and therefore the observed correlations between them after a series of runs, do not depend on the order in which they are run or the precise times at which they take place. They only depend on the orientations of Alice's and Bob's measuring devices at the times when Alice's and Bob's particles, respectively, pass through those measuring devices. And since the orientation of Bob's device at the appropriate times is random, uncontrolled by the experimenter, there is no way to predict anything about what the correlations will be. They could be anything from 0.5 to 1, but whatever they are tells you nothing useful since you have put a random effect in your experiment that destroys your ability to make any useful predictions about it.

Bob's (and Alice's) outcome is unambiguously delivered by his measurement.

Um, yes, of course? Why is this even a question? That's what "outcome" means.

if I understand you correctly, that moment is well defined in QM?

The moment when each particle (Alice's or Bob's) passes through its respective measuring device (Alice's or Bob's) is well defined, as a proper time by Alice's or Bob's clock. There is no other relevant "time" in the experiment.

(The collapse or decoherence?)

I don't know what role you think either of these things plays in this scenario. I think you need to fix your more basic confusions first.

 

[entropy1]

I realized my mistake. No need to get all upset. Anyway, thanks for making the effort to answer. For what it is worth.

 

[PeterDonis]

I realized my mistake.

Ok, good.

 

[vanhees71]

To answer the question in the title, I'd say it depends on the photon detector you use and how you define "the moment of measurement". In this context I'd say, assuming photon detection via the photoeffect is a most common scenario. Then I'd define the "moment of photon registration" as the time needed for the photoelectron to get out of the material when the em. wave reaches it. This is in the atto-second range, as my experimental colleagues from the nuclear-physics department recently measured:

https://aktuelles.uni-frankfurt.de/...time-it-takes-for-an-electron-to-be-released/

https://www.nature.com/articles/s41467-021-26994-2 (open access).

 

[Heidi]

I wonder if the question here is not when do we get an outcome in a projection valued measurement.
decoherence never give such a moment. what we can do is to make povms at every moment and get new states (a new operator)
has the moment the same importance then?

 

[vanhees71]

Questions of this type are pretty difficult to answer, because it's already difficult to clearly define what's meant by the "moment to get an outcome". It's somewhat similar to the question of what is the time a particle needs to "tunnel through a potential well". Here's a paper just accepted by EJP discussing your question. I'm not yet fully understanding it (particularly it's not clear to me, how the velocity $v_I$ is calculated:

https://arxiv.org/abs/2011.13254

 

[Cthugha]

To answer the question in the title, I'd say it depends on the photon detector you use and how you define "the moment of measurement". In this context I'd say, assuming photon detection via the photoeffect is a most common scenario. Then I'd define the "moment of photon registration" as the time needed for the photoelectron to get out of the material when the em. wave reaches it. This is in the atto-second range, as my experimental colleagues from the nuclear-physics department recently measured:

https://aktuelles.uni-frankfurt.de/...time-it-takes-for-an-electron-to-be-released/

https://www.nature.com/articles/s41467-021-26994-2 (open access).

Just to add my two cents about real-life detectors in case this thread goes on: More is different and the (indeed excellent) experiment above is about removing a single electron from a single molecule. Unfortunately, a single molecule does not make a good detector and any real detector has to trade off temporal resolution versus detection efficiency.

Considering a real material with several layers for added efficiency essentially results in lots of indistinguishable atoms where upon registration of the electron it is not clear from which atom the electron was removed. The materials are typically semiconductors with bands where the electrons are delocalized over many atoms. Therefore, it is also not clear how long the electron took to be detected and this uncertainty is much larger than the time it takes to actually remove an electron from a single atom/molecule. This is true for anything resembling a lattice, even if one has only few layers of material. Detectors relying on avalanche effects such as single photon sensitive diodes also need to cope with the problem of jitter in the amplification process.

Therefore, for typical incoherent detectors that can operate on the level of individual events, the temporal resolution one may actually achieve for unknown processes is certainly not at the attosecond level. Typical photo diodes get to a temporal resolution around 30 to 100 picoseconds at moderate quantum efficiency. The quite novel superconducting nanowire detectors which move from the superconducting to the normal state when hit by a single photon may achieve about 3 picoseconds: https://www.nature.com/articles/s41566-020-0589-x
Eternities ago my diploma thesis was on speeding up the detection process using special detectors called streak cameras which got us slightly below 2 picoseconds - of course at various other severe drawbacks: https://www.nature.com/articles/nature08126

At this level, time-energy uncertainty may already become relevant so that the spectral resolution you have may already influence the temporal resolution you will be able to achieve. If one is not interested in the timing of an individual detection event, but only in the mean time at which an detection occurs for an ensemble of identically prepared experimental systems, things of course become much easier. So I fully agree that this question requires a very precise definition of what one actually wants to measure and what is considered as the measurement.