Are entangled particles really separated?

[chrisrp]

TL;DR Summary

If entangled photons experience no time and distance after separation, are they really separated in their frame of reference?

I would greatly appreciate answers or perspective on these questions, thank you in advance!
Since entangled photons are traveling at the speed of light relative to our spacetime, my understanding is that they experience no time or distance from the moment they are generated to the moment they are interacted with (e.g. observed, absorbed, etc.). While entangled photons may seem to be great distances apart in our perceived spacetime, is it possible that they are not truly separated from each and they are still together in their frame of reference? Could the properties of entanglement we observe in our spacetime be a result of these photons being in the process of incomplete transition from their production to their next interaction or separation?

 

[jambaugh]

My gut reaction to your question is to say "Photon's do not have a frame of reference". I would also point out that we get the same entanglement phenomena with heavy slow moving particles (quanta), not just photons. Since photons are no more nor no less able to be entangled than slow moving massive particles there isn't any evidence for some explanation of the type you suggest.

In more detail, entanglement is a form of statistical correlation. Locality is only a means to assert no causal interactions. It is not at the heart of the issue. One can, for example establish entanglement between the spin and momentum of a single particle. Within standard QM you can set up the entanglement, assert no causal interactions between the two component systems after the setup, and observe the same Bell's Inequality violating correlations between spin measurements and momentum measurements. This is less interesting as a physical experiment since it would be problematic to assure in the lab that the two component subsystems have not interacted as part of the measurement process. It is easier to assume Einstein's SR applies and work with spatially separated component measurements.

But in the end QM predicts this entanglement absent a causal component in the dynamics of the system. Attempting to explain it via hidden variables and hidden causal interaction is an attempt to explain quantum predictions in a classical framework i.e. as an ontological theory (describing states of reality) rather than a phenomenological theory (describing what happens).

We are intuitively biased towards ontological theories because they work so well at the scale of our everyday existence and survival behavior. When we throw a rock to hit a rabbit to eat, we don't have to worry that our "reality model" of "rock" and "rabbit" not being fundamental. As we are averaging over a massive number of phenomenological actions the aggregate phenomena fit very well into an objective reality model. By the same token we also don't have to worry about relativistic effects when hitting rabbits with rocks and so our intuitions, which evolved in this scenario, plays us false when it comes to understanding relativity of time and frame dependent simultaneity.

 

[chrisrp]

My gut reaction to your question is to say "Photon's do not have a frame of reference". I would also point out that we get the same entanglement phenomena with heavy slow moving particles (quanta), not just photons. Since photons are no more nor no less able to be entangled than slow moving massive particles there isn't any evidence for some explanation of the type you suggest.

In more detail, entanglement is a form of statistical correlation. Locality is only a means to assert no causal interactions. It is not at the heart of the issue. One can, for example establish entanglement between the spin and momentum of a single particle. Within standard QM you can set up the entanglement, assert no causal interactions between the two component systems after the setup, and observe the same Bell's Inequality violating correlations between spin measurements and momentum measurements. This is less interesting as a physical experiment since it would be problematic to assure in the lab that the two component subsystems have not interacted as part of the measurement process. It is easier to assume Einstein's SR applies and work with spatially separated component measurements.

But in the end QM predicts this entanglement absent a causal component in the dynamics of the system. Attempting to explain it via hidden variables and hidden causal interaction is an attempt to explain quantum predictions in a classical framework i.e. as an ontological theory (describing states of reality) rather than a phenomenological theory (describing what happens).

We are intuitively biased towards ontological theories because they work so well at the scale of our everyday existence and survival behavior. When we throw a rock to hit a rabbit to eat, we don't have to worry that our "reality model" of "rock" and "rabbit" not being fundamental. As we are averaging over a massive number of phenomenological actions the aggregate phenomena fit very well into an objective reality model. By the same token we also don't have to worry about relativistic effects when hitting rabbits with rocks and so our intuitions, which evolved in this scenario, plays us false when it comes to understanding relativity of time and frame dependent simultaneity.

Wow, thank you for your thoughtful, detailed and kind reply jambaugh. It is clear that you support knowledge/education in physics and the genuine interest of others who have not dedicated so much time to further our understanding like you have. Your response will give me many days of thoughts, learning and further curiosity. I will take some time to research and think about your reply before responding so I do justice to the very generous and excellent response you gave me.

 

[f95toli]

I think this is yet another case of where the fact that photons are so weird make people confused about quantum mechanics in general. Photons are "easy" to work with experimentally since they don't interact very strongly with their environment, but the effects of quantum mechanics are much clearer when other experimental systems are used. Photons are -in my view- a bad system to use to teach QM.

The fact that your idea does not work should be quite obvious from the fact that we can also entangle many different types of "normal" objects. A"simple" example would be two ions in an ion trap or, for a recent example, two different superconducting qubits in two different cryostats
See
https://arxiv.org/abs/2008.01642

 

[chrisrp]

Thank you so much f95toli, experimental evidence to help answer my questions is exactly what I was hoping for. There is a bit more to my questions but I want to review replies, and think it through some more, to see if those are already answered. I appreciate your time and kindness in replying, thank you!

 

[PeterDonis]

my understanding is that they experience no time or distance from the moment they are generated to the moment they are interacted with

This is not correct. The correct statement is that the concept of "experiencing time or distance" does not make sense for photons.

Another way of stating this is that photons cannot be at rest in any reference frame, so the concept of "reference frame of a photon" doesn't make sense. We have a brief FAQ on this in the relativity forum:

https://www.physicsforums.com/threads/rest-frame-of-a-photon.511170/

is it possible that they are not truly separated from each and they are still together in their frame of reference?

No, this is not possible, for two reasons. First, as noted above, the concept of "frame of reference of a photon" doesn't make sense. Second, if you do use any valid frame of reference, it is clear that the photons are separated.

One possible source of confusion here is that the spacetime "length" along the worldline of a single photon is zero. (This is true for anything that moves at the speed of light.) However, when you talk about two photons, what you are interested in is the spacetime length of a curve that goes from one photon to the other. Such a curve will not be a null curve and will have a nonzero spacetime length, and that nonzero spacetime length is what is properly viewed as the "separation" of the photons.

 

[vanhees71]

It's also problematic to say "photons are separated". This insinuates that photons would be point-like objects having a position. To problem is that as massless "quanta" (just to avoid the word "particle") with spin 1 you cannot define a position operator. A photon is a certain state of the (asymptotic) free electromagnetic field, namely a on-photon Fock state.

What's observable are the positions of detection events. What's usually involved in photon detection is the photoelectric effect, i.e., you have, e.g., an atom with which the photon reacts and kicks out an electron of the atom which can be detected. For an atom, which has a finite mass, you can define a position observable. If you analyse the photo effect in the usual way by 1st-order perturbation theory it's also clear that the detection probability distribution is proportional to the energy density of the photons, which is a well-defined physical (i.e., particularly not gauge dependent!) quantity.

The didactic trouble with photons is that it is difficult to define it according to our modern understanding of it, for which you need relativistic QFT and necessarily even a gauge theory with all the formal complications to be overcome before being able to define it. The main problem with the often used introduction to QM using photons is that one doesn't use the modern notion of photon but a kind of photon in Einstein's sense of the scalled "old quantum theory". This, of course, emphasized then the inconsistencies of the old quantum theory, picturing photons as localizable particle-like objects and "wave-particle dualism", which are overcome by our modern "new quantum theory". The same holds for the Bohr-Sommerfeld model of the atom, which also unfortunately provides wrong qualitative pictures like "orbits of electrons around the nucleus" and extra rules for "non-radiating orbits". All this had to be overcome by the theorists at the time and finally lead to the discovery of "modern quantum theory", which has none of the mentioned inconsistencies and should be taught from the very beginning instead of hammering the confusing and qualitatively misleading concepts of the "old quantum theory" in students' brains. It's as if you'd teach Aristotelian mechanics before Newtonian mechanics in the first semester ;-)). For good reasons nobody starts with Aristotle instead of Gailei and Newton ;-).

 

[DrChinese]

While entangled photons may seem to be great distances apart in our perceived spacetime, is it possible that they are not truly separated from each and they are still together in their frame of reference? Could the properties of entanglement we observe in our spacetime be a result of these photons being in the process of incomplete transition from their production to their next interaction or separation?

To add to the excellent answers above:

If you are not familiar with it, there is a thing called Bell's Theorem*. It shows us that the statistical outcomes of measurements of entangled particles cannot be dependent only on factors at the time of creation. Rather, they are due to HOW they are measured. It is the observer's reference frame that would be relevant - although in most cases that isn't much of a factor either.

Further, it is possible to create entangled photon pairs that have never interacted - which would take the air out of any attempt to pin entanglement on the point of pair creation. Here's the reference from a top team:

https://arxiv.org/abs/0911.1314*Yes, I worked Bell into this thread...

 

[vanhees71]

Further, it is possible to create entangled photon pairs that have never interacted - which would take the air out of any attempt to pin entanglement on the point of pair creation. Here's the reference from a top team:

https://arxiv.org/abs/0911.1314*Yes, I worked Bell into this thread...

As discussed some time ago, entanglement swapping also doesn't need non-local interactions and a violation of the microcausality condition. What's needed are entangled photon pairs (entangled, because being created as such) and local measurements of two photons (one from one of the pairs and one from the other), which can be as far distant as you want. The important point also is that in order to make the correct statement that here two photons get entangled though they have never interacted you need the assumption of the validity of the microcausality condition of QED. That's why I still don't see, where entanglement swapping would show non-local interactions in contradiction to QED. To the contrary, it's fully consistent with QED and the entanglement of the two photons after the described measurement is again only possible because of the quantum correlations described by the entanglement of the original photon pairs.

 

[kimbyd]

The way I think of entanglement is that the entangled objects are part of the same system, no matter how far separated they become.

Now, technically, the entire universe can (in principle) be described with a single wavefunction. But isolated parts of the universe can be described as a wavefunction independent of the rest. And that's one way of looking at entanglement: a set of particles that can be described together as separate from the rest of the universe, but cannot be described separately from one another.

Why can't they be described separately? That all has to do with how the system was set up. The classical case is one where two photons are emitted from the same source, and conservation of angular momentum requires that they have opposite spins. As long as those two photons don't interact with anything else, then they will retain this relationship to one another, as they share a state. They share that state because of how they interacted with one another in the past.

But once they interact with other parts of the universe, they "decohere", which can be mathematically described as becoming entangled with the other bits. And that process looks like the collapse of the wavefunction to observers within the universe.

So to keep things entangled, you have to keep them from interacting with other things. Even thermal radiation (which is why qubits have to be supercooled).

 

[jambaugh]

I think it is unfortunate that we coined a separate word "entanglement" rather than using the qualified exiting term "quantum correlation". It imbues too much mystique into what is, by itself, simply statistical correlation between two observables.

This is not to say that there isn't something importantly different going on with quantum vs classical probabilities, namely quantum probabilities will not always satisfy Bell's inequality which is equivalent to saying quantum probabilities cannot be modeled by classical probability distribution over a set of states.
Quantum probabilities for commuting observable events are not additive.

I'm going to post a "derivation" of Bell's inequality in a new post. [will edit link into this post.]

 

[kimbyd]

I think it is unfortunate that we coined a separate word "entanglement" rather than using the qualified exiting term "quantum correlation". It imbues too much mystique into what is, by itself, simply statistical correlation between two observables.

This is not to say that there isn't something importantly different going on with quantum vs classical probabilities, namely quantum probabilities will not always satisfy Bell's inequality which is equivalent to saying quantum probabilities cannot be modeled by classical probability distribution over a set of states.
Quantum probabilities for commuting observable events are not additive.

I'm going to post a "derivation" of Bell's inequality in a new post. [will edit link into this post.]0≤d(A,B)+d(B,C)−d(A,C)

I don't think correlation really captures what's going on either, though.

A statistical correlation implies that random parameters A and B tend to vary in the same direction together.

Entanglement is a stronger statement, in that it enforces observed relationships between particles based upon their shared histories. For the angular momentum case, for instance, measuring the angular momentum of one particle in an entangled pair doesn't just give you information about the probable result of the measurement of the other pair: it can, with the right setup, actually give you the exact result.

In principle it doesn't have to be this way: just because quantum mechanics has conservation laws doesn't mean that they'll always be observed to hold. From a naive examination, one might only expect that conservation laws might only apply to the global wavefunction. As we can only ever observe a fraction of the whole, one might expect there to be cases where conservation laws simply don't hold because the observable is exchanged with parts of the wavefunction we can't observe.

In fact, there do appear to be some situations in which this is the case for quantum mechanics (see here for example). But for the most part, the conservation laws are observed to hold even for the fraction of the wavefunction we can observe. Quantum entanglement is at the heart of this fact. And that, to me, is very interesting.

 

[Fra]

I don't think correlation really captures what's going on either, though.

A statistical correlation implies that random parameters A and B tend to vary in the same direction together.

I agree.

Entanglement is a stronger statement, in that it enforces observed relationships between particles based upon their shared histories.

And this is the key question.

We know quantum mechanics describes it, but how can we understand this? (Especially given that the Bells mechanisms apparently does not work)

This question IMO take us into foundational or interpretation questions though, so I will omit my personal views. But I think this is an open question with no consensus. But it is an interesting question that i think is actually deeply connected to the more messy parts of unification and foundational questions.

/Fredrik

 

[vanhees71]

I think it is unfortunate that we coined a separate word "entanglement" rather than using the qualified exiting term "quantum correlation". It imbues too much mystique into what is, by itself, simply statistical correlation between two observables.

This is not to say that there isn't something importantly different going on with quantum vs classical probabilities, namely quantum probabilities will not always satisfy Bell's inequality which is equivalent to saying quantum probabilities cannot be modeled by classical probability distribution over a set of states.
Quantum probabilities for commuting observable events are not additive.

I'm going to post a "derivation" of Bell's inequality in a new post. [will edit link into this post.]0≤d(A,B)+d(B,C)−d(A,C)

The mystery is not related with names but with ideas. The problem is that we are used to the behavior of macroscopic objects which are almost impossible to be isolated from "the environment" such that decoherence "coarse-grains" the observables relevant for the macroscopic description to behave according to classical physics, i.e., we are not used to interference phenomena a la quantum theory, and "entanglement" is indeed just a word to describe associated correlations between different parts of systems which are generically quantum. There's nothing very mysterious in it.

The greatest obstacle against understanding is that it seems inevitable to accept that there is objective randomness in Nature, i.e., that observables only have determined values if the system is prepared in a corresponding quantum state and that it is impossible to prepare it in a state, where all observables of the system take determined values. Once one accepts this, there are no mysteries left, just a very successful and quite comprehensive description of the behavior of Nature.

 

[jambaugh]

A statistical correlation is literally a -- statistical -- correlation --. It fails to imply anything; it is descriptive.

I can hand you two physical systems and a 1-to-1 mapping between potential measurements between them and say if you measure corresponding observables you will see corresponding values. The two systems have correlated outcomes. I give you a whole bag of such paired systems and you can statistically map out the correlations between pairs of measurements other than those in correspondence.

At this point there's no mystery, I have said nothing above that would distinguish classical vs quantum correlated systems. There's no puzzle until you overlay an implicit assumption that the systems are in objective states of reality and the probabilities of all outcomes can be expressed in terms of some probability distribution over that set of possible states. Only then do you have to scratch your head because, if I have given you "entangled" quantum systems your assumptions about objective states is inconsistent with the distribution statistical correlations between measurements, a la Bell's inequality violation.

Bell's inequality is equivalent to the assertion that
$$P(A\veebar B) + P(B \veebar C) \le P(A \veebar C)$$ which itself is implied by additivity and positivity of probabilities. ($\veebar =$ xor/sym diff.)

 

[vanhees71]

But there's still no mystery, because quantum theory provides probabilities different from "classical probability", and that's why Bell's inequality is invalid for the "quantum probability" and makes quantum theory distinguishable from any local deterministic (probabilistic) theory. One has simply accept the observed facts: Quantum theory describes the phenomena correct, local deterministic hidden-variable theories don't. That's a profound result of scientific research and simply must be accepted. We don't decide, how Nature behaves, but we can observe her and find the best description we can, and that's at this time QT. As you say: "it's descriptive"!

 

[Fra]

But I think few physicists claims to understand WHY the quantum description of probability is right. This question can be understood without a desire to restore Bell type realism. The mystery is bigger than the loss of old times realism.

Ie. why has nature chosen to make use of quantum logic? As I ask that, the implicit presumed answer (that is yet to be explicit) lies in some generalisation of a theory of inference, possible in the context of ineracting agents. This is why I consider the open question. (Mystery is a bad word though.)

I am not satisfied with the description, I think there is a deeper explanation as well to be found.

/Fredrik

 

[vanhees71]

It's right, because the scientific method has brought us to discover quantum theory. Science never answers "why questions".

 

[Fra]

You mean questions like: Why an apply falls to the ground? Why a hydrogen atom is stable?

/Fredrik

 

[jambaugh]

"why?" only goes so far as we reduce specific behavior to certain generalizations. Apples fall "because" masses attract. That masses attract is not further explainable in a "why" it is only describable in a way consistent with observations, such as apples falling to the ground.

 

[Fra]

I think where our ambition to "stop asking for another explanatory level" stops is determined only by progress and when we see a possible benefit from it. To ask why nature implements quantum logic is IMO not a meaningless question as long as there is a context of where it may be answered, and especially if it might have something to offer to the open questions.

To just shout out a why, without any ideas of what kinds of possible answers you are looking for, is not constructive.

(My context is that of interacting agent, in a extremal qbism interpretation, here the choice of logic for calculating guiding probabilities for actions, has the potential to make testable claims about the hamiltonians of a agent-agent system.)

/Fredrik

 

[kimbyd]

A statistical correlation is literally a -- statistical -- correlation --. It fails to imply anything; it is descriptive.

I can hand you two physical systems and a 1-to-1 mapping between potential measurements between them and say if you measure corresponding observables you will see corresponding values. The two systems have correlated outcomes. I give you a whole bag of such paired systems and you can statistically map out the correlations between pairs of measurements other than those in correspondence.

At this point there's no mystery, I have said nothing above that would distinguish classical vs quantum correlated systems. There's no puzzle until you overlay an implicit assumption that the systems are in objective states of reality and the probabilities of all outcomes can be expressed in terms of some probability distribution over that set of possible states. Only then do you have to scratch your head because, if I have given you "entangled" quantum systems your assumptions about objective states is inconsistent with the distribution statistical correlations between measurements, a la Bell's inequality violation.

Bell's inequality is equivalent to the assertion that
$$P(A\veebar B) + P(B \veebar C) \le P(A \veebar C)$$ which itself is implied by additivity and positivity of probabilities. ($\veebar =$ xor/sym diff.)

Bell's theorem is a little different, though. In particular it describes how the statistical correlation between the measurements of an entangled state can't be described in a classical manner.

Yes, you do need to discuss the correlation to get the full picture of what is going on with entanglement, and in particular how it differs from the classical expectation of how such observables might be correlated. But correlation alone also does not describe the whole of what is going on. In particular I don't think it's a good way to understand the behavior of pure states. It also misses the point that wavefunction dynamics as described by the equations of motion of the wavefunction are not statistical in nature. The statistical nature of QM derives only from the behavior of the system during wavefunction collapse (or the appearance of collapse).

Because entanglement is all about how the system behaves when there is no collapse over significant distances, focusing only on the collapse aspect misses some important features of the behavior of the system.

 

[EPR]

I think where our ambition to "stop asking for another explanatory level" stops is determined only by progress and when we see a possible benefit from it. To ask why nature implements quantum logic is IMO not a meaningless question as long as there is a context of where it may be answered, and especially if it might have something to offer to the open questions.

To just shout out a why, without any ideas of what kinds of possible answers you are looking for, is not constructive.

(My context is that of interacting agent, in a extremal qbism interpretation, here the choice of logic for calculating guiding probabilities for actions, has the potential to make testable claims about the hamiltonians of a agent-agent system.)

/Fredrik

In which interpretation is macroscopic causality fundamental?

I think we are not on solid ground with these why questions. We don't have why answers we can confidently regard as true.

 

[Fra]

I think we are not on solid ground with these why questions. We don't have why answers we can confidently regard as true.

Agreed. But I think the edge of scientific discovery is never on solid ground. Evolution does not follow a straight deductive path (this is what gave Popper headache). This is what i meant in post 13. As long as we have only foot off solid ground, we are fine.

(The why questions are essential linked to "ideas" that may or may not bear fruit, and thus be part of the future mature science. This is part of the scientific process, and it's edge is ugly)

/Fredrik