When does entanglement actually end?

[DrChinese]

I haven't seen a paper which answers this particular question, maybe someone else has... (I have scanned the preprint archive but to no avail so far).

Most Bell tests use polarizing beam splitters (PBS) to check photons at Alice and Bob. Typical are 2 detectors at Alice and 2 at Bob. Results of all 4 are correlated and analyzed. You would normally say the entanglement ends once we know which way the photon goes through the beam splitter.

What if we takes the 2 beams at Alice and merge them back very precisely together again? I.e. such that it is no longer possible to tell which path the photon took through the PBS. I would expect that the resultant reconstructed beam (Alice) is still entangled with Bob. If you tested Alice and Bob at this point, I would expect us to see the perfect correlations and the Bell inequality violations per usual. Is this correct?

So when does the entanglement actually end? If what I am saying is right, the PBS is not actually capable of ending the entanglement itself. Instead, it is the detection of the photon - and what we know about it at that point - which ends the entanglement. I believe this is fully consistent with the QM prediction.

 

[friend]

I think all entanglement means is that the particles have become correlated unless one or both bounce off some other particle. Why is this so mysterious

 

[DaveC426913]

I think all entanglement means is that the particles have become correlated unless one or both bounce off some other particle. Why is this so mysterious

OK, so your contention is that entanglement ends when the particles collide with other particles. Is that verifiable or is it a guess?

 

[DrChinese]

I think all entanglement means is that the particles have become correlated unless one or both bounce off some other particle. Why is this so mysterious

When a particle goes through a polarizing beam splitter or a filter: as far as anyone knows there is no physical contact between the polarizer apparatus and the photon itself. I believe it is more of a field effect. Clearly, if a series of polarizers is involved, the entanglement does NOT continue in the normal case (as opposed to the special case I described in the OP). So perhaps the mechanism is simply passing through a filter...

...Except that the case I am asking about would actually mean 2 filters are involved and so would negate that conclusion (since the first PBS did not completely end the possibility of entanglement. That is what I am asking about. In other words, the end of the entanglement seems to be contingent on what we have the possibility of knowing. This implies that the underlying mechanism is not specific to one particular observational apparatus.

Besides, you can definitely bounce entangled photons off a mirror or an optical fiber and that has no apparent effect on the entangled state. This is done routinely in Bell-type experiments.

 

[peter0302]

I think you're right. It ends when there is an _irreversible_ measurement - i.e. detection - made, and when decoherence occurs. What you're talking about is like a delayed choice quantum eraser isn't it? If the measurement can be reversed, the particles can be "re-entangled" back to the state they were in before the measurement.

 

[Phrak]

Particles A and B are entangled when they are described by a single wave function. I’m not sure if it even makes sense to give them distinguishing labels like A and B, except to say what Alex might measure is not what Bobbie would measure.

If the wave passes through a beam splitter it’s entangled with the splitter, because in principle it’s possible to measure the direction it passed through the splitter due to the momentum imparted to the splitter. In measuring the momentum imparted to the beam splitter, the path of the wave is known.

If Alex measures a particle then Alex is entangled with particles A and B.

If Bobbie also measures a particle, she’s entangled with Alex.

Edit: It makes sense to say the last two statements as a third observer, observing Alex and/or Bobble. I don't know if it's correct to say, "I'm entangled with paricles A and B."

 

[DrChinese]

I think you're right. It ends when there is an _irreversible_ measurement - i.e. detection - made, and when decoherence occurs. What you're talking about is like a delayed choice quantum eraser isn't it? If the measurement can be reversed, the particles can be "re-entangled" back to the state they were in before the measurement.

Yes, I think that is always the case. Kinda odd, doesn't it seem?

 

[peter0302]

Not if you like MWI. :)

I think what you're talking about is more evidence that there's no physical link between them and that the only physical reality of entanglement is manifested when measurements are made - which is why we don't see any evidence of it unitl two measurements are compared. Regardless of what interpretation you like (collapse, decoherence, many-worlds), in all of them it's still the irreversible measurement that causes the results we see. The photon bouncing off the mirror - for which there is no evidence afterwards - isn't a measurement, so it has no effect on the "link."

 

[moving_on]

With respect to reflection, can't this 'affect' polarization in certain circumstances?
What I mean is 'polarization by reflection'.

 

[moving_on]

Thinking more about this.
My understanding is that when you set up a 'polarization by reflection' experiment, it is possible to infer the polarization of the reflected photon based on the angle set for the reflector. Is this about right? (assuming it reflects).
What about a 'cat in the box' version. We program a 'randomizer' to choose one
of a set of possible angles. We send in some photons from a stream of entangled pairs.
We don't then know the angle and hence cannot infer the polarization of the exiting photon...
... would this cause disentanglement?
There are probably lots of reasons why this is complete tosh, so I'm going to try
to stop thinking now...

 

[peter0302]

Haha. It's not trash but you need to understand some fundamentals better first. *If* you learn anything about a particle, that is a measurement. Whether it's an active measurement - like detection - or a passive measurement - like no detection - anything you do that allows you to infer a value *is* a measurement from a QM perspective. It's truly an information based theory, which is why it's so difficult to reconcile it with what we see in the macroscopic world.

 

[vanesch]

Not if you like MWI. :)

I think what you're talking about is more evidence that there's no physical link between them and that the only physical reality of entanglement is manifested when measurements are made - which is why we don't see any evidence of it unitl two measurements are compared. Regardless of what interpretation you like (collapse, decoherence, many-worlds), in all of them it's still the irreversible measurement that causes the results we see. The photon bouncing off the mirror - for which there is no evidence afterwards - isn't a measurement, so it has no effect on the "link."

Indeed, what ends *observable* entanglement is measurement. Now, in all projection-based theories observation puts the state of the observed system in a "product state", so that there is no entanglement anymore. However, in all "purely unitary" theories/interpretations/... such as MWI, measurement IS entanglement (extra entanglement, between the observer and the system state). So in one set of views, measurement ends entanglement, in another, measurement entangles further (and hopelessly irreversibly).
Both views can be reconciled by saying that *from the point of view of a particular observer* what he's entangled with is a pure product state of the system under observation.

 

[LaserMind]

By a measurement we mean getting a value for an observable...
When a wave packet is forced to reveal the values of its states in the form of observables (operators) by some external agent (another wave packet) then that paticular wave packet's state construction is ended, as are all its possible paths it may have instantly and its new wave packet has realigned states and entanglements.

But a particle spends all of its life as a wave packet, its just that the packet states keep getting realigned/entangled by 'hitting' other wave packets.

 

[peter0302]

Yeah but even you "Detect" a particle through its absence - thereby not employing a "hit" with another wave packet - that's still a quantum measurement. So actually no "interaction" in the traditional sense is required for a measurement.

 

[DrChinese]

Indeed, what ends *observable* entanglement is measurement. Now, in all projection-based theories observation puts the state of the observed system in a "product state", so that there is no entanglement anymore. However, in all "purely unitary" theories/interpretations/... such as MWI, measurement IS entanglement (extra entanglement, between the observer and the system state). So in one set of views, measurement ends entanglement, in another, measurement entangles further (and hopelessly irreversibly).
Both views can be reconciled by saying that *from the point of view of a particular observer* what he's entangled with is a pure product state of the system under observation.

Thanks as always for your keen comments. It is interesting that our entangled particles could have their entanglement ended for one commuting observable, while remaining entangled for another. I am thinking about perhaps polarization and momentum.

 

[LaserMind]

It is interesting that our entangled particles could have their entanglement ended for one commuting observable, while remaining entangled for another. I am thinking about perhaps polarization and momentum.

I agree with you that the actual collapse of the wave function (so-called) is a key concept - when, how, where, why, how long - it strikes me that it only changes to another wave function and never comes into 'our Universe' as an actual object - for example an electron is always an electron and will exist in a wave packet only.

Sometimes I get the impression, reading the literature, that it comes out of superposition as a little gray ball (or even a cat!) or something - which is not the case at all.

Also, your point about partially collapsing some states is unclear - it must impinge on entanglement considerations.

 

[peter0302]

The electron certainly doens't morph. But according to the generally accepted models right now, the electron (and the photon for that matter) is _always_ a particle. What changes is the probability distribution of where you'll detect it.

There are many problems with the idea of a wave-packet, not the least of which is that if there is a physical wave-packet, it would exist everywhere in the universe and changes in it would be instantaneous everywhere in the universe, and therefore explicitly non-local. By considering the particles as particles, the only non-local element is the probability wave, which itself has no physical meaning.

 

[Phrak]

I wouldn't pretend to know the all about entanglement, but a lot of the discussion here has been predicated upon

1) fitting the idea of entanglement into a particular interpretation of quantum mechanics without qualification,
2) what is believed constitute an interaction, and
4) the idea that an observation obtains a universal wave collapse.

When a wave passes through a beam splitter it is entangled with the splitter. An electron is entangled with the Stern-Gerlach apparatus.

When Alice observes the spin state of an entangled pair of electrons, the pair are still entangled to other observers, including Bob. What is described by one observer as a wave can be described by another oberver as a projected state.

There's a tendency to attach an objective, observer independent interpretation to various elements of quantum mechanics, but within the null interpretation, what is unclear to me, are whether variables describe what are known or what are knowable.

 

[DrChinese]

There are many problems with the idea of a wave-packet, not the least of which is that if there is a physical wave-packet, it would exist everywhere in the universe and changes in it would be instantaneous everywhere in the universe, and therefore explicitly non-local.

And yet the physical result is pretty much as if that were the case. So that is why I ask: is collapse a physical process? If it were, the about would be true.

And yet... partial collapse of the wave function could be considered a counter-argument to the above. Because now there would have to be "half-a-wave-packet" left (which would also be non-local?) to account for the results.

Yikes!

 

[peter0302]

Hehe, I can't really tell what side you're taking. :) But my answer is collapse can't be a physical process; it's just that quantum statistics don't conform to the laws of macro-statistics.

Wouldn't you rather throw out classical statistics than throw out relativity? :)

 

[LaserMind]

And yet... partial collapse of the wave function could be considered a counter-argument to the above. Because now there would have to be "half-a-wave-packet" left (which would also be non-local?) to account for the results.

Yikes!

hmmm..., re partial collapse - what make me sceptical is the 'which path' problem.
Because obtaining just one observable (partial) would reveal which path information - in say, erasure experiment - and we would then get then a 'particle' result rather than a wave interference result.
We would probably conclude the 'wave function' collapsed (for all states).

What do you think?
Mega yikes.

 

[DrChinese]

hmmm..., re partial collapse - what make me sceptical is the 'which path' problem.
Because obtaining just one observable (partial) would reveal which path information - in say, erasure experiment - and we would then get then a 'particle' result rather than a wave interference result.
We would probably conclude the 'wave function' collapsed (for all states).

What do you think?
Mega yikes.

Actually, the "partial collapse" is demonstrated as true in virtually every Bell test - although that is a by-product rather than a specific element of the Bell test.

It is normal to place filters after the PDC crystal (which is where the input photon is split into 2 output photons). These filters are tuned to a specific frequency of light because it is critical that extraneous light (of which there is a lot coming out of the PDC that is not down-converted) does not go into the detection apparatus. Those filters *absolutely* give us knowledge of wavelength, frequency and energy of the photon that passes - it is an observation! As such, there must be collapse of that part of the wavefunction. Yet... afterwards, we perform a commuting polarization observation on those same photons and notice there is perfect entanglement.

So this is not a speculative issue... partial entanglement is real.

 

[CJames]

Indeed, what ends *observable* entanglement is measurement. Now, in all projection-based theories observation puts the state of the observed system in a "product state", so that there is no entanglement anymore. However, in all "purely unitary" theories/interpretations/... such as MWI, measurement IS entanglement (extra entanglement, between the observer and the system state). So in one set of views, measurement ends entanglement, in another, measurement entangles further (and hopelessly irreversibly).
Both views can be reconciled by saying that *from the point of view of a particular observer* what he's entangled with is a pure product state of the system under observation.

I'm trying to wrap my head around the full implications of this. Does this imply that it is in principle possible to obtain information from one particle about any other particles it has interacted with in the past? Or, put another way, quantum information is never destroyed?

 

[LaserMind]

Actually, the "partial collapse" is demonstrated as true in virtually every Bell test - although that is a by-product rather than a specific element of the Bell test.

It is normal to place filters after the PDC crystal (which is where the input photon is split into 2 output photons). These filters are tuned to a specific frequency of light because it is critical that extraneous light (of which there is a lot coming out of the PDC that is not down-converted) does not go into the detection apparatus. Those filters *absolutely* give us knowledge of wavelength, frequency and energy of the photon that passes - it is an observation! As such, there must be collapse of that part of the wavefunction. Yet... afterwards, we perform a commuting polarization observation on those same photons and notice there is perfect entanglement.

So this is not a speculative issue... partial entanglement is real.

Partial collapse and maintaining entanglement? Then one state could be given a known state preparation that the entangled particle would have 'no idea' about what the value is? How does that work? Have you got a reference for partial collpase re entanglement? Interesting.

 

[peter0302]

Quantum information can absolutely be destroyed. That's exactly what quantum eraser does.

 

[CJames]

maybe I'm not using the right terminology. My point here is that a measurement of one of the entangled particles will give you information about the other particle. In the quantum eraser experiment, I suppose it is true that "which path" information is destroyed for the OBSERVER. What is not destroyed, though, is the fact that IF "which path" information is obtained from one of the particles, the interference pattern collapses. Throughout the entire experiment, each particle contains information about the other.

My question revolves around something more complex. What happens long after the experiment takes place? Vanesch appears to be saying that (for some theoretical observer) the particles will become entangled with the entire experimental setup, and so on inexorably. So the question I'm asking is whether a particle (in principle) contains information about every other particle it has interacted with in the past.

 

[DrChinese]

Partial collapse and maintaining entanglement? Then one state could be given a known state preparation that the entangled particle would have 'no idea' about what the value is? How does that work? Have you got a reference for partial collpase re entanglement? Interesting.

This isn't perfect but it has the filter before the beam splitter:

Multi-photon entanglement

Unfortunately, my usual reference for this type of experiment (Dehlinger and Mitchell) has the filter after the polarizer so the fact that there was partial collapse is not evident.

 

[peter0302]

So the question I'm asking is whether a particle (in principle) contains information about every other particle it has interacted with in the past.

Well, the answer is no, as to "information." It is certainly true that particles are influenced by their entire history, but the extent to which usable information can actually be divined depends on how much the particle has become entangled with the environment.

Imagine tallying up items on a simple calculator. Every time you hit M+, the total updates. The total reflects all of the items that went into it. But that doesn't mean by knowing the total you know the cost of the individual items. Each time you perform a measurement on a particle, it's like hitting M+.

 

[DrChinese]

My question revolves around something more complex. What happens long after the experiment takes place? Vanesch appears to be saying that (for some theoretical observer) the particles will become entangled with the entire experimental setup, and so on inexorably. So the question I'm asking is whether a particle (in principle) contains information about every other particle it has interacted with in the past.

I don't know if I would agree that each particle contains information about all particles it has interacted with in the past. In fact, you would have to say that information is lost at about the same rate it is gained. I think Vanesch is saying that a new system is formed which is itself in a superposition of states. With that many particles, I don't think any individual particle has enough of the story to call it "information". Not sure if that addresses your point or not.

But clearly if the observer had a known net spin state before interacting with another particle with a known spin state, the combined state would be known and presumably would be entangled in a fashion. It breaks my brain to think about. :)

 

[CJames]

Thankyou peter and Dr Chinese. Your answers are very helpful.

 

[ThomasT]

Quantum entanglement is a name given to correlations (typically produced by combining the data streams of two or more spatially separated detectors) which satisfy certain criteria.

Other than the technical details of specific experimental designs and material and instrumental preparations that characteristically produce entangled (or nonseparable) data sets, there isn't any way to talk about when entanglement begins or when entanglement ends. Is there? I don't know.

The Copenhagenists tell us that we can never know what entanglement is at the level of quantum interactions themselves due to the existence of a fundamental quantum. I believe they're correct, and this seems to be supported by the application of Bell's theorem.

I learned from a previous thread on entanglement that it's fairly pointless to speculate about what entanglement actually is (other than material and instrumental preparations and behavior, that is). So, it would also seem somewhat pointless to speculate about when it begins and when it ends -- since we have no way of speaking unambiguously about what it ... is.

And, by the way, I'm not at all happy with this state of affairs.

 

[vanesch]

Quantum entanglement is a name given to correlations (typically produced by combining the data streams of two or more spatially separated detectors) which satisfy certain criteria.

Mmm, I would define it differently. To me, quantum entanglement is a *formal property* in the framework of a specific *theory* (in other words, a formal definition, not an "observed phenomenon"). You need to place yourself already within the formal framework of quantum theory, and then you can define entanglement as a quantum state which belongs to the tensor product state of two subsystems, but which is not to be written as the product of two states each belonging to the subspaces of the respective subsystems.

Of course, this has observable consequences as per the predictions of said theory. But I would keep a distinction between these observable (predicted) consequences on one hand, and the formal concept of entanglement on the other hand.

For instance, entanglement "explains" the violations of Bell inequalities (as per the predictions of quantum theory on entangled states). But these violations can also be obtained by, say, blunt action-at-a-distance. In that case, there's no point in talking about "entanglement", although the observed effects are the same.

 

[ThomasT]

Mmm, I would define it differently. To me, quantum entanglement is a *formal property* in the framework of a specific *theory* (in other words, a formal definition, not an "observed phenomenon"). You need to place yourself already within the formal framework of quantum theory, and then you can define entanglement as a quantum state which belongs to the tensor product state of two subsystems, but which is not to be written as the product of two states each belonging to the subspaces of the respective subsystems.

Of course, this has observable consequences as per the predictions of said theory. But I would keep a distinction between these observable (predicted) consequences on one hand, and the formal concept of entanglement on the other hand.

For instance, entanglement "explains" the violations of Bell inequalities (as per the predictions of quantum theory on entangled states). But these violations can also be obtained by, say, blunt action-at-a-distance. In that case, there's no point in talking about "entanglement", although the observed effects are the same.

Yes, thanks. The definition of quantum entanglement that you offer is more precise than the way I had characterized it. There is, of course, a distinction between processes (experimental preparations) which generate entangled data and an abstraction that is a general formal description of those processes. But it's the preparations and data that give the formalism any and all meaning (ie., physical referents) that it might have.

My characterization of entanglement was just a lead into the main point -- that speculating about the nature of entanglement is doomed to be a futile exercise (depending of course on how one interprets the quantum theory and Bell's theorem).

I think I'm almost ready to let go of my desire to understand the deep nature of quantum entanglement. The quantum theory isn't designed to provide this, even though one might attempt to support certain speculations about the deep nature of certain instrumental phenomena by referencing certain aspects of the development and current expression(s) of the formal theory. So-called realistic theories which involve actions-at-a-distance or quantum potentials or multiple worlds or other sorts of nebulous concepts aren't much help in this regard either.

I'm glad you put the word explains in quotation marks where you stated that [the formal treatment of quantum] entanglement "explains" the violations of Bell inequalities.
It doesn't quite do it for me either.

 

[vanesch]

Yes, thanks. The definition of quantum entanglement that you offer is more precise than the way I had characterized it. There is, of course, a distinction between processes (experimental preparations) which generate entangled data and an abstraction that is a general formal description of those processes.

No. You see, there's no such thing as "entangled data", that was my point. You can find *correlations* in data. But *entanglement* is a concept that only makes sense in quantum theory (unless one gives it another definition in another theory). There's nothing "observable" about entanglement. Of course, entangled quantum objects will, though quantum theory, give rise to predictions of certain correlations, but these correlations could also occur by, say, action-at-a-distance theories. If there weren't any quantum theory, but we had started off with action-at-a-distance theories, we would never have the word entanglement, and never have invented the concept.

BTW, speculation about the nature of fundamental theoretical concepts is always a "futile exercise" apart from giving you a mental picture.

 

[DrChinese]

You can find *correlations* in data. But *entanglement* is a concept that only makes sense in quantum theory (unless one gives it another definition in another theory). There's nothing "observable" about entanglement.

Of course I essentially agree with this. But here is something that is puzzling me. The question is often asked: Is collapse a physical process? I see (sorta) how MWI and orthodox QM handle it. But I really don't see how the dBB (Bohmian) theory would address it, because it postulates that there is an underlying mechanism (even though uncertainty is supplied to match experiment). Now I ask: if there is such a mechanism, how can we have *partial* collapse of the wave function? As long as we focus on the formalism (going no further), everything fits. But going a step further (which is the point of dBB), it seems we get into a pretty strange place.

 

[vanesch]

Of course I essentially agree with this. But here is something that is puzzling me. The question is often asked: Is collapse a physical process? I see (sorta) how MWI and orthodox QM handle it. But I really don't see how the dBB (Bohmian) theory would address it, because it postulates that there is an underlying mechanism (even though uncertainty is supplied to match experiment). Now I ask: if there is such a mechanism, how can we have *partial* collapse of the wave function? As long as we focus on the formalism (going no further), everything fits. But going a step further (which is the point of dBB), it seems we get into a pretty strange place.

In Bohmian mechanics, there is no collapse: the "guiding field" (deduced from the unitarily evolving wavefunction) goes on without collapsing (just as in MWI). The actual "collapse" just comes about because the particles HAVE specific positions, and hence go this or that way under the quantum force (and in doing so, change the quantum force on all other particles, that's the famous "action at a distance" in BM). However, because before the measurement, we didn't know what the position was, and the possible positions of the particles are such that we need the "entire wavefunction" to predict the possible evolutions of all those possible positions ; after measurement, we've reduced the probability distribution of the positions (because of the measurement result), and hence we now don't NEED anymore the "other branches" of the wavefunction. We can keep them, though. They won't affect future evolution of the particle positions anymore. So we can just as well "cut them away" from the wavefunction (collapse it). But you're not obliged to do so.
Simply because we now KNOW that the particles are in certain positions (or regions), so our probability distribution has "retracted", and we don't need the evolution anymore of pieces of wavefunction (of configuration space), simply because there's no probability there anymore.

EDIT: the behaviour of particles in BM is exactly as in statistical (classical) mechanics: you suppose that they HAVE a specific position, but you only KNOW about a distribution. So you need the dynamics that handles ALL of these potential positions until you learn more about the positions, in which case you can truncate the needed dynamics of positions (given that you won't need those anymore that you now KNOW have probability 0). So you can "leave that part of the dynamics out" if you wish - but you can just as well keep it, it won't make any difference. It is a bit (very naive analogy) as if you looked at the Newtonian gravitational potential of the sun, extending to all of space. And then you find out that the Earth and the planets only orbit the sun in a certain region of space: you can just as well "set the rest of the potential to zero" what the effect of the sun on the planets' dynamics is concerned. Or keep it the way it is. It won't make any difference for the motion of the planets.

Now, you can ask: but in about all of quantum mechanics, people always insist (me included) that you CAN'T see the wavefunction as a probability distribution, because that screws up quantum interference. How come that this is exactly what is done in Bohmian mechanics ? Answer: because BM restores quantum interference by subtle action-at-a-distance effects in the quantum force. Particle A will get a pull to the left or to the right according to whether particle B, potentially miles away, will be 5 microns more to the left or to the right.

 

[DrChinese]

In Bohmian mechanics, there is no collapse: the "guiding field" (deduced from the unitarily evolving wavefunction) goes on without collapsing (just as in MWI). The actual "collapse" just comes about because the particles HAVE specific positions, and hence go this or that way under the quantum force (and in doing so, change the quantum force on all other particles, that's the famous "action at a distance" in BM). However, because before the measurement, we didn't know what the position was, and the possible positions of the particles are such that we need the "entire wavefunction" to predict the possible evolutions of all those possible positions ; after measurement, we've reduced the probability distribution of the positions (because of the measurement result), and hence we now don't NEED anymore the "other branches" of the wavefunction. We can keep them, though. They won't affect future evolution of the particle positions anymore. So we can just as well "cut them away" from the wavefunction (collapse it). But you're not obliged to do so.
Simply because we now KNOW that the particles are in certain positions (or regions), so our probability distribution has "retracted", and we don't need the evolution anymore of pieces of wavefunction (of configuration space), simply because there's no probability there anymore.

EDIT: the behaviour of particles in BM is exactly as in statistical (classical) mechanics: you suppose that they HAVE a specific position, but you only KNOW about a distribution. So you need the dynamics that handles ALL of these potential positions until you learn more about the positions, in which case you can truncate the needed dynamics of positions (given that you won't need those anymore that you now KNOW have probability 0). So you can "leave that part of the dynamics out" if you wish - but you can just as well keep it, it won't make any difference. It is a bit (very naive analogy) as if you looked at the Newtonian gravitational potential of the sun, extending to all of space. And then you find out that the Earth and the planets only orbit the sun in a certain region of space: you can just as well "set the rest of the potential to zero" what the effect of the sun on the planets' dynamics is concerned. Or keep it the way it is. It won't make any difference for the motion of the planets.

Now, you can ask: but in about all of quantum mechanics, people always insist (me included) that you CAN'T see the wavefunction as a probability distribution, because that screws up quantum interference. How come that this is exactly what is done in Bohmian mechanics ? Answer: because BM restores quantum interference by subtle action-at-a-distance effects in the quantum force. Particle A will get a pull to the left or to the right according to whether particle B, potentially miles away, will be 5 microns more to the left or to the right.

But I think that there MUST be definite constraints on the dBB/Bohmian-type solutions if entanglement can be partial. So let's say that Alice is affected by Joe. I guess you could say they are entangled in a sense. And yet, it is Bob's measurement (i.e. how Bob is measured) - and not Joe's - that affects the correlation of Alice and Bob. And further, Alice and Bob can (and probably will) remain entangled afterwards!

Now why do I say that there is a constraint? Because the Bohmian solutions (generally) argue for the primacy of particle position. It is not reasonable that a distribution of deterministic particle positions should simultaneously determine Alice and Bob AND have Alice and Bob as entangled per the results of Bell tests. Clearly, the only variable in their correlations is their observed relative angle to each other. The positions of the remainder of the particles in the universe - indeed the relative time at which they are measured - are not factors even though you would reasonably expect then to be significant factors (by definition). So the constraint I see is: a) the impact of the positions of other particles combined with b) the relative time at which they are observed (since presumably the positions of all particles will be different) must be such that a) + b) completely cancel out. Further, they result in the end of the entanglement for those specific observables, but not for other commuting observables.

My point being: QM is silent and does not postulate mechanics for collapse. So it is mysterious in that respect - a valid criticism although there is no technical flaw. BM is not silent, but I don't think it can withstand the subtle questions that lie in the aftermath of Bell's Theorem. You still have to ask: how can Alice and Bob be entangled in such a way that Bell tests show exactly the correlations they do if their spin characteristics are predetermined but still subject to the influence of the remainder of the universe - when clearly that influence must be nil (else there would not be perfect correlations as well when there are matching angle settings but the observations are at different points in time and space).

From the Stanford Encyclopedia entry on Bohmian Mechanics by Goldstein:

"13. Nonlocality

"Bohmian mechanics is manifestly nonlocal: The velocity, as expressed in the guiding equation, of anyone of the particles of a many-particle system will typically depend upon the positions of the other, possibly distant, particles whenever the wave function of the system is entangled, i.e., not a product of single-particle wave functions. This is true, for example, for the EPR-Bohm wave function, describing a pair of spin-1/2 particles in the singlet state, analyzed by Bell and many others. Thus does Bohmian mechanics make explicit the most dramatic feature of quantum theory: quantum nonlocality.

"It should be emphasized that the nonlocality of Bohmian mechanics derives solely from the nonlocality built into the structure of standard quantum theory, as provided by a wave function on configuration space, an abstraction which, roughly speaking, combines — or binds — distant particles into a single irreducible reality. As Bell (Bell 1987, p. 115) has stressed,

'That the guiding wave, in the general case, propagates not in ordinary three-space but in a multidimensional-configuration space is the origin of the notorious ‘nonlocality’ of quantum mechanics. It is a merit of the de Broglie-Bohm version to bring this out so explicitly that it cannot be ignored.'

"Thus the nonlocal velocity relation in the guiding equation is but one aspect of the nonlocality of Bohmian mechanics. There is also the nonlocality, or nonseparability, implicit in the wave function itself and in its propagation, a nonlocality that does not in fact assume the structure — actual configurations — that Bohmian mechanics adds to orthodox quantum theory. And as Bell has shown, using the connection between the wave function and the predictions of quantum theory concerning experimental results, this nonlocality cannot easily be argued away (see Section 2).

"The nonlocality of Bohmian mechanics can be appreciated perhaps most efficiently, in all its aspects, by focusing on the conditional wave function. Suppose, for example, that in an EPR-Bohm experiment particle 1 passes through its Stern-Gerlach magnet before particle 2 arrives at its magnet. Then the orientation of the Stern-Gerlach magnet for particle 1 will have a significant effect upon the conditional wave function of particle 2: If the Stern-Gerlach magnet for particle 1 is so oriented as to "measure the z-component of spin," then after particle 1 has passed through its magnet the conditional wave function of particle 2 will be an eigenvector (or eigenstate) of the z-component of spin (in fact, belonging to the eigenvalue that is the negative of the one "measured" for particle 1), and the same thing is true for any other component of spin. You can dictate the kind of spin eigenstate produced for particle 2 by appropriately choosing the orientation of an arbitrarily distant magnet. As to the future behavior of particle 2, in particular how it is affected by its magnet, this of course depends very much on the character of its conditional wave function and hence is very strongly influenced by the choice of orientation of the distant magnet.

"This nonlocal effect upon the conditional wave function of particle 2 follows from combining the standard analysis of the evolution of the wave function in the EPR-Bohm experiment with the definition of the conditional wave function. (For simplicity, we ignore permutation symmetry.) Before any magnets have been reached the EPR-Bohm wave function is a sum of two terms, corresponding to nonvanishing values for two of the four possible joint spin components for the two particles, each term a product of an eigenstate for a component of spin in a given direction for particle 1 with the opposite eigenstate (i.e., belonging to the eigenvalue that is the negative of the eigenvalue for particle 1) for the component of spin in the same direction for particle 2. Moreover, by virtue of its symmetry under rotations, it happens that the EPR-Bohm wave function has the property that any component of spin, i.e., any direction, can be used in this decomposition. (This property is very interesting.)

"Decomposing the EPR-Bohm wave function using the component of spin in the direction associated with the magnet for particle 1, the evolution of the wave function as particle 1 passes its magnet is easy to grasp: The evolution of the sum is determined (using linearity) by that of its individual terms, and the evolution of each term by that of each of its factors. The evolution of the particle-1 factor leads to a displacement along the magnetic axis in the direction determined by the (sign of the) spin component (i.e., the eigenvalue), as described in the fourth paragraph of Section 11. Once this displacement has occurred (and is large enough) the conditional wave function for particle 2 will correspond to the term in the sum selected by the actual position of particle 1. In particular, it will be an eigenstate of the component of spin "measured by" the magnet for particle 1.

"The nonlocality of Bohmian mechanics has a remarkable feature: it is screened by quantum equilibrium. It is a consequence of the quantum equilibrium hypothesis that the nonlocal effects in Bohmian mechanics don't yield observable consequences..."

I am not arguing that there is not a non-local component to BM/dBB, as I think this is pretty clear both from the above and the more detailed descriptions of the basic formulas I have seen. I am simply saying that the proposed mechanism doesn't seem to be suited for describing both full entanglement and partial entanglement scenarios. Just having a non-local component does NOT give Bohmian solutions a "pass" on Bell's Theorem. The non-local component must fully explain the observed correlations too, in order for the pass to be valid. It is completely unreasonably to me that - to paraphrase Goldstein above: The setting for magnet A affects the outcome at B, and yet has no affect on commuting observables for A or B.

 

[ThomasT]

No. You see, there's no such thing as "entangled data", that was my point. You can find *correlations* in data. But *entanglement* is a concept that only makes sense in quantum theory (unless one gives it another definition in another theory). There's nothing "observable" about entanglement. Of course, entangled quantum objects will, through quantum theory, give rise to predictions of certain correlations, but these correlations could also occur by, say, action-at-a-distance theories.

OK, I understand that quantum entanglement is formally different from, say, quantum action-at-a-distance in that the former "is not to be written as the product of two states each belonging to the subspaces of the respective subsystems", but the latter might be.

But suppose we want to interpret the formal expression of quantum entanglement in order to give it some physical meaning. Then can't we say that data correlations satisfying certain criteria are the objectively physical manifestation of the formal expression?

There is something observable about entanglement (even though quantum states themselves aren't observable), else how would you know if you'd produced it or changed it experimentally?

Of course there's no way to tell if the correlations have been produced by FTL communication of some sort between the spatially separated filtration-detection setups, or not.

But, no matter which is the case, we're still dealing with some sort of relationship between coincidentally accumulated data attributes -- and this relationship is physically defined by the experimental preparations and designs and, ultimately, the results.

Here's Schrodinger's characterization of entanglement:
"When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own. I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. By the interaction the two representatives [the quantum states] have become entangled."

What's my point? I think that we can speak in terms of entangled data without getting into too much semantic trouble. But if you want to be nitpicky about it, then I see your point -- entanglement refers directly to quantum states, and quantum states aren't to be taken literally as real physical states.

BTW, speculation about the nature of fundamental theoretical concepts is always a "futile exercise" apart from giving you a mental picture.

Following the previous thread on entanglement in which I participated, I no longer have a mental picture of the deep nature of entanglement.

In saying that speculation about the nature of fundamental theoretical concepts is always a futile exercise, I mean that it seems that no undisputedly correct mental picture (of the deep nature of quantum processes) is even possible ... ever. This is the state of affairs that I'm unhappy about. But I guess I'll get over it.

 

[wawenspop]

In saying that speculation about the nature of fundamental theoretical concepts is always a futile exercise, I mean that it seems that no undisputedly correct mental picture (of the deep nature of quantum processes) is even possible ... ever. This is the state of affairs that I'm unhappy about. But I guess I'll get over it.

The 'mental picture' is lacking probably because we are trying to think in lengths and areas etc whereas we are operating below that level and need a different way of thinking. Is it a law that we will never know, or is it that we have not got a correct view yet? I believe the latter unless there is some proof otherwise. Consciouseness itself is a very powerful force in the Universe because it produces knowledge that is a scarce commodity in the Universe (see David Deutsch youtube lecture).

 

[ThomasT]

The 'mental picture' is lacking probably because we are trying to think in lengths and areas etc whereas we are operating below that level and need a different way of thinking.

Length scales below those which can be directly accessed either by our sensory capabilities or the machines that augment those capabilities are still length scales. There are lengths and areas and volumes even wrt the submicroscopic world. To say that we're operating below the level of "lengths and areas etc" doesn't make sense to me. Any operations that are carried out by us are on the macro, meso, or microscopic levels and our familiar, standardized concepts of "lengths and areas etc" apply.

Is it a law that we will never know, or is it that we have not got a correct view yet? I believe the latter unless there is some proof otherwise.

It seems that the existence of a fundamental quantum of action prevents (and Bell's theorem and the Copenhagen Interpretation have helped us to realize) our ever being able to visualize quantum processes the way we can visualize classical processes -- in terms of analogies from everyday experience.

One law pertaining to this would be Heisenberg's uncertainty relations -- that for a large number of similarly prepared measurements on any pair of canonically conjugate variables, the product of the statistical spread around an average value for one variable (eg., delta q, the variance in measurements of position) and the statistical spread around an average value for the other variable (eg., delta p, the variance in measurements of velocity or momentum) must be less than or equal to h (Planck's constant).

Consciouseness itself is a very powerful force in the Universe because it produces knowledge that is a scarce commodity in the Universe (see David Deutsch youtube lecture).

This is off topic, but you might start a new thread in the philosophy section.

 

[vanesch]

What's my point? I think that we can speak in terms of entangled data without getting into too much semantic trouble. But if you want to be nitpicky about it, then I see your point -- entanglement refers directly to quantum states, and quantum states aren't to be taken literally as real physical states.

If I give you 2 or 3 or ... series of data (lists of real numbers with a time tag on it), how are you going to say whether they are "entangled" data or not ?

You can find statistical *correlations* between them, but what would it mean for them to be "entangled" ?

 

[ThomasT]

One law pertaining to this would be Heisenberg's uncertainty relations -- that for a large number of similarly prepared measurements on any pair of canonically conjugate variables, the product of the statistical spread around an average value for one variable (eg., delta q, the variance in measurements of position) and the statistical spread around an average value for the other variable (eg., delta p, the variance in measurements of velocity or momentum) must be less than or equal to h (Planck's constant).

That should be greater than or equal to h.

 

[ThomasT]

If I give you 2 or 3 or ... series of data (lists of real numbers with a time tag on it), how are you going to say whether they are "entangled" data or not ?

You can find statistical *correlations* between them, but what would it mean for them to be "entangled" ?

OK, good point. Since I don't know enough about the salient features of all the different sorts and configurations of data produced via entanglement experiments to be able to abstract a set of criteria for deciding whether some data were entangled or not, then the only way I could decide if the correlated data were actually entangled would be to know the whole experimental design and procedure.

How does one know if a certain experiment has produced entanglement?

Can we speak of entangled photons, or electrons? If so, what corresponds to these things in the physical world? Is it data bits? Or, is it, following Bohr, the entire experimental procedure which defines their existence?

 

[vanesch]

How does one know if a certain experiment has produced entanglement?

Can we speak of entangled photons, or electrons? If so, what corresponds to these things in the physical world? Is it data bits? Or, is it, following Bohr, the entire experimental procedure which defines their existence?

That's my point: you cannot, without any theoretical frame, conclude that "entanglement happened", or that a certain experiment has "produced entanglement" or something of the kind. Entanglement is a formal concept within the theoretical framework of quantum theory - and outside of that theoretical framework it doesn't have any meaning. Entanglement is a property of vectors in a product hilbert space. Within quantum theory, it is possible to say that *according to the theory* this system should now be in an entangled quantum state. And it is also true that *according to the theory*, this usually leads to correlations in the data. THESE correlations can be observed and if these correlations correspond with the theoretical predictions, we can as a kind of shortcut say that "entanglement has been observed" but what's in fact meant is that the correlations are being observed in agreement with the predictions of quantum theory on an entangled state. OTHER theories can predict similar or identical correlations without ever introducing something like "entanglement".

 

[wawenspop]

... the correlations are being observed in agreement with the predictions of quantum theory on an entangled state. OTHER theories can predict similar or identical correlations without ever introducing something like "entanglement".

I understood that correlations of states of entangled particles was a postulate of QM and not a result of QM - i.e. there is no explanation as to why or how, rather 'correlations happen', then the QM put a mathematical framework around it (tensor product of Hilbert spaces etc) to formalize it and allow calculations to predict experimental results.

 

[DrChinese]

I understood that correlations of states of entangled particles was a postulate of QM and not a result of QM - i.e. there is no explanation as to why or how, rather 'correlations happen', then the QM put a mathematical framework around it (tensor product of Hilbert spaces etc) to formalize it and allow calculations to predict experimental results.

It may be mincing words, but QM made many of these predictions well before there were any results to discuss. It was not the other way around, though obviously the early (1925-1927) development of QM did consider extant lab results.

As of 1935, when EPR was written, there was no experimental knowledge of entangled particles. The EPR article was merely hypothetical in that regard. At some point, it was realized that particle pairs could appear in the singlet state - and those would have the properties Vanesch describes. But the key point is that the mathematical formalism itself led to many predictions (anti-matter, neutrinos being perhaps examples in addition to entanglement) even though there was no known mechanism (or evidence) for some of these things to occur. And even today, there is no known mechanism for entanglement per se other than the formalism.

The amazing thing is that the QM formalism supports partial collapse, which can be demonstrated experimentally. Any competing theory will need to include that too. I assume that most (if not all) virtual particle pairs are entangled too, since their spin presumably nets to zero.

 

[ThomasT]

That's my point: you cannot, without any theoretical frame, conclude that "entanglement happened", or that a certain experiment has "produced entanglement" or something of the kind. Entanglement is a formal concept within the theoretical framework of quantum theory - and outside of that theoretical framework it doesn't have any meaning.

Ok, I'll grant you that quantum entanglement is a term that is peculiar to, and only has meaning within, the framework of the quantum theory. Nevertheless, and even though quantum state evolutions take place in an imaginary space, at least some of the symbolic representations that comprise the theory itself have a meaning that can be translated into experimental manipulations.

Following Schrodinger, if the essence of quantum entanglement is the theoretical nonseparability of two or more quanta brought about via the physical interaction and mutual influence of two or more quantum scale physical entities , or the common influencing of two or more quantum scale physical entities, then theoretical quantum entanglement is inexorably linked with experimental quantum entanglement, isn't it? In fact, the way that Schrodinger talks about quantum entanglement seems to me to lend itself quite easily to classical analogy -- even though Schrodinger himself says that it doesn't -- because the separate systems can still be dealt with separately -- it's just that if they're looked at separately after they've interacted or been subjected to a common influence then any entanglement that is present won't emerge as a product of the individual probabilities, but will emerge only with respect to some global experimental parameter which reveals the statistical dependence produced via the mutual interaction or common influencing.

Entanglement is a property of vectors in a product hilbert space. Within quantum theory, it is possible to say that *according to the theory* this system should now be in an entangled quantum state. And it is also true that *according to the theory*, this usually leads to correlations in the data. THESE correlations can be observed and if these correlations correspond with the theoretical predictions, we can as a kind of shortcut say that "entanglement has been observed" but what's in fact meant is that the correlations are being observed in agreement with the predictions of quantum theory on an entangled state. OTHER theories can predict similar or identical correlations without ever introducing something like "entanglement".

If the physical essence of quantum entanglement is interaction and mutual (common) influence, then in order to produce the correlations that correspond to quantum entanglement per quantum theory it would be necessary to duplicate the experimental conditions. A rose by any other name is still a rose.

If you maintain that there is no physical understanding of the deep nature of quantum entanglement, then your argument makes sense to me. However (ironically?) your position on this would seem to affect your point of departure (ie. necessary assumptions re the meaning of the quantum theoretical formalism) in accepting MWI as a credible alternative to the orthodox probability interpretation.

Of course, there is an understanding of the experimental preparations which produce entangled quantum states -- and these involve interactions and common influences. don't they? So, even if we want to call it something else, or represent it in a different way theoretically, we're still talking about the same thing -- and we know that because of the material and instrumental preparations and the data accumulation and processing, don't we?

Having said that, I will concede that you are technically correct (DrChinese's post 46 underlines why) -- and, in the interest of unambiguous communication, I will no longer speak of entangled data.

 

[wawenspop]

When agree to take a Hilbert space product for the two entangled particles H spaces,
then we are assuming entanglement has taken place, otherwise we would have no
justification to do that. Then we get correct (as of present time) predications
to use in our experiments.

If we ask where does that justification come from? I suggest it comes concepts such
as 'when two particles collide then there total momentum (say) remains the constant
even when separated. In that sense they are correlated.

Then using QM, the unceraintities in the EXACT momemtums of each particle must still
add up to that original total. And this is where the 'strangeness' creeps in, because
how does one particle 'know' what the other's probabilty came out to be? (when they were
spacially separated).

 

[vanesch]

Ok, I'll grant you that quantum entanglement is a term that is peculiar to, and only has meaning within, the framework of the quantum theory. Nevertheless, and even though quantum state evolutions take place in an imaginary space, at least some of the symbolic representations that comprise the theory itself have a meaning that can be translated into experimental manipulations.

The experimental manipulations that give, in the frame of a quantum-mechanical treatment, rise to entangled states, would normally be called "interactions". In fact, quantum theory is such that when initially non-entangled systems interact, they usually end up in an entangled state. In classical physics, this is not the case: individual systems keep their "individuality" after an interaction, while quantum systems (with the quantum mechanical description) can have a certain "individuality" before interaction, but loose it upon interaction. So the experimental setup that "gives rise to entanglement" is interaction. If a classical physicist were looking at the experimental preparation, he'd see nothing else but "things that are set up to interact".

Following Schrodinger, if the essence of quantum entanglement is the theoretical nonseparability of two or more quanta brought about via the physical interaction and mutual influence of two or more quantum scale physical entities , or the common influencing of two or more quantum scale physical entities, then theoretical quantum entanglement is inexorably linked with experimental quantum entanglement, isn't it?

Yes, that's exactly it: two systems that are entangled have no "individual identity" anymore in their quantum-mechanical description. But again, that's a sheer property of the quantum-mechanical description.

In fact, the way that Schrodinger talks about quantum entanglement seems to me to lend itself quite easily to classical analogy -- even though Schrodinger himself says that it doesn't -- because the separate systems can still be dealt with separately -- it's just that if they're looked at separately after they've interacted or been subjected to a common influence then any entanglement that is present won't emerge as a product of the individual probabilities, but will emerge only with respect to some global experimental parameter which reveals the statistical dependence produced via the mutual interaction or common influencing.

Indeed, that's how classical action-at-a-distance can mimic perfectly the quantum-mechanical entanglement (or, quantum-mechanical entanglement can mimic perfectly action-at-a-distance ; depends on your PoV).

If the physical essence of quantum entanglement is interaction and mutual (common) influence, then in order to produce the correlations that correspond to quantum entanglement per quantum theory it would be necessary to duplicate the experimental conditions. A rose by any other name is still a rose.

I don't understand what you say here.

If you maintain that there is no physical understanding of the deep nature of quantum entanglement, then your argument makes sense to me. However (ironically?) your position on this would seem to affect your point of departure (ie. necessary assumptions re the meaning of the quantum theoretical formalism) in accepting MWI as a credible alternative to the orthodox probability interpretation.

I try to keep a distinction between what is "hard fact" and what are interpretational pictures. MWI is a way of giving a picture to the quantum-mechanical happening, which "explains" then of course entanglement and all that - but it's only that: a picture. It's not a hard fact.

Of course, there is an understanding of the experimental preparations which produce entangled quantum states -- and these involve interactions and common influences. don't they? So, even if we want to call it something else, or represent it in a different way theoretically, we're still talking about the same thing -- and we know that because of the material and instrumental preparations and the data accumulation and processing, don't we?

Entanglement is - within quantum theory - caused by interactions. That doesn't mean that "interaction = entanglement". But the experimental setup, which, to a quantum physicist, prepares an entangled state, would, to a classical physicist, just let some systems interact.

It is true that, through the quantum formalism, entangled states give rise to weird correlations which cannot always be explained by classical interaction, locality and some other reasonable assumptions (re Bell's theorem and all that). So our classical physicist will then invent "action-at-a-distance" or "superdeterminism" or something of the kind to explain the correlations that he finds from his experiment, because he cannot explain them in a local interaction picture (with some additional assumptions), while our quantum physicist just "reads off" the expected correlations from his entangled states in his formalism.

 

[vanesch]

When agree to take a Hilbert space product for the two entangled particles H spaces,
then we are assuming entanglement has taken place, otherwise we would have no
justification to do that. Then we get correct (as of present time) predications
to use in our experiments.

If you ask why one needs to use the product hilbert space H1 x H2, then there's an easy answer: the superposition principle. Because all |h1> |h2> states are possible states (that's like in classical mechanics), then, by the superposition principle, non-product superpositions of these product states must also be physical states of the system. Hence the tensor product.