Entanglement and Simultaneity

[Terdbergler]

Instantaneous action-at-a-distance (which is how we explain quantum entanglement) implies event-simultaneity, but we know (from SR) that an observer's "now" is dependent upon their velocity/reference frame.

Imagine that we have two observers, Scott and Sean, and two entangled particles. Scott and the two particles are onboard a starship while Sean is inside a nearby space station. Scott and the two entangled particles aboard the starship are moving through space at 99% of c, while Sean's space station is in a low geosynchronous orbit around the Earth (moving only slightly faster than the Earth's rotational speed; i.e., nowhere near c). Scott's starship quickly flies past Sean's space station. As they fly past each other, Scott remains at rest relative to the entangled particles, but Sean is in motion (at near light speed) relative to the entangled particles. As Scott flies past Sean, Scott checks the spin of one of the entangled particles, thereby "instantaneously" determining the spin of its entangled partner-particle, and Sean witnesses the events during the fly-by. Does the action-at-a-distance between the two entangled particles appear to be instantaneous to BOTH Scott AND Sean?

 

[Nugatory]

As Scott flies past Sean, Scott checks the spin of one of the entangled particles, thereby "instantaneously" determining the spin of its entangled partner-particle, and Sean witnesses the events during the fly-by. Does the action-at-a-distance between the two entangled particles appear to be instantaneous to BOTH Scott AND Sean?

Scott's measurement of the spin of particle A does not instantaneously determine the spin of particle B; it just tells him what the result of a measurement of the spin of B would be when and if if such a measurement is made.

If either Sean or Scott or some unrelated third party measure the spin of B, they will get the opposite result from Scott's measurement of A. If the two measurement events are space-like separated, then it is possible that Sean will see the measurement of B happening before the measurement of A, while Scott will see the measurement of A happening first (this is basic relativity of simultaneity from special relativity). If so, Sean's story will be "B was measured, we got a result, then Scott measured A and found the opposite spin"" while Scott's story will be "I measured A, I got a result, then B was measured and found the opposite spin". Either way, all we have is a measurement of A and a measurement of B, with opposite spin; there's no sense in we can say that one "caused" the other.

 

[Terdbergler]

This sounds like a purely epistemic account of entanglement; i.e., the measurement of A's spin doesn't CAUSE B to have the opposite spin, rather, it simply let's the measurer of A KNOW (or infer) what the spin of B is.

But this seems to me to be very close to Einstein's take on entanglement, best expressed through the "gloves" example.

Whether entanglement is a causal (and therefore ontological) phenomenon, or a purely epistemological one, is the sort of issue that I thought Bell's theorem settled (in favor of the ontological interpretation). But I don't know Bell's theorem so I can't say much else on the matter.

I'm a layperson so I'm definitely looking to learn here and not argue :) Please teach me what the real deal is with entanglement.

I think I understand what you mean about the second measurement (the measurement of B's spin). Whether or not our observation of A's spin is causally linked to B's spin (across arbitrarily large distances), a measurement of B in conjunction with A's measurement is still required, and then all you have is a classic, textbook, "lightbulb on a moving train and an observer at the station" scenario; nothing novel.

 

[Nugatory]

i.e., the measurement of A's spin doesn't CAUSE B to have the opposite spin, rather, it simply let's the measurer of A KNOW (or infer) what the spin of B is.

That's not quite right, as the part that I've bolded is the purely classical view - you're saying that B has a spin, and A's measurement is telling him what it is. But quantum mechanically, B does not have a spin unless and until it's measured. Thus, A's measurement doesn't tell A what the spin of B IS, it tells A what the result of a measurement of B would be.

OK, now you're screaming in exasperation "But that's the same thing! The only way that I can know what a measurement of B's spin will yield is if I know what B's spin is!". But that's just restating the hidden assumption that B has a spin even if we don't measure it.

Whether entanglement is a causal (and therefore ontological) phenomenon, or a purely epistemological one, is the sort of issue that I thought Bell's theorem settled (in favor of the ontological interpretation). But I don't know Bell's theorem so I can't say much else on the matter.

Bell's theorem is remarkably accessible to laymen, much more so than many of the other deep results of quantum physics. You might start with our own DrChinese: http://www.drchinese.com/Bells_Theorem.htm

 

[DrChinese]

Welcome to PhysicsForums, Terdbergler!

There are some interpretation dependent issues here. You certainly can think of entanglement as instantaneous action at a distance (that's one interpretation). There are interpretations in which c is respected too.

However, in all variations it is not possible to say "measuring A causes a result at B" is more true than "measuring B causes a result at A". That situation remains true regardless of ordering of measurements at A and B, regardless of relative motion, concepts of simultaneity, etc. In other words, your ideas about causal ordering will influence your perception of the events, but there is no scientific way currently to back those up.

 

[bhobba]

Instantaneous action-at-a-distance (which is how we explain quantum entanglement) implies event-simultaneity,

Some populist accounts can give that impression - but its wrong.

Please teach me what the real deal is with entanglement.

Technically entanglement has to do with the vector space structure of pure states.

Bells theorem, which uses entanglement, says it can't be explained by models that are both local and realistic - which has a meaning in a technical sense you can look up. If you insist on realism, which means things have properties independent of measurement context, then locality goes down the drain and you have instantaneous action at a distance. But one can throw realism out and save locality.

Thanks
Bill

 

[Terdbergler]

Even though particles A & B are entangled, you cannot collapse B's wave function by measuring A. I see that now. Thanks everyone. I'm much more interested now in this trade-off between locality and reality entailed by Bell's Theorem. Those who insist on realism forsake locality and those who insist on locality forsake realism.

I'm not sure which one I find it easier to give up. By locality, do you simply mean obedience the lightspeed speed limit?

 

[Nugatory]

By locality, do you simply mean obedience the lightspeed speed limit?

That's the modern interpretation of exactly what is meant by "locality"; it works so well because the lightspeed limit gives us a solid and quantitative way of distinguishing what's local and what's non-local.

Before the development of relativity, there was no natural way of saying when something was far enough away to count as non-local. However, many serious thinkers still found the idea of non-locality, that (for example) moving a mass from one location to another would instantaneously, immediately, and simultaneously change all the gravitational fields everywhere in the entire universe, very troublesome. Isaac Newton (who had a deeper awareness of the weaknesses of his creation than did many of his successors) once wrote:

It is inconceivable that inanimate Matter should, without the Mediation of something else, which is not material, operate upon, and affect other matter without mutual Contact…That Gravity should be innate, inherent and essential to Matter, so that one body may act upon another at a distance thro' a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain laws; but whether this Agent be material or immaterial, I have left to the Consideration of my readers.[

[That's copied from the wikipedia article on non-locality, mainly because that was the easiest way for me to find the quotation that I was thinking of. If it's wrong, blame wikipedia not me]

 

[Terdbergler]

Where do we currently stand on the speed of gravitational influence? Is it c? Instantaneous? Or somewhere in between?

 

[universal_101]

If you insist on realism, which means things have properties independent of measurement context, then locality goes down the drain and you have instantaneous action at a distance. But one can throw realism out and save locality.

Thanks
Bill

Are you sure about that definition of reality? I don't think realism is objects having properties which does not depend on measurement context, since measurement is nothing but the interaction with other objects, which inevitably depends also on the object which we are using as a probe(measuring device) especially at atomic scale. Therefore "reality" can also include measurement results depending on the measuring device even in principle.

 

[Nugatory]

Are you sure about that definition of reality? I don't think realism is objects having properties which does not depend on measurement context, since measurement is nothing but the interaction with other objects, which inevitably depends also on the object which we are using as a probe(measuring device) especially at atomic scale. Therefore "reality" can also include measurement results depending on the measuring device even in principle.

What if the "measurement context" is that the property isn't measured at all because we've measured something else? The realist position is that the property exists even in that context, and that's the position that cannot be reconciled with locality in Aspect-style experiments.

 

[naima]

We may recall that particles may be fully entangled (EPR particles) or very close to separable particles.
take 0.9999 |uu> + 0.0001 |dd> they are entangled.
are you still interested by the answer of the same questions?

 

[DrChinese]

Are you sure about that definition of reality?

There are, in fact, different ways to define realism. Obviously, the most common ones are ones that play into the EPR and Bell papers. Generally, you end up with something like the following:

a) Realism is the existence of simultaneous EPR elements of reality, regardless of whether they can actually all be measured simultaneously or not.

b) Realism implies that any observable property counterfactually has a defined value at all times.

And if you tinker with the definition too much, you can come up with results that differ from the norm. But that is also true anytime you monkey with commonly accepted definitions. I can prove a table is a chair if I need to, for example.

 

[universal_101]

What if the "measurement context" is that the property isn't measured at all because we've measured something else? The realist position is that the property exists even in that context, and that's the position that cannot be reconciled with locality in Aspect-style experiments.

I think you are talking about incompatible properties like position and momentum which are in conjugation. Now, the fact that Hamiltonian Mechanics formulation uses 'p' and 'x' as independent variable properties of a particle, has nothing to do with, what is "reality".

That is, even in classical mechanics it is very well understood that measuring one quantity inevitably disturbs the other, but the effect is so small that it can be safely ignored. Implying that conjugated properties are always get effected when we try to measure one or the other,even classically(which I think people consider a description of reality).

 

[Nugatory]

I think you are talking about incompatible properties like position and momentum which are in conjugation. Now, the fact that Hamiltonian Mechanics formulation uses 'p' and 'x' as independent variable properties of a particle, has nothing to do with, what is "reality".

No, that's not what I'm talking about. Consider two spin-entangled particles. I measure one of them and I get spin-up, so I know that if someone were to measure the spin of the other, it would come out spin-down (for all I know that measurement has already been made, but that's beside the point here).

A realist (using a definition that is pretty much aligned with DrChinese in #13 of this thread) would say that the other particle is spin-down, that there is no logical gap between "if we measure, we will get spin-down" and "it is spin-down". That's a perfectly respectable position (and quite natural if you think in terms of collapsing the wave function of the two-particle system) but you cannot have it and locality as well.

 

[universal_101]

There are, in fact, different ways to define realism. Obviously, the most common ones are ones that play into the EPR and Bell papers. Generally, you end up with something like the following:

a) Realism is the existence of simultaneous EPR elements of reality, regardless of whether they can actually all be measured simultaneously or not.

It means the property(EPR elements of reality) has a value even if we don't bother to measure it. I agree.

b) Realism implies that any observable property counterfactually(incorrectly) has a defined value at all times.

I think above statement is not an implication, rather its an assumption, and it is fairly easy to see through it, that the value is liable to change whenever there is a measurement on that value.

Therefore the two values one which we did not measured and one which we measured are inevitably different, and all this is under classical mechanics (i.e. reality).

 

[universal_101]

A realist (using a definition that is pretty much aligned with DrChinese in #13 of this thread) would say that the other particle is spin-down, that there is no logical gap between "if we measure, we will get spin-down" and "it is spin-down". That's a perfectly respectable position (and quite natural if you think in terms of collapsing the wave function of the two-particle system) but you cannot have it and locality as well.

Spin of a particle does not come under the domain of reality(classical physics), it is an 'unreal' concept. And even if we assume particles really spinning(like a top), we know that the direction of spin will get affected by using highly non-homogeneous Magnetic Field (SG apparatus). Moreover, you are forcing a non-real concept to be valid in reality, and subsequently disproving reality.

This is analogous to finding the number $i$(complex number iota) in real number. Even though iota owes it's existence to real numbers, it is an unreal concept. Similarly, forcing iota to be a valid real number, does not disprove the real numbers.

 

[Nugatory]

Spin of a particle does not come under the domain of reality(classical physics), it is an 'unreal' concept. And even if we assume particles really spinning(like a top), we know that the direction of spin will get affected by using highly non-homogeneous Magnetic Field (SG apparatus). Moreover, you are forcing a non-real concept to be valid in reality, and subsequently disproving reality.

Although quantum mechanical spin isn't the same as the classical notion of something rotating around its axis, that doesn't mean that it's not real, just that it's badly named. It meets the definition of an "element of reality" as used in the original EPR paper, it is the property that Bell chose to consider in his paper, and it can be measured with a Stern-Gerlach device. Although most tests of Bell's inequality are done with polarization-entangled photons, there has been at least one experiment that used spin-entangled particles.

But if you still object to me using spin in my example, we can use the direction of the magnetic moment as the property we measure or don't measure in the members of the entangled pair - surely you'll accept the direction of the magnetic moment as real? The same incompatibility between the realist position and locality is still present.

 

[universal_101]

But if you still object to me using spin in my example, we can use the direction of the magnetic moment as the property we measure or don't measure in the members of the entangled pair - surely you'll accept the direction of the magnetic moment as real? The same incompatibility between the realist position and locality is still present.

And that is my point, that direction of magnetic moment changes when we measure it, inevitably.

 

[Nugatory]

And that is my point, that direction of magnetic moment changes when we measure it, inevitably.

You are still missing the point.

Yes, in an EPR-type experiment we measure the magnetic moment of one member of the entangled pair and yes, of course this leaves it in a state in which the magnetic moment of that particle is either up and down on the axis of the measurement.

But what about the other member of the pair? We know that if we measure its magnetic moment on the same axis we will get the opposite result. But does this mean that the second particle actually has a magnetic moment pointing in the opposite direction, we just may not have measured it yet? A realist (sticking with DrChinese's post #13 in this thread) would say yes, and that is the claim that cannot be reconciled with locality.

 

[universal_101]

But what about the other member of the pair? We know that if we measure its magnetic moment on the same axis we will get the opposite result. But does this mean that the second particle actually has a magnetic moment pointing in the opposite direction, we just may not have measured it yet? A realist (sticking with DrChinese's post #13 in this thread) would say yes, and that is the claim that cannot be reconciled with locality.

Nice post,

Then I think, the (realist)claim has nothing to do with reality. I guess what I'm trying to say is, that if we know what a photon/spin is classically(in reality), we would be able to describe the Bell's results without violating anything. That is, realism can handle the results of measurement that depends on measurement perfectly.

 

[DevilsAvocado]

It looks like Lee Smolin disagrees with some of you guys. In his latest book Time Reborn he claims that if we want a hidden-variables theory (i.e. the world is real), it must violate the Free will theorem, where one of the assumptions is Relativity of Simultaneity.

However a hidden-variables theory is possible, if it violates relativity...

Our choice then becomes epistemic/statistical QM or Aristotle was right!

Could there be a hidden-variables theory compatible with the principles of relativity theory? We know that the answer is no. If there were such a theory, it would violate the free-will theorem—a theorem implying that there’s no way to determine what a quantum system will do (hence no hidden-variables theory) as long as the theorem’s assumptions are satisfied. One of those assumptions is the relativity of simultaneity.

The aforementioned theorem of John Bell also rules out local hidden-variable theories—local in the sense that they involve only communication at less than the speed of light. But a hidden-variables theory is possible, if it violates relativity.

As long as we’re just checking the predictions of quantum mechanics at the level of statistics, we don’t have to ask how the correlations were actually established. It is only when we seek to describe how information is transmitted within each entangled pair that we need a notion of instantaneous communication. It’s only when we seek to go beyond the statistical predictions of quantum theory to a hidden-variables theory that we come into conflict with the relativity of simultaneity.

To describe how the correlations are established, a hidden-variables theory must embrace one observer’s definition of simultaneity. This means, in turn, that there is a preferred notion of rest. And that, in turn, implies that motion is absolute. Motion is absolutely meaningful, because you can talk absolutely about who is moving with respect to that one observer—call him Aristotle. Aristotle is at rest. Anything he sees as moving is really moving. End of story.

In other words, Einstein was wrong. Newton was wrong. Galileo was wrong. There is no relativity of motion.

This is our choice. Either quantum mechanics is the final theory and there is no penetrating its statistical veil to reach a deeper level of description, or Aristotle was right and there is a preferred version of motion and rest.