Simple Question about Entanglement

[rkn]

Hi,

Lately I've been reading up on quantum entanglement, Bell's inequality, and EPR experiments. My question is fundamental, but I'm asking it here because I haven't yet read an explanation that answers this question (that I recall).

Take this typical description of what goes on in an EPR experiment (http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/bell.html):

"Let's suppose that we get a green light [one of two possible outcomes, red or green- e.g., spin up or spin down], so we know electron A is pointing in direction 3. Because of the way the electrons are entangled we now also know that electron B is pointing directly away from direction 3. This is where the spooky action at a distance comes in. The fact that we chose to measure electron A in this particular direction not only affected that electron, it also forced electron B to be pointing exactly towards or away from this direction! So what results do we get at detector B? If detector B is set to position 3 then it will definitely flash green. (Remember that green means opposite things at the two detectors.)"

To say that electron A "forced electron B" to point in the opposite direction means that, at some point after the entangled particles got split apart, nothing in their previous entangled state could be determining how they will be detected later at the detectors.

If this were not the case, then A doesn't "force" B into any position- B's position is the opposite of A's due to the fact that the sum of their spins must = 0 since they were just split apart from a coupled state. On this view, once you detect A's position, precisely what one would expect is for B to be detected in the opposite direction. ??

But clearly this is not the correct understanding, since "spooky action at a distance" entails that at some point the particles, after splitting apart, are no longer causally/deterministically "attached" to their previous state.

Can someone explain why the particles (photons, electrons) are not determined by their previous states- that is, by being coupled and then split apart? Especially since some sort of determinism must be operative if physicists know that, even after being split apart, their spins will = 0 (thus knowing the spin of one, you can know the spin of the other)?

I'm guessing also that what must come into play here is the fact that two different measurements can be made at each detector- one along the x-axis and one along the y-axis (I don't know what this mathematical abstraction represents in reality). Such that when Alice takes a measurement on the x-axis, somehow that "spookily" affects even the y-measurement at Bob's detector (in what way his detector is affected after Alice makes a measurement I know not).

Eek, I don't understand what's going on here (clearly). Can someone please explain what exactly is "spooky" about these experiments? Some enlightenment would be greatly appreciated! Please be gentle on my non-physicist mental capabilities.

 

[DrChinese]

...

Can someone explain why the particles (photons, electrons) are not determined by their previous states- that is, by being coupled and then split apart? Especially since some sort of determinism must be operative if physicists know that, even after being split apart, their spins will = 0 (thus knowing the spin of one, you can know the spin of the other)?

I'm guessing also that what must come into play here is the fact that two different measurements can be made at each detector- one along the x-axis and one along the y-axis (I don't know what this mathematical abstraction represents in reality). Such that when Alice takes a measurement on the x-axis, somehow that "spookily" affects even the y-measurement at Bob's detector (in what way his detector is affected after Alice makes a measurement I know not).

Eek, I don't understand what's going on here (clearly). Can someone please explain what exactly is "spooky" about these experiments? Some enlightenment would be greatly appreciated! Please be gentle on my non-physicist mental capabilities.

Welcome to PhysicsForums, rkn!

The examples in which you measure both along x or y generally don't lead to an obvious issue. This is sometimes called the "Bertlmann's socks" analogy. Only when you measure at most *other* angles, the problem becomes clear. Examples include 0 and 120 degrees. You must follow the Bell Theorem logic to see this, it involves a small amount of math. I might suggest you look at my web site, which walks you through that part of the argument using a well respected Bell variation from Mermin.

http://drchinese.com/David/Bell_Theorem_Easy_Math.htm

Then come back for some additional questions. So the answer lies with Bell.

 

[rkn]

Thank you, Dr. Chinese. I am about halfway through the article, and have a question that needs addressing I think before continuing with the rest of the article.

You ask: "do A, B and C correspond to SIMULTANEOUS elements of reality?" (Similarly, later you say: "ASSUME that a photon has 3 simultaneously real Hidden Variables A, B and C at the angles 0 degrees, 120 degrees and 240 degrees per the diagram above. These 3 Hidden Variables, if they exist, would correspond to simultaneous elements of reality associated with the photon's measurable polarization attributes at measurement settings A, B and C.")

My confusion stems from the use of the word "simultaneous." When you ask the question, "do A, B and C correspond to SIMULTANEOUS elements of reality?" for instance, do you mean, "Does this single photon have all three polarizations at once"? Or do you mean, "Will the polarizer measure three polarizations of this photon, if this photon has these three polarizations at the same time?" Or (my best guess) do you mean something else entirely? As I don't suppose it's possible for a single particle to have multiple polarizations at the same time (that is, simultaneously)...?

Thank you again for your help, it is much appreciated.

 

[DrChinese]

Thank you, Dr. Chinese. I am about halfway through the article, and have a question that needs addressing I think before continuing with the rest of the article.

You ask: "do A, B and C correspond to SIMULTANEOUS elements of reality?" (Similarly, later you say: "ASSUME that a photon has 3 simultaneously real Hidden Variables A, B and C at the angles 0 degrees, 120 degrees and 240 degrees per the diagram above. These 3 Hidden Variables, if they exist, would correspond to simultaneous elements of reality associated with the photon's measurable polarization attributes at measurement settings A, B and C.")

My confusion stems from the use of the word "simultaneous." When you ask the question, "do A, B and C correspond to SIMULTANEOUS elements of reality?" for instance, do you mean, "Does this single photon have all three polarizations at once"? Or do you mean, "Will the polarizer measure three polarizations of this photon, if this photon has these three polarizations at the same time?" Or (my best guess) do you mean something else entirely? As I don't suppose it's possible for a single particle to have multiple polarizations at the same time (that is, simultaneously)...?

Thank you again for your help, it is much appreciated.

Here is the issue: suppose we have a 2 normal dice which can be examined from several directions. They are oriented such that when the directions being examined are the same, we get the same answer on both. This is the analogy.

Now, you would normally say that if these are examined in the same way and yield the same answers, there is no surprise. They are simply predetermined. And they have their respective values independent of the act of observation, and specifically independent of how you choose to observe them.

But entangled photons lack this quality. The relative result (correlation) of observations on such a pair is dependent on their relative angle difference and nothing else. More importantly, there are no data sets in which values can exist for unmeasured settings which will be consistent with the predictions of QM.

So it is true what you say about a photon not having multiple polarizations simultaneously ("As I don't suppose it's possible for a single particle to have multiple polarizations at the same time"). They don't. But that goes against my analogy in the first paragraph, where the dice have values in different directions at all times.

 

[oli4]

Nin Hao DrChinese, thanks for the nice read (I didn't read it all yet though)
In the "Photon Polarization" paragraph, you have a double 'with':
"its polarization will be aligned exactly *with with* the lens thereafter"

Cheers...

 

[rkn]

Thank you for the analogy. That helped clarify things a bit. I also read the rest of the article.

My latest question, then, is (and forgive me if I'm not drawing obvious connections!): Why is "the hidden variables interpretation" made synonymous with "the set of probabilities that one derives when considering measurements on a set of three dichotomous random variables?" In other words, wouldn't a theoretical hidden variables interpretation specify "hidden" variables which made the same predictions as QM (e.g. a violation of Bell's inequality; specifically, a value of .250 rather than .333)?

 

[DrChinese]

Thank you for the analogy. That helped clarify things a bit. I also read the rest of the article.

My latest question, then, is (and forgive me if I'm not drawing obvious connections!): Why is "the hidden variables interpretation" made synonymous with "the set of probabilities that one derives when considering measurements on a set of three dichotomous random variables?" In other words, wouldn't a theoretical hidden variables interpretation specify "hidden" variables which made the same predictions as QM (e.g. a violation of Bell's inequality; specifically, a value of .250 rather than .333)?

There is no such data set using hidden variables. And believe me, people have tried every trick in the book. It is sort of like the 4 color map theorem. Of course Bell's Theorem actually disposes of all of them, but that hasn't stopped people from trying.

Keep in mind that the EPR paper specifically states in its conclusion that if the "simultaneous" requirement is dropped, there is no issue. But they considered that position unreasonable.

So essentially: if you insist on an observer independent reality, you *must* accept spooky action at a distance. In my opinion, almost any physicist will deny that observer independence is tenable. In other words, reality is a function of the context in which it is observed; it is contextual. Even most Bohmians acknowledge this.

 

[rkn]

Cool! Thanks for your responses. Questions are forever arising in my brain, and learning about this stuff has sort of been like crack for me lately- I always want to think and read about it.

So, another question, if you don't mind:

You say that, "reality is a function of the context in which it is observed; it is contextual. Even most Bohmians acknowledge this." There are two ways to interpret this, based on how one uses the term "observed": Bohmians, for instance, from my understanding anyway, conclude that measurements are contextual, because the experimental apparatus (physically and causally) affects what is being measured (behavior of a photon, or the pilot wave, for instance). So "observed" here means "observing with instruments such that the instruments affect what is being measured." However, one could also mean "observed" as "the mere act of a conscious being looking at (but in no way physically disturbing) an object (e.g. a photon)". Is one of these the way in which you meant "observed", or do you have something else in mind?

Also, I've come across several papers that discuss what they consider to be incorrect assumptions in Bell's applying the particular probability framework (like, an incorrect application of a common probability space) to EPR experiments. Specifically, the author here: http://arxiv.org/abs/1205.4636 makes an analogy between what he sees as Bell's mistake to Bertrand's paradox. He cites several other papers in his paper, many of which are recent, though I have yet to read these.

All told, I wish I'd studied math so that I'd have a better way to adjudicate what all these people are talking about! But, perhaps it isn't too late, yet...

 

[San K]

Can someone explain why the particles (photons, electrons) are not determined by their previous states- that is, by being coupled and then split apart? Especially since some sort of determinism must be operative if physicists know that, even after being split apart, their spins will = 0 (thus knowing the spin of one, you can know the spin of the other)?

not sure if this got answered.

In the meantime here is a guess and let's wait for a better answer:

they are determined by their previous states however the effect remains for only for a
very tiny period of time (after entanglement is broken) due to environmental effects/disturbances

 

[DrChinese]

You say that, "reality is a function of the context in which it is observed; it is contextual. Even most Bohmians acknowledge this." There are two ways to interpret this, based on how one uses the term "observed": Bohmians, for instance, from my understanding anyway, conclude that measurements are contextual, because the experimental apparatus (physically and causally) affects what is being measured (behavior of a photon, or the pilot wave, for instance). So "observed" here means "observing with instruments such that the instruments affect what is being measured." However, one could also mean "observed" as "the mere act of a conscious being looking at (but in no way physically disturbing) an object (e.g. a photon)". Is one of these the way in which you meant "observed", or do you have something else in mind?

Also, I've come across several papers that discuss what they consider to be incorrect assumptions in Bell's applying the particular probability framework (like, an incorrect application of a common probability space) to EPR experiments. Specifically, the author here: http://arxiv.org/abs/1205.4636 makes an analogy between what he sees as Bell's mistake to Bertrand's paradox. He cites several other papers in his paper, many of which are recent, though I have yet to read these.

There are dozens of different "disproofs" of Bell. None of these have ever gained any traction, and none have passed the typical challenges (such as the DrChinese challenge to provide a sample dataset). I won't bother to address this one, other than to point out that his comment that "unperformed experiments have no results" is essentially a restatement of quantum contextuality.

Regarding observation: I personally don't mess with issues regarding the requirement of a conscious observer. Depending on your philosophical bent, there are pros and cons to that element of observation. So I tend to think of it that the final context controls. I say "final" to include the end measuring apparatus, which can be located at space-like and/or TIME-like separated points.

A point that is often missed is that there can be time separation too! Get this: it is possible to entangle particles that have never interacted! This has been done. It is possible to entangle particles AFTER they have been detected/observed (and no longer exist)! This too has been done. Also, it is theoretically possible to entangle particles that have never even existed at this same time! (This has not been done yet.)

 

[San K]

It is possible to entangle particles AFTER they have been detected/observed (and no longer exist)! This too has been done.

interesting fact DrChinese and you have mentioned this before but I could not get it.

What does it mean? ...to entangle particles after they no longer exist...
what is being entangled then?...if the particles are no longer there

Also do particles go "out of existence" ever?

Also, it is theoretically possible to entangle particles that have never even existed at this same time! (This has not been done yet.)

does this, sort of, say/mean that -

the entanglement can be held between other "entities" and being swapped till the desired/end particle comes into existence and the entanglement, can then, be transferred to it...

in other words...entanglement can be "stored" and "transferred/swapped" between particles...

 

[DrChinese]

interesting fact DrChinese and you have mentioned this before but I could not get it.

What does it mean? ...to entangle particles after they no longer exist...
what is being entangled then?...if the particles are no longer there

One of the hallmarks of entanglement is so-called "perfect" correlations. Entangled photons will have correlated outcomes at any identical angle settings, unentangled photons will not.

2 photons, Alice and Bob, are created at T=0 by different lasers. I can detect Alice at T=1 and Bob at T=1 somewhere else. They will be perfectly correlated, and no longer exist. However, I do not choose to entangle them until T=2. Seems strange, but that is the following experiment:

http://arxiv.org/abs/quant-ph/0201134
Experimental Nonlocality Proof of Quantum Teleportation and Entanglement Swapping

 

[rkn]

What is a sample data set, with regard to what we are talking about? Do you mean a table, like the one in your article?

I say "final" to include the end measuring apparatus

This seems perfectly reasonable to me. The question is: What happens in the interval between when the particles are shot from the source and when they are detected on this end measuring apparatus? (Of course, we don't really know this yet...)

So, there are a couple of other points that seem perfectly reasonable to me as well:

1. The detectors are measuring something, i.e., something causes the detectors to register a signal. Therefore, something exists which sets this signal off, and this something thus exists prior to the detection and thus to our measurement. Nature might react to our measuring apparatuses, and in a way different from how it acts when not interacting with these devices, but that certainly does not mean something pops into existence just because humans "look at it" (I should say I did not take this to be what you meant, but it seems that many articles on quantum mechanics suggest this, which makes by brain want to implode.) (Again, this something may change its motion or other behavior in reaction to its interacting with the end measuring apparatus.)

2. If QM predicts probabilities of correlations to be .250 (and not .333), and these are consistently the results we get in experiments, then something (what an unsatisfactory word, I know) is clearly (to me, at least) causing particles to have correlative spins at a rate that violates Bell's Inequality. I mean, this seems especially true when the results of experiments are highly consistent, as the results of EPR experiments have appeared to be (in other words, correlations aren't just happening to occur at a rate of .250).

 

[DrChinese]

A. What is a sample data set, with regard to what we are talking about? Do you mean a table, like the one in your article?



B. This seems perfectly reasonable to me. The question is: What happens in the interval between when the particles are shot from the source and when they are detected on this end measuring apparatus? (Of course, we don't really know this yet...)

So, there are a couple of other points that seem perfectly reasonable to me as well:

1. The detectors are measuring something, i.e., something causes the detectors to register a signal. Therefore, something exists which sets this signal off, and this something thus exists prior to the detection and thus to our measurement. Nature might react to our measuring apparatuses, and in a way different from how it acts when not interacting with these devices, but that certainly does not mean something pops into existence just because humans "look at it" ...

2. If QM predicts probabilities of correlations to be .250 (and not .333), and these are consistently the results we get in experiments, then something (what an unsatisfactory word, I know) is clearly (to me, at least) causing particles to have correlative spins at a rate that violates Bell's Inequality. I mean, this seems especially true when the results of experiments are highly consistent, as the results of EPR experiments have appeared to be (in other words, correlations aren't just happening to occur at a rate of .250).

A. An example data set would look something like this:

A B C (these are angles such as 0/120/240 degrees, not particles)
+ - +
- + +
- + -
+ + -
- - +
+ - -
+ - +
etc.

And of course only 2 can be measured at a time. But if we are assuming realism, the third has a value and we simply don't know it. Now, the requirement is that in an observer independent reality, the results for one observer are not dependent on the other observer (and vice versa).

B.1. You say it must pre-exist, but that is precisely what we seek to learn. So this is an assumption, and therefore subject to disproof. Keep in mind that time ordering in QM does not support the idea that the earlier event causes the later one.

B.2. Bell tests are accurate to many standard deviations (some tests to over 100 SD).

 

[rkn]

B.1. You say it must pre-exist, but that is precisely what we seek to learn. So this is an assumption, and therefore subject to disproof.

I agree entirely. Still, it is an assumption that has not been disproven yet in the history of science and our study of nature, so that is why I lean towards it and not the contrary. So, we shall see, so to speak... (hopefully!)

Keep in mind that time ordering in QM does not support the idea that the earlier event causes the later one.

Could you point me towards some good papers on this?

 

[DrChinese]

1. I agree entirely. Still, it is an assumption that has not been disproven yet in the history of science and our study of nature, so that is why I lean towards it and not the contrary. So, we shall see, so to speak... (hopefully!)

2. Could you point me towards some good papers on this?

1. Well, Bell disproved it. So you are basically throwing out a good proof on nothing more than gut instinct. And you have no alternative local mechanism to replace it.

2. The reference in post #12 should do it. Zeilinger's teams/co-authors are tops in the field.

 

[rkn]

"Gut instinct" isn't the only thing, or even the important thing, involved in my take on how nature works. One important thing may be my lack of understanding of the material that discusses QM, however, and this certainly may be (in fact, in many cases, I know it is) the case. I am only beginning my endeavor and hopefully more enlightenment will come of a continued pursuit of understanding this material.

I can't just take your, or anyone else's, "word for it". So just saying "Bell disproved it" doesn't satisfy me! (Thankfully)

Thank you for the link. I really appreciate your quick and thoughtful responses.

 

[DrChinese]

I can't just take your, or anyone else's, "word for it". So just saying "Bell disproved it" doesn't satisfy me! (Thankfully)

He merely disproved that nature cannot be both realistic AND local.

Of course, you should try to understand the material as well as possible. If you have not already done so, you may benefit from reading the original EPR and Bell documents.

One problem you will rapidly encounter is how to explain experiments such as I referenced in #12: entangling particles after the fact. This shouldn't be possible if your premise were correct.

Good luck, and ask more questions as needed.

 

[lugita15]

rkn, I recommend http://quantumtantra.com/bell2.html by Nick Herbert. I think it may be the most straightforward explanation of Bell's theorem I've seen.

 

[rkn]

Thanks lugita15! I'll check it out

 

[rkn]

Thanks lugita15! I'll check it out

Must be wary, though... as he "uses physics to derive limits on local psychic powers [and] is currently obsessed with quantum tantra which he envisions as a brand new way of doing science."

Er... noted...

 

[lugita15]

Must be wary, though... as he "uses physics to derive limits on local psychic powers [and] is currently obsessed with quantum tantra which he envisions as a brand new way of doing science."

Er... noted...

Yes, the guy is otherwise a total weirdo, but this one page on his site is legitimate. Herbert has published his version of Bell's proof in peer-reviewed scientific journals, and in fact the numbers he uses (0, 30, and 60) are the same ones J.S. Bell himself in explaining his theorem to popular audiences. So you can trust the article, just be wary of everything else on his website.

 

[rkn]

Yes, the guy is otherwise a total weirdo, but this one page on his site is legitimate. Herbert has published his version of Bell's proof in peer-reviewed scientific journals, and in fact the numbers he uses (0, 30, and 60) are the same ones J.S. Bell himself in explaining his theorem to popular audiences. So you can trust the article, just be wary of everything else on his website.

Yeah that article is really well written. It's "bare bones" but does a great job of laying out all of the steps involved. Thanks!