EPR Paradox and Local Variables

Factual Questions
1

Note: If you don’t know what the EPR Paradox is, you won’t be able to answer my question – trust me on this.

Background: Within the EPR Paradox, it seems to me that if the two “entangled” photons had made up their minds about their spin at the moment of creation, we wouldn’t have any way to know what they’d chosen until we measured them. Thus, the moment we tested one, the wave front of the other one would appear to collapse.

Problem: I was reading somewhere that this clever “solution” to the paradox is, like, really obvious, and has been disproven. Apparently, for the photons to already have pre-selected spins, you’d have to have something called “Local Variables” – and apparently that’s not possible (at least, according to the late, great John von Neumann).

Another Note: Please don’t tell me about guide/pilot waves, because I’m not asking about that, 'kay?

My Question: Is it possible to explain to somebody like me (who doesn’t know enough physics to baffle a gnat) just how they know that the photons don’t have some variables they can’t detect? I mean, how do they know that the process of measurement isn’t destroying whatever magic pixie was telling the photon what its spin was?

They certainly can’t know what’s going on until they measure it, so how dare they (by golly!) say what isn’t attached to something that by definition they know nothing about (because they haven’t measured it yet)?

2

The late, great John von Neumann’s error was found in the fifties by Bohm. Bell’s theorem made certain predictions about local hidden variables that were later disproven by experiments–all the EPR experiments that have been in the news the last twenty years. That still leaves non-local hidden variables as an untested (maybe untestable) possibility.

So, what’s with the attitude about pilot waves?

3

My “attitude” about pilot waves is precisely because they invoke non-local variables. I was asking why it was supposed that local variables were verboten.

If, as you say, “Bell’s theorem made certain predictions about local hidden variables that were later disproven by experiments”, then is it not possible that the spin of the photons is determined when they are created? If that’s the case, the EPR Paradox vanishes – kapoof!

On top of that, Einstein wins!

4

But that is what is meant by local variables, essentially. That is what has been disproven by the EPR experiments: that there are no local variables. Einstein had his money on the other side. Einstein “loses.” The one option left for Einstein is non-local variables–which is why I wondered why you didn’t want to hear about them.

On the other hand, this is not a loss for Einstein. Clearly, this research, which he pursued late in his career, is still giving other scientists something to think about. That, and the recent publicity about the Bose-Einstein condensates, are probably what led Time magazine to choose him as the Century’s lead personality–as he shook physical foundations from one end of the century to the other.

5

Two brief remarks:

  1. Einstein was not alone in wanting to dispense with “spooky action at a distance”. Current theory has been stable for a while, despite the army of those trying to show that we can do without the possibilty of non-local “causes”.

  2. Those who seek to “get rid of” paradoxes within existing intellectual schema should be careful. “A paradox is the truth standing on its head to attract attention” (N. Falletta)

picmr

6

To understand Bell’s Inequality and the proof of the absence of local hidden variables, you have to understand the way polarization is measured.

The polorization of a photon is measured relative to the detector. Let’s say for a moment that we “know” a photon has a polorization of 0°. We try to pass it through a detector set at 0°; it passes through 100% of the time. We try to pass it through a detector set at 90°; it never passes through. BUT! We have not determined the “true” polarization of the photon; we have determined its state vector relative to the detector: I has two possible states (0° & 90°) with relative probability 100% and 0%.

So, we try to pass this same photon through a detector set at 45°. We find that it passes through 50% of the time! The same photon has a different state vector relative to the new setting: 45° and 135°, with relative probability 50% and 50%.

So let’s go back to Bell’s experiment. We have two photons with complementary polorizations. This means that if we have two detectors set at the same setting (0°, 45°, 90°, etc.) one photon will go through one detector, and the other will be blocked. Likewise, if we set one detector at 90° relative to the other, either both photons will always go through, or both photons will always be blocked. The photons’ polarizations are perfectly correllated (by knowing the relative angles of the detectors, I can perfectly predict the reaction of one photon to the detector by observing only the other). This proves that the photons have complementary polarization.

When we set the detectors to a relative angle between 0° and 90°. At 45°, if one photon goes through (or is blocked by) one detector, the other photon has a 50/50 chance of going through the other detector. At this point, the polarization of the photons relative to the two detectors is completely uncorrellated; I cannot accurately predict the response of one photon to its detector by observing the other photon’s response to its detector.

The change is correlation is continuous. At 1° relative orientation of the detectors, the correlation is high, but not perfect. Every now and again, you’ll get both photons going through, instead of always having one go through and one blocked when the detectors have the same relative orientation.

Here’s where Bell’s Inequality comes in (and my lack of math sadly becomes apparent). If the relative polarization of the photons are determined by local variables (i.e. variables whose effects propagate at the speed of light) then we must see a particular pattern of correlation as we move the detectors from alignment (perfect correlation) to a 45° relative orientation (zero correlation). However, Quantum Mechanics predicts a different pattern; more specifically, the polarization of the photons will be more highly correlated (i.e. I can predict the response of one photon from the behavior of the other with better accuracy) than would be possible assuming local variables.

Essentially, the photons cannot just know each others’ polarizations at the time they are generated (local variables). They must also “know” how the other reacts to its detector and instantaneously modify its reaction to its own detector to preserve the QM-predicted levels of correlation. And there can’t be any kind of subtle effect where the position of the detectors propagates to the generation of the photons; the experiment works even if you randomly change the orientation of the detectors picoseconds before they measure the relative polarization of the photons.

IIRC this experiment has been performed in real life (even to the random re-orientation of the detectors before the measurement) and its predictions have been confirmed.

7

Some interesting links to discussion more detailed than can be posted here:

Does Bell’s Inequality Principle rule out local theories of quantum mechanics?. A tad out of date on the experimental results, somewhat but not overly technical. You can understand most of it without even thinking about the math, but there’s no difficult math.

Bell’s Theorem. An explanation of Bell’s Theorem in terms of playing cards.

The Everett FAQ. EPR discussed from the point of the many-worlds interpretation.

Bell’s Theorem

Quantum Nonlocality

Recent experiments (technical!):

Violation of Bell’s Inequality under Strict Einstein Locality Conditions

Violation of Bell Inequalities by Photons More Than 10 km Apart

8

Thanks for the explanation, SingleDad. One thing that I still can’t grasp: how do we know that the photons didn’t depart with a master plan of their polarizations for the entire trip? They could agree upon separating that for the first 10 ps, their orientation would be X, then for the second 10 ps, it would be Y, etc.

So when you detect them at some later time, you’re just detecting the master plan that they agreed to when they left. I’m not arguing that this is the case, because I don’t have enough knowledge about it, but this is the question I arrive at when presented with the data you describe.

9

CurtC

That’s where non-local hidden variables come in.

10

Read some of the links I provided {grin}, especially the second one. SingleDad’s explanation is pretty good, but I think it’s not quite detailed enough to contain the answer to your question.

The answer to your question is contianed at some of those links, and is too long to tyr to type out here, but here’s a top-level answer without explanation. The experiments are carefully designed so there is no possible way that the photons could have agreed on a master plan when they were together, because the information required to choose a master plan from an infinite set of possible master plans did not exist at the time the photons were generated.

The initial demonstration of the truth of Bell’s inequality tried to do this, but the times weren’t handled correctly; it was possible for the photons to agree on a master plan. That error has been rectified.

11

Okay, SingleDad set me straight: the experiments dealing with the paradox take into account the configuration of the detectors, so the nature of the detection influences the outcome. Since the detectors have never met (“Hi! I’m the detector from the other side of the room – what’s your sign? Positive or negative?”), local variables can’t explain the result.

Nifty.

Since I started this thread, I’m going to pull rank, give you all mental whiplash, and utterly change the subject. (Hey, I got all you smart folks into the thread, and now I’m gonna take advantage of this!)

Every physics book I read that mentions Pauli’s Exclusion Principle includes the same parenthetical “explanation” about two systems not being able to be in the same quantum state.

What the heck does that mean? From context, I have gradually come to believe that this means that you can’t have two electrons with precisely the same motion/energy probability and precisely the same location probability (roughly speaking, two things can’t be in the same exact place).

Am I even close?

12

Pretty accurate. For something a little more technical but not very difficult, see The Pauli Exclusion Principle. I especially like:

“Was Wolfgang Pauli such an imposing figure that electrons do as he says? (Perhaps this isn’t so preposterous; it was claimed that proximity to this Austrian-born theoretician could make experimental apparatus go haywire, a phenomenon
that became known as the Pauli Effect).”

13

Do you mean that non-local variables have also been ruled out? They don’t seem to be addressed by that link.

14

I believe that non-local hidden variables have not been ruled out, but I think that current thinking and research on that question hasn’t yet trickled down to the level on which I keep track of such questions. So there’s a reasonable probability I’m wrong.

Non-locality, whether or not there are hidden variables, is pelenty to make me dizzy!

15

There’s a pretty good article about guided wave theory in this month’s Skeptical Inquirer, if you’ve let that go and want to know more. :wink:

16

Democritus: Actually, it was that article in Skeptical Inquirer that made me start this thread in the first place!

By the way, did you notice that Skeptic and Skeptical Inquirer are running many of the same “Mass Delusion” stories this month? I wonder what brought that up.