|Dec26-07, 08:26 PM||#52|
Need Understandable Explanation Of Bell's Theorum
Here is a quote I found in an article on DrChinese' very nice and interesting website.
It is from Alain Aspect, apparently in an 1999 article in Nature and/or on nature.com.
photons keep in contact through space and
Alain Aspect is clearly someone who is familiar with all the if's and but's of Bell's theorem.
[Edit:] At the end of the article, he points out that it is meanwhile a matter of 30 standard deviations.
|Dec27-07, 10:35 AM||#53|
The two subsystems in the quote above are two entangled particles, A and B.
When A acquires a specific spin (caused by measurement), then B is required, due to the dependencies in their wave function, to acquire the opposite spin (when measurement angles are the same).
If one assumes Heisenberg Uncertainty in a non-realist fashion, this means (in my understanding) that one assumes that there is no underlying cause for why particle A acquires this specific spin (out of the two possibilities depending on the measurement angle). This means that there cannot be the same cause already present at particle B, since there is no such cause. Which in turn means that there must be a non-local connection between A and B, since experiments verify that particle B will indeed acquire the opposite spin when measured along the same angle, whichever one that is. (Experiments verify this even when the shortness of the time window between relevant events excludes communication between A and B at speeds comparable to the speed of light).
So in my understanding, as long as one takes it as a given that the wave functions are indeed interdependent in this way (as Quantum Theory says AFAIK), the assumption of Heisenberg Uncertainty to have no underlying cause (non-realism in this regard) implies non-locality.
|Dec27-07, 06:56 PM||#54|
Also, regarding the relative settings of the measurement apparati: it was the apparati that are being ruled out as being in non-local communication (in tests of strict non-locality such as the Innsbruck experiment you mention). The point is that Bell imagined as follows:
"In a theory in which parameters are added to Quantum Mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant."
|Dec27-07, 09:51 PM||#55|
Do they not realize that the experiments themselves demonstrate effects that need to be explained, regardless of Bell's theorem? Or am I perhaps mistaken about this?
Why would it be necessary to rule out that the apparati might communicate non-locally? Usually the loophole that needs to be ruled out is that they might communicate classically. And in any case, how would that be related to what we are, or what we have been, discussing?
|Dec27-07, 11:07 PM||#56|
Thus it is that my understanding follows from the assumption that allowable states lie on a loop (ie, a path that begins and ends at the same point). So when Alice finds (via a measurement interaction) that her photon A has an allowable state a then we know (from their birthing correlation) that B also has an allowable state a. (a and b being unit-vectors denoting the direction of the measured polarizations; the loop then being a circle.)
Then, for all of Alice's tests that reveal A -> a, when Bob is measuring for the state b, (ie, B -> b) he is (unknowingly) evaluating the conditional probability:
P(B -> b| B -> a) = cos^2 (a,b); all elements in this formulation being local for Bob by virtue of the photonic birthing circumstances/correlations associated with the singlet state!
|Dec28-07, 02:19 AM||#57|
The mathematics behind these papers are usually very complex, even if in this case the presented results look very simple; they are often shorthands for much more complex expressions, and usually beyond my understanding.
As far as I can tell, the functions for the particles' results have only the measurement angle as a meaningful input (aside from the hidden variables), and if they belong to a local model, they must be independent of each other, that is, the function for each particle can only use that particles measurement angle as an input, none of the other angles. For the cases which allow definite predictions, the result of the last particle is a simple function of the other particles' results, similar as for the spins of two particles where the second is always the opposite of the first.
With multiple particles it is however a bit trickier, so that one can define a set of four experiments such that any possible local-hidden-variable model will make the right predictions only for at most 3 of those 4 experiments, AFAIK. This is because a local model then has more cases to care about than it can accommodate based on having only the measurement angle (and the hidden variables) as an input. The impact of the other measurement angles creates to many different cases, as though it could do something that would be right for any such case. As far as I understand.
Heisenberg uncertainty implies that the spin does not have a 'predefined' value for the first measurement, and that no hidden variables are recognized. (Even though in the case of Bohmian mechanics, the spin will be pseudo-random, so to speak, instead of random).
This is why I don't understand the attempts to accept Heisenberg uncertainty and, at the same time, to assume that the information comes from the common "birth". If one accepts uncertainty, then that means exactly that there will be no such information available, such as from any common "birth". I would think. From my point of view, this kind of local non-realism therefore looks like a non-starter. Yet I might be missing something, and if so, would like to find out.
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