From: bdemlo@higher-me.com (Brad Demko) Subject: Re: Faster than light Date: Fri, 18 Aug 2000 05:58:33 GMT Newsgroups: sci.physics.research Summary: [missing] On 17 Aug 2000 (Jonathan Thornburg) wrote: >Here's an analogy that I've found useful in explaining what quantum >entanglement does and doesn't mean vs the speed of light: The analogy you described doesn't represent anything like quantum entanglement. I'm sure this has been explained in this newsgroup many times before, but maybe it's worth another review. The essence of quantum entanglement (as exhibited in things like EPR experiments and tests of Bell's inequalities) is that the joint probabilities for combinations of spacelike-separated events depend on the choices of particular measurement operations that are applied to entangled systems at those separate events, and moreover that this dependence is non-linear. It is the non-linearity that makes it impossible to account for the dependence in conventional terms (in stark contrast to the analogy you proposed, which can be trivially accounted for in conventional terms). In order to convey any sense of quantum entanglement, we must first introduce a CHOICE of measurements to be made on each of the two coupled systems, and then we need to examine the correlations resulting from various combinations of choices. For example, suppose each of your sealed envelopes is prepared so that we can perform any one (and only one) of three measurements, A, B, or C, on its contents. Whichever measurement is performed, the result will be either 0 or 1. Several pairs of envelopes are prepared in this way, and one member of each pair is sent off to Mars while the other stays here. Then in both locations (here and Mars) we perform one of the three allowable measurements on each envelope and record the results. Our choices of measurements (A, B, or C) may be arbitrary, by flipping coins or whatever. We find, in accord with quantum mechanics, that regardless of which measurement we decide to make, the chances are 50% of getting "1", and the folks on Mars discover the same thing. This is all that either of us can determine separately. However, when we bring all the results together and compare them in matched pairs, we find the following correlations (again in accord with quantum mechanics) Earth A B C A 0 3/4 3/4 Mars B 3/4 0 3/4 C 3/4 3/4 0 The numbers in this matrix indicate the fraction of times that the Mars and Earth results agree (both 0 or both 1) when the indicated measurements have been made on the two members of a matched pair of sealed envelopes. Notice that if Earth and Mars happenned to choose to make the same measurement for a given pair of envelopes, the result NEVER agree. In other words, they are always the opposite (1 and 0, or 0 and 1). Also notice that the overall probability of agreement if both measurements are selected at random is 1/2. This shows the true nature of quantum entanglement. As you can see, it's of an entirely different character than the analogy you proposed, because there is no way of preparing the pairs of sealed envelopes in advance of the measurements such that they will give these probabilities. To see why, notice that each envelope must be ready to respond to any one of the three measurements, and if it happens to be the same measurement as is selected on its matched partner, then it MUST give the opposite answer. Hence if the Earth envelope will answer "0" for measurement A, then the Mars envelope MUST answer "1" for measurement A. Likewise for the other measurements, so there are only eight ways of preparing a pair of envelopes Earth Mars A B C A B C a 0 0 0 1 1 1 b 0 0 1 1 1 0 c 0 1 0 1 0 1 d 0 1 1 1 0 0 e 1 0 0 0 1 1 f 1 0 1 0 1 0 g 1 1 0 0 0 1 h 1 1 1 0 0 0 These preparations, and ONLY these, will yield the perfect anti- correlation when the same measurement is applied to both envelopes. Unfortunately, if we simply randomly select one of these eight preparations (with equal probabilities) for each pair of envelopes, we won't match the other correlations predicted by quantum mechanics. Instead we get Earth A B C A 0 1/2 1/2 Mars B 1/2 0 1/2 C 1/2 1/2 0 Notice that the overall probability of agreement if the two measurements are selected randomly is NOT 1/2 (as quantum mechanics says it must be). Instead, it is 1/3, so this isn't right. Still we might imagine that some other selection strategy for choosing from the eight possible preparations might give the right overall results. However, regardless of our strategy, the overall preparation process must result in some linear combination of the eight cases, i.e., there must be positive constants a,b,..,h whose sum is 1 and such that the "agreement probabilities" in the first table are satisfied. This implies, among other things, that c+d+e+f = 3/4 b+d+e+g = 3/4 b+c+f+g = 3/4 Adding these up gives 2(b+c+d+e+f+g) = 9/4, and so the sum of the coefficients b through g is 9/8, which exceeds 1. Hence there is NO linear combination of those eight preparations that can yield the joint correlations predicted by quantum mechanics. This just illustrates that the questions presented by quantum mechanics are deeper and more profound than is sometimes realize. On 17 Aug 2000 (Jonathan Thornburg) wrote: >Does this constitute faster-than-light communication? >No, it doesn't, no more than the quantum entanglement >experiments do. The analogy you proposed certainly does not constitute faster- than-light communication, nor does anything that even remotely resembles that analogy, because it has a purely conventional representation. The more serious question arises when dealing with genuine quantum entanglement, i.e., phenomena that have no conventional representation, and for which the conditional probabilities seem impossible to establish prior to the actual selection of a measurement basis. I would argue that the answer is still a qualified "no" (no superluminal communication), but this has nothing to do with the purely conventional process that you described.