At 7:49 PM 10/17/4, Keith Nagel wrote: >Hi Horace. > >Your posts are like a fine French cheese, they need to age >a bit before reaching the peak of flavour... Are we there yet?
Well it was smelling pretty bad, so I suppose so. 8^) My only defense for the confusion is momentary excitement and youthful exhuberance ... well I had the excitement anyway. At least it only took me about a day to get it right. > >Anyway, as you seem to be taking some liberties >with your models, let me try this notion on you. > >Let's question the assumption of 3 quantum variables. >String theory suggests that more than our 3 visible >dimensions exist; the number varying depending on the >theory, time of day, etc. Consider for a moment >the case of four dimensions... > >A B C D E F G H >0 0 0 0 1 1 1 1 >0 0 0 1 1 1 1 0 >0 0 1 0 1 1 0 1 >0 0 1 1 1 1 0 0 >0 1 0 0 1 0 1 1 >0 1 0 1 1 0 1 0 >0 1 1 0 1 0 0 1 >0 1 1 1 1 0 0 0 >1 0 0 0 0 1 1 1 >1 0 0 1 0 1 1 0 >1 0 1 0 0 1 0 1 >1 0 1 1 0 1 0 0 >1 1 0 0 0 0 1 1 >1 1 0 1 0 0 1 0 >1 1 1 0 0 0 0 1 >1 1 1 1 0 0 0 0 > >AE 16/16 >AF 8/16 >AG 8/16 >AH 8/16 >BE 8/16 >BF 16/16 >BG 8/16 >BH 8/16 >CE 8/16 >CF 8/16 >CG 16/16 >CH 8/16 >DE 8/16 >DF 8/16 >DG 8/16 >DH 16/16 > >4 matches over 16 combinations >4*16 + 12*8 > >160/256 = .625 Interesting!! Suppose we assume that the entanglement prevents all 4 "axes" from having identical spin. We now have the following 14 possible combinations: A B C D E F G H 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 AE 14/14 AF 6/14 AG 6/14 AH 6/14 BE 6/14 BF 14/14 BG 6/14 BH 6/14 CE 6/14 CF 6/14 CG 14/14 CH 6/14 DE 6/14 DF 6/14 DG 6/14 DH 14/14 4*14 + 12*6 = 128 Now if there were only some justification for counting all 16 rows instead of just the 14 we'd have 128/256 = 0.50. Suppose similar liberties were taken with the 3 dimensional array, Table 1. i A B C D E F 1 0 0 0 1 1 1 Key: 2 0 0 1 1 1 0 3 0 1 0 1 0 1 i - possible combination (row) number 4 0 1 1 1 0 0 A, B, C - Alice's possible observations 5 1 0 0 0 1 1 D, E, F - Bob's corresponding observations 6 1 0 1 0 1 0 7 1 1 0 0 0 1 8 1 1 1 0 0 0 Table 1 - Possible observations by Alice and Bob a b matches - - ------- A D 6/8 A E 2/8 A F 2/8 B D 2/8 B E 6/8 B F 2/8 C D 2/8 C E 2/8 C F 6/8 Table 2 - Expected results Taking the same liberty of not counting any matches when all 3 spins are the same, we have 6*2 + 3*6 = 30/64 = 0.46875, even better than needed. Maybe too much. We need an excuse to reduce the 64 to 60? Or maybe add 2 to the 30? At any rate there seems to be no physical interpretation available for this. Something looks a bit magical about 4 dimensions with the all-4-spins-alike combinations getting a special treatment, though there is no apparent physical justification. Regards, Horace Heffner
