Comments on: Derivation of Heisenberg Uncertainty from Kaluza Klein Geometry http://jayryablon.wordpress.com/2008/03/20/derivation-of-heisenberg-uncertainty-from-kaluza-klein-geometry/ Tue, 14 Jul 2009 16:04:49 +0000 http://wordpress.com/ hourly 1 By: Jay R. Yablon http://jayryablon.wordpress.com/2008/03/20/derivation-of-heisenberg-uncertainty-from-kaluza-klein-geometry/#comment-1368 Jay R. Yablon Sat, 29 Mar 2008 16:29:33 +0000 http://jayryablon.wordpress.com/?p=193#comment-1368 Hi Mike, I fixed your typos in the original post. Jay. Hi Mike, I fixed your typos in the original post. Jay.

]]> By: Mike Leggett http://jayryablon.wordpress.com/2008/03/20/derivation-of-heisenberg-uncertainty-from-kaluza-klein-geometry/#comment-1366 Mike Leggett Fri, 28 Mar 2008 19:04:15 +0000 http://jayryablon.wordpress.com/?p=193#comment-1366 Thanks for converting - I had 2 typos. $latex g_{\mu\nu}(5d) = g_{\mu\nu}(4d) + \kappa^2 A_\mu A_\nu \;\;\&\;\; g(5)_{ab} g(5)^{bc} = \delta_a^c $ Thanks for converting – I had 2 typos.

g_{\mu\nu}(5d) = g_{\mu\nu}(4d) + \kappa^2 A_\mu A_\nu \;\;\&\;\; g(5)_{ab} g(5)^{bc} = \delta_a^c

]]> By: Mike Leggett http://jayryablon.wordpress.com/2008/03/20/derivation-of-heisenberg-uncertainty-from-kaluza-klein-geometry/#comment-1363 Mike Leggett Tue, 25 Mar 2008 18:58:06 +0000 http://jayryablon.wordpress.com/?p=193#comment-1363 previous attempt failed I did a Google search on KK a year ago and found myself following this up (struggling more like) via Wikipedia and Physics Forum. Last week I started searching Google again and am delighted to see your work. I find your spin idea fascinating and your maths clear. I wish you well. I like your use of T and \tau. I think I may have made serious errors in not keeping these ideas clear. Relevant comment-1: intrinsic-spin-20 page 2 - I thought (see post 6 of ref below): $latex g_{\mu,\nu}(5d) = g_{\mu,\nu}(4d) + \kappa^2 A_\mu A_\nu $ I found I needed the $latex \kappa^2 A_\mu A_\nu $ term to get $latex g(5)_{ab} g(5)^{bc} = \delta_a^c $ and (in post 15 - in progress) to get otherwise awkward terms to cancel in R1(5) of post 14. Perhaps you omitted this term as it is small. I don’t think this will be a big problem. Best wishes, Mike. P.S. Irrelevant comment-2: I do have a problem with the enormous $latex d x^5 / d\tau = R d \phi / d\tau = u^5 $ which makes $latex d\phi / d\tau $ even more enormous. But this is not your problem - it is built into KK (which started from GR). Where: $latex u^5 = \lambda / \kappa = 10^{21} $ (approx) $latex \lambda = q/m $ $latex \kappa = your \bar \kappa $ and $latex c = 1 = \hbar $. I got round this by setting $latex u^5 = 1 $ (as I started from elementary QM). Then I got errors of $latex 10^{21} $!!!! (see post 6 especially appendix 3). My struggle is recorded in the Physics Forum thread at http://www.physicsforums.com/showthread.php?t=171945 (In post 13 I had a stab at reconciling this 10^21 error, and am working out how to tidy this up.) (In post 14 I asked for help in getting the sign right in R(5) = R(4) - EM. I think I have solved this. Half texts & papers have one sign, half the other. I don’t think it is to do with the sign of \eta_00, it may just be that some authors are more careful than others. I have prepared answer in post 15 in a word document, but am still mulling it over.) previous attempt failed

I did a Google search on KK a year ago and found myself following this up (struggling more like) via Wikipedia and Physics Forum. Last week I started searching Google again and am delighted to see your work.

I find your spin idea fascinating and your maths clear. I wish you well.

I like your use of T and \tau. I think I may have made serious errors in not keeping these ideas clear.

Relevant comment-1:
intrinsic-spin-20 page 2 – I thought (see post 6 of ref below):
g_{\mu,\nu}(5d) = g_{\mu,\nu}(4d) + \kappa^2 A_\mu A_\nu

I found I needed the \kappa^2 A_\mu A_\nu term to get g(5)_{ab} g(5)^{bc} = \delta_a^c and (in post 15 – in progress) to get otherwise awkward terms to cancel in R1(5) of post 14. Perhaps you omitted this term as it is small. I don’t think this will be a big problem.

Best wishes, Mike.

P.S. Irrelevant comment-2:
I do have a problem with the enormous d x^5 / d\tau = R d \phi / d\tau = u^5 which makes d\phi / d\tau even more enormous.
But this is not your problem – it is built into KK (which started from GR).

Where: u^5 = \lambda / \kappa = 10^{21} (approx) \lambda = q/m \kappa = your \bar \kappa and c = 1 = \hbar .

I got round this by setting u^5 = 1 (as I started from elementary QM). Then I got errors of 10^{21} !!!! (see post 6 especially appendix 3). My struggle is recorded in the Physics Forum thread at http://www.physicsforums.com/showthread.php?t=171945

(In post 13 I had a stab at reconciling this 10^21 error, and am working out how to tidy this up.)
(In post 14 I asked for help in getting the sign right in R(5) = R(4) – EM. I think I have solved this. Half texts & papers have one sign, half the other. I don’t think it is to do with the sign of \eta_00, it may just be that some authors are more careful than others. I have prepared answer in post 15 in a word document, but am still mulling it over.)

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