| Raider of the lost time
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Join Date: Nov 2003 Rep Power: 73 | gauge supremacy -
03-30-2007, 12:08 PM
Gauge symmetry is a theory of invariance for all space-time transformations that must work locally as well as globally. To be effective, the rules describing the elements of a particular gauge group must also apply locally as well as globally.
The gauge groups for standard model of elementary particles are U(1), SU(2), and SU(3). Their respective Hadamard bases are: (1), (-1); (1,1), (1,-1), (-1,1), (-1,-1);
(1,1,1), (1,1,-1), (1,-1,1), (-1,1,1), (1,-1,-1), (-1,-1,1), (-1,1,-1), (-1,-1,-1). On the other hand, the 16 bases of special relativity are (1,1,1,1), (1,1,-1,1), (1,-1,1,1), (-1,1,1,1), (1,-1,-1,1), (-1,-1,1,1), (-1,1,-1,1), (-1,-1,-1,1), (1,1,1,-1), (1,1,-1,-1), (1,-1,1,-1), (-1,1,1,-1), (1,-1,-1,-1), (-1,-1,1,-1), (-1,1,-1,-1), (-1,-1,-1,-1). However, out of these 16 linearly independent bases only (-1,1,1,1) or (1,-1,-1,-1) are ever used in describing the space-time interval invariance called metric tensor.
Simply using Hadamard gauges the gross simplification done by special relativity has been raised to the surface. The reason lies within the lightcone geometry, which neglects all possible solutions involving negative spaces and negative time. However, for time independence the lightcone geometry is contracted to SU(3) geometry. This is possible if and only if the 8 distinct bases are converted into 8 directional invariance properties. If these properties correspond to the sign convention used by different authors up to the year 1973 regarding three principal tensors of general relativity: (1) metric tensor, (2) Riemann tensor, and (3) Einstein tensor then it is clear that none of these authors ever considered using a sign convention where the metric tensor is positive, the Riemann tensor is negative, and the Einstein tensor is positive, (1,-1,1). Its significance or insignificance will be investigated further. Could it be the missing gauge that finally unites quantum mechanics and general relativity? For a complete listing which author uses which sign convention see pages behind front cover of Misner, Thorne, and Wheeler, Gravitation, Freeman, New York, 1973.
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
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Re: gauge supremacy -
03-30-2007, 09:16 PM
Linear Mode
