gauge supremacy

[AntonioLao]

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.

[mkirkpatrick]

Great idea,what is the quiddity of this conundrum? You ask,could a missing gauge theory
possibly unite quantum mechanics with general relativity? Yes I suppose it could,but where would you look to pluck such a prize?

This could be expressed;3-1-1-1=0=1?How would you gauge this equation?




regards michael.

[AntonioLao]

This could be expressed;3-1-1-1=0=1?How would you gauge this equation?

This looks like an inequality and depending which side is bounded, the unbounded side would contain infinite solutions.

[mkirkpatrick]

This looks like an inequality and depending which side is bounded, the unbounded side would contain infinite solutions.

Thats far too many solutions!Needs narrowing down to reveal real from the temporal.



regards michael.

[AntonioLao]

Needs narrowing down

This is why mathematics is bounded by its definitions and nothing more.

[mkirkpatrick]

This is why mathematics is bounded by its definitions and nothing more.

That is certainly logical,but is there room for illogical maths,which is less bounded?


regards michael.

[AntonioLao]

illogical maths

Personally, I consider all dynamic nonlinear mathematics as illogical. Not lack of solution but on the contrary there are infinite solutions. Einstein's field equations of general relativity is a good example of nonlinear equations with infinite solutions. Some people are working on the blackhole solutions and others on http://xxx.lanl.gov/abs/gr-qc/0004016

[mkirkpatrick]

Personally, I consider all dynamic nonlinear mathematics as illogical. Not lack of solution but on the contrary there are infinite solutions. Einstein's field equations of general relativity is a good example of nonlinear equations with infinite solutions. Some people are working on the blackhole solutions and others on http://xxx.lanl.gov/abs/gr-qc/0004016

Thats interesting,I understand this better now.Will check out the link.



regards michael.