Re: Entropy

Barry wrote:
There are known linkages between Symmetries and Conservation Laws.

Yes, where "symmetry" means an invariance of the Lagrangian. That is, not everything one might consider a "symmetry" qualifies.

The famous theorem by Emmy Noether is one of the most important mathematical underpinnings of modern physics. It states that for every continuous symmetry of a Lagrangian (i.e. a continuous Lie group that leaves the Lagrangian invariant) there is a corresponding conserved quantity (usually called a "current"; moreover the theorem explicitly computes either from the other (I'm omitting lots of details and caveats). This is of course in the context of Lagrangian mechanics or field theory, in which the equations of motion are obtained from the Lagrangian by an appropriate variational principle.


It's becoming clear that there's a fundamental symmetry between space
and time.

Hmmm. This is not an invariance of the Lagrangian in any theory of modern physics. And I for one don't see much of a "symmetry" here: rulers measure space and clocks measure time, and they are not "symmetric" in any observable way!

At another level, space and time are _unified_ (not "symmetric") -- all theories of modern physics use spacetime as the underlying manifold, not space and time separately. Perhaps this is what you are thinking of. This affects the geometry of the manifold in important ways, but is not an invariance of the Lagrangian and does not yield any corresponding conserved quantity.


If space and time were symmetric, what Conservation Law might result?

I have no idea, but in modern physics they aren't "symmetric" in the sense that is required to apply Noether's theorem.


It might well be something that current wisdom says isn't conserved.

Seems unlikely to me....


Tom Roberts
.

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