On 12/28/2022 9:01 PM, Bruce Kellett wrote:
On Thu, Dec 29, 2022 at 3:29 PM Brent Meeker <[email protected]>
wrote:
Of course one reason there are "laws of physics" is what my late
friend Vic Stenger called Point Of View Invariance. This was his
generalization of Emmy Noether's theorem that showed every
symmetry implied a conservation law.
That is not strictly true. It is only continuous symmetries of the
Lagrangian that imply conservation laws -- not all symmetries. For
example, the symmetries of a square under rotation and reflection do
not generate any conservation laws. Neither do discrete symmetries
like parity and charge conjugation.
So momentum is conserved because we want any law of physics to be
invariant under translation of a different location. Energy is
conserved because we want the laws of physics to be the same at
different times, etc.
It is not what we want, it is what we find. We find that nature is
invariant under these continuous transformations, so we build those
symmetries into our laws.
Vic called in POVI because he wanted to extend it to transformations in
abstract spaces, e.g. gauge invariance. Of course the invariance
depends on the "point of view" in a sense. Things didn't look at all
space translation invariant to Aristotle. Galileo said ignore that your
ship is moving along the shore, just look at the dynamics in the cabin.
So we discovered these symmetries by learning what ignore as well as
what to measure.
Brent
Bruce
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