On 5/25/2015 10:45 AM, John Clark wrote:
On Sat, May 23, 2015 , Pierz <[email protected] <mailto:[email protected]>> wrote:> Bruno /did/ acknowledge that his theory predicts that the laws of physics are invariant across space and time, because they are supposed to arise out of pure arithmeticWe know from pure mathematics (by way of Noether's theorem discovered in 1915) that if the fundamental laws of physics do not change with time then the conservation of mass/energy must exist. And Noether also tells us that if the fundamental laws of physics do not change from one place to another then the law of conservation of momentum must exist. By the way, I don't think Emmy Noether received the credit she deserved for this enormously important discovery.
And to expand on that point, note that if we find a law of physics that depends explicitly on time or location, we would be reluctant to consider it fundamental and we would look for some more fundamental law that explained its dependence. Incidentally, what Noether proved is that for each symmetry in the Lagrangian of a physical system there is a corresponding conserved quantity and vice versa. So for an expanding universe, one that has no time-like Killing vector field, there is no conserved mass/energy. John Baez (Joan's cousin) has a good essay on this online.
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