RE: Describing the impossible
October 10, 2018 at 8:20 pm
(This post was last modified: October 10, 2018 at 8:23 pm by polymath257.)
(October 10, 2018 at 5:10 pm)Whateverist Wrote:(October 10, 2018 at 2:28 pm)Jörmungandr Wrote: The conservation of energy is actually backed by Noether's theorem. It's not purely empirical.
But surely the measured result is primary and the theorem descriptive, no?
Not actually. What happens is when a *new* theory is presented, Noether's Theorem is used to *derive* the expression for energy in that new theory. That is then used to make predictions based on conservation of that new quantity.
In essence, energy is *defined* to be the conserved quantity in Noether's theorem when the lagrangian is time invariant.
(October 10, 2018 at 10:17 am)vulcanlogician Wrote: So in the case of energy being created or destroyed, I don't think scientists ever claim that it is "impossible." The merely say that it cannot be created or destroyed in an isolated system (as far as they know). The parenthetical "as far as we know" is assumed to follow all statements of scientific law, so it is never said in order to avoid redundancy.
Dark energy, for instance, may be a case of the universe breaking the first law of thermodynamics. Or it may just be an innate instability in spacetime. Scientists are still puzzling it out.
In fact, the conservation of energy in General Relativity is problematic. The basic equations are NOT time invariant, so Noether's theorem does NOT give a conserved quantity.
And this makes some sense because energy is the time coordinate of the energy-momentum vector and in curved spacetime, the translation of this vector to a common point (for various places where there is energy) may not be well-defined. The divergence theorem has to take curvature into consideration.
