On Saturday, May 9, 2020 at 4:58:20 AM UTC-6, Lawrence Crowell wrote: > > On Friday, May 8, 2020 at 9:28:02 PM UTC-5, Alan Grayson wrote: >> >> >> >> On Friday, May 8, 2020 at 4:50:55 PM UTC-6, Lawrence Crowell wrote: >>> >>> There is no global meaning to energy conservation. There is the >>> Hamiltonian constraint Nℌ = 0, which just says that for a local region >>> where the lapse function can be parallel translated to the energy is zero. >>> This is for Petrov type O solutions >>> >>> Nℌ = 0 = ½(da/dt)^2 - 4πGρa^2/3c^3 - k >>> >>> Which leads to the FLRW constraint >>> >>> (a’/a)^2 = 8πGρ/3c^3 – k/a^2 a’ = da/dt >>> >>> Where the Hubble parameter H = 70km/s-Mpc is (a’/a)^2 = H^2. This means >>> that in a local region we have energy conservation FAPP. The difficulty is >>> this is not a property of the symmetries of the system so we have no way to >>> extend this globally. >>> >>> What this ultimately means is that all physics is local. It does not >>> mean we have mass-energy locally vanishing. The apparent increase in the >>> kinetic energy due to expansion is well enough compensated for by a decease >>> in gravitational potential energy. >>> >> >> This is the claim, but I haven't seen any proof of it. Do you have one? >> Take a planet. Can you show that Mc^2, where M is the planet's mass, is >> equal to its negative gravitational potential energy? AG >> > > The Hamiltonian constraint above and the FLRW equation are all you need. > It is right there. >
If it's so obvious, there'd be no dispute about this. But there definitely is! Bruce, e.g. Can you cite a paper where it's explicitly proven? TIA, AG > > >> >> >>> There is nothing mysterious going on here. All this means is there is a >>> limitation or horizon to our ability to know if there are global symmetries >>> to the universe. >>> >> There are surely limitations on our observational abilities, but why is a symmetry necessary? Nature seems pretty asymmetric; e.g., imbalance of matter and anti-matter. AG > As such there is no meaning to conservation principles. >>> >> >> We can estimate the volume of the observable universe and its average >> mass-energy density. So it seems we can estimate its total energy. Does >> that energy remain constant or not as the universe expands? This seems like >> a reasonable question to ask. AG >> > > Consider a quantum gravitational wave, say at or near the Planck scale, in > the earliest phase of the universe. For that now redshifted or expanded to > the scale of the CMB this means such data, from the near Planck time of the > earliest universe, is around 2 trillion light years away. I have indicated > numerous times how this comes about, This is as far as we can say anything > about the physics of cosmology. Beyond that scale we are faced with a > fundamental horizon of unobservability. As a result all we can say is that > for any local system energy is conserved, but this conservation law is not > due to any global symmetry. The Hamiltonian constraint is a manifestation > of a local gauge-like principle of general relativity, and it has no global > content. On a global level we cab' say anything; it is unknowable. > > Quantum mechanics is curiously similar. We have nonlocality of a wave, but > we can only infer some things from that by local measurements that > localizes waves or fields. We are not able to ever perform a perfect > observation of a global wave. There is an epistemic horizon in QM that I > think is dual or complementary to that of spacetime or general relativity. > > LC > > >> >>> LC >>> >>> >>> On Friday, May 8, 2020 at 3:00:18 AM UTC-5, Alan Grayson wrote: >>> >>>> If it's not conserved, as seems implied by the red shift due to >>>> expansion, where does it go? TIA, AG >>>> >>> -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/893e4103-eade-461a-ba0e-ea0536bc6f96%40googlegroups.com.
