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. > > >> 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. 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/27a71852-84da-4b37-9711-26f8985ed4ba%40googlegroups.com.
