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 > 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 > > 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/17826f8e-cdf8-4b25-9803-3c4bdfa6a92e%40googlegroups.com.
