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. 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. 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/1d248d40-ee28-4b58-9822-78f59fe3d173%40googlegroups.com.
