On Saturday, May 9, 2020 at 5:49:07 AM UTC-6, Lawrence Crowell wrote: > > On Saturday, May 9, 2020 at 6:22:44 AM UTC-5, Alan Grayson wrote: >> >> >> >> 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 >>>> >>> *Sorry; I may have been confused about what you were claiming. I thought you claimed the total energy of the cosmos is zero, in which case the role of rest energy cannot be ignored. But apparently you just meant that kinetic energy and gravitational potential energy sum to zero, which is apriori plausible. 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 >> > > Tolman computed some of this early on, His old book Relativity, > Thermodynamics, and Cosmology. Oxford: Clarendon Press. 1934 is a source. > There is nothing about physical cosmology that says we will witness some > horrendous violation of energy conservation locally. It does tell us that > since GR is a local principle, based on local translations of vectors etc, > there is then no general symmetry rule for energy conservation. > > > >>>> >>>>> 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 >> > > That has nothing in particular to do with this. > *You're probably right. I was just inquiring why symmetry principles are so important. AG * > > LC > > >> 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/c20b1b81-c9d1-415b-a6e2-80ce021fa8b0%40googlegroups.com.
