On Monday, August 26, 2019 at 5:14:08 AM UTC-6, Lawrence Crowell wrote: > > On Sunday, August 25, 2019 at 9:38:51 PM UTC-5, Alan Grayson wrote: >> >> >> >> On Friday, August 23, 2019 at 8:12:55 PM UTC-6, Lawrence Crowell wrote: >>> >>> On Friday, August 23, 2019 at 9:01:42 PM UTC-5, Alan Grayson wrote: >>>> >>>> >>>> >>>> On Friday, August 23, 2019 at 7:48:19 PM UTC-6, Lawrence Crowell wrote: >>>>> >>>>> On Friday, August 23, 2019 at 5:48:13 PM UTC-5, Alan Grayson wrote: >>>>>> >>>>>> >>>>>> >>>>>> On Friday, August 23, 2019 at 3:31:36 PM UTC-6, Lawrence Crowell >>>>>> wrote: >>>>>>> >>>>>>> On Thursday, August 22, 2019 at 12:37:40 AM UTC-5, Alan Grayson >>>>>>> wrote: >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> On Wednesday, August 21, 2019 at 7:12:14 PM UTC-6, Alan Grayson >>>>>>>> wrote: >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> On Wednesday, August 21, 2019 at 3:13:11 PM UTC-6, Lawrence >>>>>>>>> Crowell wrote: >>>>>>>>>> >>>>>>>>>> On Tuesday, August 20, 2019 at 4:56:23 PM UTC-5, Alan Grayson >>>>>>>>>> wrote: >>>>>>>>>>> >>>>>>>>>>> https://en.wikipedia.org/wiki/Conformal_cyclic_cosmology >>>>>>>>>>> >>>>>>>>>>> Is this a viable theory for avoiding a BB interpreted as a >>>>>>>>>>> singularity? AG >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> Penrose proposed a conformal identification of spatial infinity >>>>>>>>>> in the past and future i^±∞ of FLRW spacetimes. A cosmology expands >>>>>>>>>> and in >>>>>>>>>> the limit time → ∞ it transitions into a new cosmology. The de >>>>>>>>>> Sitter >>>>>>>>>> vacuum is not eternally stable, so the idea may have some germ of >>>>>>>>>> relevancy. I am not sure about how this would work with vacuum to >>>>>>>>>> vacuum >>>>>>>>>> transitions. The exponential expansion of the universe is a sort of >>>>>>>>>> time >>>>>>>>>> dependent conformal transformation with a small vacuum expectation >>>>>>>>>> for the >>>>>>>>>> scale field. To transition to a new cosmology, say with inflationary >>>>>>>>>> expansion, this means the vacuum expectation is increased. >>>>>>>>>> >>>>>>>>>> The overall physics community response to this has been tepid at >>>>>>>>>> best. There are some possible conflicts with observed data. >>>>>>>>>> >>>>>>>>>> LC >>>>>>>>>> >>>>>>>>> >>>>>>>>> FWIW, ISTM that what GR might be indicating about the BB, is that, >>>>>>>>> insofar as it's a singularity, it couldn't have occurred, and didn't >>>>>>>>> occur. This is to say the universe didn't become infinitely small in >>>>>>>>> spatial extent, like a mathematical point, but rather that there was >>>>>>>>> a >>>>>>>>> maximal finite value of its energy density, hugely high but not >>>>>>>>> infinite. >>>>>>>>> For this reason I find the cyclic models promising, although, as you >>>>>>>>> rightly indicate, they're far from complete or bug-free. AG >>>>>>>>> >>>>>>>> >>>>>>>> Which brings up a possibly relevant question: If the total energy >>>>>>>> of the universe occupied zero spatial volume (the presumed condition >>>>>>>> of the >>>>>>>> universe at t=o according to the BB theory), wouldn't that contradict >>>>>>>> the >>>>>>>> Uncertainty Principle? AG >>>>>>>> >>>>>>> >>>>>>> The total mass-energy content of the universe is zero. >>>>>>> >>>>>>> LC >>>>>>> >>>>>> >>>>>> Is that a provable fact, or something that can be measured? TIA, AG >>>>>> >>>>> >>>>> It is provable, because in general spacetimes there does not exist a >>>>> Gaussian surface to define mass. This sets the energy to zero. Think of >>>>> it >>>>> as meaning gravitational potential energy as negative is equal in >>>>> magnitude >>>>> to positive mass-energy. >>>>> >>>>> LC >>>>> >>>> >>>> If, using E=mc^2, one computes the rest energy of the material Earth, >>>> it seems implausible that this equals the negative potential energy of the >>>> Earth's gravitational field, to yield a net energy sum of zero. AG >>>> >>> >>> Consider the gravitation with expansion and cosmological constant. This >>> was first pointed out by Tolman many decades ago. >>> >>> LC >>> >> >> If you're referring to the conjecture or alleged "fact" that the net >> energy of the Cosmos is zero, that concept, whatever its status, arose long >> before cosmologists became convinced in the existence of dark energy, which >> is thought to account for 73% of all energy in the Cosmos. Assuming dark >> energy exists, how does this fit in with the conjecture or alleged "fact" >> that the net energy of the Cosmic is exactly zero? AG >> > > The gravitational potential energy content from dark energy or a vacuum > energy is V = -8πGρ/3c^2. This is a negative content. To really get into > this means I have to write a fair amount on general relativity, but frankly > I am very busy right now. I have a paper accepted for publication on the > condition of rewriting some parts, though the meat of this was given > approval. I have quite a bit scheduled over the next week. > > LC >
I understand. Thanks for your time. I am trying to get a PDF version of Tolman's monograph, so I can evaluate his argument that the net gravitational energy of the Cosmos is zero. It's quite remarkable if true, and I remain somewhat skeptical because, as I have previously indicated, gravitational potential energy doesn't seem well defined. 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/f7564674-c606-4a94-bad9-0dfa981bf3cb%40googlegroups.com.
