On Mon, Jun 29, 2020 at 12:40 AM smitra <smi...@zonnet.nl> wrote: > On 28-06-2020 01:18, Bruce Kellett wrote: > > On Sat, Jun 27, 2020 at 11:19 AM 'Brent Meeker' via Everything List > > <everything-list@googlegroups.com> wrote: > >> > >> How about this one? > >> > >> https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.124.251302 > > > > The trouble is that this paper relies on the same fallacious > > assumptions as those that underlie most of this work. > > > > "The uncertainty principle in an expanding universe permits a -- > > minimal amount of -- violation of energy conservation, Delta-t ~ > > H^{-1}." > > This is a heuristic justification, the conclusions of the paper are not > based on this. >
I have to disagree. The analysis of quantum effects as one possibility for the origin of density fluctuations is central to the paper. And as they explicitly acknowledge, such quantum effects necessarily involve violations of energy conservation. Their explanation for such conservation violations in quantum mechanics is the application of the uncertainty principle, as outlined in the above quote. No other explanation is offered, and it is not suggested that the UP heuristic is anything other than the correct explanation. In fact, in all of the inflation papers I have looked at, if any explanation for the energy violations is offered at all, it always boils down to this misuse of the uncertainty principle. The fact that no other justification is ever offered or suggested indicates that these authors think that the UP argument is valid, and is all that is required. If you think that the UP argument is valid, then say so. If you agree that it is not valid, then what is your explanation for the violations of energy conservation that are clearly involved in the origin of fluctuations in a smooth background.? > As I have pointed out, this is false: the UP is an inequality, which, > > if it permitted ANY amount of energy non-conservation, would permit an > > arbitrary amount for arbitrarily long times, and the whole concept of > > conservation would collapse. And that is contrary to observation. The > > caption to Fig. 1 of the paper also points out that their argument > > relies on energy non-conservation in flat space. But space is locally > > flat, even during inflation, and GR ensures local energy conservation. > > The whole lot is a load of nonsense. > > > > Bruce > > > > Inflation starts out with a false vacuum which rapidly expands and then > decays into the real vacuum. But your arguments are based on a flawed > way of mixing quantum mechanics with classical reasoning. The inflation argument always involves adding quantum fluctuations to a smooth classical background field. > As I pointed > out earlier, but your reasoning the Green's function would be identical > zero. You then countered by saying that closed loops don't contribute to > the energy, but that's besides the point (and also irrelevant as this is > then the total energy not the local energy). The two point function in > the vacuum state is clearly not zero, while by your reasoning it is, > therefore your whole reasoning is flawed. > The two point function that is connected to external legs is the standard particle propagator, and this is subject to quantum perturbation corrections. If there are no external legs, the two-point functions do not necessarily vanish, but they are of zero net energy, and do not contribute to the observable physics. > Why not just compute the fluctuation is the local energy density for a > free field in the vacuum state <H(x) H(y)> - <H(x)>H(y) where H is the > Hamiltonian density? Then <H(x)> is independent of x, so we need to > evaluate <H(x) H(y)>, which by Wick's theorem reduces to products of > propagators. This is then not zero so, you do have fluctuations in the > local energy density. > In so far as this makes sense, you are just talking about the disconnected graphs that have no physical content. If you think that there is a term in the interaction Hamiltonian that violates energy conservation, then what is this term? If Hamiltonian evolution conserves energy, then there can be no such energy-conservation-violating term. It is not a matter of differences between local and total conservation: you cannot conserve the total energy of a system if local energy is not conserved. Again I ask, what are the non-conserving interactions in the Hamiltonian? Bruce > > Saibal > > > -- > 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 everything-list+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/1d64e7ebf274b2fdc6d46d86624dfc59%40zonnet.nl > . > -- 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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLSSR6jQ034rh%3DsyLA2tAhF4%3D_136n0Gp%2B_dtrvFrjdv7A%40mail.gmail.com.
