On Mon, Jun 8, 2020 at 10:33 PM smitra <smi...@zonnet.nl> wrote: > On 08-06-2020 13:01, Bruce Kellett wrote: > > On Mon, Jun 8, 2020 at 7:09 PM smitra <smi...@zonnet.nl> wrote: > > > >> On 07-06-2020 01:16, Bruce Kellett wrote: > >> > >>> Applying the idea of quantum fluctuations to the inflaton field is > >> a mistake, since inflation is based on a classical field. And you do > >> not quantize a classical field by adding "quantum fluctuations". > >> > >> It's an approximate way to do computations that can be justified > >> rigorously, see e.g. these lecture notes: > >> > >> https://www.nikhef.nl/~mpostma/inflation.pdf > >> > >> section 3 on page 15 and further. > > > > If that is your idea of a rigorous justification.............my mind > > boggles. > > It seems to rely on the old failed heuristic of "vacuum fluctuations" > > as particle-antiparicle pairs: "The quantum vacuum is never empty, > > particle and anti-particle pairs constantly pop out of the vacuum and > > annihilate again. During inflation, due to the enormous expansion, the > > particle and antiparticle are ripped apart, and they may get separated > > by a distance larger than the causal horizon H−1, and cannot find > > each other again to annihilate. They remain as perturbations on the > > background." > > > > This is nonsense, since there are no such particle-antiprticle pairs > > continuously formed in the vacuum state -- the vacuum does not > > fluctuate. > > You are confusing the nontechnical introduction for the rigorous content > that comes later. >
Where later? The only justification offered for the addition of a random "fluctuation" field to the classical background inflaton field is the hand-waving heuristics of the introduction. Sure, he is reasonably rigorous in his quantization of this added "fluctuation" field, but that does not justify it in the first place. >>>> It is this phenomena what Jason referred to. In the > >>>> scientific papers on inflation they may go about computing the > >>>> effects > >>>> of the fluctuations in a semi-classical way by putting in the > >>>> fluctuations by hand in classical equations of motion, but there > >>>> is a solid theoretical basis for such an approach. > >>> > >>> No, there is not. It is entirely ad hoc. The problem stems from > >>> the fact that the scalar inflaton field has the dimensions of energy, > >>> so, because energy is strictly conserved, the field value cannot > >>> fluctuate. > >>> > >> > >> It's not ad hoc, it's all explained here: > >> > >> https://www.nikhef.nl/~mpostma/inflation.pdf > > > > That article is a reasonably comprehensive account of the standard > > notions of inflation -- but it still relies on failed heuristics and > > ad hoc notions. Nothing rigourous here. > > > > Closed virtual particle loops in the vacuum are a well-known > > phenomenon in perturbation approaches to QFT, but because of energy > > conservation, these loops are strictly of zero energy-momentum. Since > > they are not coupled to anything, so they do not affect any measurable > > physics. At most they add an overall undetectable phase to the wave > > function. > > > > They do proceed in a heuristic way, but this is not unjustified. Your > arguments against it based on energy conservation are not valid. Oh! Where do my arguments based on energy conservation fail? And if > it were as simple as that then no one in that field who are all big > experts in QFT would write articles saying that quantum fluctuations are > a source of the density fluctuations. That is just an argument from authority -- which justifies nothing. After all, there was a time when all the authorities thought that the stars were attached to a crystalline "celestial sphere", and that the earth was the centre of the universe (and flat!). The energy density of a field does > have a variance just like the field strength itself has, and this then > does couple to gravity. > In quantum mechanics, all that can have variances are superpositions of eigenstates. Conservation laws forbid variations of energy (or other conserved quantities) in eigenstates. The vacuum is, by definition, an energy eigenstate (the lowest possible energy state), so its energy cannot fluctuate, and does not have a variance. Similarly for a simple harmonic oscillator, and the SHO is a model for the modes (energy eigenstates) that make up a general quantum field. The vacuum energy from zero point energies of quantum fields does not couple to gravity -- that is the 120 orders of magnitude mistake about the origin of the cosmological constant. The non-connected vacuum loops of perturbation theory are all of strictly zero energy, and they do not cou[ple to gravity. If they did, they would no longer be non-connected, and would merely form standard radiative corrections to propagators or vertex functions. Bruce -- 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/CAFxXSLTxx7epnHX6f_b99mKEmTuiqnYTugvTByx%2BNQrmEybhsQ%40mail.gmail.com.
