On Fri, Jun 26, 2020 at 12:25 PM smitra <smi...@zonnet.nl> wrote: > On 26-06-2020 03:24, Bruce Kellett wrote: > > On Fri, Jun 26, 2020 at 9:31 AM smitra <smi...@zonnet.nl> wrote: > > > >> On 14-06-2020 01:30, Bruce Kellett wrote: > >>> > >>> There seems to be something wrong with this. QFT is equivalent to a > >>> picture in which there are independent SHOs at every point in space. > >> > >> This is false, the SHO are only independent in momentum space, not in > >> real space where they are coupled via the (nabla phi)^2 term which leads > >> to nontrivial spatial correlations. > > > > The (nabla phi)^2 term does not get you energy fluctuations. As I > > understand it, we imagine an independent SHO for each mode (k value, > > or energy) at every spacetime point. > > > For each mode separately, these > > oscillators are coupled, basically because a momentum eigenstate > > (single value of k, or single mode) is a plane wave over all space. > > But because the modes are not coupled to each other, there can be no > > fluctuations of energy. A real field value is a superposition of > > independent modes (independent degrees of freedom). > > That energy is not located, so you can end up with non-smooth energy > distribution. >
Plane waves have the same energy everywhere. The superpositions of modes that would be required to get a non-smooth energy distribution cannot arise spontaneously. >> Where else would the propagator of > >> the free field theory come from if is weren't for this term? > > > > The free-field propagator comes from the Green's function > > corresponding to the creation of a particle at one point and its > > annihilation at some other point. When one does a perturbation > > expansion of this Green's function (in terms of Feynman graphs, for > > instance), there are coupled terms, corresponding to the tree diagram > > plus corrections, and the so-called vacuum "fluctuations", which are > > the non-coupled diagrams to all orders. These non coupled diagrams are > > all of strictly zero net energy, and contribute at most an overall > > phase to the amplitude. In no circumstances does any of this give rise > > to conservation-violating "energy fluctuations". > > Total energy is conserved, that doesn't mean that there cannot be local > fluctuations. > This physics is local, with local energy conservation, so your statement is absurd. Show me the Feynman diagram that violates energy conservation! >>> If these are all in their lowest energy state, then the field is in > >>> its lowest energy state. Excitation of one or more of the oscillators > >>> corresponds to the presence of more energy (and particles). The higher > >>> energy configuration can be analysed in terms of the modes, which are > >>> the plane waves of determinate wavelength. If you start with a smooth > >>> field with all the oscillators in their ground state, this lowest > >>> energy configuration persists until some energy is added from > >>> somewhere. > >>> > >>> > >>> Consequently, the usual mythology about quantum fluctuations is not > >>> true. > >>> > >> > >> While it is true that reasoning based on uncertainty principle are not > >> rigorously correct, they are only used to illustrate the effect > >> qualitatively. > > > > The trouble is that such heuristics are generally the only motivation > > given for the introduction of "fluctuations" . One paper I saw > > recently went so far as to say that it involved the exchange of > > virtual photons, which could only travel as far as allowed by the UP > > limit on their lifetime. It is nonsense like this that should be > > stamped out. If there is a rigorous derivation of energy-violating > > "quantum fluctuations", then I have yet to see it -- such terms do not > > arise in the conventional perturbation approach to QFT. > > > >> The theory as published in the literature is based on > >> rigorous treatment based on standard QFT. > >> > >>>> So quantum fluctuations cannot cause spatial variations in the field. > >>>> > >>>> False, this doesn't follow from the above. Also it the opposite has > been > >>>> demonstrated in a massive body of literature on this subject to which > >>>> thousands of experts who are all extremely well versed in QFT have > >>>> contributed to. > >>> > >>> Can you point me to some recent key papers? > >> > >> See e.g. here: > >> > >> https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.251302 > > > > This does not give anything rigorous for the origin of fluctuations, > > it simply compares and contrasts two possibilities in the context of > > inflation. > > > > Bruce > > Recent articles will not publish a rigorous derivation, you need to read > the cited references and then perhaps the cited references in those > articles to get to the original articles that date back from the early > 1980s. In other words, you do not have any idea how to make this rigorous either. But the fact that there are two possibilities according to the > experts in the field, shows that your argument is wrong (because it is > elementary, if it were correct it would have been noted very early on in > the development of inflation theory and no one in that field would > invoke quantum fluctuations as a possible source of density > fluctuation). > Your naive faith in authority is touching -- I am a lot more sceptical. If energy density fluctuations can arise spontaneously, then show me how! 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/CAFxXSLTVdk0JKJyJrabWuibXzC7T8Oj-BEjn9oqJHggr%2Bj%2BEVw%40mail.gmail.com.
