On Sun, Jun 7, 2020 at 12:39 AM Bruce Kellett <[email protected]> wrote:
> On Sun, Jun 7, 2020 at 3:13 PM Jason Resch <[email protected]> wrote: > >> On Saturday, June 6, 2020, Bruce Kellett <[email protected]> wrote: >> >>> On Sat, Jun 6, 2020 at 11:54 PM smitra <[email protected]> wrote: >>> >>>> On 06-06-2020 01:07, Bruce Kellett wrote: >>>> > On Sat, Jun 6, 2020 at 3:11 AM smitra <[email protected]> wrote: >>>> >>>> >> These fluctuations at zero temperature are what we call "quantum >>>> >> fluctuations" >>>> >> in physics. >>>> > >>>> > I think you are confusing the zero point energy of quantum fields with >>>> > "quantum fluctuations". The zero point energy, whatever it might be, >>>> > does not "fluctuate". "Fluctuate means change with time, and the zero >>>> > point energy is just a value, and it does not change with time -- it >>>> > does not "fluctuate". >>>> >>>> The ground state energy does not fluctuate, but other observables such >>>> as the field strengths obviously do in the sense of having a variance. >>>> The energy is quadratic in the field and this has nonzero expectation >>>> value, while the expectation value of the field will usually be zero. >>>> So, one can say that the zero point energy represents the quantum >>>> fluctuations of the field, because it is the variance of the field. >>>> While one can argue about the word "fluctuation" used here, what >>>> matters >>>> is that the field strength will take on random values when measured in >>>> the ground state. >>> >>> >>> >>> OK, so nothing actually "fluctuates": it is just that measurement gives >>> random values. That is what the standard deviation or variance is actually >>> about -- the statistical scatter over repeated measurements of similar >>> systems. >>> >>> I think a lot of confusion arises from statements such as this in >>> Wikipedia: "quantum systems constantly fluctuate in their lowest energy >>> state as described by the Heisenberg uncertainty principle >>> <https://en.wikipedia.org/wiki/Heisenberg_uncertainty_principle>." >>> (Wiki article on zero point energy.) This is false, because the HUP >>> again refers to results from repeated measurements, not intrinsic variation >>> in the state. >>> >>> 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". Jason was >>> claiming that quantum fluctuations in the energy of the inflaton field >>> caused variation in the time of exit from inflation, and this led to the >>> density perturbations. Such a model is incorrect. To get density >>> variations, you have to have variations in energy density. And these cannot >>> be "quantum fluctuations", because energy is conserved in all quantum >>> interactions -- given a state of a particular energy, that energy does not >>> fluctuate. Variation between different measurements can arise only if the >>> original state is a superposition of components of different basic energy, >>> and that state is then repeatedly measured. That does not happen in >>> inflation. >>> >> >> When you look up at the sky you are indirectly performing a measurement >> of the inflaton field's energy in different parts of the early universe. >> > > > That is the mythology that remains to be explained. Energy conservation > forbids fluctuations in the energy density of the inflaton field. > > Uncertainty implies you can't know the energy density exactly, does it not? Accordingly, wouldn't measurements of it at different places and times yield differing results? Jason -- 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/CA%2BBCJUh%2By6ipTw0gH_Yy_02Y8Sx9UffLUBauC59zXvzKhCdKqg%40mail.gmail.com.
