On Saturday, June 6, 2020, Bruce Kellett <bhkellet...@gmail.com> wrote:
> On Sat, Jun 6, 2020 at 11:54 PM smitra <smi...@zonnet.nl> wrote: > >> On 06-06-2020 01:07, Bruce Kellett wrote: >> > On Sat, Jun 6, 2020 at 3:11 AM smitra <smi...@zonnet.nl> 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. Jason > > > >> 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. > > 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/CAFxXSLSj_aLCpD-m9iu71hXoJVoWWb9aEXBOnfa83B78o > ZkTEQ%40mail.gmail.com > <https://groups.google.com/d/msgid/everything-list/CAFxXSLSj_aLCpD-m9iu71hXoJVoWWb9aEXBOnfa83B78oZkTEQ%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > -- 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/CA%2BBCJUjJc8TR0K-K0DcdBygmMT9nmjJSd4dc_YcbCDsgpJHPug%40mail.gmail.com.
