On 07-06-2020 01:16, Bruce Kellett 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
[1]." (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.
Yes, I agree with this.
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.
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.
There are fluctuations in the local energy density, and there is also
nontrivial correlation between the local energy density at two different
points. But I was wrong about the average of the filed vanishing. While
that's generally true, i case of the inflaton, a local fluctuation in
the field average is going to be stretched out so much that the entire
region inside the horizon gets a nonzero value for the field.
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.
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
Saibal
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