On 13-06-2020 02:57, Bruce Kellett wrote:
On Sat, Jun 13, 2020 at 2:05 AM smitra <smi...@zonnet.nl> wrote:
On 12-06-2020 06:33, Bruce Kellett wrote:
On Fri, Jun 12, 2020 at 2:08 PM smitra <smi...@zonnet.nl> wrote:
Indeed, it doesn't have the same value everywhere. And that makes
the original point you were arguing wrong.
No, all I was arguing twas that the time value at any point does not
change arbitrarily -- it does not fluctuate. There is no requirement
for the value to be the same at every point. But that does not violate
energy conservation -- it just started out that way.
The mere fact that the Casimir force exists proves you wrong. It
doesn't
matter that the naive method to compute this doesn't always work.
Get a grip, Saibal. Are you really claiming that local
energy-momentum
conservation is false?
I never said that it it false.
You implied that energy was not conserved when you related density
fluctuations in the inflaton field to quantum fluctuations.
Fluctuations are variations with time. Spatial variation is distinct.
I never said that.
My point is that your arguments are
totally flawed. You stated that a free field theory is analogous to
a
set of independent harmonic oscillators in real space, which is
nonsense
as they are coupled via the (nabla phi)^2 term, it's only in k-space
that you have independent oscillators.
Momentum space and position space are related by a Fourier transform.
Are you claiming that a Fourier transform violates the conservation
laws?
By taking the Fourier transform to decouple the osscilators, you are no
longer considering the local energy. Your argument was that because a
free field theory is basically the same as a collection of
noninteracting SHOs, the fact that energy is conserved means that there
cannot be local fluctuations. But each such independent SHO in k-space
isn't localized in real space. In real space the oscillators are coupled
by the (nabla phi)^2 term and local energy momentum conservation does
invilve a transfer of energy and momentum from one oscillator to
another.
QFT is strictly local. Micro-causality, implemented by the fact that
field commutators vanish for space-like separations, enforces
locality.
True
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.
Then you argued that it's really
the time derivative square term that's the most important in case of
inflation, but that's only because of the rapid expansion of the
universe causing the field to become homogeneous and gain an nonzero
expectation value over regions larger than the horizon, which the
allows
one to treat the filed as musical and the fluctuations in there
using
QFT. But you then pretend that all the scientists in that field are
wrong for treating the field classical and only treating the
fluctuations quantum mechanically, which is in principle if the
proper
conditions are met, a rigorous approximation method.
There is no need to misrepresent what I have said. I have no problem
with treating the background as a classical field, and quantizing only
the variations from uniformity. That works, and is not a conceptual
problem. The issue has always been the justification for the gaussian
random field superposed on the classical background in terms of
quantum fluctuations. Variations from a uniform density everywhere
require different changes in energy at different locations. Quantum
effects cannot do this, because quantum effects cannot change the
energy anywhere -- energy and momentum are locally and strictly
conserved in QFT. The random gaussian variations in energy density
must be part of the boundary conditions -- they do not have a quantum
origin.
There is a large amount of literature on this subject which you simply
ignore. They are mostly given in the references of the articles
published recently. The fact that you don't see it is not a good
argument that the entire literature on this subject is wrong.
Now, the Casimir effect, whether or not you consider it as van der
Waals force or something else, makes it clear that the total energy
content inside an isolated box made of conducting plates in which we
put
a conducting plane, depends on way the plate partitions the volume
of
the box. This follows from the fat that the total energy inside the
box
is conserved and that there exists a Casimir force between
conducting
plates. How you do the calculations, whether or not you attribute
the
force to a van der Waals force etc. doesn't matter here.
The Casimir force in the plate is then different from that of two
infinite plates, but there will in general be some Casimir force.
Moving
the plate all the way until it merges with a boundary plate the box
is
made out of will thus change the total energy contained in the box.
So what? If you move the plate against the Casimir force you must do
work on the plate. This naturally changes the energy -- the box is not
a closed system in that case.
Bruce
It simply demonstrates that the two states of the box with the plate in
different positions have different energy contents.
Saibal
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