On Monday, April 20, 2020 at 2:30:53 AM UTC-5, Alan Grayson wrote:
>
>
>
> On Sunday, April 19, 2020 at 7:23:00 PM UTC-6, Lawrence Crowell wrote:
>>
>> On Sunday, April 19, 2020 at 4:50:52 PM UTC-5, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Sunday, April 19, 2020 at 2:37:28 PM UTC-6, Lawrence Crowell wrote:
>>>>
>>>> Sure the Casimir effect involves QED. The virtual photons are in a
>>>> sense a set of gauge redundancies that can be removed, though one need the
>>>> moduli from these redundancies. This still defines a form of quantum
>>>> topological number.
>>>>
>>>> LC
>>>>
>>>
>>> You refer to QED, but aren't wan der Waal forces non quantum? AG
>>>
>>
>> Van der Waal force is just a dipole-dipole interaction, such as what
>> happens with water on the fluid surface. This can well enough be quantized.
>>
>> LC
>>
>
> But if you can explain Van der Waal forces without QED, why would you
> invoke it? I mean, if it's not necessary, and there's no need to invoke it,
> doesn't that put the EM vacuum energy on a dubious basis? AG
>
You are missing the big picture. The pointing to Van der Waal forces is
just a way of saying this is a boundary effect. However, the VdW force is
quantized to look at molecules on liquid and material surfaces. The dipole
for is 1/r^3 in it property, and the dipole-dipole interaction is then
1/r^6 and is then fairly weak.
The issue is with a bundle construction
H^1(A) → H^1(A/G) ─d→ H^2(A)
which is a short exact sequence on the space of connections A. This is a
form of deRham cohomology. The first map is from the connections to its
moduli or moduli space. This is then mapped by the differential operator to
the second cohomology ring over the fields, which in QED would be the
electric and magnetic fields. The A/G means connections modulo
diffeomorphisms or gauge changes.
Now this middle cohomology ring has another map as H^0(ψ) ─d→ H^1(ψ), with
the ψ a state, really I should have a state space, that connects to the
gauge potential as ψ → ψe^{-i∮A∙dx} under a gauge induced phase change,
such as the Aharanov-Bohm effect. The map in effect removes this phase
term, just as in the diagram above we have modulo-diffeomorphisms. This is
a map from a Hilbert space ℋ to a projective Hilbert space ℋ → Pℋ. which
defines the Fubini-Study metric.
This can be taken to more general geometries, which in a short post such as
this I do not have time to go into. These involve entanglements, and
entanglements are invariant under gauge transformations or unitary
transformations of states.
We can remove the whole business of virtual particles, and really Feynman
diagrams in general. These are nice cartoons that have helped up think
about things, but in many ways, they are just representations of
redundancies that are not that necessary. The BCFW method comes close to
removing some of these redundancies. We can see a part of this with Feynman
diagrams, for a virtual loop is an entangled pair of particles that just
happen to “exist” off-shell. We can remove the idea of virtual particles
and replace this with the topology and geometry of entanglement. This is a
part of why I think entanglement and gauge symmetries exist in a dualism or
complementarity.
Now let us get back to more brass-tacks physics. If you have two parallel
plates and the Casimir force pushes them together, the force in a
displacement FΔx = ΔW, or work. The elementary work-energy theorem of
mechanics tells us that work is kinetic energy. This then clearly means
there is a difference in potential energy between the plates relative to
outside. So we can call this what we want, but clearly there is an energy
associated with empty space or the vacuum.
LC
>
>>
>>>
>>>> On Sunday, April 19, 2020 at 11:30:51 AM UTC-5, Alan Grayson wrote:
>>>>>
>>>>>
>>>>>
>>>>> On Sunday, April 19, 2020 at 9:11:46 AM UTC-6, Lawrence Crowell wrote:
>>>>>>
>>>>>> The only thing that is measured is a difference in energy, and the
>>>>>> modes between two parallel plates are different from those outside. So
>>>>>> the
>>>>>> difference in energy results in this slight pressure.
>>>>>>
>>>>>> LC
>>>>>>
>>>>>
>>>>> From Wiki, below. Apparently there's an interpretation of the Casimir
>>>>> effect which doesn't depend on vacuum energy, which, as I recall, is
>>>>> Bruce's position on this issue. If no vacuum energy, then the claim that
>>>>> photons and other elementary particles arose from the vacuum in the very
>>>>> early universe is on dubious grounds. AG
>>>>>
>>>>> Relativistic van der Waals force[edit
>>>>> <https://en.wikipedia.org/w/index.php?title=Casimir_effect&action=edit§ion=5>
>>>>> ]
>>>>>
>>>>> Alternatively, a 2005 paper by Robert Jaffe
>>>>> <https://en.wikipedia.org/wiki/Robert_Jaffe> of MIT states that
>>>>> "Casimir effects can be formulated and Casimir forces can be computed
>>>>> without reference to zero-point energies. They are relativistic, quantum
>>>>> forces between charges and currents. The Casimir force (per unit area)
>>>>> between parallel plates vanishes as alpha, the fine structure constant,
>>>>> goes to zero, and the standard result, which appears to be independent of
>>>>> alpha, corresponds to the alpha approaching infinity limit," and that
>>>>> "The
>>>>> Casimir force is simply the (relativistic, retarded
>>>>> <https://en.wikipedia.org/wiki/Retarded_potential>) van der Waals
>>>>> force between the metal plates."[17]
>>>>> <https://en.wikipedia.org/wiki/Casimir_effect#cite_note-17> Casimir
>>>>> and Polder's original paper used this method to derive the Casimir-Polder
>>>>> force. In 1978, Schwinger, DeRadd, and Milton published a similar
>>>>> derivation for the Casimir Effect between two parallel plates.[18]
>>>>> <https://en.wikipedia.org/wiki/Casimir_effect#cite_note-18> In fact,
>>>>> the description in terms of van der Waals forces is the only correct
>>>>> description from the fundamental microscopic perspective,[19]
>>>>> <https://en.wikipedia.org/wiki/Casimir_effect#cite_note-19>[20]
>>>>> <https://en.wikipedia.org/wiki/Casimir_effect#cite_note-20> while
>>>>> other descriptions of Casimir force are merely effective macroscopic
>>>>> descriptions.
>>>>>
>>>>>>
>>>>>> On Saturday, April 18, 2020 at 10:40:45 PM UTC-5, Alan Grayson wrote:
>>>>>>>
>>>>>>> Does the Casimir effect establish that the vacuum has intrinsic
>>>>>>> energy, and if so, what is its form? TIA, AG
>>>>>>>
>>>>>>
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