On Monday, April 20, 2020 at 5:00:50 AM UTC-6, Lawrence Crowell wrote:
>
> 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 vacuu
>
> LC
>
As I understand it, the vacuum energy is a residue of various fields we're
familiar with, such as the EM field. But how can the EM field contribute
anything to the vacuum energy in a region of empty space far away from
charged particles? Same for the nuclear and weak forces which are effective
over very short distances. AG
>
>
>
>
>>
>>>
>>>>
>>>>> 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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