On Tuesday, April 21, 2020 at 6:05:36 AM UTC-6, Lawrence Crowell wrote:
>
> On Tuesday, April 21, 2020 at 3:42:16 AM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> 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'
>>
>
> There is energy in the vacuum for the same reason an EM wave far removed
> from charges have energy.
>
> A harmonic oscillator that is not vibrating classically will by the
> Heisenberg uncertainty principle have an uncertainty in position, think of
> a mass on a spring or a pendulum, which means by the potential V = ½kx^2
> where with the Heisenberg uncertainty principle ΔxΔp ≥ ħ/2 there is an
> energy of uncertainty V(Δx) = ΔV = ½k(Δx)^2. There is a kinetic energy part
> K = p^2/2 and we have a spread in that as well with momentum uncertainty.
> This gives a complete energy uncertainty ΔE.
>
> Now suppose you have to such oscillators with different spring
> coefficients k, or pendula with different lengths. We then couple these
> together with some means, say another spring, a single mass connected to
> two springs or as a pendulum suspected under another. There will then be
> some complicated motion. This interaction of two harmonic oscillator this
> way is analogous to the existence of different Fourier modes of the vacuum
> inside and outside the Casimir plates.
>
> LC
>
The latest research by planetary scientists shows that planets formed due
to, at first, electrostatic forces of attraction, not gravity. (Gravity
became dominant only when bodies became fairly large.) Could it be the
case that Casimir plates attract each other due to electrostatic forces and
not vacuum energy? Maybe this is what Bruce had in mind when he, IIRC,
rejected the apparently usual interpretation for the existence of vacuum
energy. But he doesn't seem interested in offering his opinion. Moreover,
and less important, is the fact that when assuming a vacuum, a true vacuum,
we are denying the existence of far away charges (which is my response to
your first paragraph above). TIA, 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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