On Friday, April 24, 2020 at 12:24:38 AM UTC-6, Alan Grayson wrote: > > > > On Thursday, April 23, 2020 at 4:52:11 AM UTC-6, Lawrence Crowell wrote: >> >> On Wednesday, April 22, 2020 at 7:56:05 PM UTC-5, Alan Grayson wrote: >>> >>> >>> >>> On Wednesday, April 22, 2020 at 6:52:43 PM UTC-6, Lawrence Crowell wrote: >>>> >>>> On Wednesday, April 22, 2020 at 7:48:41 PM UTC-5, Alan Grayson wrote: >>>>> >>>>> >>>>> >>>>> On Wednesday, April 22, 2020 at 6:43:22 PM UTC-6, Alan Grayson wrote: >>>>>> >>>>>> >>>>>> >>>>>> On Wednesday, April 22, 2020 at 6:09:43 PM UTC-6, Lawrence Crowell >>>>>> wrote: >>>>>>> >>>>>>> On Wednesday, April 22, 2020 at 3:48:24 PM UTC-5, Alan Grayson wrote: >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> On Wednesday, April 22, 2020 at 2:39:45 PM UTC-6, Alan Grayson >>>>>>>> wrote: >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> On Wednesday, April 22, 2020 at 10:19:52 AM UTC-6, Lawrence >>>>>>>>> Crowell wrote: >>>>>>>>>> >>>>>>>>>> On Wednesday, April 22, 2020 at 8:21:30 AM UTC-5, Alan Grayson >>>>>>>>>> wrote: >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> On Wednesday, April 22, 2020 at 5:22:23 AM UTC-6, John Clark >>>>>>>>>>> wrote: >>>>>>>>>>>> >>>>>>>>>>>> On Wed, Apr 22, 2020 at 1:39 AM Alan Grayson < >>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>> >>>>>>>>>>>> > Could it be the case that Casimir plates attract each other >>>>>>>>>>>>> due to electrostatic forces and not vacuum energy? >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> Of course not! Don't you thing getting rid of electrostatic >>>>>>>>>>>> forces would be the very first thing any even halfway competent >>>>>>>>>>>> experimental scientists would think of before he even dreamed of >>>>>>>>>>>> performing >>>>>>>>>>>> such a super delicate experiment? >>>>>>>>>>>> >>>>>>>>>>>> John K Clark >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> Experiments done on the space shuttle and in Germany (where free >>>>>>>>>>> fall is simulated) have shown that dust particles accumulate due to >>>>>>>>>>> electrostatic forces, thus changing the model for how planets >>>>>>>>>>> formed. And >>>>>>>>>>> if you read the excerpt from the Wiki article I posted, MIT >>>>>>>>>>> physicists, in >>>>>>>>>>> 1997 IIRC, were able to explain the Casimir effect without >>>>>>>>>>> appealing to >>>>>>>>>>> vacuum energy. AG >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> If the two Casimir plates are grounded there will be no >>>>>>>>>> electrostatic potential between them. Elementary electricity. >>>>>>>>>> >>>>>>>>>> LC >>>>>>>>>> >>>>>>>>> >>>>>>>>> I'm not sure how the MIT physicist did the experiment. I just know >>>>>>>>> the claim; that he accounted for the forces on the plates without >>>>>>>>> need of >>>>>>>>> appealing to vacuum energy. I'll see if I can find the paper and post >>>>>>>>> it. >>>>>>>>> AG >>>>>>>>> >>>>>>>> >>>>>>>> Try this, by another physicist: >>>>>>>> Proof that Casimir force does not originate from vacuum energy >>>>>>>> https://arxiv.org/abs/1605.04143 AG >>>>>>>> >>>>>>> >>>>>>> There has to be something wrong. For one he says the EM Hamiltonian >>>>>>> commutes with the matter Hamiltonian, and so there is no interaction >>>>>>> between the EM field and matter. This would be the case if the matter >>>>>>> possesses no charges. There can be two Hamiltonians that commute with >>>>>>> each >>>>>>> other, and it is the case the two sectors are independent. However, >>>>>>> there >>>>>>> is the interaction H_i = ∫d^4x j*A that the two operators separately do >>>>>>> not >>>>>>> have involution with. This is where the interaction happens. So I have >>>>>>> suspicions about this claim. >>>>>>> >>>>>>> LC >>>>>>> >>>>>> >>>>>> Then try this: The Casimir Effect and the Quantum Vacuum >>>>>> https://arxiv.org/abs/hep-th/0503158 AG >>>>>> >>>>> >>>>> The above is authored by Robert L. Jaffe, another heavy dude! >>>>> https://web.mit.edu/physics/people/faculty/jaffe_robert.html AG >>>>> >>>> >>>> >>>> Jaffe is more in line. He is just demonstrating how one gets the >>>> Casimir effect even if one removes the vacuum with procedures such as >>>> normal ordering. >>>> >>>> LC >>>> >>> >>> Which suggests the vacuum energy has nothing to do with the Casimir >>> effect (if you get the same result by removing the vacuum!) AG >>> >> >> There is this procedure called normal ordering where raising operators >> a^† are pushed to the left and lowering a operators are pushed to the >> right. This by hand removes the [a,a^†] commutator responsible for the zero >> point energy. The harmonic oscillator Hamiltonian is H = ½(a^†a + aa^†} >> and to add and substract ½a^†a gives H = a^†a +½ [a,a^†]. Normal >> ordering removes that commutator term, which eliminates the zero point >> energy. This is alright because the ZPE does not interact with anything in >> this free field theory. >> >> The thing is this commutator by itself does not produce the Casimir >> effect anyway. It is the term H_i = *℘*∙*A* or in a relativistic setting >> ∫d^4x *j*∙*A* where we can start to see this physics. With the first >> term the *℘* is the dipole moment of an atom *℘* = *p*(σ_+ + σ_-), which >> in this reduce theory is two states toggled by the σ operators, and *A* >> = *A*_0(a^†e^{kx} - ae^{-kx}), Thus if there is a vacuum state, no >> photons, the interaction Hamiltonian has the operator terms from >> σ_-a^†e^{kx}, >> the rotating term, and σ_+a^†e^{kx} the counter rotating term apply. It >> is from here that we can get the interaction of the zero point modes with >> matter states. This does not though directly give Casimir effect. We have >> to go to a higher order quadupole interaction term *A*∙*Q*∙*A*. This >> will appear as a*Q*a^†, for the quadrupole moment operator Q ~ σ_+σ_-. >> With a vacuum the raising operator a^† makes |0> for photons into |1> an >> upper atomic state is lowered, but then raised again and the lowering >> photon operator a recovers the |0> state again. >> >> This term can be thought of as the virtual generation of a photon that >> winks in and out of existence with the atomic state lowering and raising >> back up. There are also counter rotating terms as well. The evaluation of >> this term <0| a*Q*a^† |0> is not zero. In a perturbation series there >> can be a product of *j*∙*A* terms which give rise to much the same >> physics. From a Feynman diagram perspective a single vertex, an electron >> transition with a photon, is built up to make the interaction of two >> electrons with a photon, and from there higher order terms are built up. >> >> LC >> > > I assume the charged particles in the plates somehow excite the quantized > EM field, to produce real photons, which produce the forces on the plates. > Where, in the math above, is this interaction taken into account? AG >
More specifically, in your model, is the excitation of the quantized EM field dependent on the use of virtual particles? AG > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/962d32ff-bba0-49c6-8d85-05ed30df6bd5%40googlegroups.com.
