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 <agrays...@gmail.com>
>>>>>>>>>> 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
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