On Thursday, May 1, 2025 at 10:17:19 PM UTC-6 Alan Grayson wrote:
On Thursday, May 1, 2025 at 8:42:45 PM UTC-6 Brent Meeker wrote:
On 5/1/2025 7:25 AM, Alan Grayson wrote:
On Wednesday, April 30, 2025 at 11:06:07 PM UTC-6 Brent Meeker wrote:
On 4/30/2025 5:54 PM, Alan Grayson wrote:
On Wednesday, April 30, 2025 at 2:41:43 PM UTC-6 Brent
Meeker wrote:
On 4/30/2025 4:29 AM, John Clark wrote:
On Tue, Apr 29, 2025 at 8:09 PM Brent
Meeker <[email protected]> wrote:
*>> If you place two macroscopic
conductive plates close to each other the Casimir Effect will
cause the two plates to attract each
other; this occurs regardless of if you make any
measurements or not. It happens because
there are fewer virtual particles between the two
plates than there are outside the plates. And virtual
particles exist because it's impossible
for the energy in the electromagnetic field to be exactly zero
for any arbitrary length of
time; **and the shorter the time the greater the deviation from zero
it's likely to be. JC*
*>That's why the qualification about measure like interactions. The two
conductive plates exclude longer wavelengths. *
*Yes.*
* > I don't recall that the effect depended on duration. *
*Heisenberg's uncertainty principle is not just about the relationship
between momentum and position, it also insists there is a similar
relationship between energy and time; the shorter amount of time the
greater the random variation from a zero value there is. *
In quantum mechanics *energy* and the *time per unit change of a variable*
are conjugate variables. So they satisfy an Heisenberg uncertainty
relation, often written $\Delta E \Delta t \geq \hbar$ . This is sloppy
though and not quite right. What is right is given any operator $A$ and the
Hamiltonian $H$ defining the time evolution of $A$, then $\Delta A \Delta H
\geq \frac{1}{2} \hbar [d<A>/dt]$ . In this case I don't see what is the
time per unit change in the expected value of the energy density between
the plates? The plates are assumed stationary.
Brent
In the time-energy form of the HUP, what is the role of time as an
operator? What does *time per unit change of a variable* mean? Which
variable is referenced? About virtual particles; aren't they elements of a
perturbation expansion and thus not to be considered real since those terms
violate conservation of energy? TY, AG
That's why I include the equations (although I see they didn't get
converted to display). It can be any variable whose change is encoded by
the Hamiltonian, A and H respectively in the equation. It doesn't have
anything to do with how you might solve the equations; which is where
perturbation expansions and virtual particles enter.
Brent
Can you give some examples of what A could be, and mustn't A be an
*operator,* not a variable, that commutes with H?
*Sorry, I meant that the operator A does NOT commute with H. AG *
Yes, A is an operator, but it doesn't commute with H. That would imply the
variable measured by A is constant in time. The time per unit change in
the expected value of the variable is the inverse of [d<A>/dt].
*What is d? Can you give one or two specific examples of A? I thought the
HUP is applicable only for non-computing operators. Am I mistaken? AG*
If your claim is correct, ISTM that Clark cannot apply the Time-Enegy form
of the HUP to make his claim about the Casmir Effect. Do you agree? AG
I don't know. I don't understand the proposed role of time.
*Same here, and more generally, so I find applying the time-energy form of
the HUP dubious at best, but this is how the Casmir Effect is presumably
established in quantum EM theory. If you recall, Bruce Kellet, an
excellent physicist IMO, claimed the **Casmir Effect can fully accounted
for classically. He also vehemently denied that virtual particles are real
due to energy considerations, given that virtual particles violate energy
conservation. AG*
It doesn't seem to have anything to do with conducting plates. Perhaps he
means the period of EM fields filling the gap between the plates. Those of
long period being excluded from between the plates would thereby remove
their repulsive pressure and leave an unbalanced compressive pressure.
*Hopefully, Clark can explain what he meant. AG*
Brent
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