Respect my religious belief in operators! On Friday, 2 May 2025 at 07:50:49 UTC+3 Alan Grayson wrote:
> 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 > > -- 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 visit https://groups.google.com/d/msgid/everything-list/6dd28771-2b0e-4c04-a501-074e169e4ba1n%40googlegroups.com.
