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. * *>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? 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? TY, 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 visit https://groups.google.com/d/msgid/everything-list/fb1df801-e5b4-47ee-b7c0-1c364a565ec3n%40googlegroups.com.
