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 otherthe 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
*And without that there wouldn't be any wavelengths (or virtual
particles) inside or outside those plates and the Casimir Effect
would not exist. *
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