Re: Casimir Effect and Time-Energy form of the Uncertainty Principle

[Brent Meeker]

On 5/18/2025 9:58 PM, Alan Grayson wrote:

On Sunday, May 18, 2025 at 4:16:26 PM UTC-6 Brent Meeker wrote:



    On 5/18/2025 10:02 AM, Alan Grayson wrote:

    On Tuesday, May 13, 2025 at 4:54:55 AM UTC-6 Alan Grayson wrote:

        On Monday, May 12, 2025 at 4:15:52 PM UTC-6 Brent Meeker wrote:



            On 5/12/2025 1:58 PM, Alan Grayson wrote:

            On Friday, May 9, 2025 at 10:40:42 PM UTC-6 Brent Meeker
            wrote:

                On 5/9/2025 7:08 PM, Alan Grayson wrote:

                *I can see that the measurement spreads due to
                instrument limitations are usually immensely larger
                than the much smaller spreads accounted for by the
                UP, but what causes these much smaller spreads? Is

this a quantum effect? AG*

                Yes.  Quantum evolution is unitary, i.e. the state
                vector just rotates in a complex Hilbert space so
                that probability is preserved.  Consequently the
                infinitesimal time translation operator is U=1+e6/6t
                or in common notation 1-i(e/h)H where H=ih6/6t and h
                is just conversion factor because we measure energy
                in different units than inverse time. It's not
                mathematics, but an empirical fact that h is a
                universal constant.

                Brent


            *If one wants to prepare a system in some momentum state
            to be measured, doesn't this imply a pre-measurement
            measurement, *

            Right, given that it's an ideal measurement. Most
            measurements don't leave the system in the eigenstate
            that is the measurement result.  An ideal measurement is
            one that leaves the system in the state that the
            measurement yielded.

            *and the observable to be measured remains in that state
            on subsequent measurements? *

            Only if they're ideal measurements of that same variable
            or of other variables that commute with it.

            *If so, how can the unitary operator, which just changes
            the state of the system's wf, create the quantum spread? *

            You don't need a change in the wf to "create the quantum
            spread".  Having prepared in an eigenstate of A just
            measure some other variable B that doesn't commute with
            A.  In general A will be a superposition of other
            variables, say A=xC+yD; that's just a change of
            coordinates. But the system is not in an eigenstate of C
            or D.

            Brent


        *Sorry, I really don't get it. Not at all! If we want to
        prepare a particle with some momentum p, why would we measure
        it with some non-commuting operator, and why would this, if
        done repeatedly, result in a spread of momentum? And what has
        this to do with a unitary operator which advances time? TY, AG *

    *
    *
    *Is the spread in momentum caused by an imprecision in preparing
    a particle in some particular momentum? Generally speaking, how
    is that done? TY, AG
    *

    *The HUP doesn't limit how precisely you can prepare a particle's
    momentum.  The HUP just says that the more precisely the momentum
    is determined the less precisely defined will be the conjugate
    position. *


*I know. What I don't know is the cause of the spread. AG*

*See attached.

Brent*

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