On Monday, April 27, 2020 at 4:45:02 PM UTC-6, Brent wrote: > > > > On 4/26/2020 6:37 PM, Alan Grayson wrote: > > > > On Sunday, April 26, 2020 at 6:39:15 PM UTC-6, Brent wrote: >> >> >> >> On 4/26/2020 3:22 PM, Alan Grayson wrote: >> >> >> >> On Sunday, April 26, 2020 at 1:46:59 PM UTC-6, Brent wrote: >>> >>> >>> >>> On 4/26/2020 9:24 AM, Alan Grayson wrote: >>> >>> >>> >>> On Sunday, April 26, 2020 at 9:48:45 AM UTC-6, John Clark wrote: >>>> >>>> On Sat, Apr 25, 2020 at 12:49 PM Alan Grayson <[email protected]> >>>> wrote: >>>> >>>> *> How does QM tell us that conservation of energy can be violated for >>>>> brief durations? If you apply the time-energy form of the UP for your >>>>> proof, please state the context of your proof, that is, exactly what do E >>>>> and t stand for.* >>>> >>>> >>>> The shorter the time (t) a system is under observation the larger the >>>> amount of energy (E) could pop into existence from nothing without direct >>>> detection, enough energy to create virtual particles. And you can >>>> calculate >>>> how large the indirect effects these virtual particles would have on the >>>> system. >>>> >>> >>> As I understand the UP, it's a statistical statement about an ensemble >>> of observations, say for position and momentum of identical particles. It >>> says nothing about the result of events, say for the position and momentum >>> of a single particle or event. Doing some arithmetic to get the time-energy >>> form of the UP does not change this reality. As a result, your description >>> of what happens to a single particle, virtual or not, is not intelligible. >>> Please try again. AG >>> >>> >>> The UP doesn't apply to virtual particles because it refers to the >>> result of conjugate measurement (projection) operators. You can't measure >>> virtual particles. >>> >>> Brent >>> >> >> In its usual form, does the UP allow us to measure position and momentum >> *simultaneously*, or must we measure each variable independently (for an >> ensemble of identical particles, of course)? What is proper interpretation >> of the time/energy form of the principle in statistical terms? TIA, AG >> >> >> You can measure them simultaneously; but when you repeat the pair of >> measurements on many identically prepared particles you find that there is >> a scatter in the position and a scatter in the momentum such that the HUP >> is satisfied. >> >> Brent >> > > Can you give an example of the ensembles used in applying the time-energy > form of the UP? TIA, AG > > > https://arxiv.org/pdf/quant-ph/0511245.pdf >
This article seems to establish a lower bound on time, but nothing related to ensembles. I have no idea about the meaning of the terms in the time-energy form of the UP. AG > > > There's also an interesting discussion of how to measure time in QM. > Since time is not an operator you have to construct a clock which defines > the physical meaning of time. > http://www.god-does-not-play-dice.net/clock_peres.pdf > > 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 on the web visit https://groups.google.com/d/msgid/everything-list/a2b45bb4-a345-407f-8c4c-213f21891ed5%40googlegroups.com.
