On Monday, April 27, 2020 at 6:47:39 PM UTC-6, Alan Grayson wrote: > > > > 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 >> > Since the "uncertainty" in the UP is a statistical entity with a well-defined definition, aka "the standard deviation", how large must the sample size be, to calculate it? TIA, AG
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