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
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
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