On 15-04-2020 04:20, Alan Grayson wrote:
On Tuesday, April 14, 2020 at 4:28:23 PM UTC-6, Bruce wrote:
On Wed, Apr 15, 2020 at 2:07 AM Jason Resch <jason...@gmail.com>
wrote:
There has been controversy [1] in the meaning/interpretation of
the Time-Energy uncertainty relation in quantum mechanics, but
relatively none regarding the meaning of the position-momentum
uncertainty.
However, can these not be viewed equivalently in terms of a
4-dimensional space time?
For example, I have seen some describe mass/energy as momentum
through time. Massless particles don't age, and have no momentum
through time.
Similarly, cannot a point-in-time measurement be viewed as a
measurement of position in the time dimension?
In my view, you can go from the position-momentum uncertainty to
the time-energy uncertainty simply by flipping the time-space
orientation. Is this valid? Is there something I am missing?
You are missing the fact that energy is bounded below, whereas
momentum can take on any value between plus and minus infinity. Time
is not an operator in quantum mechanics.
Bruce
Isn't there a valid interpretation/ application of the time-energy
uncertainty relation in the context of emission of radiation? If so,
what is it? TIA, AG
The rigorous versions of these interpretations involve having some
physical object included in the system that serves as a clock. So, if
you actually perform a measurement involving time, then the measured
time is represented by a physical clock. So, by including a quantum
mechanical description of a simplified model clock, you then do get an
observable for the measured time, despite the fact that there is no
observable that allows you to measure the parameter t in the Schrodinger
equation.
Saibal
Jason
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[2].
Links:
------
[1] https://arxiv.org/pdf/quant-ph/0105049.pdf
[2]
https://groups.google.com/d/msgid/everything-list/369bbe29-2821-47a0-b269-7e43ef4b97ac%40googlegroups.com?utm_medium=email&utm_source=footer
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