On 4/15/2020 10:37 PM, Alan Grayson wrote:
On Wednesday, April 15, 2020 at 10:49:45 AM UTC-6, smitra wrote:
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 <[email protected]>
>> 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
Can you give a concrete example where the time-energy form of the UP
can be applied to? I once had an example, but can't recall what it
was. TIA, AG
It's used all the time in interpreting collision spectra in particle
physics. A sharp resonant line in the energy spectrum implies the
generation of a long live particle, while a broad line implies a short
lifetime.
Brent
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