Re: Position-Momentum vs. Time-Energy Uncertainty

[Alan Grayson]

On Wednesday, April 15, 2020 at 11:59:00 PM UTC-6, Brent wrote:
>
>
>
> 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  
>> >> 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
>

If time isn't an operator, why does this work? And I'm not sure how to 
interpret it physically. If one waits some time t, and measures in some 
interval t, t + delta t, do we get a spread of energies? And of what? TIA, 
AG

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Re: Position-Momentum vs. Time-Energy Uncertainty

[Bruce Kellett]

On Thu, Apr 16, 2020 at 3:59 PM 'Brent Meeker' via Everything List <
everything-list@googlegroups.com> wrote:

> On 4/15/2020 10:37 PM, Alan Grayson wrote:
>
>
> 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.
>


But that is applying a generalised UP to an ensemble of similar short-lived
particles. There is no significant uncertainty in the energy of each
particle, although it may be uncertain when it will decay.

Bruce

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Re: Position-Momentum vs. Time-Energy Uncertainty

['Brent Meeker' via Everything List]

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 
>> 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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Re: Position-Momentum vs. Time-Energy Uncertainty

[Alan Grayson]

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  
> >> 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

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Re: Position-Momentum vs. Time-Energy Uncertainty

[smitra]

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 
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:
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[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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Re: Position-Momentum vs. Time-Energy Uncertainty

[Lawrence Crowell]

On Tuesday, April 14, 2020 at 11:07:42 AM UTC-5, Jason wrote:
>
> There has been controversy  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?
>
> Jason
>

The Fourier transform of time and frequency would naively mean there is 
negative frequency, which by E = ħω, and if we restrict the angular 
frequency away from negative then the energy is positive. That is one 
departure. If we did have a time operator such as T = iħ∂/∂E it would mean 
that energy is a generator of time. There would then be time eigenstates 
|t> such that T|t> = t|t>. We can think then of the time eigenstate |t> = 
e^{it(E - E_0}/ħ} such that energy is a continuous generator. This forbids 
the existence of discrete bound states. 

As a result, we do not normally think of a time operator. This operator 
would then have some Schrödinger equation of the form

iħ∂ψ/∂E = Tψ

If we can’t have a continuous energy then we can’t have a continuous time 
either. The existence of a time operator then requires that it have a 
discrete measure and that time and energy be bounded away. Is there 
something of this form? Yes, it is called the Taub-NUT spacetime, but it is 
not the universe we observe. 

The Taub-NUT spacetime is analogous to a black hole, but where the horizon 
condition occurs with time rather than with radius. There is also only one 
horizon. So this time version the black hole has only one black hole, at 
least if we take the spacetime as a global condition. I attach an image of 
this spacetime below. The green region is a region that has chronology 
protected and no timelike curves. The yellow region has closed timelike 
curves. The green region has this cyclicity condition on time, and I wrote 
a short letter on how a limited sort of time operator exists for a discrete 
time that cycles around. One of the oddities is that what plays the role of 
mass is a dual to mass, called the NUT parameter μ. This is analogous to 
the magnetic monopole. It shares with the gravitation mass m = GM/c^2 the 
S-duality condition m

mμ = 2πħ

laid down by Montenen and Olive.
 

[image: Taub-NUT spacetime1.PNG]


This spacetime does not reflect our observable universe. However, as a 
local region that “bolts” a de Sitter spacetime to an anti-de Sitter 
spacetime it may have some applicability We exist in a spacetime that is at 
least approximately de Sitter, which has no closed timelike curves etc. The 
inflationary spacetime is dS as well. A dS and AdS may have some 
correspondence with a “bolt” between them that is a Taub-NUT spacetime. It 
this is so there may then be some topological charge corresponding to the 
NUT parameter μ. This of course will probably be more mercurial to find 
than the EM magnetic monopole, if it exists.

The nice thing is that in this setting there is ultimately an equivalency 
between momentum-position and energy-time conjugate variables. However, in 
our observable world, certainly on the vacuum of low energy or physical 
vacuum, the physics we observe is constrained away from any such 
equivalency.

LC

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Re: Position-Momentum vs. Time-Energy Uncertainty

[Alan Grayson]

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  > wrote:
>
>> There has been controversy  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 

>
>
>> Jason
>>
>  
>

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Re: Position-Momentum vs. Time-Energy Uncertainty

[Bruce Kellett]

On Wed, Apr 15, 2020 at 2:07 AM Jason Resch  wrote:

> There has been controversy  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


> Jason
>

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