On Sunday, June 17, 2018 at 2:05:58 AM UTC-5, Bruce wrote:
>
> From: Lawrence Crowell <[email protected] <javascript:>>
>
>
> On Friday, June 15, 2018 at 11:55:17 PM UTC-5, Brent wrote:
>>
>>
>> On 6/15/2018 6:46 AM, Lawrence Crowell wrote:
>>
>>
>> I might be wrong here, but my point is that energy occurs in discrete
>> eigenvalues and we never measure energy in between. With spin for instance
>> it occurs in any direction and is determined by the orientation of a
>> magnetic field I set. I do not tune some variable to get the energy
>> spectrum of an atom. There is something odd about energy in both quantum
>> mechanics and relativity.
>>
>>
>> But the energy of photons is a continuum.
>>
>> Brent
>>
>
>
> I am not sure that changes the argument. Photons are often emitted by
> systems with discrete energy levels or resonance scattering peaks.
>
>
> Of course it makes a difference! I am amazed at the depth of the confusion
> that seems to surround something as fundamental as einselection of a
> preferred basis.
>
> The fact that energy spectra of atoms and the like are discrete does not
> change the fact that energy eigenvalues are a continuous set of delta
> functions on the real line. And generally, when one is measuring atomic
> spectra one determines energies by the deviation occasioned by a prism or
> diffraction grating. In other words, one actually measures a position on a
> screen, or a wavelength, which is also a position measurement.
>
> Bruce
>
You are in a way saying what I am saying. The energy eigenvalue is peaked
on the real number line. We do not have a time basis in QM; there is no
time operator. We have a Heisenberg uncertainty with respect to energy and
time, ΔEΔt ≥ ħ, but we do not have a case where we can put the basis of a
system into a mixed |E> + e^{iφ}|t> basis because there is no |t> basis at
all.
The connection observables have to position and momentum was one motivation
for the Wigner quasiprobability distribution. The measurement of a system
can involve the operator V = κpq that will squeeze the vacuum into the
position representation. The Wigner function results in squeezed coherent
states in a similar fashion.
LC
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