Time-energy uncertainty constraints on non-energy measurements
Lou Pagnucco
The Time-Energy uncertainty principle imposes a constraint on the
time required to measure the energy observable - i.e., if a
system has a discrete energy spectrum with a minimal spacing of
(delta E) between levels, then the time required to measure the
energy eigenvalue is on the order of 1/(delta E).
How does this uncertainty principle affect other non-energy
observables?
Consider an observable "OBS" derived by infinitesimally
perturbing the energy observable.
Could OBS ever require (infinitesimally) less time to measure
than energy does?
Thanks,
L. Pagnucco
John Baez
Lou Pagnucco <pagn...@htdconnect.com> wrote:
>The Time-Energy uncertainty principle imposes a constraint on the
>time required to measure the energy observable - i.e., if a
>system has a discrete energy spectrum with a minimal spacing of
>(delta E) between levels, then the time required to measure the
>energy eigenvalue is on the order of 1/(delta E).
If you like thinking about this, you might enjoy
http://math.ucr.edu/home/baez/uncertainty.html
>How does this uncertainty principle affect other non-energy
>observables?
>
>Consider an observable "OBS" derived by infinitesimally
>perturbing the energy observable.
>
>Could OBS ever require (infinitesimally) less time to measure
>than energy does?
Sure. For an annoyingly trivial example, consider the
observable .99E. If you're trying to measure this to a
specific accuracy, it takes only 99% as long as measuring
the energy to that accuracy. Here of course by a "specific
accuracy" I mean up to a certain number of joules.
Wasn't that annoying? There are lots of other small perturbations
of the energy observable with the same property, but this is the
the simplest one.
Arkadiusz Jadczyk
>The Time-Energy uncertainty principle imposes a constraint on the
>time required to measure the energy observable - i.e., if a
>system has a discrete energy spectrum with a minimal spacing of
>(delta E) between levels, then the time required to measure the
>energy eigenvalue is on the order of 1/(delta E).
I think that it is rather important to distinguish between "uncertainty
relation" as a mathematical formula and its physical interpretation.
While the mathematical derivation of a formula is usually correct
(not so though as regards the famous Wigner paper "On the time-energy
uncertainty relation" - see the discussion in
http://xxx.lanl.gov/abs/quant-ph/9702019
),
its physical interpretation, its phrasing, is usually biased by the
philosophical view of the author of the given text. I wouldn't rely on
these interpretation too much - if you follow the discussion in the
literature you will see that almost every statement has been challenged
by some other author.
Please note that the term "to mesure" is not even defined in quantum
theory - at least in the opinion of John Bell (see his paper "Against
Measurement).
Therefore I would advise to be very careful when reading on
the subject you are asking about.
ark
--
Arkadiusz Jadczyk
http://www.cassiopaea.org/quantum_future/homepage.htm
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