| Topic: |
Science > Physics |
| User: |
"Neil" |
| Date: |
24 May 2005 01:35:30 PM |
| Object: |
Inferred energy paradox in QM |
Here's a correlation paradox about the required relationship between two
particles (more precisely, an emitter and a photon.) It is even more
challenging than entanglement, because it would probably have local
consequences and not just show correlated patterns of measurements.
Entangled particles typically begin as “twins” that correlate to each other
regardless of their progression away from their mutual origin. In a
celebrated example, measuring the polarization of one of two entangled
photons - however far apart - sets the necessary parameters for the other
photon. That case is intuitively strange, and challenges local realism, but
is thought to not produce genuine contradictions or FTL communication.
However, there is a different kind of correlation that seems, to me at least,
capable of causing real trouble for our world view and could lead to new
physics. Similar things may have been proposed before, but I don't think the
implications (in terms of local measurement of coherence length of a wave
packet) have been appreciated. Consider that the Heisenberg inequality
Delta E * Delta t >= hbar/2, where Delta E is the uncertainty in energy and
Delta t is the time interval of measurement or creation, limits the precision
of the energy of a state created during a time interval. Let’s do a
leisurely, and thus very accurate, measure E1 of the energy of an impending
emitter. Stimulate it to emit a photon during a short time, producing a large
uncertainty in the photon’s energy (i.e., a short wave packet with a short
coherence length and time, and a wide Fourier spread of possible energy
values.) Then, measure the emitter again, slowly, for an accurate
post-emission value E2. If we assume conservation of energy, the photon
should by inference be forced to have a sharply defined energy
Ep = E1 - E2! This is not an airy metaphysical distinction with no
consequences. Coherence length can be checked in an interferometer,
especially if we apply this to a sequence of photons, and the effect should be
“immediate” (per which standard?) regardless of distance. Is this a way to
have superluminal communication? Maybe not, but what about the implications
for energy conservation of inference from measurements of the emitter? This
point needs further attention.
Neil Bates
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| User: "Repeating Rifle" |
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| Title: Re: Inferred energy paradox in QM |
24 May 2005 07:52:46 PM |
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in article 1196sv2mk5dbt67@corp.supernews.com, Neil at
neil_delver@yawwho.com wrote on 5/24/05 11:35 AM:
Let¹s do a
leisurely, and thus very accurate, measure E1 of the energy of an impending
emitter. Stimulate it to emit a photon during a short time, producing a large
uncertainty
Here is your conceptual problem. If you cause emission with a broadband
simulator, you modify the energy.
Bill
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| User: "Neil" |
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| Title: Re: Inferred energy paradox in QM |
28 May 2005 09:07:08 PM |
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[My original reply was dropped by Google, unless it floats in very late...]
"Repeating Rifle" <salmonegg@sbcglobal.net> wrote in message
news:BEB91A85.3B83C%salmonegg@sbcglobal.net...
in article 1196sv2mk5dbt67@corp.supernews.com, Neil at
neil_delver@yawwho.com wrote on 5/24/05 11:35 AM:
Let¹s do a
leisurely, and thus very accurate, measure E1 of the energy of an
impending
emitter. Stimulate it to emit a photon during a short time, producing a
large
uncertainty
Here is your conceptual problem. If you cause emission with a broadband
simulator, you modify the energy.
Bill
Thanks for the prompt reply. Could you explain more and clearly what you
mean about modifying the energy, and per a "broadband simulator" versus
referring to the source more directly? (I get only 18 hits for that phrase
in all of Google.) I was thinking of the "emitter" as an entire closed
system, except for the photon allowed out, which could be "weighed" in some
way (e.g. literally, or other) before and after. Note that the
characteristic emission time (that determines coherence time,length) can be
much less than the time we take to carefully measure before and after energy
of the system. Also, I didn't mean to imply we must stimulate the emitter -
couldn't it be something that emits on its own, like a nucleus?
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| User: "=?ISO-8859-15?Q?J=FCrgen?= Appel" |
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| Title: Re: Inferred energy paradox in QM |
04 Jun 2005 07:06:40 PM |
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Neil schrieb:
I was thinking of the "emitter" as an entire
closed system, except for the photon allowed out, which could be
"weighed" in some way (e.g. literally, or other) before and after.
Probably you have heard that in Quantum mechanics there are observables
that cannot be measured precicely simultaneously (like momentum and
position for example). That's what the Heisenberg uncertainty relation is
about. [*]
If you want to treat emission correctly, you also have to include the
quantum nature of the electromagnetic field.
In such a system the sum of the energy of the atom and the energy of the
field cannot be measured simultaneously with the energy of the whole
system.
If you have an excited atom and a field with no photons in it, you know the
sum of their energies precisely. This however is not equal to the total
energy since there is an additional interaction energy term, which does
not commute with the former two.
Hence in such a quantum state with a well known state of atom and field the
energy of the whole system is not a sharp value. (The total Hamiltonian
does not commute with the sum of atomic and photonic part. If the total
energy were sharply defined, the system would not evolve, since energy
eigenstates are time independent (up to a unmeasurable global phase)).
This very fact that in such a state the total energy is not a sharp value
is the mechanism that leads to a finite linewidth of atomic
emission/absorbtion lines.
If you prepare the system in an energy-eigenstate so that you know the
total energy of the system precisely, you will find - if you do the
calculations - that the system is in a superposition of the state with an
excited atom and no photons and states with a ground-state atom and a
photon in some field mode.
So the solution to your paradoxon is that you can _either_ prepare the
system in a state of well defined energy _or_ know the state of the atoms
and the photon numbers simultaneously.
Best Regards,
Jürgen
[*] Strictly speaking there is no such thing as an uncertainty relation for
energy and time in quantum mechanics, since time is not an observable but
just a parameter. Unlike noncommuting observables, in quantum theory
nothing contradicts a system having a well defined energy at a certain
time.
(f'up to sci.physics)
--
GPG key:
http://pgp.mit.edu:11371/pks/lookup?search=J%FCrgen+Appel&op=get
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