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QFT
Name: Jagmeet S.
Status: other
Age: 30s
Location: N/A
Country: N/A
Date: 5/28/2003
Question:
Sir,
We put up the following question on physics-zone (a yahoo discussion
group) but could not reach a consensus.We shall be obliged if you reply.
Jagmeet
--- Jagmeet S;wrote:
Two identical events occur very close by in time(at roughly the same
location)--consider e.g. emission of 2 identical photons by an assembly
of atoms.The time difference between the emissions is exceedingly small
(say ten to the power minus ten seconds). The question is:-can we say
with certainty which photon is emitted earlier and which later? If not
what does this imply? "Creation operators commute amongst themselves" is
asserted but not proven
DISCUSSIONS so far:-
--- Ravi B.
Total unambiguity is impossible because of the Uncertainty
Principle.However if the time lag between the events is much much larger
than the intrinsic time uncertainty of the events one can sequence with a
good degree of accuracy- the degree of which would be better and better if
the events are separated by larger and larger time differences.
--- Jagmeet S.
Seems correct.Now what does this imply: -it can mean one of the two
possibilities mentioned below: 1. One photon say A is definitely emitted
ahead of the other photon say B-- it is just that we cannot tell because
of the limitations of our detection device.
2.There is a fundamental indeterminacy in the system of two photons:-the
two photons can very well be interchanged (the time order of the two
identical events can not be defined--whereas the time delay can be defined).
Which option do you think is right?
--- Ravi B.
Option 2.
--- Jagmeet S.
Option 2 would mean the following: -'a photon detector may not receive the
photons from a source in the same order as they were emitted by the
source'(provided the photons are identical in every respect). We
considered the case of two identical photons emitted from a source at a
very small time interval.Creation of the two photons would be described by
twice applying a creation operator on |0.
Creation operators commute amongst themselves--I take this to mean that
the two instances of creation may be considered non-interfering or
distinct. There is thus a definite time order in the creation of the
photons--and so also in the detection. Now to imagine that the two photons
can interchange in mid-flight is something hard to accept--I do not really
know if this could be a possibility.
Let me add the following:-
If creation operators E^{-}(x) and E^{-}(y) commute with each other(where
E^{-} stands for the -ve frequency part of the electric field, x and y
represent space-time points (x,t) & (y,t)) it means that the two
operations of creation are distinct or well discriminated from each other.
Commutation may also seem to suggest that the operations are
interchangeable,but one cannot create in future first and then in present,
so that time ordering is implied.
In any case time ordered products are used in QFT--causality and Lorentz
invariance are both respected. In simple language QFT respects relativity
plus causality--so you cannot interchange past and future events no
matter how close they are or how identical
they are.
May be this question should be referred to a quantum field theorist--ask
Dr. Soni what he thinks about this.
---Ravi B.
I shall definitely ask Dr.S.But remember that superposition of wae
functions exist and collapse to a projection only on measurement.
Replies:
Sounds to me like the discussion group is getting entangled in some arcane
quantum mechanical sprinkled with some would-be erudite name dropping that
does not come across as being well thought out by the responding members.
For example, what is the statement, "Total unambiguity is impossible
because of the Uncertainty Principle." How about partial unambiaguity --
is that impossible, possible, or partially impossible? If we cancel out
the two negatives in the statement, it reads, " Total ambiguity is
possible because of the Uncertainty Principle." That's not very helpful.
What does, "...intrinsic time uncertainty of events..." mean? How is this
determined? And please explain what, "that superposition of wave functions
exist and collapse to a projection only on measurement." This is jargon
out of the Copenhagen interpretation of quantum mechanics, which is by no
means accepted by all theorists as the only interpretation of quantum
mechanics, and is discounted by many. One participant claims that, "(the
time order of the two identical events can not be defined--whereas the
time delay can be defined)." Huh??? That is a tautology. It is not at all
clear that the creation operators commute, certainly the creation and
annihilation operators do not. See:
http://scienceworld.wolfram.com/physics/CreationOperator.html
Finally, the inquirer offers a set of conditions for the 2-photon
experiment of identical photons and a time difference of 10^-10 sec. By my
calculations, given the speed of light ~3x10^8 m/s, corresponds to about
10 cm. Since pico-second spectroscopy is fairly common now, there should
be no problem distinguishing the order of firing of the sources.
Vince Calder
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