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From: Jesse Mazer <lasermazer.domain.name.hidden>

Date: Sat, 14 Aug 2004 10:40:08 -0400

Russell Standish wrote:

*>
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*>Let |i> refer to the state where the photon travels on path i. Then
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*>one can write down a few relations, such as:
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*>
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*>|1> = 1/sqrt{2}|3> + 1/sqrt{2}|4> = |5>
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*>|2> = 1/sqrt{2}|3> - 1/sqrt{2}|4> = |6>
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*>
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*>If a photon is detected on path 5, then the probability it travelled
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*>along path i is <5|i>. Since <5|1>=1 and <5|2>=0, we have "which way"
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*>information.
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*>
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*>Now inserting an absorber on path 4 is mathematically equivalent to
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*>inserting a projection operator |3><3| in the middle of the
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*>propagator. The the probability of a photon detected at path 5 taking
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*>path i becomes <5|3><3|i>. Computing these values by the above
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*>formulae gives:
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*>
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*> <5|3><3|1>=1/2 and <5|3><3|2>=1/2
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Thanks for the elaboration, it's been a while since I studied QM. A

question: I had thought the notion of "probability" only makes sense when

talking about actual measured outcomes, and that paths in a path integral

can only be assigned a probability amplitude, not a probability, since if

you tried to talk about the "probability" of each path (just by squaring the

path's amplitude, I guess) the probabilities would not necessarily add

together classically. Is my memory wrong, or when you talk about the

"probability" that a photon took a path i do you really mean the probability

amplitude?

Jesse Mazer

Received on Sat Aug 14 2004 - 10:46:41 PDT

Date: Sat, 14 Aug 2004 10:40:08 -0400

Russell Standish wrote:

Thanks for the elaboration, it's been a while since I studied QM. A

question: I had thought the notion of "probability" only makes sense when

talking about actual measured outcomes, and that paths in a path integral

can only be assigned a probability amplitude, not a probability, since if

you tried to talk about the "probability" of each path (just by squaring the

path's amplitude, I guess) the probabilities would not necessarily add

together classically. Is my memory wrong, or when you talk about the

"probability" that a photon took a path i do you really mean the probability

amplitude?

Jesse Mazer

Received on Sat Aug 14 2004 - 10:46:41 PDT

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