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Old 2nd March 2015, 03:56 AM   #49
wogoga
Critical Thinker
 
Join Date: Apr 2007
Posts: 334
Originally Posted by wogoga in #46 View Post
However, if we assume that the original signals S1 and S2 of the combined signal S do not interact in any way when passing the slit, then we get four different sub-signals behind the slit:
S1 becoming Sa1 with phase 0
S2 becoming Sa2 with phase Pi/2

S1 becoming Sb1 with phase 0 + Pi
S2 becoming Sb2 with phase Pi/2 + Pi
This obviously cannot result in 100% destructive interference between Sa and Sb as in the already abovementioned case, where "the phase difference at the slit" is "the only relevant phase difference":
Originally Posted by Ziggurat in #47 View Post
Actually, this situation DOES result in 100% destructive interference. Sa1 cancels Sb1, Sa2 cancels Sb2. It's right there in your numbers. Treating the components separately doesn't change the end result.

The mistake that you are making is in thinking that this "adjustment" consists of anything other than BLOCKING the component of the waves which are not already in phase at the slit.

Ok. My reasoning with two phase-shifted radio signals (each divided into two sub-signals) is analogous to the 'one photon takes all paths' hypothesis, and this (in my opinion untenable) hypothesis can indeed explain (at least lateral) coherence.

Nevertheless, your statement that a slit makes the superposed phase of photons (passing at the same time) "the only relevant phase" isn't true either. Your conclusion "the slit becomes a coherent source" (#39) logically depends primarily on the 'one photon takes all paths' hypothesis, and not on blocking photons which are not in phase.

Two photons passing a slit can only be fully blocked if they have exactly opposite phase (e.g. one photon with phase 0 and the other with Pi). In the case of a phase shift between two photons of phi = Pi/2, the probability of passing the slit is Cos[phi/2]2 = 50% for each photon. So there is a 25% chance of both photons passing the slit. Because of their phase shift of Pi/2, the two photons cannot interfere in the same way, as two coherent photons with phase shift 0 would do. Therefore the slit cannot cause incoherence to completely disappear.

By the way, no interference takes place between orthogonally polarized photons. From Wikipedia: "Temporal (or longitudinal) coherence implies a polarized wave at a single frequency whose phase is correlated over a relatively great distance (the coherence length) along the beam."

So, for explaining that "the slit becomes a coherent source", you need apart from "the superposed phase becomes the only relevant phase" also something like "the superposed polarization becomes the only relevant polarization".

Cheers, Wolfgang

Last edited by wogoga; 2nd March 2015 at 04:26 AM.
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