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The Elitzur-Vaidman bomb detector is a theoretical device that can detect whether photon-activated bombs are functional without detonating all of the test bombs by using quantum mechanics principles. It was proposed by Avshalom Elitzur and Lev Vaidman in 1993. This experiment can easily conduct practically by replacing the bombs with a detector and a path alternator that can bypass the detector and still keep the phase shift relevant according to the experiment requirements.

In the above diagram,

"t" indicates the time positions of the photon along the path after emission from the source. (times positions are indicated just for the convenience of the question asked) "MN" and "MB" are 100% reflectors, "BSS" and "BSD" are 50:50 beam splitters & "$D_1$" and "$D_2$" are narrow-band single-photon detectors while "B" is a photon-triggered hypothetical test bomb.

There are four possibilities:

  1. Photon is detected at $D_1$
  2. Photon is detected at $D_2$
  3. Photon is not detected at either $D_1$ or $D_2$
  4. Photon is detected at both $D_1$ or $D_2$

Now for this experiment, since the photon source is prepared in such a way that (nearly) only one photon is emitted at a time, "possibility 4" can (almost) only appear to happen due to background photonic noise which can be mostly filtered out (what little remaining can be disregarded) by carefully designing the experiment and choice of conditions. So only three possibilities left.

  • If the bomb is a dud only situation 1 is possible.
  • If the bomb is live there is a 50% chance of possibility 3 happening and 25% chance per each of possibilities 1 or 2 happening.

The above results can be understood by the wave nature of the photon until detected and the constructive and destructive interferences at the final beam splitter (BSD) as a result of the phase shift of the photon due to reflection off mirrors and beam splitters.

Question:

Does removing the bomb after t=5 but before t=16 affect the final detection results stated above?

In other words, is the probability of interference or no interference decided at each component at the speed of light on the fly or at the moment photon is at the last beam splitter where actual interference takes place or at the final moment of the photon at the detectors just before collapse or change of wave function?

I think the answer to the above would explain the nature of the quantum mechanical probabilistic wave. That is why I asked those questions about a possibly critical intervention in the experiment.

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The photon interacting with the bomb acts as a collapse event, so at t=5 there is a 50% chance that it will explode.

Removal of the bomb after that interaction has occurred wont change anything about the experiment as the interaction between the photon and the bomb has already occurred.

Also the interference between the photons in the case of a dud or a true bomb doesnt change either as the photons have already interacted with the bomb after that point, and will continue to do that interference.

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  • $\begingroup$ Oh! Thanks that explain a lot. So according to that probability is decided on the moment the interaction occurred at the speed of the light, not at the final beam splitter or just before the wave function of the photon changes/collapses at the detector. So the probability is a passing wave, not something that is decided at the last moment of detection. This gives more physical nature to it rather than pure mathematical. $\endgroup$
    – Duke William
    Jun 30 at 13:12
  • $\begingroup$ I think you understand, but I would advise going over the logic of what is special about this experiment. Here you are working out what happens when the bomb is removed with a certain timing, but make sure you are not missing the point of the idea. The idea is that you can somehow with 25% probability be able interact with something without actually interacting with it....its very strange $\endgroup$
    – Steven Sagona
    Jun 30 at 16:18
  • $\begingroup$ The crazy thing is that in the event of collapse of the photon, there's a 50% probability that your measurement (by placing the bomb in the path and providing the possibility of explosion) causes the photon to go the OTHER WAY and not interact with the bomb. $\endgroup$
    – Steven Sagona
    Jun 30 at 16:24
  • $\begingroup$ I think it is the BOMB that causes a psychological dilemma. If we think bomb as a detector it feels no longer strange. It is either the circumstances decide wave function collapse at the mid-way detector or at the destination detectors. The analogous bomb is never visited by the photon but by its wave function which is not enough to trigger it. But we don't know what other changes done to it by wave function but may be some weak measurement happens? Maybe the photon's frequency hence the energy little bit changed? I don't know how we can measure it because mirrors can affect photon energy too. $\endgroup$
    – Duke William
    Jun 30 at 16:52
  • $\begingroup$ If you're asking what happens when the "dud" is there: The "dud" is a bomb that doesnt have a sensor attached to it, and is therefore transparent to the photons because there's no detector for it. If this dud actually slightly changes things then this would have to be included in the math and would be something extra. $\endgroup$
    – Steven Sagona
    Jun 30 at 17:58

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