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Meatlofe

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I understand that photons have a poorly define “position” parameter, but interaction sites do not, so we can use the position parameter of them in place of that of the photons. Let’s say we have 2 photons emitted from a location that we have measured to an arbitrarily high level of precision (henceforth "precisely measured") that interact somehow at a separate, precisely measured position. My question is, will both photons always take precisely the same time to get there, or will Heisenberg’s uncertainty principal alter the position of the photon forwards or backwards (in the direction of travel). If it ever alters the position of the particle (after a “measurement”) in the direction of travel, then that implies that the photon’s average speed was not equal to c, thereby allowing for FTL communication. If however it does not cause alteration in the direction of travel, then this property can be exploited to find the exact position and momentum of a massive particle (using a system too complex for this question, but one I'll get into in another post if it ends up being necessary). Below is an example of how the start and end point could be measured so precisely (and the rough foundation of the complex system).

We have 2 electrons which we have precisely measured the position of. After this measurement is taken, both of them instantaneously* drop from excited level X to ground level Y and emit a gamma photon (this is t=0). This is repeated until 2 photons collide and pair production occurs forming electron-positron pair. The produced particles then travel some distance, where they hit detectors which precisely measure their position and the times of these measurements. Because we know the energy and momentum going in as well as the mass of the particles, we can calculate the velocity of the particles, which we can then use with the time difference between measuring to work backwards to find the point of origin of the particles. This also happens to be the place where the photons interacted. (the other being where they were emitted from)

In this scenario, would the collision site always be at precisely equidistant from the 2 emitters? Or would it sometimes be closer to one than the other due to the position being uncertain? My gut suggests that in this specific case, because a measurement was last made to the position of the light, it will retain this information and therefore it will always happen at the halfway point, however if we had last measured the velocity of the light, it would then randomize the position. The problem arises though, what counts as a measurement of momentum? If you know the start point, end point, mass and time, you can calculate velocity, so does that count?I should also mention that there are substitutes for the 2 initial electrons to get the 2 gamma photons started at the same time from a known location, they're just the simplest way to explain. Examples would include: Splitting a laser with a semi-transparent mirror into 2 pinholes, each with the width of wavelength of the photon. Fission reaction. Annihilation. Etc. I could be wrong but I don't think any of these would make a difference.

*Yes, I know that "instantaneously" is likely unfeasible with this method, however by using some fancy graphs you can compare the distribution of when you'd expect it to be emitted with your actual results to see if the distribution lines up, thereby working around the fact that "instantaneously" is unobtainable. Also, some of the other methods of initiation may allow for “simultaneously” or better yet “at precisely measurable starting times”, both of these can be used as substitutes if you use a bunch of math to compensate.