I'm challenging anyone who can answer the following question objectively:
As usual, imagine a railway station and trains which are equipped with single photon sources (one each in the platform and inside the trains) and a narrow strip of detector which is positioned right above the photon sources. The photons are fired vertically upwards, perpendicular to the train’s direction of travel. In addition, let us assume that apart from the photo detectors on the train and the platform, the roof of the train is open, and that the ceiling of the station above the train also has photo detectors, corresponding to the position of the photo detectors on the platform. Now, the photon sources in the station and the trains are set to trigger at the same moment – i.e. when the train’s photon source passes in front of Alice. Now, Bob is sitting in front of the photon source in the train which is travelling at approximately half the speed of light, towards the station.
When the train in which Bob travels crosses Alice, both photon sources emit a photon (on platform and on the train). Hence, one photon is emitted towards the roof of the railway station by the photon source stationed in the platform; another is emitted inside the train above which is the photo detector on the train (moving w.r.t. Alice) and the photo detector on the station’s roof (stationary w.r.t. Alice) above the train. Which means, Alice will (? might) record two photons hitting the photo detectors on the ceiling of the station (the photon from the platform and the photon from the train). The photon emanating from inside the train should hit the station’s ceiling since the train’s detector would have moved away by the time the photon travels upwards. Now from Bob’s view point, the photon emitted inside the train will be detected by the sensor IN the train; the photon emitted by the emitter on the platform will miss the detector on top of it (since the station is moving relative to Bob’s train). Either way, SR would not work for both observers at the same time.
In case you are thinking that there is some trickery with which this question can be answered in a manner similar to the barn door paradox, let Charlie travel in the track parallel to Bob, in the opposite direction (both Bob and Charlie are equidistant from Alice’s view point and are approaching with the same speed). Now we will have three different observers with different predictions; but due to law of conservation of energy, the photons can be detected by only one of the sensors, which should settle the confusion (or if they do separate, we would be able to tell because of the lesser energy liberated by the photon). In general, the experiment suggests that depending on the relative speed of the train to the station, there are an infinite number of positions in which the photon can be found, which could either support the many worlds theory, or is at least at odds with the Special relativity.
I have been digging around this for almost 13 months; still no solution. Any ideas? Would theory of General relativity help?
Should I rephrase my question -or- add details?