|Hello! I was wondering about the following experiment: lets say that you have a laser, and that (single) laser is positioned parallel to one side of a triangle, and perpendicular to the second side, with the hypotenuse being 45 degrees to the left (or right - it doesnt matter) of where the laser would shoot a single photon. This is how the experiment goes: you turn on your laser and it shoots a single particle, moving at the speed of light (which you measure). But, you also record (using another camera or whatever) the reflection of the particle across the hypotenuse. (Or maybe this could be done in a dark room and you just measure the speed of the laser beam/photon across it visually. Another way you could do it is if you measure the speed by having two points on the hypotenuse that measure when light passes across them, and you could measure the time it would take for the reflection to go between those points... that way if you know the distance between them you can calculate the speed of the reflection) Because the hypotenuse is longer than the distance that the particle moved (and was traversed in the same amount of time) the reflection should be measured as moving faster than light, or "back in time". From what I have been able to figure out I dont think you'll have to deal with time dilation effects or anything fancy like that, so: Would this be the case?! Please explain why or why not. Thank you so much for your help!! Have a great day!
This is an interesting "paradox" type of question. An analogous scenario would be the sun setting and the shadow of a flag pole growing at an ever-increasing rate. In fact, right before the sun dips below the horizon, the flag pole's shadow is "moving" at a super-luminal infinite speed!
The question with these "paradox" questions is always whether any information can be transmitted faster than the speed of light (i.e. super luminally). In your scenario, if we were really talking about a single photon, we would not see it unless it was detected by your eye or an instrument. Alternately, we could consider a particle moving at essentially the speed of light (sat .999999999999999c) along the path you described in the question. It is then illuminated from the side by a light source such that the shadow "moves" along the face of the mirror at a velocity 1.414*.999999999999999c.
But keep in mind nothing here is truly moving. And all information is being transmitted by light (photons). If the mirror has sensors at different locations that signal to you when shadowed, this information could be received by you no faster than the speed of light. Now, for two adjacent sensors separated by a distance d, you would receive their signals in a difference in time t = d/1.414*.999999999999999c. Or, alternately, you would know d and measure t, which would confirm that the velocity of the shadow is v = 1.414*.999999999999999c. But since the shadow itself transmits no information, the paradox is resolved without violating special relativity.
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