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You are coming up against the relativistic effect known as the "relativity of simultaneity". Bob, if he sends light pulses to two mirrors, parallel to the relative line of motion and opposite each other, then, for Bob, those pulses will reach those mirrors at the same time. For Alice, the light will reach the trailing mirror first and then the leading mirror. Bob and Alice will not agree as what event are simultaneous if they are separated along the line of motion. But now consider the reflections. Again according to Bob, they take an equal time to return and meet back up with him again at the same time. For Alice, the trailing refection takes longer to catch up to Bob than the leading reflection take to run into Bob. The end result is that both pulses return to Bob as the same time. The upshot is that One "tick" must be a round trip and it makes no sense to only consider only one leg of the trip. Length contraction come into play in that it assures that the parallel pulses make the round trip in the same time as the perpendicular ones do. The end result looks like this from Alice's frame: length_con2.gif (127.71 kB . 640x100 - viewed 2988 times)( I only am showing one of the parallel mirrors here, as this is an existing animation I had already made, but adding the other mirror would not change the end result.)From Bob's frame, His clock would behave like the stationary one in this animation, while Alice's clock moved off to the Left, being length contracted and ticking slow.
Quote from: Janus on 10/06/2019 16:50:12You are coming up against the relativistic effect known as the "relativity of simultaneity". Bob, if he sends light pulses to two mirrors, parallel to the relative line of motion and opposite each other, then, for Bob, those pulses will reach those mirrors at the same time. For Alice, the light will reach the trailing mirror first and then the leading mirror. Bob and Alice will not agree as what event are simultaneous if they are separated along the line of motion. But now consider the reflections. Again according to Bob, they take an equal time to return and meet back up with him again at the same time. For Alice, the trailing refection takes longer to catch up to Bob than the leading reflection take to run into Bob. The end result is that both pulses return to Bob as the same time. The upshot is that One "tick" must be a round trip and it makes no sense to only consider only one leg of the trip. Length contraction come into play in that it assures that the parallel pulses make the round trip in the same time as the perpendicular ones do. The end result looks like this from Alice's frame: length_con2.gif (127.71 kB . 640x100 - viewed 2988 times)( I only am showing one of the parallel mirrors here, as this is an existing animation I had already made, but adding the other mirror would not change the end result.)From Bob's frame, His clock would behave like the stationary one in this animation, while Alice's clock moved off to the Left, being length contracted and ticking slow.Thanks Janus, I am familiar with the Relativity of Simultaneity. That is why I posted the question, because of an issue with it.If we consider the scenario with just one light clock first. Alice on the platform observes Bob's clock to be ticking slowly because the photon traces a longer, diagonal path between tick and tock. The conclusion in Einstein's interpretation of relativiity is that "time slows down for the relatively moving observer".Now, conider the same clock turned on it's side. What does Alice see. Well, she sees the clock tick faster in one direction than in the other - your gif demonstrates it clearly. So, she sees "time" speed up in one direction and slow down in the other.
Now, put the two clocks in together. For the floor to ceiling clock "time slows down", but for the end-to-end clock, time speeds up as the photon goes to the rear of the train (because the mirror is moving towards it) while time slows down when the photon is going in the opposite direcction (because the mirror is moving away from it).Surely pardoxical, no?
No, As I said before, is doesn't you really can't think of it that way when considering the one way travel for light. Let's put it this way, Let's say we put ideal clocks at Bob's mirrors. According to Bob's frame, those clocks are synchronized to each other. and to a clock at with Bob, halfway between those clocks. If, as measured by Bob, those mirrors are 300 meters apart, then according to him if the pulses leave his clock when it reads 0, then will arrive at the mirrors when all three clocks read 0.5 microsec (we'll round c up to 300,000,000 m/sec), and returns to Bob when all three clocks read 1 microsecond. However, according to Alice, All three of those clocks are not in sync, the Lead clock lags behind the middle clock and the trailing clock runs ahead. So even though it takes less time for the pulse to reach the trailing clock, its "head start insures that it reads 0.5 microsec when the pulse reaches it, and while it takes longer for the pulse to reach the leading clock, the fact that lagged behind the other clocks means that it will also read 0.5 microseconds when the pulse arrives, even though this pulse arrived later than the pulse arrived at the trailing clock. If you were to run a string of clocks between the mirrors, each one recording its time when a light pulse passed it, Both Alice and Bob would agree as to what time was on any given clock when that light pulse passed it, even though they would not agree as to which two clocks pulses fired in opposite directions where passing at any given moment.
No. It doesn't make any sense to say that Time "speeds up" for a pulse going one way, as Bob and Alice will not agree on the simultaneity of events that are separated along the line of relative motion. while one pulse takes less time going in one direction according to Alice, you cannot make a one for one comparison between this and Bob's measured rate of time.
If you are considering A "tick" as when the light pulse leaves the central source and a "tock" as when the pulse reaches an end mirror, Then you have to consider how Bob measures the time between "tick" and "tock". Measuring the time between "ticks" or between "tocks" is straight forward, because the interval is being measured by a single clock (either at the source or end mirror). When Bob measures the interval between "tick" and "tock", he has to use two clocks, One that measures the time at the source when the pulse leaves, and one at the end mirror when the pulse arrives. Now as long as Bob can consider these clocks as being synchronized to each other, then he can also assume that the time measured by an end mirror clock at a "tock" is the same as the time measured by the clock at the source.
When dealing with a vertical pulse, to be strict, you should also only consider the total round trip. However, since both Bob and Alice will agree that both source clock and end clock remain in sync with each other, we can "cheat" and only consider just the one way trip and not encounter any problem. And while this "cheat" works in this case, it is technically a cheat, one that only works in this particular case and can not be applied to the horizontal light clock.
The emboldened part above is the subject of debate in this thread:https://www.thenakedscientists.com/forum/index.php?topic=77116.0
@Janus is answering the question in the OP, not the one you referenced.Please read https://www.thenakedscientists.com/forum/index.php?topic=66954.0 which explains how we manage new/alternative/variations-of theories on this site.