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Physics, Astronomy & Cosmology / Re: Can a test of reciprocal time dilation be constructed from this?
« on: 10/07/2019 13:03:59 »
Thanks for the replies here. I understand the issue much clearer now.
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For starters, how might Alice measure her own speed relative to the tracks? How is 0.4c arrived at? The answer to that might give us a clue as to what is known and what isn't. I might suggest shining a light to a mirror on the tracks and one on the other train and observe the blue shift of the reflected beam. That's how the police do it.I suppose she measures the relative velocity between herself and the tracks in a similar manner to how she measures the relative velocity between herself and Bob. I was thinking about how police use the radar but also she might use the speedometer on her train.
I don't see the point of points A,M,B above. We don't need to know about them to do this.Those are for a different purpose, but it is dependent on the first part.
Surely you know better than this. Evan points out this error.I was thinking RVA would play a role but given that Alice is using her own instruments, in her own reference frame I was struggling to see why it should play a role.
I get .588c for Bob relative to the tracks given the above two measurements.
What will Bob measure his own velocity relative to the tracks to be?[/quote]0.588cQuoteWill Bob make similar meaurements/calculations for Alice's velocity relative to the tracks?Why not? Is Alice special? Bob can do the exact same thing and get .4c.
0.8c. - 0.4c = ~0.588cThis is the part I don't get. If Alice conducts all measurements within her own inertial frame, using her radar equipment, why does she apply RVA? She's not trying to determine the values that Bob gets in his intertial frame, she's doing everything in her own IF.
Bob is going faster down the tracks for Alice to have measured those figures.
If she cannot use her instruments to measure that value then she deduces it as a matter of logical necessity.She uses her instruments to get that figure. None of it is assumed.[/quote]
Cheers Evan. I still need to get more familiar with the calculation for relativistic velocity addition (RVA) but it looks quite simple there.Quoteshe measures the relative velocity between herself and Bob as 0.8cI'm afraid not.
0.4c + 0.4c ≠ 0.8c
At speeds that are a significant fraction of c, you cannot just do an arithmetic addition; you have to use the relativistic formula.
This becomes even more extreme when you consider bunches of protons in the LHC, which are travelling at just a smidgeon under c, in both directions around the ring. In their frame of reference, the oncoming bunch of protons is not travelling at (roughly) 2c, but scrapes in at just under 1c.
See: https://en.wikipedia.org/wiki/Velocity-addition_formula
I get 0.8c/(1+1/16) = 0.7529...c as the speed Alice would measure for Bob (and vice-versa).I'm not entirely sure what this figure represents though. Is it what Alice says that Bob's measurement "actually" is?
@Janus is answering the question in the OP, not the one you referenced.Yes, I was linking him to that thread to avoid starting a discussion on it in this one because his statement seemed to beg the question.
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.
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.Introducing more clocks doesn't help the situation. The light clock is the clock. It is used bcos it represents an "ideal" clock. If you introduce a clock at each mirror, then we may as well introduce a clock at each mirror for those clocks and so on ad infinitum.
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.This is the key point here - I understand about observers agreeing on clock readings.
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.I'm not disputing that they will agree on the clock times.
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.Why doesn't it make sense? In the traditional thought experiment with the floor-to-ceiling-clock the observer in "the stationary system" - let's call her Alice - observes the photon in Bob's clock traveling a longer, diagonal path between the mirrors - meaning a longer time betweeen "tick" and "tock". Alice concludes that "time has slowed down for Bob".
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.Thanks Janus, I am familiar with the Relativity of Simultaneity. That is why I posted the question, because of an issue with it.
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 2989 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.