The forum discussion centers on a hypothetical experiment involving the repositioning of two synchronized clocks within a vessel traveling at 0.9C. The analysis utilizes special relativity principles, particularly Lorentz transformations, to predict the time difference between the clocks as one clock moves from the leading to the trailing end of the vessel. Calculations reveal that the time difference in the observing frame is 0.288675 seconds, while in the vessel frame, it is -0.57735 seconds. The discussion emphasizes the importance of understanding simultaneity and time dilation in different frames of reference.
PREREQUISITESPhysicists, students of relativity, and anyone interested in the implications of time dilation and simultaneity in high-speed travel scenarios.
starthaus said:I am not "maintaining". 13.33ns is the correct result.
yossell said:How can you say that this is the correct result without maintaining it?
JesseM said:No, you have been talking about simultaneous events in F, but I have not. I have been talking about how "out-of-sync" or "desynchronized" the clocks are in the frame of the observer F'. If the observer F' measures the leading clock reading T=0 at the same moment (in frame F') that the trailing clock reads T=8, it makes sense to say that in frame F' the two clocks are "out-of-sync by 8 seconds" (with vL/c^2 = 8). This is how other authors talk, for example this page says at the bottom:
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so that although the ground observer measures the time interval between the starting of the clock at the back of the train and the clock at the front as \gamma vL/c^2 seconds, he also sees the slow running clock at the back actually reading vl/c^2 seconds at the instant he sees the front clock to start.
No, he's not contradicting himself, he's just talking about different measurements involving different pairs of events. If he "measures the time interval between the starting of the clock at the back of the train and the clock at the front", then he's measuring the time interval between the events of each clock starting, i.e. the time between the event "clock at back reads T=0" and the event "clock at the front reads T=0". This time is indeed gamma*vL/c^2. On the other hand, if he measures the clock at the back "at the instant he sees the front clock to start", then here "at the instant" refers to simultaneity in his own frame, so he must be looking at the event on the back clock's worldline which is simultaneous with the event of the front clock starting according to his own frame's definition of simultaneity. As I already showed, this would be satisfied if he picked the events "clock at back reads T=8" and "clock at front reads T=0".starthaus said:So, the author is confused of what the moving observer actually measures <shrug>. He calculates correctly and claims one thing and then he contradicts himself and claims another thing.
Suppose there is a clock at the planet P synchronized in S with Homer's clock at Earth. In S', these clocks are unsynchronized by the amount L0V/c^2.
JesseM said:No, he's not contradicting himself, he's just talking about different measurements involving different pairs of events. If he "measures the time interval between the starting of the clock at the back of the train and the clock at the front", then he's measuring the time interval between the events of each clock starting, i.e. the time between the event "clock at back reads T=0" and the event "clock at the front reads T=0". This time is indeed gamma*vL/c^2.
But it's not what I have been talking about all along, and I was the one who made the original statement in post #10 that "Relativity of simultaneity says that if two clocks are a distance L apart and synchronized in their mutual rest frame, then they are out-of-sync by vL/c^2 in the frame that sees them moving at v", which you objected to in post #13 by saying "They are out of sync by \gamma(v)\frac{vL}{c^2}". Given what I meant by the phrase "out-of-sync by" (which matches what physicists would normally mean by that type of phrase in this context), my statement was perfectly correct.starthaus said:...which is exactly what I have been talking about all along.
And I never said your math was wrong, I just said that your objection to the statement "they are out-of-sync by vL/c^2" was misguided, since the statement doesn't concern events that have a time difference of dt=0 but rather events that have a time difference of dt'=0. If you acknowledge natural language is ambiguous, maybe you shouldn't be so quick to raise objections to natural language statements that you don't understand, and should instead ask questions to try to clarify what the accepted terminology is.starthaus said:This is why mathematics is much better than natural languages. I have said all along dt=0. I did not say dt'=0.
JesseM said:two clocks are a distance L apart and synchronized in their mutual rest frame,
JesseM said:And I never said your math was wrong, I just said that your objection to the statement "they are out-of-sync by vL/c^2" was misguided, since the statement doesn't concern events that have a time difference of dt=0 but rather events that have a time difference of dt'=0. If you acknowledge natural language is ambiguous, maybe you shouldn't be so quick to raise objections to natural language statements that you don't understand, and should instead ask questions to try to clarify what the accepted terminology is.
JesseM said:two clocks are a distance L apart and synchronized in their mutual rest frame,
No, it doesn't mean that, not if we aren't considering a pair of events that are simultaneous in the clocks' rest frame, like the pair "front clock reads T=0" and "back clock reads T=8". If the clocks are synchronized in frame F, then for these two events dt=8. It's only meaningful to give a value of dt when you have first specified what two events you want to calculate the time-interval between.starthaus said:...meaning dt=0
I phrased it in the standard way that other physicists phrase similar claims. Again, you might have asked what I meant before jumping into accuse me of saying something incorrect. Anyway, I explained almost immediately what I meant in more precise language, like this from post #16:starthaus said:If this is what you wanted to say, then you needed to phrase it precisely.
I don't think this is at all ambiguous, if you had been paying attention rather than rushing to object you might have seen that I was just using "out-of-sync in the observer's frame" in a way that didn't match how you interpreted this phrase, so that your objection was a purely semantic one.But that's not telling us the amount they're out-of-sync in the observer's frame! To find that, we need to find two events on each worldline that are simultaneous in the observer's frame, and then find the time interval between them in the rest frame of the clocks (since the observer judges how out-of-sync the clocks are by looking at what each clock reads at a single moment in his own frame).
In the observer's frame, the clocks are only separated by a distance of L/gamma(v), so suppose in the observer's frame the two simultaneous readings occur at these coordinates:
x=0, t=0
x=L/gamma, t=0
In that case the time of the first event in the clock frame is t'=0, while the time of the second event is:
t' = gamma*(0 - vL/gamma*c^2) = -vL/c^2
Again you seem to be assuming a certain use of language which doesn't match how physicists normally talk. It is standard in relativity to talk about anything that is true in one frame to be what is "measured" by an observer at rest in that frame (for example, the bottom of p. 1 of http://web.mit.edu/sahughes/www/8.022/lec11.pdf earlier saying "Suppose there is a clock at the planet P synchronized in S with Homer's clock at Earth. In S', these clocks are unsynchronized by the amount L0V/c^2.") In any case I didn't actually use the word "measure" to describe how out-of-sync the clocks are in frame F', for example my original post #10 which you objected to just said "Relativity of simultaneity says that if two clocks are a distance L apart and synchronized in their mutual rest frame, then they are out-of-sync by vL/c^2 in the frame that sees them moving at v."starthaus said:Two events separated by dt,dx in frame F are perceived simultaneously in frame F'. What is their time separation in frame F?
0=dt'=\gamma(dt-vdx/c^2)
so:
dt=vdx/c^2
The observer in frame F' does not "measure" a de-synchrnization of vdx/c^2. The observer in F' only infers a de-synchronization from the fact that the events appeared simultaneous in F'.
JesseM said:No, it doesn't mean that, not if we aren't considering a pair of events that are simultaneous in the clocks' rest frame, like the pair "front clock reads T=0" and "back clock reads T=8". If the clocks are synchronized in frame F, then for these two events dt=8.
In any case I didn't actually use the word "measure" to describe how out-of-sync the clocks are in frame F', for example my original post #10 which you objected to just said "Relativity of simultaneity says that if two clocks are a distance L apart and synchronized in their mutual rest frame,
then they are out-of-sync by vL/c^2 in the frame that sees them moving at v."
They do always show the same time at any given time in F. At t=0, the trailing clock reads T=0, and the leading clock reads T=0. At t=8, the trailing clock reads T=8, and the leading clock reads T=8. That's what any physicist would understand the phrase "synchronized in frame F" to mean--that if you compare their readings at a single time in frame F, both clocks show the same reading at this time. Do you interpret "synchronized in frame F" to mean something different?starthaus said:Synchronized means showing the same exact time, i.e. dt=0.
JesseM said:They do always show the same time at any given time in F. At t=0, the trailing clock reads T=0, and the leading clock reads T=0. At t=8, the trailing clock reads T=8, and the leading clock reads T=8. That's what any physicist would understand the phrase "synchronized in frame F" to mean--that if you compare their readings at a single time in frame F, both clocks show the same reading at this time. Do you interpret "synchronized in frame F" to mean something different?
If not, just note that in the equation dt' = gamma*(dt - v*dx/c^2), dx and dt can stand for the distance and time interval between any two events I choose, so if I choose event #1 to be "the leading clock reads T=0" and I choose event #2 to be "the trailing clock reads T=8", t
OK, so do you agree that for the synchronized clocks I described, the event "leading clock reads T=0" occurs at time t=0 in frame F, and the event "trailing clock reads T=8" occurs at time t=8 in frame F, so between this specific pair of events we have dt=8, and this doesn't contradict the fact that the two clocks are "synchronized" in frame F?starthaus said:No, what gives you the idea?
I'm not talking about the events you chose, I'm talking about the events "leading clock reads T=0" and "trailing clock reads T=8". Do you disagree that in frame F dt=8 for these events, and in frame F' dt'=0 for these events? If you don't disagree with that, do you disagree that according to the definition of "unsynchronized by" I gave above, it is correct to say that in frame F' the two clocks are "unsynchronized by 8 seconds", since in frame F' the event of the leading clock reading T=0 occurs simultaneously with the event of the trailing clock reading T=8?starthaus said:I chose "trailing clock AND leading clock at the same time T", hence dt=0
JesseM said:OK, so do you agree that for the synchronized clocks I described, the event "leading clock reads T=0" occurs at time t=0 in frame F, and the event "trailing clock reads T=8" occurs at time t=8 in frame F, so between this specific pair of events we have dt=8, and this doesn't contradict the fact that the two clocks are "synchronized" in frame F?
I'm not talking about the events you chose, I'm talking about the events "leading clock reads T=0" and "trailing clock reads T=8". Do you disagree that in frame F dt=8 for these events, and in frame F' dt'=0 for these events? If you don't disagree with that, do you disagree that according to the definition of "unsynchronized by" I gave above, it is correct to say that in frame F' the two clocks are "unsynchronized by 8 seconds", since in frame F' the event of the leading clock reading T=0 occurs simultaneously with the event of the trailing clock reading T=8?
Yes, that's the equation I already mentioned I was using, in post #41 for example:starthaus said:If you insist on this choice then:
dt'=\gamma(dt-vdx/c^2)
And also earlier, in post #24:If not, just note that in the equation dt' = gamma*(dt - v*dx/c^2), dx and dt can stand for the distance and time interval between any two events I choose, so if I choose event #1 to be "the leading clock reads T=0" and I choose event #2 to be "the trailing clock reads T=8", then since event #1 occurs at t=0 in frame F and event #2 occurs at t=8 in frame F, the dt for this specific pair of events is dt=8, despite the fact that the events both occur on the worldlines of two clocks which are "synchronized in frame F" according to the definition above.
Your equation dt' = gamma*v*dx/c^2 is incorrect for those two events, because dt was nonzero for the events I picked. The full Lorentz transformation equation is
dt' = gamma*(dt - v*dx/c^2)
If dt is not zero, you can't reduce this to dt' = gamma*v*dx/c^2. For the two events I chose (the event of the leading clock reading T=0, and the event of the trailing clock reading T=8), dt was not zero, here dt=8.
JesseM said:Yes, that's the equation I already mentioned I was using, in post #41 for example:
The way physicists talk, "synchronized" is a property of the clocks themselves, not a property of the pair of events on each clocks' worldline we choose to analyze. If at every time coordinate t, both clocks read T=t in frame F (like my example where both clocks read T=0 at time coordinate t=0, and both read T=8 at time coordinate t=8), the clocks themselves are said to be "synchronized" in frame F, and that remains true of the clocks even if we choose to look at a pair of events on each clock's worldlines which occur at different times in F. If you define "synchronized" relative to the pair of events we choose as opposed to the clocks themselves, you are using language in a bizarre way that you shouldn't expect any physicist to understand without a detailed explanation.starthaus said:Now, you can get a physically measurable result from it by accepting that "synchronized" means dt=0
And you replied:They do always show the same time at any given time in F. At t=0, the trailing clock reads T=0, and the leading clock reads T=0. At t=8, the trailing clock reads T=8, and the leading clock reads T=8. That's what any physicist would understand the phrase "synchronized in frame F" to mean--that if you compare their readings at a single time in frame F, both clocks show the same reading at this time. Do you interpret "synchronized in frame F" to mean something different?
But you can see that according to the definition of "synchronized in F" I give above, all that matters is that the clocks always show the same reading at any single time in F, that remains true even if we choose to analyze two events on their worldlines which don't occur at the same time in F.No, what gives you the idea?
You don't think it's possible for an observer in F' to measure what both clocks read at a single time t'? If not, you must be using some weird definition of "measure" which again doesn't match the terminology used by physicists. As I said earlier in post #39:starthaus said:or you can get a non-measurable entity by continuing to insist that the "measurement" is done by imposing dt'=0. Of course, in the latter case, there is no measurement that can be done.
It is standard in relativity to talk about anything that is true in one frame to be what is "measured" by an observer at rest in that frame (for example, the bottom of p. 1 of http://web.mit.edu/sahughes/www/8.022/lec11.pdf says "inertial observers in different frames of reference measure different intervals of time between events")
JesseM said:The way physicists talk, "synchronized" is a property of the clocks themselves, not a property of the pair of events on each clocks' worldline we choose to analyze. If at every time coordinate t, both clocks read T=t in frame F (like my example where both clocks read T=0 at time coordinate t=0, and both read T=8 at time coordinate t=8), the clocks themselves are said to be "synchronized" in frame F, and that remains true of the clocks even if we choose to look at a pair of events on each clock's worldlines which occur at different times in F.
It doesn't mean that according to how physicists use the term "synchronized", no, it only means that at the clocks always show the same reading simultaneously in their rest frame. I can provide quotes showing them using it my way rather than your way if you like.starthaus said:The point is that you don't even have to "look at them" from frame F' "(if you ever accept that "synchronized" means dt=0).
The standard textbook procedure for physically defining the meaning of an inertial frame's coordinates involves a grid of measuring-rods and clocks at rest in that frame, with the clocks synchronized according to the Einstein synchronization convention, and with the coordinates of any event being defined in terms of local readings on this system of measuring-rods and clocks. So, suppose F' has a ruler at rest relative to him which defines his x'-axis, and at each marking on the ruler there's a clock which is also at rest in F'. Then if he's observing a pair of clocks moving relative to himself in the -x' direction, he might observe through his telescope that at the moment the leading clock passed the x'=0 light-second marker on his ruler, the leading clock read T=0, while his own clock at rest at that marker read t'=0 seconds. Then he might also observe through his telescope that at the moment the trailing clock passed the x'=6 light-second marker on his ruler, the trailing clock read T=8, while his own clock at rest at that marker read t'=0 seconds. Regardless of how long it takes the light from these events to reach his telescope (wherever he is sitting), because of these local readings on his measuring-rod/clock system, he will assign the event of the leading clock reading T=0 coordinates of x'=0, t'=0 and he will assign the event of the trailing clock reading T=8 coordinates of x'=6, t'=0. That's the standard meaning of how inertial observers "measure" the coordinates of different events in SR, using local readings on this sort of system of measuring rods and clocks.starthaus said:For chuckles and grins, how do you look at two clocks separated by say 100m whizzing past you at 0.8c? Please explain.
JesseM said:he might observe through his telescope that at the moment the leading clock passed the x'=0 light-second marker on his ruler, the leading clock read T=0, while his own clock at rest at that marker read t'=0 seconds. Then he might also observe through his telescope that at the moment the trailing clock passed the x'=6 light-second marker on his ruler, the trailing clock read T=8,
starthaus said:You mean the observer manages to swivel the telescope instantaneously such that he can observe both clocks simultaneously (as mandated by your condition dt'=0) while they whizz by him at 0.8c?
Aaron_Shaw said:I'm sure one could manufacture a device like a telescope which is able to observe in two different directions at once.
Well, for one thing the observer might be at different distances from the x'=0 mark and the x'=6 mark, in which case the light from the two events wouldn't reach him at the same time. But you can also just imagine there is a camera next to each mark that takes continuous footage of events in the vicinity of that mark, and that each camera is continuously sending data to the observer's computer via cables, or that the observer periodically flies out to the different cameras to see what they've recorded. This is just meant to be a theoretical procedure for defining each frame's coordinates anyway, as long as it'd be possible in principle you don't have to worry about how practical it would be (since in practice you can use other methods like parallex to gauge the distance of different events, and divide distance by speed of light to figure out the time interval between when the event occurred in your frame and when the light from the event actually reached you).starthaus said:You mean the observer manages to swivel the telescope instantaneously such that he can observe both clocks simultaneously (as mandated by your condition dt'=0) while they whizz by him at 0.8c?
JesseM said:Well, for one thing the observer might be at different distances from the x'=0 mark and the x'=6 mark, in which case the light from the two events wouldn't reach him at the same time. But you can also just imagine there is a camera next to each mark that takes continuous footage of events in the vicinity of that mark, and that each camera is continuously sending data to the observer's computer via cables, or that the observer periodically flies out to the different cameras to see what they've recorded.
This is just meant to be a theoretical procedure for defining each frame's coordinates anyway, as long as it'd be possible in principle you don't have to worry about how practical it would be
You have to distinguish between theoretical statements about what would be true in idealized experiments which don't violate any fundamental laws of physics, and practical statements about what we might actually measure. In practice we've never been able to accelerate a pair of clocks to relativistic speed to observe how if they are synchronized in their own frame according to Einstein's procedure they will be out-of-sync in our frame, but we know this is a theoretical prediction of SR.starthaus said:Indeed. What about the motion blur? You think that they can do something about the 0.8c?
You don't have to worry about light delays if you are using local readings on your own set of synchronized clocks. If I am sitting at position x'=100, and at t'=94 I see the image of an event happening right next to the x'=6 marker on my ruler, and my clock at that marker reads t'=0 in the image, then I will assign that event a time coordinate of t'=0 even though I didn't actually learn about it until t'=94.starthaus said:You must also solve the problem that the two light paths from the two clocks aren't equal, so you will need to adjust the clock readings (that is, after you manage to de-blur the images you are getting at 0.8c).
Again, by looking at local clocks at rest in his frame which are in the immediate vicinity of where the snapshot was taken, clocks which have been previously "synchronized" in the observer's frame according to the Einstein synchronization convention.starthaus said:...and how does the observer ensure that the snapshots are simultaneous? How does he physically realize the condition dt'=0?
Well, things work different in theoretical physics, where physicists often explore the predictions of the laws of physics for situations that would be too difficult to realize as practical experiments for now.starthaus said:In my profession, I do.
JesseM said:Well, things work different in theoretical physics, where physicists often explore the predictions of the laws of physics for situations that would be too difficult to realize as practical experiments for now.
Austin0 said:Desynchronization is not dependent on specific events but can be calculated purely as a function of velocity and spatial separation between clocks in their own rest frame. Yes??
If you think it would apply to L as per JM i.e. proper length, then either you are simply wrong or I have to relearn relative simultaneity.
starthaus said:it is the latter
Austin0 said:Given an inertial frame F1 with two clocks separated by 10 units of 1 ls ,,as measured in that frame and an observation frame F2 ...v= 0.8 c
WOuld you question that as observed and measured in F2 that the degree of desynchronization between the clocks in F1 would be 0.8* 10 = (+) or( - ) 8.0 sec. ?
You are maintaining that the desynch would be 1.666667 * 0.8*10 =13.3333 ?
starthaus said:I am not "maintaining". 13.33ns is the correct result.
It's "physically realizable" in the sense that it could be realized without violating any laws of physics, but it's not practically realizable with present technology, no. But the point is that no experiment comparing two events on clock worldlines from the perspectives of two frames moving at relativistic velocities relative to one another is practically realizable, because we can't really achieve relativistic velocities relative to the Earth. So, it's also not practically realizable to look at two events with dt=0 in the clock rest frame and then show experimentally that the time between these events in a frame moving at relativistic velocity relative to the clocks is dt'=gamma*L*v/c^2.starthaus said:In other words, the experiment is not physically realizable with the convention dt'=0 for labeling the clocks as synchronized.
JesseM said:It's "physically realizable" in the sense that it could be realized without violating any laws of physics, but it's not practically realizable with present technology, no.
But the point is that no experiment comparing two events on clock worldlines from the perspectives of two frames moving at relativistic velocities relative to one another is practically realizable, because we can't really achieve relativistic velocities relative to the Earth. So, it's also not practically realizable to look at two events with dt=0 in the clock rest frame and then show experimentally that the time between these events in a frame moving at relativistic velocity relative to the clocks is dt'=gamma*L*v/c^2.