Repositioning clocks: continuing from the switch paradox

[Aaron_Shaw]

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?

I'm sure one could manufacture a device like a telescope which is able to observe in two different directions at once.

 

[starthaus]

I'm sure one could manufacture a device like a telescope which is able to observe in two different directions at once.

Indeed. What about the motion blur? You think that they can do something about the 0.8c?
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).

 

[JesseM]

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?

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]

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.

...and how does the observer ensure that the snapshots are simultaneous? How does he physically realize the condition dt'=0?

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

In my profession, I do.

 

[JesseM]

Indeed. What about the motion blur? You think that they can do something about the 0.8c?

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.

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).

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.

 

[JesseM]

...and how does the observer ensure that the snapshots are simultaneous? How does he physically realize the condition dt'=0?

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.

In my profession, I do.

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]

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.

In other words, the experiment is not physically realizable with the convention dt'=0 for labeling the clocks as synchronized.

 

[Austin0]

Desynchronization is not dependant 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.

it is the latter

I think I may hold off on any adjustments to my understanding of relative simultaniety.

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 ?

I am not "maintaining". 13.33ns is the correct result.

With your understaning of the Lorentz math it should be blindingly obvious that simply given a relative velocity of 0.8 c it can be stated with certainty that the relative degree of desynchronization between the two frames must be (+) or (-) 0.8 sec per light second of proper spatial separation of clocks . Without further information or recourse.
This applies reciprocally from either frame.

Your 13.33333 sec is only correct for specific locations x',0 and x', 16.6667=dx'= 16.6667 . I t has no general truth regarding the desynchronization between the frames and is only correct at all because you have idiosyncratically turned the conditions as stated upside down and insisted on working from the other frame.
I can accept correction when warranted but I fail to discern either point or purpose in your exercise as it educates none , apparently not even yourself IMHO

 

[JesseM]

In other words, the experiment is not physically realizable with the convention dt'=0 for labeling the clocks as synchronized.

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]

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.

Which means that such a definition of synchronization has no practical use.

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.

This is incorrect, the synchronization definition employing dt=0 does not imply any observation of the clocks. All you need to know is that they had been accelerated slowly enough such that they did not get out of synch. For that extent, the clocks may be totally enclosed in arocket, unobservable, you will still be able to determine their desynchroonization in frame F' based only on two things : proper length L and coordinate speed v.

 

[JesseM]

Which means that such a definition of synchronization has no practical use.

So do you also think the Lorentz transformation equation dt' = gamma*(dt - v*dx/c^2) has no practical use? Is there any practical way to verify that for two events that have a dx of 10 light-seconds in our frame and a dt of 8 seconds in our frame, the events would have a dt' of 0 in a frame moving at 0.8c relative to us?

This is incorrect, the synchronization definition employing dt=0 does not imply any observation of the clocks.

I don't know what "synchronization definition" you are using that's different from mine. My definition had nothing to do with a specific pair of events so I am not considering any particular value of dt, my definition is just that if two clocks show the same reading at every time-coordinate in a given frame, they are "synchronized" relative to that frame. Are you using a different definition?

All you need to know is that they had been accelerated slowly enough such that they did not get out of synch.

"Did not get out of sync" in your frame, or in the rest frame of the clocks? If you accelerate both clocks at the same coordinate acceleration in your rest frame, then both clocks will remain synchronized in your frame, which means according to my definition of synchronization above, they will become out-of-sync in their new rest frame.

For that extent, the clocks may be totally enclosed in arocket, unobservable, you will still be able to determine their desynchroonization in frame F' based only on two things : proper length L and coordinate speed v.

OK, suppose that while the rocket is accelerating up to relativistic speed, both clocks are right next to each other in the middle of the rocket. This means we can know theoretically that they remain "synchronized" in all frames (both our frame and other frames) according to my definition above, as long as they are together. Then once the rocket is coasting, there's a device which automatically pushes one clock slowly along a track towards the front of the rocket, and which automatically pushes the other slowly along a track towards the back (the device is designed to push both clocks at the same slow speed relative to the rocket). In that case, we can determine theoretically that the after reaching the front and back the two clocks should still be "synchronized" in the current rest frame of the rocket (according to my definition above), and that this means that two readings on the clocks which have a separation of vL/c^2 should occur simultaneously in our frame.

 

[starthaus]

So do you also think the Lorentz transformation equation dt' = gamma*(dt - v*dx/c^2) has no practical use?

I never said such a thing, please stop putting words in my mouth and try to stick to the subject being discussed.

Is there any practical way to verify that for two events that have a dx of 10 light-seconds in our frame and a dt of 8 seconds in our frame, the events would have a dt' of 0 in a frame moving at 0.8c relative to us?

No, there isn't. You, yourself have admitted earlier on that there isn't any practical way.

I don't know what "synchronization definition" you are using that's different from mine.

You are using dt'=0 which , according to your own admission is impossible to implement practically.
I am using dt=0 which is very easy to implement (and is implemented in prcatice).

OK, suppose that while the rocket is accelerating up to relativistic speed, both clocks are right next to each other in the middle of the rocket.

This is not the original definition of the problem and has nothing to do with the original experiment. In the original experiment the clocks start separated by the distance L. Please stick with the experiment under discussion.

 

[JesseM]

I never said such a thing, please stop putting words in my mouth and try to stick to the subject being discussed.

I didn't put words into your mouth, I asked about what your position on this is.

No, there isn't. You, yourself have admitted earlier on that there isn't any practical way.

So, do you think we can ever verify that the equation dt' = gamma*(dt - v*dx/c^2) is correct practically in a case where we pick two events with dt not equal to zero? If not, does this equation have any "practical use" if we already know dt' = gamma*v*dx/c^2 applies in cases where dt=0?

You are using dt'=0 which , according to your own admission is impossible to implement practically.
I am using dt=0 which is very easy to implement (and is implemented in prcatice).

I don't know what you mean by "implement". It is not possible in practice to ever actually measure any value for dt' if the primed frame is moving at a relativistic speed relative to us, since in practice we can't actually get a system of rulers and clocks moving at relativistic speed relative to us. But if you allow theoretical conclusions based on knowledge of the time between events dt in our frame, like the conclusion that two events with dt=0 in our frame must occur with a separation of dt'=gamma*v*dx/c^2, then there's no justification for not allowing it for events with nonzero dt. For example, you don't even need to accelerate clocks at all, you can just consider two clocks at rest in F which are 10 light-seconds apart and synchronized in F. In this case if you define your events to be "left clock reading T=0" and "right clock reading T=8", then here dx=10 and dt=8--since these clocks are at rest relative to us it isn't hard to measure their positions and times. And then as a theoretical conclusion, we know it must be true that dt' = gamma*(dt - v*dx/c^2), so if the primed frame has v=0.8 this implies dt'=0 for this particular pair of events.

This is not the original definition of the problem and has nothing to do with the original experiment.

In what post was an "original experiment" specified?

In the original experiment the clocks start separated by the distance L.

I don't remember any post that said they "start" separated by L, it was just said that the clocks are at a distance of L in their rest frame F and are moving at v relative to the observer's frame F'. In my example this will be true as soon as the mechanism moves the clocks to the front and back of the rocket. We can define the "start" as some time when the rocket is already coasting and the mechanism has finished moving the clocks.

If you somehow think we must define the "start" as before the rocket leaves Earth, in this case your example doesn't meet the specified conditions at the "start" either, since at that point the clocks weren't yet at rest in F' which was one of the conditions discussed.

 

[starthaus]

But if you allow theoretical conclusions based on knowledge of the time between events dt in our frame, like the conclusion that two events with dt=0 in our frame must occur with a separation of dt'=gamma*v*dx/c^2, then there's no justification for not allowing it for events with nonzero dt.

Yes, there is. Not a theoretical disproof but a practical one, the measurement in the latter case requires the realization of the condition dt'=0 in the observer frame F'. By your own admission, this is not realizable.

 

[JesseM]

Yes, there is. Not a theoretical disproof but a practical one, the measurement in the latter case requires the realization of the condition dt'=0 in the observer frame F'. By your own admission, this is not realizable.

My own claim was about the practicality of measuring dt' in frame F', which is equally impossible in practice for dt'=0 and dt'=gamma*v*L/c^2, because we can't practically get rulers and clocks accelerated to the relativistic speed of F'. Your own argument about dt'=gamma*v*L/c^2 was based on the wholly impractical notion of a rocket being accelerated to a relativistic speed, and then on a purely theoretical calculation of what would be true in F' based on what we know is true in F. If this practically impossible scenario counts as a "realization" of dt'=gamma*v*L/c^2 in your increasingly bizarre terminology, then simply having two synchronized clocks at rest in F and picking two events on their worldlines with coordinates x=0,t=0 and x=10,t=8 in F (like the event of the first clock reading T=0 and the event of the second clock reading T=8) should also count as a "realization" of dt'=0, since a purely theoretical calculation of what would be true in F' also shows that dt'=0 for this pair of events.

Likewise, if you want a "realization" of dt'=0 not just for any pair of events but for a pair of events on the worldlines of clocks actually at rest in F' (as opposed to clocks at rest in F as above), then if "realization" can include the wholly impractical notion of a rocket that can accelerate to relativistic speeds, then my thought-experiment with the rocket that has a mechanism that slowly moves the clocks to either side should also count as just as much of a "realization" as your "realization" of dt'=gamma*v*L/c^2.

 

[starthaus]

My own claim was about the practicality of measuring dt' in frame F', which is equally impossible in practice for dt'=0 and dt'=gamma*v*L/c^2,

This is not true if you assume dt=0 instead of dt'=0. The impractical aspect goes away once you replace your condition dt'=0 with my condition dt=0.

 

[JesseM]

This is not true if you assume dt=0 instead of dt'=0.

Oh really? If F' is moving at 0.8c relative to our frame F, do you have a practical experimental method to verify that dt'=gamma*v*L/c^2 for two events which have dt=0 in F, using clocks that are actually at rest in F' to experimentally measure dt'? Or are you resorting to a purely theoretical calculation of the value of dt' in F'?

 

[starthaus]

Oh really? If F' is moving at 0.8c relative to our frame F, do you have a practical experimental method to verify that dt'=gamma*v*L/c^2 for two events which have dt=0 in F, using clocks that are actually at rest in F' to experimentally measure dt'? Or are you resorting to a purely theoretical calculation of the value of dt' in F'?

Sure I do, I am an experimentalist, remember? All I need to do is to determine v. The beauty of the method is that it works even with variable v. As long as you accept that SR is correct, the determination holds.

 

[JesseM]

Sure I do, I am an experimentalist, remember? All I need to do is to determine v. The beauty of the method is that it works even with variable v. As long as you accept that SR is correct, the determination holds.

So you are just doing a theoretical calculation in F', not actually experimentally measuring dt' with clocks at rest in F'? If so, am I also allowed to just measure dx and dt for two events in F, then do a theoretical calculation to find dt' in F?

 

[starthaus]

So you are just doing a theoretical calculation in F', not actually experimentally measuring dt' with clocks at rest in F'? If so, am I also allowed to just measure dx and dt for two events in F, then do a theoretical calculation to find dt' in F?

No, you are not since your experiment depends directly on dt'=0.

 

[JesseM]

No, you are not since your experiment depends directly on dt'=0.

I don't know what you mean by "depends directly on". The result of the theoretical calculation is dt'=0, but I start with the measured values of dx=10 and dt=8. Similarly you start with the measured values of dx=L and dt=0, and the result of your theoretical calculation is dt'=gamma*v*L/c^2. What possible difference can you point to that allows you to say your experiment is a "realization" of dt'=gamma*v*L/c^2 but mine is not a "realization" of dt'=0? In both cases we measure a dx and dt, then calculate a dt' theoretically using the equation dt' = gamma*(dt - v*dx/c^2).

 

[starthaus]

I don't know what you mean by "depends directly on".

It means that, according to your own description, you need to observe both clocks simultaneously in frame F'.

 

[JesseM]

It means that, according to your own description, you need to observe both clocks simultaneously in frame F'.

No, I already explained that this was only if you wanted to measure dt' using rulers and clocks at rest in frame F'. But your definition of what it means to "realize" dt'=gamma*v*L/c^2 does not require us to measure dt', it allows us to just calculate it theoretically from a dx and dt that we have measured in F. So you can stop linking back to that post of mine, it isn't relevant to the question of why you think it's possible to "realize" dt'=gamma*v*L/c^2 but not to "realize" dt'=0. If you allow a theoretical determination of dt' from measured dx and dt to count as a "realization" in the first case, why don't you allow it in the second case? Appears to be an irrational double-standard on your part.

 

[starthaus]

No, I already explained that this was only if you wanted to measure dt' using rulers and clocks at rest in frame F'. But your definition of what it means to "realize" dt'=gamma*v*L/c^2 does not require us to measure dt', it allows us to just calculate it theoretically from a dx and dt that we have measured in F. So you can stop linking back to that post of mine, it isn't relevant to the question of why you think it's possible to "realize" dt'=gamma*v*L/c^2 but not to "realize" dt'=0. If you allow a theoretical determination of dt' from measured dx and dt to count as a "realization" in the first case, why don't you allow it in the second case?

Because your experiment relies on simultaneous observation of the two clocks in frame F'. Mine doesn't.

Appears to be an irrational double-standard on your part.

There is no point in starting to sling ad-homs, let's keep the discussion civil.

 

[JesseM]

Because your experiment relies on simultaneous observation of the two clocks in frame F'.

No it doesn't. In both of the experiments I mentioned in post #65, I measured two events in frame F, getting dx and dt for these events in F, then I did a purely theoretical calculation to get dt' in F' (I have already stated this several times, are you reading my posts carefully?) That's exactly what you did too, so I don't see why your experiment is a "realization" of dt'=gamma*v*L/c^2 but mine is not a "realization" of dt'=0.

There is no point in starting to sling ad-homs, let's keep the discussion civil.

My point is that there's no rational argument for treating your type of experiment as a "realization" of dt'=gamma*v*L/c^2 but not treating mine as a "realization" of dt'=0.

 

[starthaus]

No it doesn't. In both of the experiments I mentioned in post #65, I measured two events in frame F, getting dx and dt for these events in F,

How do you do these "measurements"? You are located in frame F', in motion (at very high speed) wrt F.

 

[JesseM]

How do you do these "measurements"? You are located in frame F', in motion (at very high speed) wrt F.

OK, I see we were originally using F' to be the observer's frame, but in more recent posts I got mixed up and started using F as the observer's frame, sorry about the confusion. But is that the definition you have been assuming in all your posts? For example, in post #62 you said:

You are using dt'=0 which , according to your own admission is impossible to implement practically.
I am using dt=0 which is very easy to implement (and is implemented in prcatice).

Were you really saying here that it's impossible to "implement" a measurement of two events in our own primed frame such that we find dt'=0 for these events? If we synchronize two clocks at rest in our primed frame using the Einstein synchronization convention, then if we consider an event that was measured to happen next to the left clock when it read T'=5 and another event which was measured to happen next to the right clock when it read T'=5, doesn't this qualify as a measurement of dt'=0 for these two events?

If you got the notation confused too, can you clarify what you meant in this comment from post #60?

All you need to know is that they had been accelerated slowly enough such that they did not get out of synch. For that extent, the clocks may be totally enclosed in arocket, unobservable, you will still be able to determine their desynchroonization in frame F' based only on two things : proper length L and coordinate speed v.

Is F' still supposed to be the observer's frame? And were the clocks accelerated from an initial state of rest in F'? If so, then if they were both accelerated at the same rate, wouldn't they just remain synchronized in F'? Or were you assuming in this comment that F was the observer's frame and F' was the rest frame of the rocket?

 

[starthaus]

OK, I see we were originally using F' to be the observer's frame, but in more recent posts I got mixed up and started using F as the observer's frame, sorry about the confusion. But is that the definition you have been assuming in all your posts?

Yes, all along.

 

[JesseM]

Yes, all along.

OK, so can you answer my requests for clarification about your earlier posts #60 and #62? Specifically these:

If we synchronize two clocks at rest in our primed frame using the Einstein synchronization convention, then if we consider an event that was measured to happen next to the left clock when it read T'=5 and another event which was measured to happen next to the right clock when it read T'=5, doesn't this qualify as a measurement of dt'=0 for these two events?

were the clocks accelerated from an initial state of rest in F'? If so, then if they were both accelerated at the same rate, wouldn't they just remain synchronized in F'?

 

[starthaus]

OK, so can you answer my requests for clarification about your earlier posts #60 and #62? Specifically these:

The clocks are synchronized in the unprimed frame (the rocket frame), F. You (the observer) are located in the primed frame F'. (see above).

There is some work I have to do and I've been spending too much time on this website, so, with apologies, I will not be answering any more questions for another 12-18 hours. Sorry for the inconvenience but I will answer once I catch up with the work I have to do.

 

[JesseM]

The clocks are synchronized in the unprimed frame (the rocket frame), F. You (the observer) are located in the primed frame F'. (see above)

OK, I guess that's an answer to the question in the second quote, about your rocket example. But the question in the first quote wasn't asking about your rocket example at all, I was just asking why you don't think my example involving only clocks at rest in F' (and no rocket) would qualify as a "realization" of dt'=0. Again:

If we synchronize two clocks at rest in our primed frame using the Einstein synchronization convention, then if we consider an event that was measured to happen next to the left clock when it read T'=5 and another event which was measured to happen next to the right clock when it read T'=5, doesn't this qualify as a measurement of dt'=0 for these two events?

Maybe when you say it's impossible to "realize" dt'=0, you're just talking about determining that two events on the worldlines of clocks at rest in F have a dt'=0, not saying that it's impossible to determine dt'=0 for an arbitrary pair of events (like the events on the worldlines of clocks at rest in F' above)?