# Discuss events which are simultaneous in one frame?

by neopolitan
Tags: discuss, events, frame, simultaneous
P: 321
 Quote by kev When the radiactive lumps are being brought together by the inpartial robots, the rear lump is moving even faster (relative to the one and only sentient observer) than the nose lump that is transported "backwards" from the nose to the centre and so the rear lump experiences even more time dilation relative to the front lump from the point of view of the only observer. .
You asked to point out where you made the typo (it is more like an error). See above.
The difference in the speed of lumps in the frame external to the roicket is irrelevant. You are using the differences in speeds in the observer frame in order to justify a difference in time dilation. This is incorrect: if the lumps were synchronized prior to slow transport, they will remain synchronized after slow transport, the difference in speeds between the fore and aft lump in the external observer frame is irrelevant as long as the rules of slow transport were obeyed in the rocket frame (slow and equal speeds in the rocket frame).
P: 3,967
 Quote by 1effect You asked to point out where you made the typo (it is more like an error). See above. The difference in the speed of lumps in the frame external to the roicket is irrelevant. You are using the differences in speeds in the observer frame in order to justify a difference in time dilation. This is incorrect: if the lumps were synchronized prior to slow transport, they will remain synchronized after slow transport, the difference in speeds between the fore and aft lump in the external observer frame is irrelevant as long as the rules of slow transport were obeyed in the rocket frame (slow and equal speeds in the rocket frame).
In post #63 I said this:
 Quote by kev We are agreed that two clocks that are syncronised [according to Barney] will still be syncronised when they are transported to the centre of the rocket.
How does that differ from the underlined part of your post?

I also said this:
 Quote by kev In the example I gave the two tamper proof radioactive decay clocks are not syncronised after the acceleration phase of the rocket [as far as Barney is concerned] and they will still not be syncronised when transported to the centre ....
I'll say it again. "The radioactive lumps are not syncronised prior to the slow transport."

I can only assume that you also missed or skipped over the prior 2 posts (#71 and #72).

"if the lumps were synchronized prior to slow transport, they will remain synchronized after slow transport"

The point is that the lumps are not syncronised prior to the slow transport. Post #72 makes it clear that lumps are not syncronised after the rocket has accelerated from the Fred's rest frame and according to the rules of the thought experiment (post #72) the radioactive lumps are sealed or "tamper proof" and we are not allowed to to syncronise the radioactive lumps. THAT is the point of the radioctive lumps. There are conventional clock paired with each radiactive lump that can be syncronised.

So to sum up the last dozen posts where we have been repeating ourselves and making out that we are disagreeing when we are not:

1) Two clocks that are syncronised prior to slow transport will remain syncronised after slow transport.

2) Two clocks that are not syncronised prior to slow transport will not be syncronised after slow transport.

3) The radioactive lumps are not syncronised prior to slow transport (So point 2 applies)

4) The radioactive lumps are sealed in tamper proof containers and according to the rules no one is allowed to adjust, advance, retard or syncronise the radioactive lumps once the rocket has launched.

This is where me and neopolitan were at about half a dozen posts ago. The only thing neopolitan is not sure about is whether or not the the radioactive lumps will remain self syncronised during the acceleration of the rocket and after the rocket has stabilised to its cruising speed. I can assure you that the radioactive lumps will not remain syncronised after the acceleration phase.
P: 645
I thought about one thing a little late last night, when I should have been asleep. I think the replies which have appeared since then answer the question, but I want to make sure.

I have assumed that the rocket is rigid and that we are not talking about a real world situation here where there would be a lag between the commencement of acceleration along the length of the rocket. If we were assuming a (semi) real world rocket, then the motor would be in the tail and the whole length would contract physically, within its own frame. This is not how I have thought about the mind experiment. The whole frame accelerates together, if it accelerates at all.

I think that kev has considered the rocket to be rigid as well, but I am not totally sure. If the rocket according to kev is not rigid, then yes there will be a loss of synchronicity in the nominal rest frame (since motions would be created by the frame's acceleration, it would no longer really be a rest frame).

 Quote by kev This is a bit more tricky. While the rocket is accelerating it is length contracting according to Fred. The nose and tail therefore can not have the same velocity at all times according to Fred because the tail is catching up to the nose.
I think this is wrong. I think I can understand what you are saying - if it relates to length contraction - but I am pretty sure there is something wrong with the conceptualisation.

I will have to ponder it a bit more though and read the comments of other contributors.

cheers,

neopolitan
P: 321
U asked me to point the exact error in your post, so I did. I can only go by what you wrote in the respective post. If you intended to write something else, go ahead and correct it. :-)
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P: 16,969
 Quote by neopolitan I was further trying to say, perhaps not sufficiently clearly, that the unequal time dilation effects observed in another frame should explain how the clocks end up being synchronous in that other frame when they weren't initially.
This is correct, although the easiest way to show it is not directly through time dilation (because there are also synchronization issues), but through the spacetime interval as follows.

The rocket has proper length L and is moving at v in the (unprimed) observer frame. Without loss of generality the origin of both frames is taken to be the event, A, when the rear clock starts moving at u in the rocket frame. The event B is when the front clock starts moving at -u in the rocket frame. The event C is when the clocks meet.
A' = (0,0) --> A = (0,0)
B' = (0,L) --> B = (γLv/c, γL)
C' = (c L/(2u),L/2) --> C = (γL(c²+uv)/(2cu), γL(u+v)/(2u))

If the clocks are initially synchronized in the rocket frame then at A/A' and B/B' the clocks read 0. The spacetime interval |C-A|=L²(c²-u²)/(4u²), so at C the rear clock reads sqrt(L²(c²-u²)/(4u²))/c. The spacetime interval |C-B|=L²(c²-u²)/(4u²), so at C the front clock also reads sqrt(L²(c²-u²)/(4u²))/c.

So, basically, in the observer's frame, the rear clock moves for longer at a higher velocity (more time dilation) which balance out to have them synchronized at their meeting.

Note that, if the clocks are initially de-synchronized in the rocket frame by an amount dt, then they will be desynchronized by dt in all frames at their meeting.
 P: 645 DaleSpam, Can you confirm that acceleration does not cause a loss of synchonisation between two synchronised but non-collocated clocks in shared rest frame? This is kev's claim, not mine, my rebuttal is at post #75 (admittedly not with any hard data to back it up). cheers, neopolitan
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P: 41,311
 Quote by neopolitan Can you confirm that acceleration does not cause a loss of synchonisation between two synchronised but non-collocated clocks in shared rest frame? This is kev's claim, not mine, my rebuttal is at post #75 (admittedly not with any hard data to back it up).
Kev is correct. Whether clocks maintain synchronization during acceleration depends on how they are accelerated.
P: 3,967
Quote by 1effect

 Quote by kev When the radiactive lumps are being brought together by the inpartial robots, the rear lump is moving even faster (relative to the one and only sentient observer) than the nose lump that is transported "backwards" from the nose to the centre and so the rear lump experiences even more time dilation relative to the front lump from the point of view of the only observer.
You asked to point out where you made the typo (it is more like an error). See above.
The difference in the speed of lumps in the frame external to the roicket is irrelevant. You are using the differences in speeds in the observer frame in order to justify a difference in time dilation. This is incorrect: if the lumps were synchronized prior to slow transport, they will remain synchronized after slow transport, the difference in speeds between the fore and aft lump in the external observer frame is irrelevant as long as the rules of slow transport were obeyed in the rocket frame (slow and equal speeds in the rocket frame).
There is no error in my original statement. It is simply the point of view of the unaccelerated observer external to the accelerated rocket.

In the case of two clocks that are syncronised from the point of view of an observer on the rocket the clocks will read the same time when slow transported to the centre. The two clocks at the nose and tail of the rocket that appear syncronised to the onboard observer are not syncronised according to the unaccelerated external observer and the difference in time dilation during the slow transport accounts for why the external observer see the two clocks as syncronised by the time they are co-located at the centre of the rocket. Both internal and external observers agree that clocks are syncronised when they are are co-located. If the clocks were not syncronised according to the onboard observer prior to the slow transport, then both observers will agree they are not syncronised when they meet at the centre.
P: 645
 Quote by Doc Al Kev is correct. Whether clocks maintain synchronization during acceleration depends on how they are accelerated.
Can you check the conditions stated in the thread then, and see whether they qualify.
P: 645
 Quote by kev In the case of two clocks that are syncronised from the point of view of an observer on the rocket the clocks will read the same time when slow transported to the centre. The two clocks at the nose and tail of the rocket that appear syncronised to the onboard observer are not syncronised according to the unaccelerated external observer and the difference in time dilation during the slow transport accounts for why the external observer see the two clocks as syncronised by the time they are co-located at the centre of the rocket. Both internal and external observers agree that clocks are syncronised when they are are co-located. If the clocks were not syncronised according to the onboard observer prior to the slow transport, then both observers will agree they are not syncronised when they meet at the centre.
I agree with this. This is either not what you originally wrote, or not what I initially read.

In any event, this I can agree with.

I no longer understand why you need acceleration though, since the in-frame, non-collocated synchronised clocks will not be sychronised according to an external observer (not at rest relative to the clocks) irrespective of whether they undergo acceleration or not.

You might want to review post #71

 Quote by kev The tail is going faster at all times until the rocket starts cruising. The tail clock is time dilated more than the nose clock. When the clocks are syncronised in Barney's frame the nose clock should be showing a lesser time according to Fred using the formula $-L_o v/c^2$. The time dilation that occurs during the acceleration phase is doing exactly the opposite and is not self syncronising. When the clocks are brought together in the centre, the tail clock is time dilated even more making the situation worse.
cheers,

neopolitan
P: 3,967
 Quote by neopolitan I no longer understand why you need acceleration though, since the in-frame, non-collocated synchronised clocks will not be sychronised according to an external observer (not at rest relative to the clocks) irrespective of whether they undergo acceleration or not.
It is true that "the in-frame, non-collocated synchronised clocks will not be sychronised according to an external observer (not at rest relative to the clocks) irrespective of whether they undergo acceleration or not." However they will be out of sync in different ways according to the external observer. If the clocks are syncronised by someone onboard the rocket then the nose clock will show less elapsed time than the tail clock according to the external observer. If the clocks are not syncronised after the acceleration then the nose clock will show more elapsed time than the tail clock.

Basically I introduced acceleration to support your view that "the nose clock is in the future of the tail clock".

When the clocks on the rocket are syncronised according to an oboard observer (A) then to an external unaccelerated observer (B) the nose clock reads less than than the tail clock. If the rocket is 16 light seconds long and going at 0.5c relative to observer A then A will see the nose clock reading 8 seconds less than the tail clock. This is not supportive of your view that the "the nose clock is in the future of the tail clock".

When the clocks on the rocket are syncronised according to an onboard observer (A then obviously the nose clock and the tail clock will be showing the same time simultaneously as far as observer A is concerned. This is not supportive of your view that "the nose clock is in the future of the tail clock" either.

However if we place syncronised clocks on the rocket and then accelerate it, an unaccerated external observer will see that the nose clock IS in the future of the tail clock, if the onboard observer does not re-syncronise the clocks after the acceleration. The onboard observer and the external unaccelerated observer will both agree that the nose clock has aged more than the tail clock.

To give an extreme example. We place identical twin babies on a very long rocket. One twin baby is at the nose and the other at the tail of the rocket. The rocket is accelerated very hard for a very long time and then allowed to cruise for long enough to allow stresses and strains to stabilise. We bring the twins together at the centre of the rocket and we see that the nose twin is an old guy with a long white beard while the tail twin is still a baby. Since they are both co-located no observer can disagree that the nose twin is in the future of the tail twin.

By the way I am talking about a traditional rocket with a single rocket at the rear and the rocket is allowed to undergo natural length contraction.

Now if instead of accelerating the rocket that has the twins onboard, we get another rocket and accelerate away in that. We turn around and fly past the the rocket with the twins onboard and they appear to be ageing differently by our observations. Finally we land next to the twin's rocket and the twins come to meet at at the centre of their rocket. In this case we note the twins did not really age differentially. They are both older and it is us that have aged less. I am trying to show that Lorentz transformations result in real physical changes and that what may appear to be symetrical situations are not really symetrical when you take acceleration into account.
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P: 16,969
 Quote by neopolitan Can you confirm that acceleration does not cause a loss of synchonisation between two synchronised but non-collocated clocks in shared rest frame? This is kev's claim, not mine, my rebuttal is at post #75 (admittedly not with any hard data to back it up).
As Doc Al mentioned the answer depends on the details of the motion, which I don't think have been unambiguously defined here. So instead of directly answering I will refer you to

http://www.mathpages.com/home/kmath422/kmath422.htm

Which gives a more detailed treatment of Born-rigid acceleration than I could. I am sure that you could find other pages describing other acceleration schemes.
P: 645
 Quote by DaleSpam As Doc Al mentioned the answer depends on the details of the motion, which I don't think have been unambiguously defined here. So instead of directly answering I will refer you to http://www.mathpages.com/home/kmath422/kmath422.htm Which gives a more detailed treatment of Born-rigid acceleration than I could. I am sure that you could find other pages describing other acceleration schemes.
If I have this right, which is by no means a given, this theoretical effect is due to a rigidity which is not actually physically possible. One consequence is that the tail of the rocket will have to travel faster than the nose to mainain this impossible rigidity - according to an external observer - within the "rest frame" the tail will now not be at rest relative to the nose, but will have a velocity in the direction of motion as perceived by the the external observer.

That, to me, would explain why a tail observer would be younger than the nose observer.

I suspect that in reality other effects prevent this from happening.

Standing by to be corrected :)

cheers,

neopolitan
P: 645
 Quote by kev It is true that "the in-frame, non-collocated synchronised clocks will not be sychronised according to an external observer (not at rest relative to the clocks) irrespective of whether they undergo acceleration or not." However they will be out of sync in different ways according to the external observer. If the clocks are syncronised by someone onboard the rocket then the nose clock will show less elapsed time than the tail clock according to the external observer. If the clocks are not syncronised after the acceleration then the nose clock will show more elapsed time than the tail clock.
See earlier post on acceleration, I don't think that this is what I had in mind since, as DaleSpam pointed out, we have not sufficiently defined the scenario. When I wanted a rocket that didn't compress due to the acceleration, I didn't mean that I somehow wanted to do away with length contraction. The reasoning behind this is that the rocket will compress mechanically if the motor is at the tail (if the rocket is pushed) and stretch mechanically if the motor is at the nose (if the rocket is somehow pulled) and I wanted to eliminate the differences involved.

 Quote by kev Basically I introduced acceleration to support your view that "the nose clock is in the future of the tail clock". When the clocks on the rocket are syncronised according to an oboard observer (A) then to an external unaccelerated observer (B) the nose clock reads less than than the tail clock. If the rocket is 16 light seconds long and going at 0.5c relative to observer A then A will see the nose clock reading 8 seconds less than the tail clock. This is not supportive of your view that the "the nose clock is in the future of the tail clock".
First, thanks for coming out in support. I do appreciate that.

The problem, however, is that we have a disagreement about the meaning of "the nose clock is in the future of the tail clock". I explained what I meant to JesseM in post #42.

If you read that post, you can hopefully see why I think that, in the scenario you describe above, the nose clock is in the future of the tail clock.

cheers,

neopolitan
 P: 3,967 Hi neopolitan, Essentially the method of acceleration i was describing is born-rigid acceleration as described in the link. I was totally ignoring Newtonian compression forces under acceleration and that is why I mention allowing time for the rocket to settle to its natural length contracted time. For example a fast accelerating rear wheel drive car will get shorter (or a front wheel drive car get longer) for reasons that have nothing to do with relativity. The impossibility of ideal born-rigid motion is due to consideration of those Newtonian compression and tension effects under acceleration. Ideal born rigid acceleration would require each particle of the rocket to have its own rocket motor. However, we can ignore those petty details if we allow the rocket to cruise for a while after acceleration to settle down. Dalespam correctly points out that how the clocks go out of sync during acceleration depends on the acceleration scheme that is employed. However, I have been looking at acceleration methods in relation to this topic and I have come to this conclusion: There is no acceleration scheme that can be applied to two clocks (in flat space) (that are spatially separated by a non zero distance along the x axis) that will keep the clocks syncronised as viewed by an observer co-moving with the clocks when the clocks have reached a constant and equal (non zero) velocity along the x axis, relative to the initial frame.
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P: 16,969
 Quote by neopolitan If I have this right, which is by no means a given, this theoretical effect is due to a rigidity which is not actually physically possible.
It is indeed impossible to have a perfectly rigid object, but it is theoretically possible to have perfectly rigid motion. If you read more about Born rigidity you will notice that it is always used to describe motion rather than objects.

If you look at the diagram on the page I linked to such a motion is possible, but each particle would require it's own "engine".
P: 645
 Quote by DaleSpam It is indeed impossible to have a perfectly rigid object, but it is theoretically possible to have perfectly rigid motion. If you read more about Born rigidity you will notice that it is always used to describe motion rather than objects. If you look at the diagram on the page I linked to such a motion is possible, but each particle would require it's own "engine".
Would not then each particle in the engine require an engine, and so on. Which makes it sort of impossible?

cheers,

neopolitan
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P: 16,969
 Quote by neopolitan Would not then each particle in the engine require an engine, and so on. Which makes it sort of impossible?
Sure, it is practically impossible, but not logically or theoretically impossible. Additionally, it still makes sense to understand Born rigid motion as a close approximation to easily achievable situations, e.g. a short stiff rocket with gentle thrust.

On the other hand a perfectly rigid object is not even theoretically possible and inherently leads to logical contradictions. Such an idea is generally not useful even as an approximation.

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