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Discuss events which are simultaneous in one frame? 
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#73
Feb1508, 11:38 PM

P: 321

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). 


#74
Feb1608, 12:49 AM

P: 3,967

I also said this: 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. 


#75
Feb1608, 02:06 AM

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


#76
Feb1608, 07:59 AM

P: 321




#77
Feb1608, 08:49 AM

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P: 17,293

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 CA=L²(c²u²)/(4u²), so at C the rear clock reads sqrt(L²(c²u²)/(4u²))/c. The spacetime interval CB=L²(c²u²)/(4u²), so at C the front clock also reads sqrt(L²(c²u²)/(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 desynchronized in the rocket frame by an amount dt, then they will be desynchronized by dt in all frames at their meeting. 


#78
Feb1608, 11:23 AM

P: 645

DaleSpam,
Can you confirm that acceleration does not cause a loss of synchonisation between two synchronised but noncollocated 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 


#79
Feb1608, 12:08 PM

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P: 41,459




#80
Feb1608, 12:11 PM

P: 3,967

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 colocated at the centre of the rocket. Both internal and external observers agree that clocks are syncronised when they are are colocated. 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. 


#81
Feb1608, 12:39 PM

P: 645




#82
Feb1608, 12:46 PM

P: 645

In any event, this I can agree with. I no longer understand why you need acceleration though, since the inframe, noncollocated 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 neopolitan 


#83
Feb1608, 02:27 PM

P: 3,967

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 resyncronise 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 colocated 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. 


#84
Feb1608, 04:20 PM

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P: 17,293

http://www.mathpages.com/home/kmath422/kmath422.htm Which gives a more detailed treatment of Bornrigid acceleration than I could. I am sure that you could find other pages describing other acceleration schemes. 


#85
Feb1708, 12:57 AM

P: 645

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 


#86
Feb1708, 01:10 AM

P: 645

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 


#87
Feb1708, 01:29 AM

P: 3,967

Hi neopolitan,
Essentially the method of acceleration i was describing is bornrigid 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 bornrigid 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 comoving with the clocks when the clocks have reached a constant and equal (non zero) velocity along the x axis, relative to the initial frame. 


#88
Feb1708, 08:59 AM

Mentor
P: 17,293

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". 


#89
Feb1708, 10:46 AM

P: 645

cheers, neopolitan 


#90
Feb1708, 11:49 AM

Mentor
P: 17,293

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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