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Twins paradox and ageing 
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#55
Dec2909, 03:55 PM

P: 1,414

The way I interpret the experiments that I've read is that the tick rates of clocks (ie. the periods of oscillators) are affected by velocity changes. Do you think this is wrong? 


#56
Dec2909, 08:39 PM

P: 801

The tick rate of a valid clock is 1 sec per second of proper time in its rest frame, regardless of its motion or acceleration. It's the ratio between proper time in the rest frame of the clock and coordinate time in the observer's rest frame that "changes" with a change in the relative velocity between clock and observer, not anything physical about the clock itself. 


#57
Dec3009, 08:04 AM

P: 1,414

Now accelerate one clock, then bring it back aside the other again and they display different times. Doesn't it make sense to attribute this difference to the acceleration? In light of the evidence, I don't understand how one can say that a different tick accumulation (associated with an acceleration) isn't "anything physical about the clock itself." 


#58
Dec3009, 08:40 AM

P: 801

In other words, one path between two events has less elapsed proper time than the other path between those events. Each clock keeps good proper time. The difference in clock readings is due to a difference in elapsed proper time, not a difference in the clocks. 


#59
Dec3009, 09:32 AM

P: 1,414

We know that the two clocks have counted a different number of ticks, and that one clock was accelerated and the other not. So, we agree that we can attribute the difference to the acceleration intervals. Spacetime path(s) notwithstanding, I think we're forced to conclude that the periods of the oscillator(s) of the traveller's clock and the traveller himself have been temporarily, physically altered during their accelerations. 


#60
Dec3009, 09:41 AM

P: 801

Each twin's age and clock readings reflect actual time elapsed. The reason for the difference is that the actual time elapsed is different. Acceleration affects the spacetime paths, which affects the proper time elapsed. The only reason SR predicts different clock readings for the twins is because it assumes that each clock accurately records the elapsed time for each twin. 


#61
Dec3009, 11:42 AM

P: 1,060

When talking of timelike intervals, which are the only type which can be traversed by a clock, the time recorded by an ideal clock while traversing this interval is said to be proper time whatever its motion or path through that interval. It is a measure of spacetime path length. In a frame in which it is at rest the proper time recorded by the clock is the same as the coordinate time, that is the projection of the interval onto the time axis of that frame. Since the coordinates in any inertial frame can be Lorentz transformed into coordinates in any other relatively moving inertial frame, the coordinates of a clock in any infinitessimal region of its travels can be transformed into those of a frame at which it as at rest in that infinitessimal region. Since all inertial frames are equivalent in SR, each infinitessimal amount of coordinate time, which in each comoving rest frame is equal to proper time, can be summed, and, in the limit, as these infinitessimal regions are allowed to become smaller and smalle, so apprroaching zero, integrated over the path (timelike) of the clock to give the exact proper time, as a sum of coordinate times, for this path. So there is nothing in this derivation of proper time which gives any clock any preference over any other clock as all proper times can be made equivalent to the sum of coordinate times of a clock in frames in which it is at rest. In other words the time recorded by a clock can be viewed as the sum of coordinate times in inertial frames in which it is (for an infinitessimally small region) at rest, and since the use of all inertial frames is equally valid, all times so recorded are equally valid or "correct". So for a clock, any clock, the time it records, proper time, is for that clock THE time. Matheinste. 


#62
Dec3009, 01:00 PM

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P: 17,202

I don't think that this is nearly as complicated as many of the posters have made this out to be. The reason that light clocks exhibit time dilation is the second postulate. The reason that all other clocks exhibit the same time dilation is the first postulate.
There is no deeper reason than the postulates, they are fundamental. And the reason we accept the postulates is that they fit the data very well. 


#63
Dec3009, 01:09 PM

P: 1,060

Matheinste. 


#64
Dec3009, 01:30 PM

P: 451




#65
Dec3009, 02:49 PM

P: 1,414

Anyway, I think this is a better conceptual (as well as intuitive) path to follow toward a deeper physical understanding of differential aging than the spacetime geometry. 


#66
Dec3009, 02:56 PM

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#67
Dec3009, 04:50 PM

P: 1,060

Matheinste. 


#68
Dec3009, 04:51 PM

P: 1,060

Matheinste. 


#69
Dec3009, 07:18 PM

P: 801

Conceptually, it's like saying that my bathroom scales read higher because I ate too much ice cream and cake last week. The scales read higher because I'm heavier, not because of any difference in the scales' operation. This is true of any measuring device: different results do not imply a difference in the measuring device itself. 


#70
Jan910, 03:14 PM

P: 1,414

We're setting aside the spacetime interpretation for the moment. 


#71
Jan910, 03:30 PM

P: 451

Is it the velocity that alters that state of the clock or is it the acceleration that alters the state of the clock? What experiment can we do to measure which is responsible? Two things happen and a third is found to be correlated. If you can never separate the two things how will you ever be able to call one the cause and the other not the cause? 


#72
Jan910, 03:53 PM

P: 1,414

The traveller, and all other observers, watched the earthsun system rotate 20 times during the trip. Yet the traveller and his clock only ticked off 5 years. We agree that difference in tick rate is due to difference in velocity, don't we? It seems clear to me from experiments that it isn't intervals of constant, uniform velocity that exhibit tick rate changes, but intervals of acceleration. 


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