when you are measuring a length of a subject in a moving frame you get length contracted but after bringing the subject to rest frame you get the proper length. Which I understand the relativistic effects get diminished when you measure the subject in rest frame. In case of time dilation why are we getting a persistent relativistic effect (as twin paradox says) after bringing two subjects to the same frame ,one being older than other one. we will always observe two one meter scale same length in rest frame no matter how much velocities they had earlier. My question is why time dilation effect being persistent in rest. Does that mean time is like a continuous chain , so that when you manipulate a part of it ,the effect remain forever along the chain. Unlike length we can't separate it by parts of 1 unit.


I'm not sure I have a definitive answer but note that time dilation effects accumulate over time, while length contraction effects accumulate over distance. In other words, if you let two clocks run for a long time then a significant dilation difference can build up. Likewise, if you have two very long measuring rods, then the total effect of contraction will grow to a noticeable difference in the positions of the ends.

The reason we can "see" one kind of accumulation and not the other is that we are constrained to move along timelike worldlines. This also manifests in the simple fact that it only takes one observer to measure a time interval in one location (e.g., you can look at your watch!), but if you want to measure a distance interval at one time, you need two separated observers who have previously synchronized their clocks.

  • $\begingroup$ I also think this way. I don't know if this is a sufficient explanation. $\endgroup$ – user146554 Apr 28 '18 at 5:19

I suppose the natural counterpart to the twin scenario is Bell's spaceship scenario (that was first pointed out by Dewan and Beran).

While it's customary to cast the twin scenario in a form where the twins rejoin on a single location, it's actually sufficient for the twins to have no velocity relative to each other at the end. When they have no velocity relative to each other then for both twins time is elapsing at the same rate, so they can see for which one less proper time has elapsed.

(A way to visualize this variation on the scenario: take a triplet, and position sibling 1 and sibling 2 in one location, and sibling 3 in a second location. Initially they have no velocity relative to each other, so they can synchonize their clocks. Now sibling 2 goes on a journey from sibling 1 to sibling 3, traveling fast enough to cause a measurable relativistic effect. As sibling 2 joins sibling 3 they observe, as they knew they would, that for sibling 2 less proper time has elapsed than for sibling 1 and 3. Relative to siblings 1 and 3 sibling 2 has traveled more spatial distance, hence for sibling 2 less proper time has elapsed.)

In the case of Bell's spaceship scenario the length contraction is made physically apparent by the fact that the logical implication of the principles is that the highly rigid tether will snap (if the leading and the trailing spaceship have exactly the same acceleration relative to a common non-accelerating frame).

Come to think of it, I guess that with 5 siblings the two scenarios can be combined. Let me abbreviate them to s1, s2, s3, s4, s5.
Start with three locations, on a straight line, equally spaced.
Groups: (s1, s2), (s3, s4), (s5)
s1, s3, and s5 maintain a synchronized time throughout, let me refer to that as 'formation time'.
s2 and s4, connected by a sufficiently inelastic tether, journey to s3 and s5 respectively.
When they arrive then for s2 and s4 less proper time has elapsed than for the s1-s3-s5 formation, and the tether has snapped.

All in all it seems to me that it's probably wrong to have a notion of a difference along the lines of 'time dilation can accumulate' whereas 'length contraction always reverts'. It seems to me that as long as Bell's spaceship scenario is not fully understood special relativity is not fully understood.


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