Twin Paradox Without Accelerations
In the above argument it is stated that Prime undergoes accelerations whereas Unprime does not, therefore, it is perhaps no surprise that the experience different things (in particular, a different duration for Prime's trip). Just in case the reader might decide that it must be the accelerations that cause the difference in duration for the twins, this section describes how it is possible to explain the paradox entirely without accelerations.
Instead of having Prime start at rest, next to Unprime, then accelerate to speed v, then stop at the distant station, then accelerate once again until moving at speed v back toward the initial station, etc., imagine the following demonstration. Unprime sits still at the original station. According to Unprime, Prime is moving along (and always has been) at the speed v, and passes Unprime at the moment that Unprime's and Prime's watches read t = t' = 0. Prime continues on, ultimately passing the distant station. At the moment he passes the distant station, Prime's watch reads t'=0.75 years (for reasons he understands, and were explained above). At that exact moment, Doubleprime (another person), passes the same distant station in another train heading back toward the original station at speed v. Both Prime and Doubleprime notice that the station clock reads t = 1.25 years. The also notice that both their watches display the time t' = t'' = 0.75 years (Doubleprime's watch is just coincidently equal to 0.75 years). According to Unprime (or his cohorts spread all over the place) Doubleprime has always been moving this way. Eventually Doubleprime passes the original station. As he passes, Doubleprime notices that his own watch reads 1.5 years, and that the watch on Unprime's wrist reads 2.5 years. Unprime notices the two watches also. Unprime's explanation is Time Dilation (just as in the above explanation). Doubleprime's explanation is that Unprime's clocks were running slowly and out of synchronization (again, just as in the above explanation).
The resulting difference between the reading on Unprime's watch and that on Doubleprime's watch is not the result of any accelerations experienced by anyone (nobody experienced any accelerations). But notice that the full duration measured by Unprime was, of course, measured in one reference frame; the duration for the full experiment recorded by Prime and Doubleprime required the combined results acquired in two different reference frames. That is the source of the asymmetry in the results. This explanation of the twin paradox (without accelerations) shows that it takes TWO different reference frames to keep track of the time duration experienced by the twin who actually takes the trip, while it take only one frame to keep track of the duration for the twin who stays at home. Their situations are fundamentally different, and the different time durations they experience are the result.
