Understanding the Twin Paradox: Exploring Special Relativity and Time Dilation

[pervect]

Does it completely destroy the utility of SR to simply take the viewpoint that it really is only valid to talk about accelerated bodies as moving?
In other words, to say that the moving twin is in fact unjustified in saying the whole universe moved away from him and then toward him, which would have resulted in less time passing for the staying twin than himself (creating a paradox), but then doing (relatively) complex calculations with his frame of reference to show how the paradox is mathematically resolved.
That is to say, there would be no paradox in the first place if one were to accept the (wild?) proposition that when a spaceship undergoes events that cause its acceleration, less time actually passes for it than for the relevant entities that were not accelerated, and that that is the only valid viewpoint.
Therefore, 8 years passed for the spaceship and 10 for the Earth, period.
I understand (albeit loosely) that the time frame rotation considerations allow the paradox to be resolved, but doesn't that make the situation much more complex than it needs to be in order to be explained?
Why not merely make the reasonable interpretation that if an entity acclerates, and a certain time period passes until it decelerates and returns, then yes, *it* was the entity that actually moved, and therefore time dilated for it, and nothing else (respect to the IFR)...

I'm not quite sure how to answer this. In a hypothetical SR universe, It's equally consistent for the moving twin to regard himself as stationary, and the universe moving, as it is for the moving twin to consider the universe stationary, and himself moving. I'm a bit uneasy about the word "unjustified" here, the moving twin can adopt either point of view, as long as she sticks with it.

If you have two twins each driving a car, you don't expect them to both have driven the same distance when they reunite. Likewise, there is no inherent paradox to imagine two twins progressing through space-time, and being different ages when they reunite. There isn't any distance paradox, because you never expected the twins to drive the same distance in the first place.

In the case of the car driving through space, we say that the shortest distance between two points is a straight line, and thus we expect anyone who doesn't follow a straight line to drive a longer distance.

In the case of the space-time twins, the one that journeys through space-time in the space-time equivalent of a straight line, which is called a "geodesic", takes the longest time. This is perhaps confusing (because of the difference where "shortest" changed to "longest"), but it's not "paradoxical". If one draws a space-time diagram (which is highly recommended, but seems surprisingly difficult to get people to actually do for some unknown reason), the geodesic path are in fact straight lines on the space-time diagram.

The twin that ages less ages less not because they accelerated so much as because they didn't follow a geodesic path (the equivalent of a straight line path for the twins driving through space).

 

[Mister T]

Why not merely make the reasonable interpretation that if an entity accelerates, and a certain time period passes until it decelerates and returns, then yes, *it* was the entity that actually moved, and therefore time dilated for it, and nothing else (respect to the IFR)...

Because it doesn't provide a satisfactory quantitative answer at the most basic of levels. The magnitude of the difference in the twins' ages depends on the amount of time spent traveling while not accelerating. The easiest way to see this is to plot their paths through spacetime on a spacetime diagram. The longer the path lengths the greater the difference in their ages.