Hurkyl said:
It's not simply a novelty -- it's for educational purposes. People really do make that mistake and other similar ones (even people that should know better), so its important to spend some time teaching students to identify the flaw, and demonstrating that it really is flawed.
Stopping the clock during an experiment doesn't stop the experiment.
No, but I meant that we could redefine the end of the experiment, too.
State your claim precisely, please. Current problems include:
(1) Which events?
(2) If you mean the events where the twins separate and reunite, then they are timelike separated, and there is no intrinsic meaning to the 'distance' between them. (It would make sense to ask about the proper duration, but of course, everyone would measure the same value)
(3) If you mean to refer to coordinate-dependent quantities, then I think you are going to need to put some constraints on what coordinate charts each twin uses.
1) u pick em
2) I mean cumulative distance traveled.
3) no constraints, as long as each twin measures everything properly.
Really, I would just like to see why people believe that acceleration is crucial, when the experiment could be presented without acceleration with the same result. By same result I mean that the twin who measured the shorter distance has less elapsed time, not that the twins reunite. For example, it has been presented as two separate trips with a third observer traveling from the distant star system to earth, nobody accelerates, and we just add up the two trips and get the same result. Or the experiment could end when the ship passes the turnaround point. With a third observer there with a clock. The twins don't have the novelty of reuniting, but we have the same result of two defined events, and one twin has less elapsed time between them than the other.
And I think it's worth mentioning that, in the normal twins paradox, that the twins' reunion doesn't really change anything. It's not like the laws of physics change because they reunite.
I don't dispute that the traveling twin will age less, but he will age less (have less elapsed time between events) during a one-way journey as well. And we don't need to reunite the twins to show this. Unless we consider the most important thing here is to have two twins look at each other and have one say "Gee, you're older than me, how did that happen?"
Sure, in the common example, the twin who accelerates does indeed age less, but is there any evidence (or logical deduction) that shows that this is the reason? SR certainly doesn't make such a claim. Using SR, we can ignore acceleration altogether and get the same result. We can even say that the ship never accelerated, and the Earth (and distant star system) were
moved by magic/God/Unknown reasons, and when the twins reunite, the one in the ship is younger according to SR. Yes, that's silly, I know. Just making a point.
And I have seen many posts saying I'm wrong, but none that say how, or provide any substantiation of the claim that acceleration is important as a general rule, not just in a specific scenario where the accelerated twin
happens to age less.
That's what I'm asking for.
Al