It is violated in exactly the same way. The object that accelerated away from the Frame of Origin (in this case, the still ground) is the one that will be time dilated. So the train’s clock turns slower than the station’s clock.
True, but we haven’t been calculating for acceleration. We’ve just been dealing with the period of constant relative velocity after acceleration. And even with initial acceleration, the observers would see each others clocks as running slowly during the period of constant velocity.
We also don’t have a well defined “end” in this situation. If the train decelerates, then we will have a similar situation to the Twin Paradox. But if the station accelerates to reach the speed of the train (ignoring that it’s practically unlikely), the end result should be that the clocks are still synchronized.
I’m afraid you would have to prove that one. The math won’t workout (well… bend enough rules and you can make anything seem to workout).
Running the same speed, but no longer in sync. Remember, the twin A actually does age more and twin B less. Time dilation isn’t merely a perception issue.
So I take it you want to defend the stance that both station and train see the other clock moving slower than its own?
I just showed that: a clock traveling at constant velocity will be observed to run slowly by a stationary observer, because that observer will see a point on the edge of the clock traveling at the speed of line trace a longer path than will a similar particle tracing the edge of a clock in his own frame.
Right, but twin A is the only twin that accelerates in that problem. If twin A were to accelerate to constant velocity, and then twin B accelerated to the same constant velocity in the same direction (such that they are in the same frame again), the clocks would be synchronized again.
Not particularly. There are dozens of more reputable sources around the internet that do a much better and more thorough job of saying exactly what PhyBang, Farsight, and I have been saying.
This is what you have claimed;
And you haven’t supported that notion at all. Nor can you if you do your math right, because it isn’t true.
No, this is what you said;
No, merely running the same speed. The aging doesn’t reverse. The clocks would be offset.
I wouldn’t be including Farsight in your crew. And you really need to stick just to “Carleas”.
So far, you still haven’t raised any point that I can see as relevant to the OP.
I supported that notion in my last post:
Because both observers see the other observer’s clock as moving, both see the other’s clock as running slowly.
To borrow a refrain: show the math. I honestly don’t know how the acceleration equations would work out, but I know that 1) in the Twin paradox, only one twin accelerates, 2) it is that acceleration that makes their clocks read differently, 3) I’m not taking your word for it that the math works out, because as far as I can tell neither of us have an equation that calculates the effect of constant acceleration on time.
Wrong, by your own sources.
“More aging” == “clocks running FASTER”.
a = v/t
a’ = v’/t’
(falsely assuming v’ = v);
a’ = v/t’ =>> v = a’t’
a = v/t =>> v = at
since t’ = L(t - vx/c^2);
a’ = v /((L(t - vx/c^2))
or
v’ = a’ * L(t - vx/c^2)
v = a * L(t’ - vx/c^2)
It is just arithmetic/algebra.
Except that acceleration doesn’t involve a constant v, so it’s not just plug and play. As I said in one of these threads, acceleration has to require an integral over time to account for the changing velocity.
You’re conflating the two situations we’re talking about. In the spin counter example, both observers see the other’s clock as running slowly. In the Twin Paradox, one twin ages more than the other. Both still see the other’s clock as running slowly during the periods of constant velocity, but they ultimately undergo asymmetric experiences. The Twin Paradox also requires Relativity of Simultaneity to solve :-"
You have a LOT to learn about relativity and “accepted Science”. The Twin paradox has nothing at all to do with simultaneity issues and is easily resolved by merely understanding that clocks slow down for objects moving faster than the frame of origin. You can’t reverse the logic because there is only one frame of origin for the observers.
But enough religious/political debating with you.
Since every scientific textbook that actually takes the time to go through the mathematics of the twin paradox disagrees with your position, Jimmy, don’t you think that perhaps you come across as the religious zealot here?
I must admit, it is a brilliant rhetorical tactic to accuse those who know the science and present the relevant mathematics as being those who unthinkingly believe in what they have read. And then you show you can’t actually use the relevant equations. For example, your acceleration equations are laughably bad; it is literally hard to know where to begin since in your equations you seem incapable of determining the difference between a coordinate value and a delta value on a given axis.