Special Relativity Controversy: Solving the Paradox

[LukasMont]

Hey guys,

My question is a bit confusing:

When we observe a train moving close to the speed of light, passing by the platform, according to the frame of reference in the platform, the clocks in the train are ticking slower than the clocks in the platform itself. According to the frame of reference in the train, however, the platform is moving in opposite direction, close to the speed of light, so the clocks in the platform would tick slower than the clocks in the train.

The contradiction to me is:

If, to the platform, 10min ellapsed in its clocks, but only 6min ellapsed in the clocks on the train (for example), to the train , 10min would have ellapsed in its own clocks and only 6min in the plataform's clocks. To someone in the platform, his twin in the train got younger; to the twin in the train, his brother in the platform was the one to get younger. I'm supposing a situation in which there's no accelerations, curves or turning points of any sort. Isn't it a contradiction? What sense could we make of all this?

How do we solve this?

 

[phinds]

Hey guys,

My question is a bit confusing:

When we observe a train moving close to the speed of light, passing by the platform, according to the frame of reference in the platform, the clocks in the train are ticking slower than the clocks in the platform itself. According to the frame of reference in the train, however, the platform is moving in opposite direction, close to the speed of light, so the clocks in the platform would tick slower than the clocks in the train.

The contradiction to me is:

If, to the platform, 10min ellapsed in its clocks, but only 6min ellapsed in the clocks on the train (for example), to the train , 10min would have ellapsed in its own clocks and only 6min in the plataform's clocks. To someone in the platform, his twin in the train got younger; to the twin in the train, his brother in the platform was the one to get younger. I'm supposing a situation in which there's no accelerations, curves or turning points of any sort. Isn't it a contradiction? What sense could we make of all this?

How do we solve this?

"younger / older" are relative terms and in the kind of space-time you are talking about are only meaningful if/when the two are back standing side by side after having started out side by side. To get THAT, you do have to have acceleration somewhere, otherwise you have to say "younger / older" according to WHICH frame of reference, which leads to the confusion you have.

If you get clear on the relativity of simultaneity you'll understand it.

 

[Nugatory]

If, to the platform, 10min ellapsed in its clocks, but only 6min ellapsed in the clocks on the train (for example), to the train , 10min would have ellapsed in its own clocks and only 6min in the plataform's clocks. To someone in the platform, his twin in the train got younger; to the twin in the train, his brother in the platform was the one to get younger. I'm supposing a situation in which there's no accelerations, curves or turning points of any sort. Isn't it a contradiction? What sense could we make of all this?

This apparently paradoxical result comes from failing to include the relativity of simultaneity in the analysis.

Look at https://www.physicsforums.com/threads/special-relativity-time-issues.846242/post-5307390 and https://www.physicsforums.com/threads/weird-time-dilation-question.883303/post-5552719 for an explanation.
(And I’ve posted this often enough in the past weeks that I really ought to write it up as a FAQ... soon)

Once you’ve thought the relativity of simultaneity through for this problem, you’ll realize that the question “which one has aged more?” Is poorly defined. To turn it into well-defined question with an unambiguous answer we have to bring the two twins back together again, standing side-by-side at the same place so relativity of simultaneity isn’t a problem. This is the classic twin paradox, explained in many many threads here and also at http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

 

[FactChecker]

Hey guys,

My question is a bit confusing:

When we observe a train moving close to the speed of light, passing by the platform, according to the frame of reference in the platform, the clocks in the train are ticking slower than the clocks in the platform itself. According to the frame of reference in the train, however, the platform is moving in opposite direction, close to the speed of light, so the clocks in the platform would tick slower than the clocks in the train.

The contradiction to me is:

If, to the platform, 10min ellapsed in its clocks, but only 6min ellapsed in the clocks on the train (for example), to the train , 10min would have ellapsed in its own clocks and only 6min in the plataform's clocks. To someone in the platform, his twin in the train got younger; to the twin in the train, his brother in the platform was the one to get younger. I'm supposing a situation in which there's no accelerations, curves or turning points of any sort. Isn't it a contradiction? What sense could we make of all this?

How do we solve this?

Remember that the observer on the platform and the observer on the train are comparing different sets of clocks. The observer on the platform witnesses the aging of the train person based on reports he gets from fellow platform people down the line as the train goes forward. On the other hand, the observer on the train witnesses the aging of the platform person based on reports he gets from fellow train people further and further back in the train as the train goes forward. So they can both think that the other observer is aging slower due to the fact that their information is coming from completely different directions.

 

[Mister T]

The person on the platform has two clocks, and he synchronizes them. He takes note of the reading on one clock just as the train passes (call this Event A), and then later he takes note of the reading on his other clock, again, just as the train passes (call this Event B). When he compares the readings on his two clocks to the readings on the train clock at Events A and B he concludes that the clock on the train is running slow.

But the person on the train will cry foul, because he will claim that the two platform clocks were not synchronized properly, and this is what causes the guy on the platform to conclude that the clocks on the train are running slow.

There is of course no foul. It's just that the notion of what's simultaneous is different in different frames. A notion that is glossed over in many books, leaving the reader unable to grasp what appears to be a contradiction.

 

[Erland]

Hey guys,

My question is a bit confusing:

When we observe a train moving close to the speed of light, passing by the platform, according to the frame of reference in the platform, the clocks in the train are ticking slower than the clocks in the platform itself. According to the frame of reference in the train, however, the platform is moving in opposite direction, close to the speed of light, so the clocks in the platform would tick slower than the clocks in the train.

The contradiction to me is:

If, to the platform, 10min ellapsed in its clocks, but only 6min ellapsed in the clocks on the train (for example), to the train , 10min would have ellapsed in its own clocks and only 6min in the plataform's clocks. To someone in the platform, his twin in the train got younger; to the twin in the train, his brother in the platform was the one to get younger. I'm supposing a situation in which there's no accelerations, curves or turning points of any sort. Isn't it a contradiction? What sense could we make of all this?

How do we solve this?

Let me recommend an old post by myself where exactly this problem is addressed:

https://www.physicsforums.com/threa...multaneity-easier-to-see-with-a-train.468826/

The point is that simutaneity is relative.