Train platform -- light speed and time quandry

[uniqueland]

TL;DR Summary

how can a train traveling at light speed, travel at two different speeds being the same train, depending upon whether you are on the train platform or in the train

Summary: how can a train traveling at light speed, travel at two different speeds being the same train, depending upon whether you are on the train platform or in the train

You say good bye to your friend at the train station. You get into train that will travel at just under light speed (ignore the physical issues of impossible g forces for such acceleration and deceleration), There is a physical "counter", perhaps a physical bar that sticks out and the train srikes it with each revolution., Each time the train completes a revolution and strikes the bar as it passes, the counter increases by 1. There is such a counter on both the train and at the train station platform. To you, on the train, you have been on the train for 10 minutes but to your friend at the platform who you said goodbye to before getting onto the train, 10 years have passed. So how many revolutions did the train make around the planet? IT is the same train, but the counter ON the train would show 10 minutes worth of revolutions at 7 revolutions per second and the counter at the platform would show 10 years worth of revolutions at 7 revolutions per second. How can the same train show two different counters when it had to physically hit the counter physical "bar" that with each contact revolution it increase the counter by 1? How many times did it hit that counter bar? how can it be two different answers? when you get off the train, you are 10 minutes older but your friend is 10 years older.

 

[Gaussian97]

This is basically the twin paradox, read this http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

 

[sophiecentaur]

I think you are trying to impose non relativistic conditions on a very relativistic situation. It is not an intuitive thing.
If you start with the idea that everyone will measure c as the same value (not intuitive) then you (or Einstein or a textbook etc.) will get the right result - which you can believe (but maybe not ‘feel is right’).

 

[Bandersnatch]

To you, on the train, you have been on the train for 10 minutes but to your friend at the platform who you said goodbye to before getting onto the train, 10 years have passed. So how many revolutions did the train make around the planet? IT is the same train, but the counter ON the train would show 10 minutes worth of revolutions at 7 revolutions per second and the counter at the platform would show 10 years worth of revolutions at 7 revolutions per second. How can the same train show two different counters when it had to physically hit the counter physical "bar" that with each contact revolution it increase the counter by 1?

Let's say we ignore the centripetal acceleration the train would have to experience in order to do what is described, since it's incidental to the problem you have. Maybe the train travels through a toroidal space, like in the game Asteroids. Or it goes one way, turns back, and returns, as in the already mentioned twin paradox (again, ignoring acceleration at the turning point).
Then, it's a matter of applying not only time dilation but also length contraction. The distance covered is not the same. The train traveling at close to c w/r to the observer on Earth needs to travel a very short distance between each hit on the counter.

 

[Ibix]

the counter ON the train would show 10 minutes worth of revolutions at 7 revolutions per second and the counter at the platform would show 10 years worth of revolutions at 7 revolutions per second. How can the same train show two different counters when it had to physically hit the counter physical "bar" that with each contact revolution it increase the counter by 1? How many times did it hit that counter bar?

The counters will agree - they must.

Rotational motion is a pain to analyse, so I'm going to simplify your experiment. Instead of circling, the train runs backwards and forwards on a straight track, tripping the counter every time it passes the midpoint. The calculation for the station frame is pretty much as you say. However, as seen by the train, it's the station that is moving. So the station and the track are length contracted - so each leg of the journey takes almost no time to complete. Result - the counter frequency is very, very, high for a short (by the train clock) time, leading to the same count as the station observer sees.

Something similar will apply to a train moving in a circle, but you need a rotating frame, and defining exactly what you mean by that gets very messy very quickly.

 

[metastable]

(ignore the physical issues of impossible g forces for such acceleration and deceleration)

If we don’t ignore the physical issues I think you’ll see an issue with the experiment as described from the centrifugal forces — based on the answer to another recent paradox thread I don’t believe the train will remain rigid.

 

[Ibix]

based on the answer to another recent paradox thread I don’t believe the train will remain rigid.

It doesn't matter in this case. He's not trying to sync clocks in the train.

 

[uniqueland]

My point is that I understand, ignoring the multitude of impossible issues involving centrifugal forces and rotational issues that arise when traveling in a circle and ignoring the obvious acceleration and deceleration issues, assuming instant acceleration as if the train was like a beam of light coming out of a flashlight, when you are a passenger in this "instant" light speed train, and you are in the train for 10 minutes, assuming your eyes could follow it, you will watch the counter count 420 times around per minute or 4200 times in 10 minutes. You will see it strike the bar, assuming you had eyes capable of such impossibility, but to your friend on the train station, his counter counted 10 years worth of revolutions. by hitting the exact same trigger bar which would be 420 X the number of minutes in 10 years = counter result. So are you saying that I, as a passenger on the light speed train, will experience and see with my super human eyes, the counter count up to the 10 year number, ,which would have to meant that I experienced going around (leaving aside the issues of going around rather than going flat on a track) ten YEARS worth of revolutions, in only ten MINUTES which would then be exponentially faster than the mere speed of light, which would be an impossibility., ?

 

[uniqueland]

The counters will agree - they must.

Rotational motion is a pain to analyse, so I'm going to simplify your experiment. Instead of circling, the train runs backwards and forwards on a straight track, tripping the counter every time it passes the midpoint. The calculation for the station frame is pretty much as you say. However, as seen by the train, it's the station that is moving. So the station and the track are length contracted - so each leg of the journey takes almost no time to complete. Result - the counter frequency is very, very, high for a short (by the train clock) time, leading to the same count as the station observer sees.

Something similar will apply to a train moving in a circle, but you need a rotating frame, and defining exactly what you mean by that gets very messy very quickly.

so you are saying that the distance is contracted to such a tiny number, that to travel back and forth (or around if you ignore the circular issues) would be that the train, traveling at the speed of light would achieve the same amount of revolutions in ten minutes, considering the extreme length contraction, as it would in ten years traveling the actual revolution of the Earth each time around?

 

[Nugatory]

so you are saying that the distance is contracted to such a tiny number, that to travel back and forth (or around if you ignore the circular issues) would be that the train, traveling at the speed of light would achieve the same amount of revolutions in ten minutes, considering the extreme length contraction, as it would in ten years traveling the actual revolution of the Earth each time around?

“In ten minutes” according to who? That phrase has no unambiguous definition.

“Actual revolution of the Earth each time around”? What makes the train observer’s notion of what’s “actual” any less valid than that of someone on earth?

To avoid this sort of ambiguity we have to focus on the invariants: the things that measuring devices record and the events that happen. Say the orbiting spaceship makes ten orbits, incrementing the counter with each orbit, and then stops.

Everyone agrees that the counter is incremented ten times; that’s an invariant.

Everyone agrees about the reading on ship clock when it triggers the counter for the first time and everyone agrees about the reading on the ship clock when triggers the counter for the tenth time; these are invariants. (As is the difference between these two readings, which is the time recorded by the ship clock for the ten orbits).

Likewise, everyone agrees about the reading on the Earth clock when the counter is triggered for the first time and the tenth time, so these are also invariants, as is the difference between these readings, which is the time recorded by the Earth clock for the ten orbits.

However, the time recorded by the Earth clock for the ten orbits is much greater than the time recorded by the ship clock. The Earth observer explains this by saying that the ship clock is running slow. The ship observer explains it by saying that the ship clock is working just fine but the ship covered a shorter distance in less time. Both explanations are equally valid.

None of this will make any sense to you until you understand the relativity of simultaneity.

 

[Ibix]

the train, traveling at the speed of light would achieve the same amount of revolutions in ten minutes, considering the extreme length contraction, as it would in ten years traveling the actual revolution of the Earth each time around?

I think you have the gist of it, but there are several things wrong with what you've actually written.

First, the train cannot travel at the speed of light, although it can travel arbitrarily close to it (for the purposes of a thought experiment, anyway). Attempting to describe a massive object traveling at the speed of light turns out to be self-contradictory, and is a good way to end up totally confused. I responded on the basis that your train was traveling very near to the speed of light - which is what you say in the main body of your OP.

Secondly, by using "actual" to describe the rest length of the track you are treating this measurement as somehow special. It isn't. The measurements made by the moving train are just as valid. That's why we use terms like "rest length" - because the measurements an object makes of itself are interesting, but they aren't privileged.

Furthermore, when you are talking about times and distances it's important to specify who is doing the measurement. So you should say "...would achieve the same amount of revolutions in ten minutes measured by its own clocks, considering the extreme length contraction of the track that it measures, as it would in ten years traveling the actual revolution of the Earth as measured by someone at rest with respect to the Earth".

Finally, I'd be very careful of saying "if you ignore the circular issues". That will always come back to bite you. However, it is true that there must be a self-consistent explanation for the recorded number of ticks in the circular case. It's difficult to say what that would be without actually working through the maths.

So I suspect that you have the right idea. But there are a lot of traps for the unwary in relativity, which is why a degree of nitpicking is important.

 

[uniqueland]

I think you have the gist of it, but there are several things wrong with what you've actually written.

First, the train cannot travel at the speed of light, although it can travel arbitrarily close to it (for the purposes of a thought experiment, anyway). Attempting to describe a massive object traveling at the speed of light turns out to be self-contradictory, and is a good way to end up totally confused. I responded on the basis that your train was traveling very near to the speed of light - which is what you say in the main body of your OP.

Secondly, by using "actual" to describe the rest length of the track you are treating this measurement as somehow special. It isn't. The measurements made by the moving train are just as valid. That's why we use terms like "rest length" - because the measurements an object makes of itself are interesting, but they aren't privileged.

Furthermore, when you are talking about times and distances it's important to specify who is doing the measurement. So you should say "...would achieve the same amount of revolutions in ten minutes measured by its own clocks, considering the extreme length contraction of the track that it measures, as it would in ten years traveling the actual revolution of the Earth as measured by someone at rest with respect to the Earth".

Finally, I'd be very careful of saying "if you ignore the circular issues". That will always come back to bite you. However, it is true that there must be a self-consistent explanation for the recorded number of ticks in the circular case. It's difficult to say what that would be without actually working through the maths.

So I suspect that you have the right idea. But there are a lot of traps for the unwary in relativity, which is why a degree of nitpicking is important.

yes of course i meant to say near the speed of light. and yes i understand the corrections you pointed out but I was trying to get to the quandry point I was focused on and ignoring the myriad of issues that there would actually be with the phyicality of such an event occurring

 

[uniqueland]

“In ten minutes” according to who? That phrase has no unambiguous definition.

“Actual revolution of the Earth each time around”? What makes the train observer’s notion of what’s “actual” any less valid than that of someone on earth?

To avoid this sort of ambiguity we have to focus on the invariants: the things that measuring devices record and the events that happen. Say the orbiting spaceship makes ten orbits, incrementing the counter with each orbit, and then stops.

Everyone agrees that the counter is incremented ten times; that’s an invariant.

Everyone agrees about the reading on ship clock when it triggers the counter for the first time and everyone agrees about the reading on the ship clock when triggers the counter for the tenth time; these are invariants. (As is the difference between these two readings, which is the time recorded by the ship clock for the ten orbits).

Likewise, everyone agrees about the reading on the Earth clock when the counter is triggered for the first time and the tenth time, so these are also invariants, as is the difference between these readings, which is the time recorded by the Earth clock for the ten orbits.

However, the time recorded by the Earth clock for the ten orbits is much greater than the time recorded by the ship clock. The Earth observer explains this by saying that the ship clock is running slow. The ship observer explains it by saying that the ship clock is working just fine but the ship covered a shorter distance in less time. Both explanations are equally valid.

None of this will make any sense to you until you understand the relativity of simultaneity.

fair enough. your example of an orbiting spaceship is probably better than my train going around the Earth but I used the train example because both the observer at the train platform and the passenger on the train are both looking at the train station counter, triggered by the physical bar that the train hits each time it passes by and, at the moment that bar is triggered for each revolution, the passenger on the train and the observer at the train station are theoretically standing in essentially the same physical space since the trigger bar is right in front of them and the question was,assuming both had super human eyes and could actually see the bar being triggered each time, how the observer at the platform and the passenger on the train could count two different number of triggers?

 

[PeroK]

at the moment that bar is triggered for each revolution, the passenger on the train and the observer at the train station are theoretically standing in essentially the same physical space since the trigger bar is right in front of them and the question was,assuming both had super human eyes and could actually see the bar being triggered each time, how the observer at the platform and the passenger on the train could count two different number of triggers?

They don't count a different number of triggers. The number of triggers is what it is. You could simply record the number of triggers and that number could be communicated to everyone. Even to someone not looking at the experiment.

Note that one of the biggest misconceptions about SR is that it relates to what one observer in one physical locations "sees" - using light as a signal - compared to what another observer sees. This has nothing to do with SR, any more than it has to do with classical physics.

The difference between the observer on the platform and the observer on the train is that their clocks are running at different rates relative to each other. So, the time between each trigger is one thing on the platform clock, but a different thing on the train clock.

 

[Nugatory]

how the observer at the platform and the passenger on the train could count two different number of triggers?

They can’t and they don’t. However many times the moving train triggers the counter before it stops is how many trigger events will be counted.