Undergrad Relativistic Simultaneity: A Thought Experiment

[Milsomonk]

Hi guys,
I've been asked to check somebody's relativity logic and i'd love to get s second opinion as it's easy to slip up.

There is a train, with an observer (A) in the middle, with a device that fires marbles simultaneously up the train and down the train. There is also a detector at each end of the train that has a clock which records when the marble arrives.

There is also an observer (B) on a platform, they also have detectors which independently record the time the marble arrives.

scenario 1
in the case that the train is stationary observer (A) and (B) are at the same point in the axis of the train and therefore have the same frame of reference and the detectors clocks agree

scenario 2
the train is moving, observer (A) sees the marbles reach each of their detectors (on the train) simultaneously. Observer (B) also sees the marbles reach each of their detectors (on the platform) simultaneously.

scenario 3
scenario 2 is repeated but instead of marbles, photons are used, this time observer (A) and (B), detectors show different times and there for conclude that the photons reaching their respective detectors are not simultaneous events.

My first issue is with scenario 2 with the marbles, I do not think the two observers detector clocks would show the same time, and I do not think that replacing marbles with photons would make any difference other than making the relativistic effect more noticeable. it seems like for scenario 2 with marbles they have used classical physics and for scenario 2 with photons they have considered relativity. would anyone agree with my conclusion on this thought experiment? or are they correct and I am missing something? Many thanks for your help :)

 

[kuruman]

You are missing that the velocities relative to the train station of marbles depend on the velocity of the train and the velocities of the marbles relative to the train. The velocities of photons are always $c$. You cannot replace photons with marbles. Also, I don't believe that scenario 2 is plausible although I did not write the equations. If the train travels at relativistic speeds you cannot have the firing of the marbles and the detection of the marbles occur simultaneously in both frames A and B.

 

[Dale]

it seems like for scenario 2 with marbles they have used classical physics and for scenario 2 with photons they have considered relativity. would anyone agree with my conclusion on this thought experiment?

You are correct. They should have used the relativistic velocity addition. That would show that the marbles do not arrive at the same time in the platform frame.

 

[Milsomonk]

Hi, thanks for your response. I see my mistake now, the observers in the case of the photons would both agree on the speeds as it is c in both frames. but in the case of scenario 2 with the marbles are you saying you would agree with me that the the observers would not conclude that the events happen simultaneously?

 

[Dale]

Yes. In the platform frame the arrivals will not be simultaneous.

 

[Milsomonk]

Ah yeah that's what I thought about the relativistic velocity addition. thank you for your help :)

 

[PeroK]

Ah yeah that's what I thought about the relativistic velocity addition. thank you for your help :)

It's a good exercise to calculate the speeds of the marbles in both directions in the platform frame and the time it takes the marbles to reach the ends of the train (again in the platform frame).

Hint: if you know about the relativity of simultaneity and the "leading clocks lag" rule, then you should know the answer (for the time difference) in advance!

PS Note that the relativity of simultaneity between frames does not require any light sources in your experiment. Any pair of simultaneous events in one frame will not be simultaneous in another - as long as they are separated along the direction of relative motion. In that respect light has nothing to do with it.

 

[Milsomonk]

Great answers, thanks very much for the help everyone :)