Special Relativity: Understanding the Problem of Simultaneity

[Shark 774]

I just had a test at school today for special relativity and had a question almost identical to the attached question. This question was taken from a 2008 exam and in the examiner's report they gave all 4 answers as correct (obviously they decided that it was a dodgy question). I told my teacher this during the test today and he just said to choose whatever answer I thought was right and give an explanation of why, so I chose C and D and said that C is correct because if they were not equal distances apart then the light rays would reach Nancy at different times and that D is correct because if the speed of light was not a constant then the light also would not reach Nancy simultaneously. What are your thoughts? (Note: It says "all observers" in option D, which is not correct because in reality 'c' can vary for non-inertial, however in the course structure of the physics course it states Einstein's 2nd Postulate saying "the speed of light has a constant value for all observers regardless of their motion or the motion
of the source", hence this is not a technicality that they're trying to trick us on.)

 

[ajclarke]

As far as I know, this is a problem of simulteneity. Fred see's the events as simultaneous because he is within the inertial frame of the trani where the events take place.

However for Nancy, in a different inertial frame will see the train differently. I would say that she wouldn't see the two events simultaneously, because the light from fredis moving away from her, whilst the other persons light is catching up to her.

The speed of light remains constant I agree, but I think this is an issue of length contraction.

Anyone confirm? Or am I talking rubbish :D

 

[L-x]

the correct answer is A. From fred's point of view nancy is moving towards the light from alan, and so sees it first. From nancy's point of view, The light from Alan left him before bob's light did. Both are correct (it is impossible for observers in different reference frames to agree on the simultaneity of events in SR)

Edit: you may find this video instructive:

 

[Fewmet]

the correct answer is A. From fred's point of view nancy is moving towards the light from alan, and so sees it first. From nancy's point of view, The light from Alan left him before bob's light did. Both are correct (it is impossible for observers in different reference frames to agree on the simultaneity of events in SR)[/url]

I concur. Choices C and D would be if the the matches were struck simultaneously in Nancy's reference frame.

In that case, Fred would see Bob's strike first, then Alan's as he is approaching the light from Bob and receding from the light from Alan. From that, it must be that (back in Nancy's frame) Alan struck the match first, so Nancy sees it first.

 

[Shark 774]

Ok thanks for the responses. Hopefully I can still get the marks for it because it was decided, in the exam, to be either a non-clear question, or too difficult for high school students.

 

[Doc Al]

I just had a test at school today for special relativity and had a question almost identical to the attached question. This question was taken from a 2008 exam and in the examiner's report they gave all 4 answers as correct (obviously they decided that it was a dodgy question).

The only thing 'dodgy' about this question is the sloppy wording where it says: "At the instant that Fred and Nancy are directly opposite each other, Fred sees both Alan and Bob strike matches simultaneously."
I don't think they meant that Fred actually sees them striking matches at that instant. What they meant was: "At the instant that Fred and Nancy are directly opposite each other, both Alan and Bob strike matches simultaneously according to Fred (and all train observers)." He won't "see" them strike the matches until after the light reaches him.

I told my teacher this during the test today and he just said to choose whatever answer I thought was right and give an explanation of why, so I chose C and D and said that C is correct because if they were not equal distances apart then the light rays would reach Nancy at different times and that D is correct because if the speed of light was not a constant then the light also would not reach Nancy simultaneously. What are your thoughts?

Note that in the answer choices they really do mean Nancy "sees" the light from the matches. Anyway, this is a problem in simultaneity. The easiest way to understand why C (and thus D) is incorrect is to view things from the frame of the train. Which way is Nancy moving in that frame? Which beam of light will she intersect with first?