I was asked the following question on a relativity problem i

I was asked the following question on a relativity problem in modern physics. I keep seeing the answer to this question posted in different places with no explanation as to why the answer is what it is, and I can\'t abide by not knowing the reasoning behind the answer. I won\'t be providing the answer so it won\'t jade responses.

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\"A passenger train travels east at high speed. One passenger is located at the east side of the train, another is located in the west side of that train. In the train\'s frame of reference, these two passengers glance up at the same time. In the Earth\'s frame,

a) they glance up simultaneously. \"

b) the passenger at the east side glances up first. \"

c) the passenger at the west side glances up first. \"

d) the passengers glance sideways \"

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It doesn\'t say where the observer is in relation to the train in Earth\'s frame. Doesn\'t it depend on where the observer is in Earth\'s frame and whether or not the train is oncoming or passing? If the observer was behind the train, wouldn\'t the observer see the passenger on the left glance up first? If the train was oncoming and the observer was to the right, wouldn\'t they see the person on the right glance up first?

Full answers with full explanations only, please.

Solution

When we are talking about Earth\'s frame, the observer is in Earth\'s frame of reference and is at rest.

It depends on where the observer is located with respect to the train.

The second psotulate of the SPR states that the speed of light is same in all inertial frames whether moving or at rest.

we assume the observer on earth is located ta the middle of the train when the events have happend.

both the end of the train are at equal disatnce from the observer and the light from both ends reach the observer in the same time intervel.

When these two events are simultaneous they are simultaneous in Earthis frame of reference too.

If the observer is located on the east that is in front of the train, loght from the front (East) reached him first and a little later depending on the legth of the train and find the EAST event first and WEST event later.

if the observer is behing the train(WEST) then light from west reaches first and from the front(EAST) a little later and finds the East event happend later and the WEST, first.