# Special relativity: Lightning and Trains (no math involved)

Gravitino22

## Homework Statement

Consider the relativity of simultaneity: A student in a train at rest from his point of view and a professor in a train that is moving in the positive x direction from the student’s perspective. Two lightning of different colors will strike at opposite ends of the trains when both trains are in the same position. A red lightning will strike in the left side of the trains and a blue one will strike in the right side of the trains at the same time. Statement A: The student will say that both light waves reached him at the same time while in the professors frame the blue light wave reached him before the red light wave because he is moving towards the blue light relative to the student.

Now consider the same situation but from the professors point of view; the student is moving in the negative x direction while the professor is at rest. Explain how statement A is still true.

*Obviously all of this motions are non accelerated i.e special relativity

## Homework Equations

Time dilatation
Length contraction

## The Attempt at a Solution

Ive been thinking for several days about this but I can't find out how statement A will still be true. If the student is moving in the proffessors perspective he will see the red light strike first because he is moving towards it. I can't see how this is possible.

Homework Helper
Gold Member
[...] from the student’s perspective. Two lightning of different colors will strike at opposite ends of the trains when both trains are in the same position.

Keep in mind, the observation quoted above is from the student's perspective. Don't forget about the length contraction (Lorentz contraction). From the student's frame of reference, both trains (his own train and the professor's train) are the same length (i.e. they are the same length when the professor's train happens to be moving).

What does that tell you about the length of the professor's train, compared to the student's train, if both trains were measured at rest?

More-so, now consider the length of the student's train, as measured by the professor, when the student's train is moving relative to the professor's frame. In this situation, when do the front (or right side, if you'd rather) of the two trains line up? When do the back (left side) of the trains line up?

Gravitino22
I got it! i think..

the proffessors train is larger than it actually it is if they are both measured at rest!. makes sense.

Now I just have to figure how to make it work ...

Is the students train going to even smaller than it actually it is from the proffessors point of view?

or is it larger than it actually is and the trains align when the lightining had already hit therefore the blue lightining striked closer to the student instead than at one of the ends of the train?

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Homework Helper
Gold Member
I got it! i think..

the proffessors train is larger than it actually it is if they are both measured at rest!. makes sense.

Now I just have to figure how to make it work ...

Be careful of your wording, here. I know what you mean, but some instructors might ding you if you're not careful. If a meter stick moves past you, traveling very fast, traveling in the lengthwise direction, you will measure its length to be less than 1 meter. For example, if if the meter stick moves past you at 0.9c, you will measure its length to be 0.436 m. But given your frame of reference, 0.436 m is its actual length! Again, I know what you mean when you say "actual length" meaning "rest frame length" but you might want to avoid that. No matter what frame of reference you measure something in, your measured answer is the actual length given the frame you are in. (The same object will have different lengths when measured in different frames, but all lengths/measurements are equally valid -- there isn't one "true" length.)

So anyway, getting back to the problem. Yes, you're right. If the lengths of both the student's train and the professor's train are both measured in the same frame (with neither moving relative to the other), the professor's train is longer.

Is the students train going to even smaller than it actually it is from the proffessors point of view?

(Ignoring the suspicious wording) Yes, that's right. In the professors frame of reference, the student's train is comparatively quite small. As such, according to the professor, the fronts and backs of the trains do not line up at the same time. That's because the student's train is so much shorter. That means the lightning strikes occur at different times.

or is it larger than it actually is and the trains align when the lightining had already hit therefore the blue lightining striked closer to the student instead than at one of the ends of the train?

No, that's not it. When something moves relative to your (inertial) frame of reference, that something always contracts in length, relative to what it would be if not moving. Things around you never get longer as they move faster (relative to you).

(By the way, if you've been introduced to spacetime diagrams, it might make things particularly clear if you diagram this situation.)

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Gravitino22
Well that clears all my doubts. Thank you very much i just have to be carefull with my wording :D