Rosio Pavoris

Richard Feynman once said that all of quantum physics can be derived by carefully thinking about the double-slit experiment. All of relativity can be derived (much more easily) by carefully thinking about a flashlight on a train.
Last time, I said one of the consequences of special relativity was that there is no absolute way of telling which of two events happened first. Let’s look at what I meant by that.

Consider the following set-up: two light sensors, at a fair distance from each other, and a lightbulb in the middle, the same distance from both sensors.
If you switch on the lightbulb, which sensor will go off first? They’ll both go off at the same time, right?

Starting at the bulb, light has to travel the same distance to reach the sensor on the left as it does to reach the one on the right. So yes, they go off at the same time.

Now consider what that scene would look like if it were moving past an observer (or if an observer were moving past it; same thing).

Now the sensor on the left is actually being moved into the light beam, so light starting at a given point in time has to travel less far to reach that sensor than it does to reach the one on the right.
For “normal” objects this wouldn’t make a difference, since to the motionless observer, the objects on the left (that is, fired in the opposite direction to the movement of the system) would appear to move more slowly than the objects on the right (which would be moving at a speed equal to that of the system plus the speed at which the object appears to be fired to the person on the train with it), but light doesn’t work that way (neither do objects, but the difference is too small to be really noticeable at low speeds). Light always appears to be going equally fast to all observers.

So what does this mean? To the motionless observer, light moving to the left sensor has less distance to travel than light moving to the one on the right, but it still moves at the same speed.
The result is that to that observer, the sensor on the left will appear to be triggered before the one on the right!
Furthermore, if there were another observer, moving in the same direction as the train but faster than it, he would see the sensor on the right going off first!

We’ve already seen that all reference frames are equally valid (except accelerated ones, but really they are if you include gravity and work according to general relativity, but that’s not a concern here), so it follows that there is no absolute way of telling which sensor went off first.
It doesn’t take much imagination to see that this doesn’t just apply to this situation, but to every situation imaginable.

Relativity is really quite interesting, and it makes sense once you get used to it. The hard part is getting used to it. Human beings are generally just too slow to notice its effects, like they’re too big to notice most quantum effects and too light to get a good feel of Newtonian physics.
Nature is a great deal more fascinating than it appears at first glance.

(If you’re interested in a similar thought experiment which also makes use of the fact that objects contract along their direction of motion, the ladder paradox is pretty neat.)