# Frames of reference and why are they different

Here is a quote from "The Elegant Universe" by Brian Greene.

Imagine two countries that have been at war are sitting down to sign a treaty ending hostilities while traveling aboard a train that is moving at a constant velocity. The catch is that neither country's delegate wants to sign the treaty before the other delegate and thus, a simple system is devised to ensure that both delegates sign the peace treaty simultaneously. The solution involves setting a light bulb at the center of a table in such a way that the light bulb is exactly between the delegate from Forwardland (who is facing the direction the train is traveling) and the delegate from Backwardland (who has her back to the direction the train is traveling). When the light bulbs lights up, that is the signal for both delegates to sign the treaty.

This setup is agreeable to all parties on the train and to both security councils in the countries' respective capitals. Once the bulb lights up and the delegates have simultaneously signed the peace treaty, everyone on the train celebrates the cessation of hostilities, but they are perplexed to discover that fighting has broken out anew between the two countries. The reason given is that the delegate from Forwardland was tricked into signing the treaty before the delegate from Backwardland

Why do the delegates see the light at the same time? the forward land delegate IS approaching the light and the backwardland delegate IS moving away from it. so therefor the delegate from forward land SHOUlD see the light first. (because he traveled less distance to see the light.)

SO how come the observers on the platform outside the train see this but the ones ON the train don't??? Since the speed of light IS constant it makes sense that this would be how everybody saw it, on and off the train. I have searched for an answer to my question for about a month now and haven't a found a satisfying one. Please don't use too complex of vocabulary.

Simply put, relativistic speeds cause for events previously thought of as simultaneous to no longer be simultaneous if the velocity of the reference frame of the event changes relative to the defined observer. The best way to wrap your head around this is to pictorially trace what is happening in space time.

The case you describe is v>0

Think of v in this case as the v of the train relative to you, and you, the observer of the train are the white line, seeing what occurs in sliver of space x as time marches forward, indicated by observing events at all points in x at a time t. If the train appears to be getting further from you then delegate Forwardland is point C and delegate Backwardsland is A.

Interestingly enough if the train was approaching you you would have seen the opposite occur, where the delegate of Backwardsland signed first (like v=-0.5c). If v=0 you are traveling the same speed as the train, and you might as well be one of the people on the train observing the (now) simultaneous event.

• What a nice image! Did you make it? If not, where did you find it? – rob May 14 '15 at 4:51
• I should have added that this picture is available on wikipedia – Skyler May 14 '15 at 16:05

the forward land delegate IS approaching the light and the backwardland delegate IS moving away from it

Are they? Or are the delegates sitting perfectly still, and the Earth spinning quickly beneath them? Of course we have a convention that the Earth is stationary and the train moves across it, but we also know that the Earth is not stationary - it spins and orbits, and the sun it orbits is also circling the center of the galaxy, and the Milky Way galaxy is dancing with its galactic cluster, etc. We can choose any body+direction to designate an arbitrary "stationary" coordinate system, but because it's arbitrary, we can also easily choose a second coordinate system in which the first system is not stationary.

For example, let's take our delegates in the train: as they are preparing to sign the treaty, one of the aides asks the Forwardland delegate why he is moving so much, and reasonably the delegate replies "I am not moving, I'm sitting quite still at this table." Indeed, from the perspective of those in the train car, they are sitting still around the table with a stationary light halfway between them. If the curtains are drawn so that they can't see out the window, they have no way of knowing they're moving. The laws of physics work the same way for them sitting still in the train as they do sitting still on the ground; the speed of light is $c$, objects fall straight down rather than off to one side, etc. That's why the delegates see the light at the same time even though they are "moving toward" or "moving away" from it; because those assessments are only accurate as seen from the observer standing on the ground.

• that still doesn't make sense to me. The light does have to travel less distance to reach the forward land delegate than it does for the backward land delegate, Right? (if not, then I'm beyond confused) so why do they see the light at the same time? – Alex Taylor May 15 '15 at 0:58
• @AlexTaylor They're sitting the same distance from the light bulb, e.g. if one delegate pulls out a yardstick and begins measuring, he'll find that both of them are sitting, say, two feet from the bulb. It doesn't matter whether he measures from one end of the table or the other because the light bulb is in the middle. So why would the light travel less distance one way than the other? – Asher May 15 '15 at 7:39
• @AlexTaylor And before you answer that, also consider this: is the train traveling east, or west? In your view, this would also make a difference, since at normal train speeds the spin of the Earth is much, much faster than the speed of the train; but on top of that, the orbit of the Earth is much faster than the spin, so the time of day also effects the travel speed; but if the train is traveling due east or west, the light should go off to one side because of the tilt of the solar system in its orbit around the galaxy... et cetera. – Asher May 15 '15 at 7:46
• @AlexTaylor What it boils down to is that the researcher standing in his laboratory in Berlin measures the same speed of light as the researcher traveling on the train from Berlin to Bern, because the speed of light is the same in all inertial reference frames (and to a high degree of precision, the spin and orbit of the Earth are small enough to consider the surface "inertial"). There's no "absolute" frame from which all other frames can be measured. – Asher May 15 '15 at 7:52
• what do you mean when you say "the speed of light is the same in all reference frames. Because I feel like this seems to be the root of my problems in understanding this – Alex Taylor May 16 '15 at 1:22