Okay lets imagine that its possible that we have two space trains sat in some interstellar train station neatly placed say 1 light minute apart.
The two trains leave the station simultaneously and travel in the same direction along a parallel course at an identical speed which is a high percentage of the speed of light.
Now one bored young chap on one of the trains decides to shine his new sparkly green laser pointer at the other train where sits his friend. He shines the light directly out of the window perpendicular to the direction of travel.
1 minute later the light beam is observed by his friend, the physical distance separating the two theoretical trains being 1 light minute.
But wait isn’t the actual distance traveled by the photons much more than the distance which separates the trains? If we plot the path traveled we could reasonable draw a triangle. The distance between the trains as one side, the distance traveled by the light transmitting train until the light is received by the other train also one side, and the distance covered by the light beam is the hypotenuse.
Doesn’t this prove that light travels faster than light? :dubious: Or something?
What other fun things happen in this scenario? Is the light colour shifted?
What you are describing is the very reason for things like relativistic length contraction and time dilation. From the perspective of those on the train, they are not moving; the light travels only the perpendicular distance between the two trains, and of course travels at the speed of light. From the perspective of someone on the train station, the light travels along the triangle you mention. But they also see the trains length-contracted, so that one side of the triangle is much shorter than normal. When they do the math, the speed of light is still the same ol’ speed of light.
I had to take third semester physics either for my undergraduate degree or to qualify for engineering grad school. During a test on Relativity some football player type muttered to himself, “I don’t believe it. I’m gonna put it down, but I don’t believe it.”
The simple answer is, to the people on the train, yes, the beam will reach after 1 minute.
The people on the ground, no, it will take more than one minute (precisely because the distance travelled is greater).
Another way to look at it is: if people on the train and on the ground agree on the time that the beam left (0:00:00), they will not agree on when it arrives.
As a general aside, whenever you see a though experiment that appears to contradict relativity, it usually has a common element:
The moment you see the word “simultaneous”, or a phrase to the same effect, you can usually stop right there. The only events that are simultaneous in any meaningful manner occur at the same location. If you need to specify simultaneous for events at different locations the example is already doomed.
I’ve often been told that simultaneity (simultaneousness? simultanation?) is unattainable, but isn’t it possible to synchronise clocks to an arbitrary precision by exchanging light-speed messages back and forth between two points?
Station A sends a laser-encoded (or radio?) message to station B, saying “it’s 8:00 here”. Station B replies as soon as it receives the first message, then as soon as it gets B’s reply, station A replies with “it’s now 8:02 here” . When it receives this last message, station B should be able to figure out the time difference between its own clock and that of station A. Then both can agree that the trains will leave at 9:00 per station A’s clock. The only lack of precision should be in the “as soon as” parts.
Clocks can be synchronized in any given reference frame, yes. The issue of simultaneity comes into play when you start talking about what the clocks look like from the point of view of another inertial reference frame. In one reference frame you have synchronized your clocks, but from the point of view of someone moving past you on a train, your clocks may no longer be synchronized.
Can someone help me out with the “triangle” part? I don’t see where there’s a triangle. The photon leaves the laser and goes in a straight line to the other train. I see an H, not a triangle. Where’s the hypotenuse, if the laser is shone perpendicularly?
If you are at the train station platform, you see the train as moving. The laser that is on the train is moving. The photons coming out of the laser are moving in the train’s direction of motion in addition to perpendicular to the train.
Picture someone throwing a baseball out the window of a moving train. If the train is moving in the x-direction with speed v1, and the person throws the baseball out the window (y-direction) with speed v2, then the baseball is moving with speed sqrt(v1^2+v2^2) diagonally in the x-y plane.
See the diagram in the section “Looking at Someone Else’s Clock” here. This example has two mirrors rather than two train cars, but you can imagine that the guy in the second train car is holding a mirror or something.
