Quote (fingerling @ Feb 10 2013 09:41pm)
would like to see that equation if you know it

in the following diagram, the units are cooked up so that space is in units of 1 light second, and time is 1 second. Light travels 1 light second per second, and since
the speed of light is a constant for all observers, it always travels on lines of slope 1 (45 degrees). Space is being represented as a single dimension, so we are only considering movement in a straight line (this is a limitation of 2d graphs).
In our story there are several friends who are at rest at time = 0.
Friends:
Bob, Dave, John, and Sue
Bob, and Dave will be at rest the entire problem, so they travel down the time axis. Time moves forward for them, but they don't move in space. They are represented by the purple arrow that is on top of the time axis.(slope 0)
Bob and Dave have an agreement, after 3 seconds, Bob is going to emit a flash of blue light. (blue line). This will be a cause.
Dave has agreed that when he sees the blue light, he will wait 2 seconds and emit a flash of green light. (green line) This will be our effect.
John will be taking off on his rocket ship 2 seconds after the start of the graph. His rocket ship quickly accelerates to 1/2 the speed of light then just coasts along at that speed. So in 1 second he travels 1/2 a light second. So he will travel on a line of slope 1/2. (orange line)
Sue will be taking off on her rocket ship after 6 seconds. Her rocket ship is a magical rocket ship that quickly accelerates to 3 times the speed of light then just coasts along at that speed. So in 1 second she travels 3 light seconds. So she will travel on a line of slope 3. (red line)
Bob and Dave see the blue flash and the green flash, and agree that 2 seconds took place between them.
John sees the blue flash first, and later sees the green flash (cause first, then effect later). An interesting side note: You will notice that while John still agrees with Bob and Dave on what was the cause, and what was the effect, he will disagree on how much time took place between them. John experiences more than 2 seconds between the flashes.
When Sue takes off on her rocket ship, she sees the green light first, and the blue light second, the effect before the cause. On a side note: she experiences less than 2 seconds between the green light and the blue light.
You will find that if you add any observer at any speed less than light (slope less than 1), who sees both flashes of light, they will always agree with each other that the blue flash came first, and some time later, they saw the green flash. They will however disagree on how much time transpired between flashes.
Observers that travel slower than light always see causes before effects.You will also find that if you add any observer at any speed greater than light (slope greater than 1), who sees both flashes of light, they will always agree that the green flash came first, and that some time later, they saw the blue flash. They will however disagree on how much time transpired between flashes.
Observers that travel faster than light always see effects before causes.This post was edited by Azrad on Feb 11 2013 12:29am