Okay, now you know I’m a conspiracy freak, or simply a nutcase. But just for argument, I always tried to understand how Einstein’s thought experiments lined up exactly with the mathematics of relativity.
First thought experiment: A person is standing on a platform beside the railroad track, and another person is approaching him at high speed on a train, sitting exactly at the center of the train. Just as the person on the train and the person standing on the platform come directly parallel to each other, lightning hits at both ends of the train at exactly the same instant.
Lightning travels at a certain speed, so we know it will take a certain very small amount of time to reach the two observers. However, the observer on the train is moving toward the flash at the front of the train, and away from the flash at the back of the train. By the time he sees the flash, he will see the one at the front of the train first, and the one at the back of the train last.
Nothing complicated about that. But the observer, not moving at all, will see that the two flashes occurred eaxctly the same instant, since he was directly at the center of the train with the observer on the train when the lightning struck.
The implication is that movement of the train observer made a difference in perception from the stationary observer on the platform. Did it?
Let’s simply repeat the experiment in our minds. Suppose the train was equipped with an electronic spike and hammer, so that when the lightning struck at each end of the train, a spike was slammed into the ground at each end, marking the exact spot where the lightning hit. We now have a fixed marked position in time and space, showing where the lightning hit.
Instead of leaving the observer on the train, take him out of the trian and place him on the platform exactly parallel to where he was on the train. With each observer in a stationary position, imagine two lightning flashes at the same instant, hitting the spikes marked by the last strike.
Withiout moving at all, the two observers will experience the lightning flashes just as they did before, since each of them are in the same positions as they were at the first experience. In the first, the train observer moved toward he flash, in the second, he was simply standing where he was the first time he saw the flash.
The relations in time/space are exactly the same in either case, moving or not moving. The only thing that matters is where each observer was standing(sitting) when he saw the flash.
Second example, the “parabola” effect. In describing this thought experiment, many have said that the appearance of a falling rock from a train wil be seen differently from the perspective of the observer on the train, and the stationary observer watching the train go by.
Here’s the thought experiment: A person stands on the ground watching a train go by. He sees a man standing on an open railroad car, holding a stone in his hand. As the man on the train and the man on the ground come exactly parallel, the man on the train drops the stone. The man on the train will see the stone fall straight down, while it is said that the observer on the ground will see a “parabola”, the rock moving in the same direction as the momentum of the train as it falls downward.
Not so, and easily disproven. Let’s do the experiment again, but assume the person who was on the ground now stands on a platform that is moving in the opposite direction that the train was moving in the first experiment, at the very same speed.
As the observer on the now moving platform draws parallel to the man on the now stationary train, the man on the train releases a stone. Assuming that the speed is the same, the stone will fall on a spot on the platform corresponding to the same spot as before, when the train was moving. The stone has merely fallen straight down, while the surface underneath has changed, with exactly the same effects of measurments. No parabola.
But there does exist a parabola. Where did it come from?
Simply draw a graph, with the vertical line representing the beginning point at which the man released the stone. Then draw a horizontal line showing where the stone struck on the ground when released. Only by combining these two “trajectories” can a parabola be claimed. Time/space as a gemoetric function is created by treating movement on a graph as if there was no movement, as if the whole thing was static. It is combining two different systems into one by geometric representation. But as we see from simply reversing the process of movement, the stone did not fall in a parabola. It fell straight down.
In the first thought experiment, the only real consideration was the position of the two observers when the flash of light reached them. Any movement in the meantime was incidental to the experiment.
There was no “shortening” or “lengthening” shown in this process. It merely demonstrated that, given a certain position in one instant of time, two different observers will see two different manifestations. One will see simultaneous flashes of light the other will not. Were the flashes simultaneous? Of course. How do we know? because simply by marking the flash with the spikes the instant each flash hit, and measuring that distance from the stationary observer, we can then ask the observer if he saw the flashes at the same time. If he says “yes”, then we know, with light traveling at the same speed in either case, that the two flashes actually were simultaneous, since the stionary observer was positioned exactly at the center of the two flashes.
The stationary observer standing just up the track will experience the same thing as he did while moving, simply because he was at the same spot as when he was moving. But we DO know, by simple measurement, the flashes WERE simultaneous, simply by the observation of the stationary observer, and the experience of the other observer will simply reflect a difference in measurement regarding the same time needed for lightning to reach him.
There is no “curvature” nor “shortening” effect in either experiment.