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shminux comments on Ask an experimental physicist - Less Wrong
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That is a very good explanation for the workings of time, thank you very much for that.
But it doesn't answer my real question. I'll try to be a bit more clear.
Light is always observed at the same speed. I don't think I'm so crazy that I imagined reading this all over the place on the internet. The explanation given for this is that the faster I go, the more I slow down through time, so from my reference frame, light decelerates (or accelerates? I'm not sure, but it actually doesn't matter for my question, so if I'm wrong, just switch them around mentally as you read).
So let's say I'm going in a direction, let's call it "forward". If a ball is going "backward", then from my frame of reference, the ball would appear to go faster than it really is going, because its relative speed = its speed - my speed. This is also true for light, though the deceleration of time apparently counters that effect by making me observe it slower by the precise amount to make it still go at the same speed.
Now take this example again, but instead send the ball forward like me. From my frame of reference, the ball is going slower than it is in reality, again because its relative speed = its speed - my speed. The same would apply to light, but because time has slowed for me, so has the light from my perspective. But wait a second. Something isn't right here. If light has slowed down from my point of view because of the equation "relative speed = its speed - my speed", and time slowing down has also slowed it, then it should appear to be going slower than the speed of light. But it is in fact going precisely at the speed of light! This is a contradiction between the theory as I understand it and reality.
My god, that is probably extremely unclear. The number of times I use the words speed and time and synonyms... I wish I could use visual aids.
Also, I just thought of this, but how does light move through time if it's going at the speed of light? That would give it a velocity of zero in the futureward direction (given the explanation you have linked to), which would be very peculiar.
Anyway, thanks for your time.
Maybe this angle will help: "relative speed = its speed - my speed" is an approximate equation. The true one is relative speed = (its speed - my speed)/(1-its speed * my speed / c^2). Let one of the two speeds = c, and the relative speed is also c.
Thanks for your answer, this equation will make it easier to explain my problem.
Let's say a ball is going at the speed of c/4, and I'm going at a speed of c/2. According to the approximate equation, before the effects of time slowing down are taken into account, I would be going at a speed of -c/4. Now if you take into account time slowing down (divide -c/4 by the (1-its speed*...)), you get a speed of -2c/7.
So that was the example when I'm going in the same direction as the ball. Now let's say the ball is still going at a speed of c/4, but I'm now going at a speed of -c/2. Using the approximate equation: 3c/4. Add in time slowing down: 2c/3.
So the two pairs are (-c/4, -2c/7) and (3c/4,2c/3). Let's compare these values.
For the first tuple, when I'm going in the same direction as the ball, -c/4 > -2c/7. This means that -2c/7 is a faster speed in the negative direction (multiply both sides by -1 and you get c/4<2c/7), so from the c/2 reference frame, after the time slow effect, the observed speed of the ball is greater than it would be without the time slow down. So far so good.
For the second tuple, however, when I'm going in the opposite direction of the ball, 3c/4 > 2c/3. So from the -c/2 reference frame, after the time slow effect, the ball appears to be going slower than it would if time didn't slow down.
But didn't the first tuple show that the ball is supposed to appear to go faster given the time slow effect? Does this mean that time slows down when I'm going in the same direction as the ball, and it accelerates when I'm going in the opposite direction of the ball? Or does it mean that the modification of the approximate equation which gives the correct one is not in fact the effects of time slowing down? Or am I off my rocker here?
This might be just a confusion between speed and velocity. In one case relative velocity (not speed), in fractions of the speed of light, is -1/4 (classically) vs -2/7 (relativity). In the other case it is 3/4 vs 2/3. In both cases the classical value is higher than the relativistic value.
That the classical value is always higher than the time-slowed value is precisely what doesn't make sense to me.
If -1/4 is the classical value, and -2/7 is the relativity value, -2/7 is a faster speed than -1/4, even though -1/4 is a bigger number. So the relativity speed is faster. However, if 3/4 is the classical value, and 2/3 is the relativity value, 3/4 is a faster speed relative to me than 2/3. So in this case, the classical speed is faster.
So when I have a speed of 1/2, time slowing down makes the relative speed of the ball greater. And when I have a speed of -1/2, time slowing down makes the relative speed of the ball smaller. More generally, this can be described by my direction relative to the ball. If I'm moving in the same direction as the ball, time slowing down makes it appear to go faster than the classical speed. However, if I'm going in the opposite direction of the ball, then it appears to go slower than the classical speed. And that doesn't make sense. Time slowing down should always make the ball appear to go faster than the classical speed, and the effects of time slowing down should definitely should not depend on my direction relative to the ball.