When in relative motion near the speed of light, two observers each think that the other observer's clock runs slow. Neither observer believes his own clock to be running slower.
that's an implication of relativity, as opposed to a fact, correct?
I had a thought about why time dilation and velocity are linked in Relativity. Imagine that time is caused by our 3 dimensional universe moving at the speed of light through a 4th dimension. We move through this 4th dimension at a constant rate and direction, which is why time seems to flow one-way at a contant rate. The kicker to this idea is, that the velocity limit of the speed of light applies to the SUM of our motion in the 3 spatial dimensions and the 4th time dimension. So, any spatial motion would have to reduce the velocity of an object through time, since everything is already moving at the speed of light in the 4th dimension. Of course, this effect wouldn’t be noticeable at everyday speeds, since they are so much smaller than the speed of light, the time distortion is negligible.
I’m still trying to work out a few things about how that could actually work, but I think it’s an interesting idea.
Begs the question: Time slows down relative to whom?