There's something about my understanding of time which seems to contradict relativity and I can't understand why. I wonder if some of the gurus here can help.
The problem is quite simple, at least it looks simple to me. I once tried to understand the phenomenom of time dilation by imagining a clock flying through space away from earth. If the clock travels fast enough, from our point of view it would appear to have slowed down. This has nothing to do with any relativistic effects but simply due to the fact that the clock's images take longer and longer to reach us.
At first I thought that that was essentially the idea behind relativity except for a problem. If the clock travels away from us it would seem to slow down but if it travels toward us the effect would be the opposite, it would speed up. If I understand it well, relativity says that the direction of movement is irrelevant because the speed is squared in the equation. That rang two bells.
The first bell is a pet peeve I have since high school. I always thought that the fact that exponentiation is not a perfectly reversible operation if the exponent is an even number is a tremendous source of inconsistency in math. I always watched every new equation I learned for possible loopholes due to that inconsistency but in all cases the equations either provided two solutions or signal was not relevant. I can't say anything about relativity but it's interesting that the root of a squared number is the reason why it doesn't agree with my intuition.
The second bell has to do with the idea of time dilation, which is also counter-intuitive. If time dilation is simply a consequence of the fact that a finite speed of light affects our measurement of moving bodies, then our understanding of relativity is fundamentally wrong. Not the theory itself, because our measurements would still agree, but the idea that two clocks traveling through different paths will go out-of-sync is wrong because the time dilation effects would cancel out at the points their trajectories intersect. The so-called twin paradox is solved because there was never a paradox to start with.
Any thoughts? I'm very curious about that.