What’s also bothering me is gravitational time dilation. I don’t get how the acceleration causes time to dilate. I see that it happens, and don’t get me wrong, I make no claim that it doesn’t, but what exactly happens due to gravity that gets clocks to change? It’s possible, too, that this is a question that doesn’t need to be asked, though.
It helps if you imagine that everything is moving at the speed of light. However, for objects with mass, some of that motion is along the time axis and some of it is along a spatial axis.
If I am stationary in your reference frame, all of my motion is along the time axis and my watch appears to tick normally. But if I’m moving relative to you, some of my motion is directed along a spatial axis. I’m not moving as fast through time, so my watch ticks slower. However, the situation is symmetrical. From my perspective, YOU’RE the one who’s moving in space. You’re not moving as fast through time, so YOUR watch ticks slower.
The way out of this apparent paradox is to realize that there is no absolute time axis. What I call “the time axis” looks like a mix of time and space to you and vice versa.
When you accelerate, you’re altering the vector of your time axis. As a result, your path through spacetime is curved instead of straight. Any curved path between two points is necessarily longer than a straight path, so clocks in accelerated reference frames run slower.
Mass curves space. When you’re in a gravitational field, you have to follow a curved path through spacetime in order to remain stationary. Curved paths are longer than straight paths, so clocks in a gravity field run slower.
I actually thought it was the other way around. That is, with gravity, time gets all wonky, and consequently the frequency of light gets wonky, too.
If this is right, then it makes perfect sense. The only reason that I say “if” is because it’s almost too easy. What I’m imagining here is something akin to a vector space, where everyone has a different basis. So, everyone is basically kind of the same, but more appears to not be the same because of the wonky stuff that can happen when you move from one to the other. Time is linked to space somehow (how, though?), and time kind of “leaks” into space as one changes reference frames.
I guess my question now becomes: in any particular reference frame, how does time know to be time? Or, what I guess is the same question, why is time the same for each reference frame considered in itself? And what is the difference between space and time anyway?