I understand that by definition dimension is defined by just another coordinate to pin-point something in space-time. Therefore we need to know not only where but when. At the same time, this somehow over the time changed to imply that there's a "copy" of universe at each time. Meaning if we had a time machine we could go back to in time by just reversing vector's time component.
But how can this be, if time is relative and dependent on speed of reference frame? Does this assume some universal speed the whole space-time is quantified? Is there some constant Planck distance of time?
More over spatial dimensions are constantly exponentially expanding. So if we imagine the time as for example 2D cartoon, it's frame would be ever expanding as the movie goes on. But what effect would relativity/quantum fluctuation have on the frame and it's pixels? A distortion of some kind, surely.
I understand it is just a model and works OK on Earth (meaning locally), and with relativity accounted for in a nearby space. But how about as a whole? Why is this model then expanded to hypothetically allow time-travel? I'm not talking about sci-fi movies, but about scientific papers trying to achieve this (hypothetically).
Is there even a possibility to pin-point a coordinate in this mess? Doesn't that disprove that time is a dimension, not only to travel in, but also just as a coordinate definition? It doesn't have any stable coordinates (except in non-relativistic speeds locally). If time is measurement of the curve an object took in a time dimension, what is this curve tight to? Any spatial coordinate? But those can't be fixed in time, they change all the time (expansion).
If I wanted to go back in time to 1950, I would have to account not for only speed of all the entities (Earth, Sun, Milky Way, Universe?), expansion of the Universe, but also my speed (time velocity) relative to what? Some arbitrary point?
In short: If I have precise coordinates now in 3D [x, y, z, t(now)] and the point exists, how can time be a dimension if this point didn't existed in [x, y, z, t(before)].
Can someone help to explain?