Is time believed to be a constant or is it merely a function of the perception of the observer? My understanding is that if Astronaut Poole was just outside of an event horizon and Astonaut Bowman was just inside the event horizon, their repsective perceptions of time would be drastically different.
As such, is there any sort of objective measurement of time? Would Hal’s silicon clock be able to give an objective measurement? Is the perception of time a human thing? Is the speed of light a constant that could be used to derive an “absolute second in time” or something?
Further, is there some sort of scientific notation for time that indicates an oberver’s viewpoint or some sort of notation for a theoretical “objective” time like a superscipt or subscript? I don’t know how to properly describe what it is I want say in a fomulaic manner.
Neither. It is certainly not constant. However, while it can be different for different observers, this difference is not caused by the observers’ perception, but rather by their different rates of acceleration.
An atomic clock is an objective measurement of time. However, it is not an absolute measure of time. There is no such thing as “universal” or “absolute” time. It’s all relative.
Sort of. As an object speeds up, it becomes compressed in the direction of travel (from the viewpoint of a “stationary” observer).
To be perfectly honest, though, I have only a basic understanding of special relativity. Some of your questions might be better answered by either waiting for someone more versed in physics to notice this thread, or by searching on Google for “special relativity”. For instance, I found this page, which has a fairly easy-to-understand rundown on special relativity, including time dilation and length contraction.
No “sort of” about it. Time and space are intrnsically linked, and you can’t meaningfully discuss one without the other, in the context of relativity. To give an idea of how closely related they are, inside the event horizon of a black hole, time and distance from the center are swapped in their roles: Once inside the hole, you can move freely in the t direction, but you can only move closer to the center, in exactly the same manner that you can only move towards the future, when outside a black hole.
You have to move up to GR for that. Everything is moving through spacetime at a certain 4-velocity which is (necessarily) timelike for a massive particle. Fascinatingly enough, the lengths of all these 4-velocities are the same: -1 (with the sign convention g[sub]00[/sub] ~= Diag[-1,1,1,1] ).
In other words: you can’t move “freely”, but are carried along by your worldline at a constant rate. “Relative motion” is percieved when two observers have different spatial components of their 4-velocities (suitably parallel-transported to a common basepoint etc…).