ubertuber

So in my layman's understanding (meaning conceptual, not mathematical) of the theory of general relativity it seems that Einstein is telling us that there is no truly objective vantage point from which to observe objects. For instance, if I was standing next to the highway and a car drove by, i would be able to clock its speed at a certain number, say 69 mph. This number would seem to corroborate what my senses tell me. Now, if someone in that car was able to bounce a signal from their radar gun off of me, it would also return a reading of 69 mph. Thus, this measurement does not truly tell me how fast the car is moving, it only tells me how fast the car is moving relative to me. This is further born out by my knowledge that the earth is not only rotating, but is also hurtling through space, so even though I fell as though I am not moving, I clearly am. To sum up, motion is relative to perspective and there is no meaningful way to objectively determine trajectory and velocity unless one first specifies a vantage point.

Secondly, I think that general relativity is telling me that the perceived rate of passage of time is dependent on velocity. Namely, local time passes slower for objects moving more quickly. So, for instance if I am sitting still and I measure a particle that is moving at 90% of the speed of light, time passes more slowly for that particle. Even better, if there was a clock ON the particle, it would register less elapsed time than my wristwatch would in any given period, as long as that particle keeps moving close to the speed of light.

Now (finally) my question is this... If motion is relative, how do these clocks know which one should slow down and which one should speed up? If it is the particle that is moving, my watch will register more elapsed time. If it is me that is moving, my wristwatch should register less elapsed time. Logic would seem to suggest that only one of these things could be true at a time, but my first paragraph would suggest there is not any difference between our motions save the vantage point of the observer. Now, I seem to recall reading once that this time dilation is a real and measurable phenomenon, not just a theoretical abstraction. So I have a contradiction here, and one of my favorite authors says that there are no contradictions in the natural world. When we are faced with one we should check our premises. Have I misunderstood one of these two points concerning relativity? Or is this somehow similar to the physics experiment of the two holes (in which light can behave as a particle or as a wave [meaning displaying phase interference or not] depending on which result the observer is looking for) and so the position of the observer somehow determines the outcome of the experiment? If you have a better understanding of the specific mathematics here, please help me out!