That covers a lot of physics, Marcel. I'll try to summarize as best I can. The quote is directly from Einstein, in his introduction to general relativity--following the explanation of special relativity. Special relativity is the "special case" of uniform motion; general relativity is the generalized case of accelerated motion.
To understand accelerated motion, we have to go back to Newton's theory of gravity. Newton had found that acceleration in a gravity field accounted for both the attraction of bodies toward the center of the Earth, and for celestial orbits.
In Newton, however, space is an absolutely smooth background and time is also absolute (i.e., clocks run at the same rate everywhere in the universe).
Einstein, with a deep background in classical mechanics, saw what Ernst Mach had done. By disregarding the role of space altogether, Mach had proposed that the motion of any body in the universe depends on the motion of every other body in the universe. That is, if one could determine the initial state (position and momentum) of all bodies at one moment, one could in principle predict future states in all other moments. In Mach, then, time is "physically real"--there is a non-arbitrary zero point of motion and space is just a convenient fiction. Of course, Mach's idea also depended on Newton's assumption of absolute time.
Einstein recognized that other than in a closed, isolated system, what he called "Mach's Principle" would be impossible to show experimentally valid. Like every good physicist (especially of the classical variety) Einstein was driven by the need to demonstrate correspondence between theory and physical result. And like almost every theorist of his era, he was troubled by Newton's theory that required "action at a distance"--the instantaneous influence of one body on another .
With Mach, since space doesn't matter, invisible gears crank the universe and all action is local. This property--locality--is how Einstein arrived at the idea that if Mach's Principle holds, there is no nonlocal influence on the motion of bodies. So there must be some physical boundary that prevents action at a distance. Since special relativity had already incorporated the absolute speed of light, Einstein reasoned that not only did the speed of light limit uniform motion, but that it limits local action as well--because accelerated motion (i.e., motion in a curved path rather than a straight line) would be bounded by the curve. If you think of this in terms of geometry, and you know that a straight line is a special case of a curve, you see that while the line extends from minus infinity to plus infinity, the curve limits the path of the straight line so that the distance-time relation to the common coordinates of three dimensional space adjusts the coordinates so that a body in time is continuous with its position in space. The metric signature of general relativity is +++-, which means that the straight line (the three plus signs) is truncated by the minus sign, and this is a physical boundary. The derivation is x^2 + y^2 + z^2 - (dt)^2. The xyz coordinates describe a body's position in space; dt is the distance-time term. At nonrelativistic distances and speeds, it doesn't mean much, but is significant otherwise. (All of this is experimentally validated.)
So. If all physical influences are local, there can't be a universal clock, because the measurement of local processes viewed by one observer at a relativistic distance (or speed) from another's locality differs from the measurement that the other makes. Every observer carries her own clock, in other words, which reads differently from one observer's state in relation to the other.
Not only is time physically real, as in Mach's mechanics--space is also physically real in general relativity. However, neither space nor time can be _independently_ real, because of the observer dependence. Time is treated as an extra dimension, a coordinate point continuous with space. In mathematics, this is called Minkowski space, or space-time. In explaining how this continuum acts on the apparent position and momentum of bodies, Einstein reminded us of what "physically real" means, in order to distinguish the true physics from the apparent: " ... independent in its physical properties, having a physical effect but not itself influenced by physical conditions." Time is not physically real. Space is not physically real. Spacetime is physically real.
Tom
