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You've asked a very interesting question... one that cuts to the heart of Newtonian mechanics and the theory of relativity (we'll be limiting our discussion to just the Special Theory of Relativity). Newtonian mechanics, which reigned supreme for about 300 years, is built on the assumption that there is an absolute time. An absolute now. There is no absolute state of rest in Newtonian mechanics but time was given a special status and assumed to be unique and absolute. Under Newtonian mechanics, the system you suggest (of a simultaneous "now" across reference frames) is absolutely valid. Since time itself is absolute, there is no reason whatsoever to limit it's progress by correlating it somehow with the speed of light. After all, if time is absolute and universal, what does it matter if it takes light thousands of years to travel the distance and convey the message to us... time itself is still separate and universal, right?
Well, maybe not... that view, which is inherently logical and common-sensical, was the accepted view exactly because it corresponded to everyday experience. Velocities might be relative (as in two cars approaching each other seeming to go faster) but how could time, a separate and universal entity, be at all affected by motion??? Simple... it couldn't! And this was the state of things until a few experiments started to suggest that everything might not be as cut and dried as all this. Experiments like the historic Michelson-Morley experiment were increasingly showing that the speed of light was turning out to be the same no matter how you measured it. It seems that velocities, as you got close to the speed of light, weren't adding as they should! A few brilliant men started to suggest what might be happening (namely, Lorentz, Fitzgerald, Mach, etc.) but it wasn't until a certain patent clerk by the name of Albert Einstein came along that the picture became clear.
What Einstein showed was that when we start talking about things going near the speed of light, this concept of simultaneity could no longer be thought of in the same way as we experience it in our normal world. Our common sense evolved on a world that operates, for all intents and purposes, at non-relativistic speeds. All our interactions occur at speeds much, much less than the speed of light so none of the subtleties of relativity revealed themselves until these investigations. What these investigations revealed, and what Einstein consolidated, is today known as the Special Theory of Relativity. There are reams and reams of pages written (and published on the web) about this so instead of going into the details of relativity itself, I'll briefly bring to bear on the points relevant to your question. But, I'll add at the outset that you should definitely explore the various books and pages out there on this intricate and beautiful theory. There are also many answers posted here on MadSci that you can browse through. At the end, I'll include a little bibliography of links to help get you started.
So, back to relativity... what Einstein showed in his landmark paper was that the speed of light was constant in all reference frames. One of the implications of this seemingly innocuous statement is that it destroys the idea of an absolute or universal time. Time, like velocity, is now relative and, in fact, time itself is no longer allowed a separate and unique existence; instead, it's partnered forevermore with space into one congregate space-time. Once you accept the idea of a spacetime without absolute time, you have to redefine what it means for two events in spacetime to be labeled simultaneous. There are many lucid and simple expositions on what this means so I'll defer to them for proofs and just state the result here: events that are simultaneous within one reference frame are not, in general, simultaneous in another reference frame moving with respect to the first! This amazing conclusion leads directly to the well-known relativistic consequences of time dilation and length contraction.
But this conclusion also has dramatic consequences for the situation you pose. For example, let's say a sun goes nova just as you sit down to your afternoon tea. We assume that both you and the exploding sun are in the same reference frame and so we can say that both events (your tea break and the sun going nova) are simultaneous; i.e., they both happen now. Since the sun exploded quite a distance away (but still in your reference frame), it will take light a finite amount of time to travel that distance and deliver the message to us. But, as we know, although it's simultaneous in our reference frame it won't necessarily be simultaneous in another person's reference frame (say, someone near Alpha Centauri). Thus, simultaneity within a reference frame can be easily preserved and you can define a local, absolute "now" but not a universal, absolute "now" for all reference frames.
I hope that made some sense. Relativity is a tricky theory because it's so contrary to our everyday experience. But it's important to remember that there's nothing magical about our everyday experiences and our ideas of common sense... we adapted to and evolved on a world that moves at extremely slow speeds (compared to the speed of light) so there's no reason to expect us to have a natural intuition into what happens when things go really fast. This is when it's helpful to start developing a mathematical intuition in addition to our physical (and intrinsically biased) intuition. Unfortunately, this is not an easy thing at all for those of us who aren't mathematical prodigies so we end up struggling along and thinking about these things for hours on end before coming across some small insight or realization. But I can guarantee you that the time you spend thinking on the way nature really is will be time well spent... for in these matters you catch a glimpse of what the universe, and life, really is. No wonder, then, that men are inspired to see the hand of God in science... but such matters are better left for philosophers to sort out, I think. :) I hope that helped... but if something I said seems shady or you'd like to discuss this further, please feel free to drop me a line at firstname.lastname@example.org.
And, as promised, here are some interesting links:
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