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Phew! I blinked and fell way behind in these posts! Here is my 2 cents:
JoeC,
RE "Are we traveling at near light speed in relation to some part of the universe... or is some part of the universe traveling at near light speed in relation to us? Which one is moving?..."
This is unresolved, but the hump (as you suggested we get over) rests squarely on Relativity's shoulders. The question doesn't go away. Why should we think because WE are here, the rest of the universe should care? BTW, the answer to the paradox above is that we NEVER are at velocity zero.
RE "As for how useful relativity is: Physicists need to use relativity when working with particle accelerators, to account for the increased mass of the particles they are slamming together at high speed. GPS satellites need to account for tenets of relativity since their clocks tick slower than clocks on earth. These are two examples of relativity coming into play in real life."
Okay, I dig that. But two things come into mind:
1. What have particle accelerators achieved of usefulness in real life, other than creating more reasons for research? Mind you, not critical of this research, but sense that given limitations on our energy parameters, we may be reaching a research dead end.
2. GPS clocks tick slower in orbit than on Earth... So? If my clocks at home run slow, do I conclude time is slowing down, or do I conclude the clocks are slow? Why not instead that there are as yet misunderstood reasons why atomic oscillations slow down while traveling through gravity fields, in the same way light redshifts in gravity fields? Is Relativity, though it does explain this, the ONLY answer? Not saying this is wrong, mind you, only that we have come to this conclusion via a circular type of reasoning, where our math predicts slowing atomic clocks (not mechanical clocks), so that in finding indeed they do slow down, we then assume that TIME is slowing down. Any critical mind would call "foul!", though physics seems to be okay with this and accepts it as fact.
RE "I think you're looking for a way to figure out what your "real" velocity is (with respect to the universe?). This concept does not exist in Special Relativity. There is no "universal reference frame" by which you can determine velocity."
Aha! This is a kinda "because" answer, which disappoints more than satisfies. Nevertheless, the question remains as a fundamental inquiry into the nature of universal relativity. Is a Terracentric reference, we on Earth, truly valid? For most physicists, the answer is "yes", without further questions. Again, because we do not have an answer for this, it does not preclude more questions. In effect, here we are asking the basic question of what is "rest mass", and what is "velocity"? This is not a chicken or egg question, rather it is asking what is the universe using as a reference frame, a very valid question. The answer to this determines whether the universe is already relativistic in how it is constructed, which means we are then recreating this needlessly; and if so, the "rest mass" may have no meaning. We invent terms and want to give them a reality which they may not have.
So, if the answer is that velocity is never zero, and rest mass doesn't exist, does this not throw the whole idea of SR/GR into doubt? Now you see why this is such a curiosity, why I am asking these questions. They are fundamental to our understanding of how the physics of the universe work.
Lastly, does science ever reach the point where such questions are not allowed? Of course not, since if it does, then science becomes religion, and once it is written open inquiry becomes forbidden, which is a contradiction. No need to put down anyone doubting and asking, for it is only natural. As thinkers and scientists, this is what we are supposed to do.
What does all this mean to me? Think about it: If rest mass is in doubt, and mass velocity is in doubt, and the physical application of a time dimension is in doubt (only atomic oscillations slow down, not time), what is Relativity left with? It may be that the universe is already Relativistically manifest into the reality we see, for which we are "hardwired" to understand three dimensionally. We do not need to re-invent another Relativity, since it already is at work. The result is a universe that is more Newtonian, though not perfectly, than it is Einsteinian. Einstein, Minkowski, and others, for all their brilliant ideas, may have sent us on a merry chase. There may be a much simpler explanation to how it all works. Possibility: Gravity is NOT a universal constant. Dark matter, light redshift, neutron stars spin, black holes, the atom, as products of how Energy and Gravity interact, all these fall into place. If so, this is worth pursuing. Why? Because it would release a whole new understanding how works the universe, and how to tap into the inexhaustible energy source that runs it intrinsically, gravity. Quantum electromagnetic energy, on which all our research is based, is perhaps only its modifier.
Truly appreciate all your thoughts on this, as always.
C2
Ps: In UR above: "Someone who is familiar with relativity would not say that Coppernicus2 "makes plenty of sense" when he implies that an object can be at rest with respect to the universe." My statement about velocity at zero was taken out of context and misunderstood, so false as stated by you. Do not wish to get into a "tit for tat" argument, but thought to correct obvious error. I hope more open minds are willing to read this, or arguments over "it is written" become too stinky of dogma. 
__________________
I have formally 'resigned' (tactical withdraw) from the Space-Talk boards; mine were many questions, ideas, but no real answers. Thanks. 04/10/04.
Disclaimer: Please note the ideas expressed here by me are cutting edge theory, very speculative in nature, and not physics as it is being currently taught. Caveat lector.
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Thread 
08/22/03 19:42
speed of ligt
Aether