and don't know a thing when it comes to relativity ... or poor ol' Alex is wrong (although inconceivable!, the possibility can't be ruled out).
In Richard's post above... he makes the statement, --"If a rest frame exists for an object in Einstein's space (in the rest frame the object does not move through space, only through time),"--
Hmmmmm, "moves through time"... I guess I'm not alone with my outlandish and "stupid" ideas as Alex implies.
It seems I'm not the only one who interprets relativity correctly, contrary to Alex's strongly held position that I don't know squat.
How can I define "moving through time"?... It's the pace at which events take place in one F.O.R. as compared to another reference frame; be it oscillations of a given field, the heart rate of an observer, the ticking of a clock, or the pace at which a system transitions into a different state... however you want to "define" time. So at this very moment, as compared to the rest frame (my F.O.R is perceived by me as motionless), the events that I witness in this frame occur with natural unaltered pace. If I were to take the room I'm now sitting in, and rocket it up to speeds that are a considerable fraction of the speed of light (say 99.999%) whilst leaving me behind to watch from the grass, then the "motion through time" that this room experiences has been slowed almost to a halt AS PERCEIVED BY MY F.O.R.! So I'm not saying that this room has ceased to experience time... far from it! In fact, were an observer sitting in this room as it were flung out into space, neglecting lethal G forces, there would be no noticeable change in the rate of time as observed by him from his point of view. This is the invariance of proper time that Alex is so insitent upon; I realize this concept and account for it. My take on an excerpt from a popular book (Brian Greene's Elegant Universe), is that we all travel with speed c through space time. In the rest frame, this speed is manifested as maximal speed through time (speed c). However, if two observers were suddenly separated by motion, in fact a great deal of motion... each would argue that the other has diverted his speed through time into speed through space. In the limit that this speed through space approaches c, motion through time approaches 0. For all frames as measured by some observer to be in between these upper and lower extremities, we convert using the equation "t' = t0/(1-v2/c2)1/2. Notice how the perceived motion through time with respect to how a given observer measures it, is directly dependent upon the speed with which this frame is observed to move through space, which in turn is measured by a fraction relating it to the speed of light (v2/c2). Therefore it is not to outlandish to conceive of space and time as being to equal partners who play equally important roles in the mechanics of the universe. One could even say that they are not partners, but different sides of the SAME COIN. There is no distinction between space and time when it comes to relative observers. What's my space is your time and what's your time is my space. We all move with the same speed "c" through space-time. The direction of our motion is the only thing that changes (be it through space or time). This can concept can be animated by the tipping of the light cone. The axis of the cone is the time dimension while the axis perpendicular to "time" is space. If you tip one persons cone, his axis now becomes more space oriented than time, as perceived by the other observer. But the rate of time always remains invariant for the observer in his own cone. The act of tipping a light cone is felt as acceleration. From a 4-dimensional point of view, there is no acceleration of speed, only a change in direction takes place. Since gravity curves space-time, it follows that our light cone will inevitably change direction in the presence of gravity... once again, this is perceived as acceleration. What is a change in speed in 3-D is a change in direction in 4-D.
We all move with speed c, forever. Such is the essence of "proper frame invariance".
What'dya know, Alex actually can be wrong. No I didn't make those equations up, and no I didn't take a course in Star Trek physics. I'm not impressed with those who can mechanically remember facts (that's what books and hard drives are for), what impresses me is those that have enough genius and keen eye to discover the facts in the first place. They deserve the real credit. The most important tool a physicist possesses is that which no book, university, calculator, or amount of money could ever give him... it's his imagination. That's what separates the Einstein's from the Joe Shmo college graduate. Einstein by the way, didn't have a degree when he envisioned special relativity and uncovered the secrets of the universe most impressively by nothing more than powerful insight and genius imagination. How unfortunate that someone like Alex feels he has the authority to call that great man's theory "wrong", without having a reason to do so.