Why is motion in spacetime impossible? It has to do with the definitions of space and time and the equation of velocity v = dx/dt. What the equation is saying is that, if an object moves over any distance x, there is an elapsed time t. Since time is defined in physics as a parameter for denoting change (evolution), changing position from one point in a time dimension (time axis) to another is self-referential. Why? Because the equation for velocity along the time axis would have to be v = dt/dt which is meaningless, of course. It is logically impossible for the t coordinate of an object to change in spacetime. Et voil´! It's that simple. No time travel, no motion in spacetime, no spacetime and no time dimension.
I've always been unconfortable with the notion of time being considered the fourth dimension. You just don't have the freedom of motion as with the other three spatial dimentions and that wierd things start happening if you reverse time or otherwise can affect the past. The fourth dimention as another spatial dimention I can live with.
But I'm not about to go calling Richard Feynman a crackpot though!
The most amazing thing I was taught as a graduate student of celestial mechanics at Yale in the 1960s was that all gravitational interactions between bodies in all dynamical systems had to be taken as instantaneous. This seemed unacceptable on two counts. In the first place, it seemed to be a form of "action at a distance". Perhaps no one has so elegantly expressed the objection to such a concept better than Sir Isaac Newton: "That one body may act upon another at a distance through a vacuum, without the mediation of any thing else, by and through which their action and force may be conveyed from one to the other, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it." (See Hoffman, 1983.) But mediation requires propagation, and finite bodies should be incapable of propagate at infinite speeds since that would require infinite energy. So instantaneous gravity seemed to have an element of magic to it.
The second objection was that we had all been taught that Einstein's special relativity (SR), an experimentally well established theory, proved that nothing could propagate in forward time at a speed greater than that of light in a vacuum. Indeed, as astronomers we were taught to calculate orbits using instantaneous forces; then extract the position of some body along its orbit at a time of interest, and calculate where that position would appear as seen from Earth by allowing for the finite propagation speed of light from there to here. It seemed incongruous to allow for the finite speed of light from the body to the Earth, but to take the effect of Earth's gravity on that same body as propagating from here to there instantaneously. Yet that was the required procedure to get the correct answers.
You know, I've always wondered about this, and I was also under the impression that if the sun were to suddenly snuff out of existance, we wouldn't know for another eight minutes or so. But this seems to say that gravity, while not instantaneous, is certainly faster than the speed of light so a savy scientist might be able to make a sucker bet with the janitor (“Say Bob, I bet my house that the sun will snuff out in five minutes.”), not that it will do the scientist much good.
There is abundant literature on SR dealing with the seeming inconsistencies which Van Flandern brings up in his “paper”, and then mentions in passing as being "non-trivial". They are forbiddingly described as non-trivial, perhaps, because he is ultimately advocating a common-sense approach to cosmology, requiring no special knowledge of mathematics nor original experimentation to generate grand, sweeping hypotheses on how the universe works. His message seems to be that mainstream cosmological researchers are pointy-headed acolytes who either purposely or through accidental oversight have made things out to be far more complex than they really are, and that the “truth” of the matter is readily discernible by Everyman, if only he had all the facts laid out for him in plain English. No mathematics required.
Pass the popcorn, physics just got interesting again …
The GPS has revolutionized the transportion industry, as well as offering unprecedented position and chronometer accuracy to field researchers involved in biology, botany, ecology, geology, and petroleum exploration, among others. While the system was not designed as a test of gtr, it turns out that in addition to numerous extremely complex Newtonian physical issues which must be taken account of, there are also about a dozen distinct str and gtr effects which must be taken into account in the design and operation of the system. This takes quite a bit of explaining, since the actual system is quite complex, and I certainly won't attempt to explain all the engineering details here (although I'll provide links to sites where you can obtain more detailed information).