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General Relativity Is At Least 99.95% Right
ultracool writes to mention a ScienceDaily piece on compelling proof of general relativity. A team at the University of Manchester have used three years' worth of data on a pair of pulsars as a litmus test, against which they've benchmarked Einstein's theory. From the article: "Though all the independent tests available in the double pulsar system agree with Einstein's theory, the one that gives the most precise result is the time delay, known as the Shapiro Delay, which the signals suffer as they pass through the curved space-time surrounding the two neutron stars. It is close to 90 millionths of a second and the ratio of the observed and predicted values is 1.0001 +/- 0.0005 - a precision of 0.05%. A number of other relativistic effects predicted by Einstein can also be observed. 'We see that, due to its mass, the fabric of space-time around a pulsar is curved. We also see that the pulsar clock runs slower when it is deeper in the gravitational field of its massive companion, an effect known as "time dilation."'"
Mathematics is a closed system, for which we know all the rules (because we define them). Thus, things can be proven as being objectively true, false, or unprovable (for as given set of axioms, there are many self-consistent sets).
Physics and the other sciences, on the other hand, are faced with the dilemma that we can never observe all the behaviour of everything in the universe at once, and thus we are forever working with partial data sets, and fitting our theories to them. As a result, the best we can say is that the theory we have put together fits the observed data to a high degree of precision - but that this may be invalidated at any time by new phenomena. See, for example, the progression from Newtonian mechanics to Relativity, or the long-running debate over the nature of light.
. . .we really shouldn't pretend his theories are anything more than a bunch of mathematical approximations. . .
.that reference intuitive concepts. . .
That's what I said. In fact, it's what Newton said as well.
. .
They reference only observable phenomenon and are valid only within the limits of those observations.
KFG
Well you certainly can measure position! What about a single slit experiment? The electron going through the slit has a quite well-defined position, but a less well defined momentum and that is the crux of quantum mechanics. Indeed, as you imply, it is not possible to say the position of the particle is exactly such-and-such because that would violate the uncertainty principle. I would prefer not to mention infinite spreads of position/momenta because this is not helpful; given you mention information propagation, do you not think that this notion might have issues with an infinite wavefunction? The wavefunction in any phase space must be normalizable and this is surely the most important concept. I'll except tunneling as there even the smallest of tails causes the finite barrier to "leak"... eventually.
An illustration - it is well known that C60 can be made to diffract. What do you mean then that position is meaningless? Do you mean to say that the atoms within the fullerene have no spatial relation to each other? How then do we know the symmetry of the molecule (from the number of absorption lines)? Of course postion is meaningful! Whether it is well defined is quite another matter.
I would also question your belief that the operators have any more meaning than the objects that the theory puports to describe! And I would certainly not advise trusting the math (although I'm a theoretician) - surely one must actually trust experiment!
I happen to be a physicist (but I don't particularly think that's relevant). I'm quite sure you grasp QM (the famous quote from Bohr aside), but I'm not sure I agree with the way you have chosen to explain it :-)
It is very common to say that "position, etc. are meaningless" but that simply isn't a correct statement at all, as I hope I've shown. Sorry for dragging this off topic (and for the profusion of exclamation marks)