I have two examples that show how terrible things have become. I think the former is far worse than the latter, because the former is just plain dumb.
1. Quantum ‘non-locality’
It is held by theoretical physics that, when you are dealing with ‘quantum objects’, there can occur action at a distance without there being any ‘time’ for the effect to propagate. Einstein called this action at a distance ‘spooky’ and didn’t believe it. John von Neumann thought he had come up with mathematical evidence for the spooky action at a distance, but eventually it was found that von Neumann had made a stupid mathematical error just like the ones you and I would make in high school. I forget what the error was. In the 1960s another guy, John Bell, came up with his own mathematical evidence, which remains the standard argument in the field. In the 1980s, however, E.T. Jaynes, a physicist at Washington University, showed that Bell had made the common error of confusing ‘correlation’ with ‘causation’. Around the year 2000, a handful more of theoreticians started presenting their own arguments debunking Bell’s mathematics; this is where I come into the matter in a tiny way, by having made people aware of Jaynes’s prior work.
There is no spooky action at a distance. We are not talking here about a theory that just happens to be wrong; physics theory actually doesn’t suggest spooky action at a distance, unless you make a mistake in your math—which is exactly what physicists are doing and have done now for decades.
Mind you, that it took until the late 1980s for a first-class brainiac like E.T. Jaynes to debunk shows that Bell’s error is especially enticing. I myself was shocked to learn that famous, ultra-lauded people like John von Neumann make the same kinds of mistakes the rest of us do, and that their peers fail to notice the errors; my picture of von Neumann had been the one of a practically supernatural brain being that Jacob Bronowski painted for us in an episode of ‘The Ascent of Man’. Nevertheless, here we are, two decades since Bell’s error was discovered, and science fiction takes spooky action at a distance as a given, research dollars are poured into ‘quantum computing’ and ‘quantum cryptography’, as are pages in journals such as Science. So it goes, all because of an obscure math error that just happens to give a result our modern theoretical physicists prefer, which they prefer because they are not practical people who prefer common sense over magic. They like magic and wish to keep physics akin to magic. Maybe it helps them to feel special.
2. Special relativity and the twin paradox.
In this case there isn’t really a mathematical error, but a failure to generalize the mathematics and see if there were another solution to the given word problem (thought experiment) that was less weird than the standard one. When Albert Einstein formulated special relativity, he failed to notice that his thought experiments were soluble without assuming that observers in different inertial frames had their own ‘times’, with the celebrated ‘dilations’ and ‘contractions’ being artifacts of observation due to the finite velocity of light rays. In the early 2000s I bothered to learn enough tensor math to satisfy myself that this different solution to the problem really existed; it could be obtained from special relativity in tensor form by including a scaling factor that canceled out.
Which solution is right, if either, can only be determined by experiment, and the only type of experiment I know of that can deal with the matter is to reproduce the conditions of the twin paradox experimentally. This has been done but the experimental methods employed are subject to criticism; supposedly Einstein’s theory is demonstrated, but to me what’s true remains to be seen. However, even if Einstein’s predictions do turn out to be true, it is striking that, for a hundred years already, physicists have failed to notice that there is a ‘common sense’ form of special relativity, that solves the usual thought experiments just as well as does the more ‘spooky’ theory of Einstein. A hundred years! Instead we are taught Einstein’s theory as if it were an unavoidable result. And who knows what the implications are for Einstein’s general theory, which is foundational to the work of such a celebrity as Larry Flynt ... er, I mean Stephen ‘I call it a Hawking Hole’ Hawking.
For more info see http://www.nonloco-physics.000freehosting.com/