And I could recommend 'A briefer history of time', by Stephen Hawking.
The part where antimatter has a negative time-direction is on page 112. It speaks of Feynman's quantum mechanical calculations. I may have made a mistake when saying negative mass, but, AFAICT, rest mass and time-rate is the same thing.
Just because a theory is found to be inaccurate does not discredit the theory's inventor. Otherwise we wouldn't still be teaching Newtonian physics in school.
Understanding quantum theory requires only understanding that you cannot know everything at once. Knowing one thing makes other things uncertain. Although, with entanglement, this sometimes works the other way around.
Understanding special relativity requires understanding that all movement is relative, the speed of light (in a vacuum) is constant and that relative motion implies relatively warped frames of reference.
The reason why I keep making mistakes with relativity theory is that it has been 8 years since I last studied it thoroughly.
And, regarding my unorthodox ideas, I try to keep them out of the discussion, but they slip in because I have been thinking about them for years. I already take them as fact even though they have not been through peer review, which is wrong of me.
Proving that we are handling zero incorrectly is real simple though:
f(x) = x
g(x) = x - 1
h(x) = f(x) / g(x) => has an asymptote at x = 1
h(x) * g(x) = f(x), except, at x=1 it has no value.
Shouldn't dividing and multiplying with the same value return one to the original value? I am quite certain that has to be in the definition of division somewhere, and that it should count for all real numbers. Maybe I should look it up.
Edit #1:
@Flaede: Usually it is not so much a case of one state or the other, but, as you confine things, the total amount of valid states decreases. So, for instance, in an unbound atom there are only discrete energy levels for electrons, because they are confined tightly along all three spatial dimensions. In a conductive crystal (like metals) there are bands of valid energy states, with gaps between them. In the case where an electron is not confined at all it can assume any energy. Hopefully this is clearer to you now.
In the case with the cat, it is not so much that the cat is both alive and dead, but rather that the one bit of information regarding whether the cat is alive or not can have any value until the external observer opens the box. From the cat's perspective things are quite different; the cat knows when it is alive and whether it dies.
@Idiom: Bending a photon into a circle
requires a significant warping of space-time. I guess you might have misunderstood the original article. (Bending due to matter-interference is another thing entirely, and will not cause warping of space-time.)
@Grek: Your explanation of the acceleration limit is only valid for the observer staying behind. For the person in the spacecraft it will seem like he is constantly accelerating, his mass staying constant, and gaining energy in accordance with that. (IIRC)
Edit #2:
I've looked up the use of zero and infinity. It has already been found useful and rigorously examined; in 1966 Abraham Robinson published the details.
http://en.wikipedia.org/wiki/Ghosts_of_departed_quantities