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Autodynamics was a theory designed to replace the Theory of Relativity in the 1940s. It didn't work. Its main tenet states that the Lorentz transformation equations used in mainstream science are formulated incorrectly, causing special relativity and general relativity equations to be invalid. It also holds that the neutrino does not exist, despite the fact that both neutrinos and antineutrinos have been detected, that there are other particles which have not been observed by mainstream physics such as the "picograviton" and the "electromuon", and that there are other models of decay for muons. It is completely rejected by the mainstream scientific community, mainly because not only does it not have good evidence, there is very, very good evidence against it (such as the existence of something it says doesn't exist).
Grains of truth
Autodynamics is almost certainly correct in saying that there are particles we do not know about. This is due to the stopped clock phenomenon. However, it should be noted that they are probably incorrect about the properties of these undiscovered particles.
Autodynamics also contends that faster than light travel is possible. While many theoretical ideas exist for sneaking around the light barrier, autodynamics makes accelerating past light speed as easy as accelerating past Mach 1.
Autodynamics contends that gravity is caused by particles they call 'pico-gravitons.' This appears to be roughly analogous to the graviton. Their website says, "Even though Einstein described his 'General Theory of Relativity' which describes gravity as a warping of space and time, it like Newton's gravity equation, does not give a mechanism to it. That is, their [sic] is no explanation for what causes gravity, just a description." This is actually true, but subsequent theories such as graviton theory have explained it.