There isn't just one scientific method. But there are two broad catagories of methods by which theories are ruled out.
1.) Falsification by experiment.
2.) Internal contradiction.
Method 1 is based on the logically valid syllogism known as
modus tollens which says, "If p is true, then q is true. q is
not true. Therefore, p is not true."
More formally:
[itex]p \longrightarrow q[/itex]
[itex]\neg q[/itex]
[itex]\therefore \neg p[/itex]
This model would be called
naive falsificationism, and has been criticized by a number of philosophers of science. But in some instances falsifying evidence is so overwhelming that such objections can be safely ignored.
The rise of quantum mechanics was brought about largely by Method 1. In one relatively short period of time it was found experimentally that there were several phenomena that could not in any way be accounted for by classical physics. For instance look up the photoelectric effect, the stability of the atom, and the ultraviolet catastrophe.
Method 2 is used when it is found that a theory is logically inconsistent. If it is possible to start from the axioms of a theory and, for some statement [itex]p[/itex], derive both [itex]p[/itex] and [itex]\neg p[/itex], then the theory is rejected. In logic this is known as a violation of the law of the excluded middle.
This method is in large part responsible for the birth of special relativity. As the 1800s were coming to a close classical mechanics and classical electrodynamics were the prevailing theories of the day. If in addition to these theories one accepts the idea that the laws of physics should be the same for all inertial observers then one encounters an apparent contrdiction. For the laws of classical mechanics are left invariant under one set of coordinate transformations (known as the Galilean transformation), and classical electrodynamics is left invariant under a
completely different set of coodinate transformations (known as the Lorentz transformation, of Special Relativity). Relativity resolved the contradiction by proposing a modified version of mechanics, of which classical mechanics is a limiting case.
wasteofo2 said:
Are there any sort of essays or generally accepted criteria for accepting one theory over another?
The entire discipline known as "Philosophy of Science" is devoted to this. Philosophers of science will readily admit that nothing in their field is set in stone.
I ask, because for most any theory, it seems that you can find evidence for it. If you did your research, you could come up with tons of evidence for a totally wrong theory (like all the evidence that existed for the geocentric model of the solar system).
You are touching on a basic issue of the philosophy of science here: the inadequacy of
confirmation theory. We gain confidence in theories not so much for withstanding many tests to confirm it, but rather for withstanding many tests to
falsify it.
And when scientists do accept a new theory over an old one, it is expected that the new theory will be confirmed in a
larger experimental domain than the old one, not a smaller domain. For example it is now recognized that relativistic mechanics is superior to nonrelativistic mechanics, and one reason is that the former is valid over a larger range of speeds than the latter. Using this criterion it is impossible for the reverse process to happen, even in principle. In other words, if relativistic mechanics had been discovered first, it could never have been supplanted by nonrelativistic mechanics, if we were to adhere to the principle enunciated above.
We don't look for theories that account for
some observational evidence, we look for theories that account for
all of it.