StarstruckKid wrote:
Then how do we ever move beyond existing theory? If everything has to happen within existing theory, doesn't that preclude being able to move beyond it, by definition? Would you say that relativity is 'within the bounds' of Newtonian mechanics?
Thing is, everything has to happen within existing theory for as far as that theory applies. 1+1 does not suddenly become equal to 3 because we discovered some new mathematics. Newton's 9.8ms^-2 did not double when we discovered General Relativity. Water didn't begin starting fires (unless you like group I alkali metals) when we discovered Molecular Orbital theory.
New theories are refinements of old ones, not replacements. You can't replace an old theory without incorporating it. You can send a rocket to Mars using Einstein, sure. You can also use Newton because Einstein's theories are a superset of Newton's to correct Newton's old theories where they weren't working well.
You have to do this by finding the area where the old theories aren't working well. Turns out that close to and at the speed of light, Special Relativity indeed does apply and works very well indeed; We see time dilation, we see increased masses. No new theory is going to change what actually happens in reality. Any challenge to Relativity is going to come on the quantum scale, where the two frameworks don't work very well at all, it is not going to come at the "close to c" scale, where they work exceptionally well.