Comment by TheOtherHobbes
7 years ago
The point isn't that you get a few more significant figures of accuracy on a slightly larger set of problems, but that you use completely new tools, techniques, and ideas to tackle completely new classes of problems.
Heliocentrism isn't a "refinement" of geocentrism. It's a completely new way of understanding the universe. The fact that you can make geocentrism work if you make your epicycles complicated enough doesn't change the fact that it's conceptually incorrect, and not a useful way to think about the solar system.
Likewise GR isn't a "refinement" of Newton. It drives a tank through the middle of the Newtonian world view and burns it to the ground. Then it says "New physics, this way" and off it goes, thinking about phenomena that are literally inconceivable in a Newtonian universe.
You can consider GR a more accurate refinement for certain problems only. There's a limited set of problems - large in everyday human terms, but extremely limited in cosmological terms - where Newton gives you all the accuracy you want.
But if your understanding stops there, you're missing the point of these revolutions. They're not about improved accuracy, they're about new world views that give access to entirely new problem classes.
You literally cannot imagine these problems if you consider Newton as a mostly correct foundation and GR as a kind of philosophical epicycle added to it later.
And that means you cannot do useful new physics.
When Asimov says that "the model of a flat earth is nearly right, it's only wrong by 8 inches per mile" it's supposed to be an outrageous statement - the earth is not flat, that way of understanding is completely incorrect, and the (Newtonian level) correct model can help you solve new problem classes such as travel to the moon.
He's making the point of how the existing understanding can't give wildly wrong answers which are ready to be "upended", or else it would not have persisted. The understanding can be upended, sure. But the new theory has to account for everything existing.
GR (amongst other things) is a generalisation of Newton's law of universal gravitation, Newton's laws can be accurately derived from both QM and from GR with the PPN framework being the most common tool which derives it's parameters from the predictions set by GR.
Newtonian gravity works perfectly well in weak fields so it is not "wrong" but rather it's just not a generalised theory. A good way to look at it is that the laws govern the flow rate in a pipe are not a good generalisation of the behaviour of fluids in motion but they are as sure as hell good for calculating how liquid will flow in a pipe.
And wile GR tied everything together the signs that Newtonian laws were not a generalised theory predate Einstein in fact the Lorenz Transformation which serves as the basis for GR pretty much proved that as if the speed of light must taken as a constant and be finite which as defined by Newtonian physics then we get variable length and time.
So no GR to Newton isn't the same as Heliocentrism to Geocentrism if anything is that Geocentrism didn't actually work even with the math and observation we had.
The Greeks understood the Helicentric model quite well and even considered stars as distant suns the only problems with their models were primarily due to measurement errors for example Aristarchus's measurements were wrong by a few degrees but that was enough to alter the distance and size ratio of the moon and the sun to being about 20 times which what the greek calculated from being about 400 times which is what we've eventually measured correctly when we had better tools.
Uh, all your examples illustrate the core fact that our current theories are pretty close (to within many decimal places, usually) and that anything new isn't going to completely upend our expectations, even if it posits a completely new way of looking at things.
As the OP said, its not about upending expectations about precision of measurement.
After all you can make the geocentric model infinitely precise with enough epicycles, it can match all and every earthbound observation to any degree of precision.
That does not change the fact that it is fundamentally wrong.
There are edgecases though, where a currently percieved constant- is shown to be only the local galactic wether - or worser- easy influencable using the right tool.
If such a shaddy-bike-shed constant falls, new physics are possible, as in the underlying mechanism influences alot of old formulas and allows for boldly tweaking what no oman has tweaked before.