bhobba said:
Physics is a mathematical model - its relation to this thing you called physical reality first needs a definition of physical reality many many of which exist, so many its useless. Think in terms of mathematical models (just like in Euclidean Geometry where you don't argue about what a point or line is 'in physical reality' - you just accept the obvious) - in your example Newton gave us a better mathematical model, Einstein an even better one - that's it - that's all. Do physicists believe we are getting closer to some truth about the world - of course - eg see Wienberg:
http://www.physics.utah.edu/~detar/phys4910/readings/fundamentals/weinberg.html
Bill
Physics is not a mathemtical model. A "mathematical model" I'd define as a certain set of axioms (e.g., the axioms of Euclidean geometry) which can be freely invented. Of course you are constrained by the fact that the axioms should not contradic themselves in an obvious way (although according to Gödel for any sufficiently interesting set of axioms you can never prove this consistency within this system of axioms itself), but otherwise you are pretty free to invent anything.
Physics is first of all an empirical science. It's about observation of phenomena in nature that show some regularity and pattern in the sense that you can reproduce these observations in an objective way, i.e., if you find something in a certain arrangement (in experiments that's called "preparation"), then you always find the same observational results (and be it only in a statistical sense). In the history of the modern sciences it turned out that you can make observations quantitative by defining measures for the most importantant quantities involved, starting from the geometrical quantity of length, the duration of times, and mass (as a measure for inertia). Already with this quite limited set you can describe everything what's now called "classical mechanics", and with the work of physicists like Galilei and Newton this could brought into an elegant mathematical system of "Natural Laws", now called Newtonian Mechanics. It's very powerful, giving us all the theoretical tools needed to construct all kinds of machines, including such a phantastic possibility as flying to the moon or landing a little lab at the spot of a tiny comet on the spot after a decade-long journey with some spectacular maneuvres all following Newtons laws as predicted, but nevertheless all this is based on observational facts, and the theory follows these observational facts, reducing the basic ones to an astonishingly simple handful of "fundamental laws" that finally can be cast into symmetry principles.
Of course, from this point on it's very mathematical, nearly like pure mathematics starting from a few axioms and building up a platonic world, but one must not forget that it's just the result of a lot of empirical evidence made ever more precise with the progress of technology of observation. As any empirical finding, it's always bound to be incomplete, and indeed the first evidence that Newtonian Mechanics cannot be the full truth are electromagnetic phenomena, which to a certain extent were found to be quite completely described by another set of fundamental laws, today called "Maxwell's Theory of Electromagnetism". It's plainly contradicting the very fundamental symmetry principles underlying Newtonian spacetime, and indeed after another struggle of about 50 years of many physicists, finally Einstein came to another better mathematical model called Special Theory of Relativity.
It's also true that without these mathematical formulation almost all physics we know to day, and which is crucial for our technological development (particularly quantum theory which is behind almost everything shaping our modern lives, particularly the laptop I'm typing this posting right now, the internet which let's me deliver it to PF where it can be read within a few microseconds or so all around the world), because often you get the idea for new experiments only through the mathematical conclusions within a given model of natural phenomena. In some sense an extreme example is the LHC (as far as I know the 2nd-most expensive experiment ever built up), which is the result of the quest for the final corner stone of the Standard Model of elementary-particle physics, the long-thought Higgs boson, which was predicted almost 50 years before it indeed has been unambigously discovered by ATLAS and CMS. I guess nearly every physicist around the world will remember what he or she did on Jul/04/2012, where the discovery was announced. I remember that we first had a seminar by a guest on another topic and then all watched the announcement of the Higgs discovery via the WWW.
So one must not forget that physics is about reproducible objective observations of nature, leading to astonishingly precise but always incomoplete mathematical models, but it's not math. If there is anything you can call "reality" in the sense of natural sciences it's the objective reproducibility of observations of nature. For sure, the mathematical models are NOT the "reality" in this sense but always incomplete pictures of it. The much I like Penrose's semipopular books (I've read some portions of "Road to Reality"), I cannot agree with his radical neoplatonism. He must have forgotten his time in the introductory and advanced science labs, where he should have learned that physics is finally an empircal science, not some system of purely mathematical axioms.
