I think Feynman said it best: 'Physics is like sex: sure, it may give some practical results, but that's not why we do it.' As was remarked earlier, having a working knowledge of physics will not help you in the vast majority of things in life; in fact, as has also been remarked already, it's even worse than that: many of the regular accepted physics explanations for complicated everyday phenomena not directly reducible to or a direct application of classical/modern physics are simply incorrect and more of a hamper than of actual utility in actually understanding said phenomena in a practical way. I will try to illustrate this, by giving an example of a culture of which I am apart, which is both deeply scientific, yet extremely practical, namely medicine.
In medicine, a discipline which is for the most part deeply based in the natural sciences, the disconnect between physics and practice is much clearer than usual. This can be immediately seen in that almost no physics or mathematics is taught during medical training nor utilized in the practice of medicine; this often comes as a surprise to anyone in medical school deeply convinced of the scientific nature of medicine, a stance which is exemplified in medical research as 'evidence based medicine'. Before and in my early years of medical school, I was also convinced that all useful knowledge in medicine could and therefore should be reduced to physics; I was astutely aware that my viewpoint was a very tiny minority view both among students and teachers. During the latter years, I began to realize that the opposite does in fact seem to be true: theoretical explanations of phenomena in medicine grounded in physics are almost entirely useless in clinical practice; for biomedical science this is of course an entirely different matter.
The fact that physics based knowledge seems specifically useless for clinicians is two-fold: namely a) the theory of physiology has not been fully reduced to a working biophysical model and pretending that it has is a dangerous delusion, especially for science; the mathematical methods required for such modelling has often not yet even been discovered and simplifying things in order to comform to standard mathematical techniques usually simply means throwing out the baby with the bathwater, and b) there is no actual full correspondence between what clinicians think is happening in a patients body based on their diagnostic investigation and what is actually happening i.e. in terms of known or unknown physics. What these physicians think to know is merely a mental model; practically speaking, the question is not whether that mental model is correct in terms of physics or natural sciences, but it is instead whether that model is efficient in identifying disease in a quick and reliable manner.
Andy Resnick said:
So, I'll present a different approach. "Physics knowledge" is more than being able to regurgitate formulas. One of the core discipline elements of Physics, something that distinguishes it from other science and engineering disciplines, is the quantitative notion of 'simplifying' real systems via approximation to arrive at an abstract idealization, which is then used to (approximately) solve an actual problem at hand. Creating an abstract model and deciding what can be ignored and what must not is an (maybe THE) essential element of problem solving, and AFAIK, is primarily (exclusively?) taught as part of the introductory Physics curriculum.
While I agree with you partially, I do not do so without sufficient hesitation. During my undergraduate years in college, doing a double major in physics and medicine, I was fully convinced that the points you are making here were true. Now many years later, I'm more convinced of the opposite: a large part of mathematical reasoning used in (theoretical) physics is based on intuitive reasoning for which there has to date been given no proper mathematical justification. For core physics knowledge i.e. classical physics as taught during undergrad, we have identified the mathematical theories which in many cases actually formalize and sometimes even subsume much of this intuitive reasoning; these are the mandatory basic mathematics courses every physics student has to take.
The remaining 'physics' part of the theory is often merely a qualitative semi-mnemonic scaffolding capable of directly exemplifying some core properties of these simplified mathematical theories and linking them to experiment. In terms of actual physics, i.e. when more carefully analyzed with more advanced physical frameworks (soft and condensed matter physics, biophysics, fluid dynamics, nonlinear dynamics, theory of critical phenomenon, etc) and more advanced experimental techniques, these simplifications, i.e. methods of approximation and linearization, tend in many cases to breakdown quickly and often spectacularly when carefully looking at an actual phenomenon in the non-idealised case.
The relative ease (and therefore seductiveness) of the mathematical methods learned early on in the simplified canonical theories is then actually a psychological bias among physicists during further theorisation or extrapolation of a theory beyond empirically tested limits, which can be summed up as the following: theories i.e. mathematical models or explanations of phenomenon of which the mathematics is already academically understood and consistent with the mathematical methods that the physicist has already learned are strongly preferred to non-standard theories; the physicist might even refer to one theory as more beautiful or more aesthetic for these reasons. This 'beauty' depends on where the mathematical focus of further training outside of the core curriculum has taken them. Particle theorists tend to find group theoretical notions beautiful, fluid dynamicists tend to find (complex) analytic notions beautiful and relativity theorists tend to find differential geometric notions beautiful, while at the same time finding the other's respective notions far less aesthetically pleasing or even downright hideous.
Historically speaking, this has always been an issue which has caused divide among mathematicians, e.g. Euler, Gauss, Riemann and many if not most of the classical mathematicians would have found generalized functions such as the Dirac delta function hideous, not even to speak of the everywhere continuous but nowhere differentiable functions, i.e. fractals, which they even termed as 'pathological' i.e. sick because they do not conform to the reigning notion of beauty from the theory of analysis, namely the intuitive connection between the key concepts of continuity, smoothness and differentiability. Due to the increased specialization of the 20th century and the lack of an actually accurate and self-consistent overarching picture, such ideological differences have become exacerbated. This innate desire to have a theory fully conform to some particular existing mathematical methods one already knows is a non-experimental systematic bias to be controlled for when mathematically and theoretically investigating known physical phenomena and their theories more deeply; this seems to be true for both theories in fundamental physics as well the more applied subjects I referred to above and many mathematical physicists actually do take this into consideration when writing reviews.
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