Even something as fundamental as Newton’s law of gravity is ultimately an approximation. Textbook authors dutifully write down the famous law without remarking that it results in infinite forces when the two attracting objects get infinitely close together. Never mind that infinite forces are a sure sign that your theory has gone up in smoke: in the current crop of textbooks sitting on my desk, not one mentions the obvious pathology.
To quote the fake president from Dave: Okay, let’s get right to the guts of it: every one of these accusations is absolutely true.
I can’t find fault with them, at least.
Sure, Edison (and perhaps as or more importantly, his staff) knew Ohm’s law and that hot things glowed (which is blackbody radiation). The details of why were far less important than those two models. It’s true that probing the question of Mach’s principle (at what does a gyroscope point?) led to general relativity, but we have that model without the answer to the question.
Physics, like all of science, tries to make models to explain how the universe behaves. It’s not a quest for the true nature of things — that’s metaphysics (and in case this gets translated into hipster, no, that’s not ironic). It may be a shortcoming that this isn;t driven home more forcefully, but it’s not an inherent flaw of science.
So I contend that it doesn’t matter. What he’s complaining about isn’t inherently a problem with physics or with physics education. But the author then acknowledges this, which leaves one to scratch their head and wonder what the point of the article is.
After decades — indeed, centuries — of employing such tricks, physicists have forgotten that they are modelling phenomena, not necessarily uncovering Divine Truth.
Newtonian centers of mass cannot get “get infinitely close together” without bodies prior touching and deforming to negate closer approach. A solid sphere is not the closest approach to a center of mass. The optimized cheat is no miracle, (radius=R, spherical coordinates [R, theta, phi]):
Sphere, r(theta) = 2Rcos(theta)
Shmoo, r(theta) = 5^(1/3)Rsqrt[cos(theta)]
(6/5)[(5/8)^(1/3)] = 2.6% better
A point mass m_0 is the origin. Its mass distribution’s surface rests on a plane. The z-axis connects m_0 to the surface kiss. A sphere would rest on the xy plane with the z-axis passing through its center.
Pack tight inside a Schwarzschild radius, but space and time go wildy nonlinear long before that. Newtons works within boundary conditions (far field; c = infinity, h = 0, k_B = 0), then General Relativity and quantum mechanics, then theorists with lace-trmmed panties snugged around their ankles. Like Euclid and 2-spheres, gravitation is fundamentally incomplete at one or more founding postulates (e.g., vacuum mirror-symmetry toward fermionic mass). A problem cannot be solved with the thinking that created it.
No well-managed concern tolerates innovation. Einstein was cashiered as a patent clerk, Galileo enraged the One True Church, and the MD awarded a Nobel Prize/Medicine for curing stomach ulcers was declared a crackpot. HP-35 vs. K&E slide rules. Entrenched management obsesses on what is measurable (zero risk) instead of promoting what is important (insubordination).
I wish I had been taught this in high school. I definitely thought that obtaining divine truth was the goal, when the goal is much more arbitrary and complicated: building a model that is simply good enough.
I seem to remember reading that Newton did recognize this flaw, and required tht bodies have measurable separation. I got this through to kids most effectively by telling them that obviously, the coincident centers of mass of a ring and the finger wearing it did not result in a black hole.