Theories in Modern Physics Are Curve Fitting Models

Dec 27, 2022
Dr Katie Mack, Hawking Chair in Cosmology and Science Communication at the Perimeter Institute for Theoretical Physics: "A physicist's task is to constantly create equations that keep up with our observations of physical phenomena."

This is the inductive method or, in more technical terms, curve fitting:

"Curve fitting is the process of adjusting a mathematical function so that it fits as closely as possible to a given set of data points. The function can then be used as a mathematical model of the underlying data."

Instructive descriptions of the inductive method in physics:

Ethan Siegel: "Scientific Theories Never Die, Not Unless Scientists Choose To Let Them. When it comes to science, we like to think that we formulate hypotheses, test them, throw away the ones that fail to match, and continue testing the successful one until only the best ideas are left. But the truth is a lot muddier than that. The actual process of science involves tweaking your initial hypothesis over and over, trying to pull it in line with what we already know...By the addition of enough extra free parameters, caveats, behaviors, or modifications to your theory, you can literally salvage any idea. As long as you're willing to tweak what you've come up with sufficiently, you can never rule anything out."

Sabine Hossenfelder (Bee): "The criticism you raise that there are lots of speculative models that have no known relevance for the description of nature has very little to do with string theory but is a general disease of the research area. Lots of theorists produce lots of models that have no chance of ever being tested or ruled out because that's how they earn a living. The smaller the probability of the model being ruled out in their lifetime, the better. It's basic economics. Survival of the 'fittest' resulting in the natural selection of invincible models that can forever be amended."

Before 1915 theoretical physics was mainly DEDUCTIVE - you cannot tweak your theory unless the tweak is deducible from initial axioms (postulates). In 1915 Einstein replaced deduction with induction, and unlimited ad hoc adjustment, unrelated to any axioms, was allowed. Here Michel Janssen describes relentless adjustment performed again and again until "excellent agreement with observation" was reached:

"Einstein did not give up the Einstein-Grossmann theory once he had established that it could not fully explain the Mercury anomaly. He continued to work on the theory and never even mentioned the disappointing result of his work with Besso in print. So Einstein did not do what the influential philosopher Sir Karl Popper claimed all good scientists do: once they have found an empirical refutation of their theory, they abandon that theory and go back to the drawing board...On November 4, 1915, he presented a paper to the Berlin Academy officially retracting the Einstein-Grossmann equations and replacing them with new ones. On November 11, a short addendum to this paper followed, once again changing his field equations. A week later, on November 18, Einstein presented the paper containing his celebrated explanation of the perihelion motion of Mercury on the basis of this new theory. Another week later he changed the field equations once more. These are the equations still used today...It is not hard to imagine Einstein's excitement when he inserted the numbers for Mercury into the new expression he found and the result was 43", in excellent agreement with observation." Janssen, M. (2002) The Einstein-Besso Manuscript: A Glimpse Behind the Curtain of the Wizard. In The Collected Papers of Albert Einstein (Vols. 1-10, pp. 1987-2006). Princeton, NJ: Princeton University Press.

DEDUCTION from clearly defined axioms (postulates) is the only reasonable method in fundamental physics:

"By a theory I shall mean the deductive closure of a set of theoretical postulates together with an appropriate set of auxiliary hypotheses; that is, everything that can be deduced from this set." W. H. Newton-Smith, THE RATIONALITY OF SCIENCE, p. 199 of science.pdf

Here Einstein suggests that deduction, not induction, is the correct method:

Albert Einstein: "From a systematic theoretical point of view, we may imagine the process of evolution of an empirical science to be a continuous process of induction. Theories are evolved and are expressed in short compass as statements of a large number of individual observations in the form of empirical laws, from which the general laws can be ascertained by comparison. Regarded in this way, the development of a science bears some resemblance to the compilation of a classified catalogue. It is, as it were, a purely empirical enterprise. But this point of view by no means embraces the whole of the actual process ; for it slurs over the important part played by intuition and deductive thought in the development of an exact science. As soon as a science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms."

The crucial question is: What if a theory in physics is not deductive (no clearly defined axioms; no explicit deductive paths leading from axioms to conclusions; unlimited ad hoc adjustment is allowed)?

Answer: Then the theory, e.g. Einstein's general relativity, is a not-even-wrong inductive concoction, essentially equivalent to curve fitting models.
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Dec 27, 2022
Sabine Hossenfelder: "The cosmological constant is a free parameter in Einstein's theory of general relativity. This means its value must be fixed by measurement."

"A fudge factor is an ad hoc quantity introduced into a calculation, formula or model in order to make it fit observations or expectations. Examples include Einstein's Cosmological Constant..."

Ken Croswell, Magnificent Universe, p. 179: "Ever since, the cosmological constant has lived in infamy, a fudge factor concocted merely to make theory agree with observation."

Can one add a fudge factor analogous to the cosmological constant to the Lorentz transformation equations? One cannot, and the reason is simple: Special relativity is DEDUCTIVE (even though a false postulate and an invalid argument spoiled it from the very beginning) and fudging is impossible by definition - one has no right to add anything that is not deducible from the postulates.

Einstein's general relativity was not deduced from postulates. It is a not-even-wrong INDUCTIVE concoction - a malleable combination of ad hoc (guessed) equations and fudge factors allowing Einsteinians to predict anything they want:

Alexander Poltorak : "In 2005 I started writing a paper, "The Four Cornerstones of General Relativity on which it doesn't Rest." Unfortunately, I never had a chance to finish it. The idea behind that unfinished article was this: there are four principles that are often described as "postulates" of General Relativity:

1. Principle of general relativity

2. Principle of general covariance

3. Equivalence principle

4. Mach principle

The truth is, however, that General Relativity is not really based on any of these "postulates" although, without a doubt, they played important heuristic roles in the development of the theory."

Sometimes Einsteinians call Einstein's 1915 final equations "postulates" (the brainwashed public sees no problem in this):

"Postulates of General Relativity
Postulate 1: A spacetime (M^4, g) is a Riemannian 4-manifold M^4 with a Lorentzian metric g.
Postulate 2: A test mass beginning at rest moves along a timelike geodesic. (Geodesic equation) ...
Postulate 3: Einstein equation is satisfied. (Einstein equation) ..."
Dec 27, 2022
In the not-even-wrong inductive concoction called "general relativity", the speed of gravitational waves is a matter of arbitrary choice. Einstein decided that gravitational waves should travel at the speed of light, and tweaked the coordinates accordingly. Arthur Eddington, Einstein's accomplice, was surprisingly honest in this particular case and exposed the hoax:

Arthur Eddington: "If coordinates are chosen so as to satisfy a certain condition which has no very clear geometrical importance, the speed is that of light; if the coordinates are slightly different the speed is altogether different from that of light. The result stands or falls by the choice of coordinates and, so far as can be judged, the coordinates here used were purposely introduced in order to obtain the simplification which results from representing the propagation as occurring with the speed of light. The argument thus follows a vicious circle." The Mathematical Theory of Relativity, pp. 130-131

Arthur Eddington: "The problem of the propagation of disturbances of the gravitational field was investigated by Einstein in 1916, and again in 1918. It has usually been inferred from his discussion that a change in the distribution of matter produces gravitational effects which are propagated with the speed of light; but I think that Einstein really left the question of the speed of propagation rather indefinite. His analysis shows how the co-ordinates must be chosen if it is desired to represent the gravitational potentials as propagated with the speed of light; but there is nothing to indicate that the speed of light appears in the problem, except as the result of this arbitrary choice."