Deductive and Not-Even-Wrong Theories in Physics
(too old to reply)
Pentcho Valev
2019-04-23 10:37:12 UTC
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 http://cdn.preterhuman.net/texts/thought_and_writing/philosophy/rationality%20of%20science.pdf

Einstein offers essentially the same definition here:

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." https://www.marxists.org/reference/archive/einstein/works/1910s/relative/ap03.htm

Two points should be noted:

1. The axioms (postulates), clearly defined, are indispensable.

2. The results of the theory are DEDUCED FROM AXIOMS, not guessed as Feynman used to teach:

Richard Feynman: "Dirac discovered the correct laws for relativity quantum mechanics simply by guessing the equation. The method of guessing the equation seems to be a pretty effective way of guessing new laws." http://dillydust.com/The%20Character%20of%20Physical%20Law~tqw~_darksiderg.pdf

The crucial questions are:

What if the theory has no axioms? What if results of the theory are just "guessed", not deduced from axioms?

Answer: Then the theory, e.g. Einstein's general relativity, is a not-even-wrong empirical concoction, essentially equivalent to the EMPIRICAL curve fitting models defined here:

"The objective of curve fitting is to theoretically describe experimental data with a model (function or equation) and to find the parameters associated with this model. Models of primary importance to us are mechanistic models. Mechanistic models are specifically formulated to provide insight into a chemical, biological, or physical process that is thought to govern the phenomenon under study. Parameters derived from mechanistic models are quantitative estimates of real system properties (rate constants, dissociation constants, catalytic velocities etc.). It is important to distinguish mechanistic models from empirical models that are mathematical functions formulated to fit a particular curve but whose parameters do not necessarily correspond to a biological, chemical or physical property." http://collum.chem.cornell.edu/documents/Intro_Curve_Fitting.pdf

Pentcho Valev
Pentcho Valev
2019-04-23 15:18:07 UTC
Post-truth science: "Einstein was able to predict, WITHOUT ANY ADJUSTMENTS WHATSOEVER, that the orbit of Mercury should precess by an extra 43 seconds of arc per century should the General Theory of Relativity be correct." http://aether.lbl.gov/www/classes/p10/gr/PrecessionperihelionMercury.htm

Sometimes the truth shows up even in Einstein cult. Countless ad hoc adjustments until "excellent agreement with observation" is reached (typical of empirical curve fitting models):

Michel Janssen: "But - as we know from a letter to his friend Conrad Habicht of December 24, 1907 - one of the goals that Einstein set himself early on, was to use his new theory of gravity, whatever it might turn out to be, to explain the discrepancy between the observed motion of the perihelion of the planet Mercury and the motion predicted on the basis of Newtonian gravitational theory. [...] The Einstein-Grossmann theory - also known as the "Entwurf" ("outline") theory after the title of Einstein and Grossmann's paper - is, in fact, already very close to the version of general relativity published in November 1915 and constitutes an enormous advance over Einstein's first attempt at a generalized theory of relativity and theory of gravitation published in 1912. The crucial breakthrough had been that Einstein had recognized that the gravitational field - or, as we would now say, the inertio-gravitational field - should not be described by a variable speed of light as he had attempted in 1912, but by the so-called metric tensor field. The metric tensor is a mathematical object of 16 components, 10 of which independent, that characterizes the geometry of space and time. In this way, gravity is no longer a force in space and time, but part of the fabric of space and time itself: gravity is part of the inertio-gravitational field. Einstein had turned to Grossmann for help with the difficult and unfamiliar mathematics needed to formulate a theory along these lines. [...] 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. This last change did not affect the result for the perihelion of Mercury. Besso is not acknowledged in Einstein's paper on the perihelion problem. Apparently, Besso's help with this technical problem had not been as valuable to Einstein as his role as sounding board that had earned Besso the famous acknowledgment in the special relativity paper of 1905. Still, an acknowledgment would have been appropriate. After all, what Einstein had done that week in November, was simply to redo the calculation he had done with Besso in June 1913, using his new field equations instead of the Einstein-Grossmann equations. 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." http://zope.mpiwg-berlin.mpg.de/living_einstein/teaching/1905_S03/pdf-files/EBms.pdf

Pentcho Valev
Pentcho Valev
2019-04-23 19:24:37 UTC
Deduction or induction in fundamental physics? Feynman:

'Greek' versus 'Babylonian' mathematics

Greek (deductive; axiomatic) models are both logically and experimentally falsifiable. Initially, critics look for an invalid argument and check for consistency. The theory could be refuted even at this pre-experimental stage. Experimental verification without preceding logical verification is pointless.

Babylonian (inductive; curve-fitting) models are logically unfalsifiable, and therefore experimentally unfalsifiable as well. The match between observations and predictions could be impressive on the surface but it is just as important as the match between data and the mathematical curves in curve fitting models.

Pentcho Valev