Discussion:
Fundamental Physics: Axiomatic or ... Not Even Wrong
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Pentcho Valev
2018-01-01 12:20:34 UTC
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Einstein's text below suggests that a physics theory is either an empirical concoction or a construction "built up logically from a small number of fundamental assumptions, the so-called axioms":

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

In other words, equations in a physics theory are either guessed or (possibly guessed initially but then) deduced from "a small number of fundamental assumptions, the so-called axioms":

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

Except for special relativity which is an axiomatic construction, theories and models in today's fundamental physics are empirical concoctions.

If the theory is axiomatic, as is special relativity, then it can only be spoiled by a false axiom or an invalid argument (one in which the conclusion does not follow from the premises). If the theory is not axiomatic, that is, if the method is "guessing the equation" and not "deducing the equation from axioms", then the theory is already fatally spoiled by the mere fact that it is not axiomatic. Such theories are not even wrong.

Pentcho Valev
Pentcho Valev
2018-01-01 16:16:37 UTC
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Axiomatic theories are falsifiable - either logically or experimentally. Empirical (not even wrong) theories are not. If an empirical theory matches some observation, this only means that suitable ad hoc equations and fudge factors have been chosen. Here Michel Janssen describes endless empirical groping, fudging and fitting until "excellent agreement with observation" was reached:

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." https://netfiles.umn.edu/users/janss011/home%20page/EBms.pdf

Pentcho Valev
Pentcho Valev
2018-01-03 10:04:04 UTC
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Non-axiomatic physics - one in which "guessing the equation" is naturally followed by "guessing the fudge factor" - consists, by definition, of "invincible models that can forever be amended":

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." http://www.math.columbia.edu/~woit/wordpress/?p=9375

Pentcho Valev

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