Empiricism and Deductivism in Physics

"Quantum Theory Rebuilt From Simple Physical Principles [...] But this so-called rule for calculating probabilities was really just an intuitive guess by the German physicist Max Born. So was Schrödinger's equation itself. Neither was supported by rigorous derivation. Quantum mechanics seems largely built of arbitrary rules like this, some of them - such as the mathematical properties of operators that correspond to observable properties of the system - rather arcane. It's a complex framework, but it's also an ad hoc patchwork, lacking any obvious physical interpretation or justification. Compare this with the ground rules, or axioms, of Einstein's theory of special relativity, which was as revolutionary in its way as quantum mechanics.. (Einstein launched them both, rather miraculously, in 1905.) Before Einstein, there was an untidy collection of equations to describe how light behaves from the point of view of a moving observer. Einstein dispelled the mathematical fog with two simple and intuitive principles: that the speed of light is constant, and that the laws of physics are the same for two observers moving at constant speed relative to one another. Grant these basic principles, and the rest of the theory follows. Not only are the axioms simple, but we can see at once what they mean in physical terms. What are the analogous statements for quantum mechanics?" https://www.quantamagazine.org/quant...ples-20170830/

Yes, deductivism is the only reasonable method in theoretical physics. Other types of reasoning may be useful but finally the model should consist of a set of axioms (postulates) and a set of valid arguments. Nothing else. Critics look for a false axiom or an invalid argument - if they are unable to find any, the model is accepted.

The alternative is empiricism - models are essentially equivalent to the "empirical models" defined he

"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/docum...ve_Fitting.pdf

Except for special relativity, models in modern theoretical physics are empirical, not deductive:

Sabine Hossenfelder: "Many of my colleagues believe this forest of theories will eventually be chopped down by data. But in the foundations of physics it has become extremely rare for any model to be ruled out. The accepted practice is instead to adjust the model so that it continues to agree with the lack of empirical support."
http://www.nature.com.proxy.readcube...nphys4079.html

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

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/janss...0page/EBms.pdf

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