Curve Fitting in Fundamental Physics
(trop ancien pour répondre)
Pentcho Valev
2018-03-20 09:44:55 UTC
"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 "small number of fundamental assumptions, the so-called axioms", clearly defined, are indispensable.

2. The results of the theory are DEDUCED from the "small number of fundamental assumptions, the so-called 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 question is:

What if the "small number of fundamental assumptions, the so-called axioms" don't exist, or, even if they exist, some results of the theory are not deduced from them?

Answer: Then the theory, e.g. general relativity, is a not-even-wrong empirical concoction, essentially equivalent to curve fitting:

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Pentcho Valev
Pentcho Valev
2018-03-21 10:08:23 UTC
Sabine Hossenfelder: "Is this still science?" has become a recurring question in the foundations of physics. Whether it's the multiverse, string theory, supersymmetry, or inflation, concerns abound that theoreticians have crossed a line. Science writer Jim Baggott called the new genre "fairy-tale science." Historian Helge Kragh coined the term "higher speculations," and Peter Woit, more recently, suggested the name "fake physics." http://backreaction.blogspot.bg/2017/11/if-science-is-what-scientists-do-what.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

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." http://backreaction.blogspot.bg/2017/12/the-cosmological-constant-is-not-worst.html

"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..." https://en.wikipedia.org/wiki/Fudge_factor

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." http://www.amazon.com/Magnificent-Universe-Ken-Croswell/dp/0684845946

Clearly there is no essential difference between "invincible models that can forever be amended", on the one hand, and Einstein's general relativity, on the other. In both cases we have "fake physics".

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 empirical concoction - a malleable combination of ad hoc ("guessed") equations and fudge factors allowing Einsteinians to predict anything they want:

What are the postulates of General Relativity? Alexander Poltorak, Adjunct Professor of Physics at the CCNY: "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." [END OF QUOTATION]

Sometimes Einsteinians call Einstein's 1915 final ad hoc equations "postulates" (we all live in Einstein's schizophrenic world, don't we):

"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) ..." [END OF QUOTATION]

Pentcho Valev