Empirical Models in Fundamental Physics
(trop ancien pour répondre)
Pentcho Valev
2017-11-27 12:16:46 UTC
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Except for special relativity which is deductive, theories and models in today's fundamental physics are empirical, that is, essentially equivalent to the "empirical 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

For a deductive theory, "guessing the equation" could be an initial step but then it is obligatorily followed by "deducing the equation" (from a few simple axioms). For an empirical theory, "guessing the equation" is both the initial and final step:

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

Technically, the difference between a deductive and an empirical model is as follows. You cannot introduce any changes to your DEDUCTIVE model that are not deducible from the initial axioms (postulates). In contrast, an EMPIRICAL model "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

Before 1915 theoretical physics was mainly deductive. In 1915 things changed. 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
2017-11-27 15:10:34 UTC
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Here is how an empirical model (Einstein's general relativity) works:

The gravitational redshift is produced by the variation of the speed of light predicted by Newton's emission theory of light, so any measurement of the gravitational redshift directly confirms this variation:

"If we accept the principle of equivalence, we must also accept that light falls in a gravitational field with the same acceleration as material bodies." http://sethi.lamar.edu/bahrim-cristian/Courses/PHYS4480/4480-PROBLEMS/optics-gravit-lens_PPT.pdf

University of Illinois at Urbana-Champaign: "Consider a falling object. ITS SPEED INCREASES AS IT IS FALLING. Hence, if we were to associate a frequency with that object the frequency should increase accordingly as it falls to earth. Because of the equivalence between gravitational and inertial mass, WE SHOULD OBSERVE THE SAME EFFECT FOR LIGHT. So lets shine a light beam from the top of a very tall building. If we can measure the frequency shift as the light beam descends the building, we should be able to discern how gravity affects a falling light beam. This was done by Pound and Rebka in 1960. They shone a light from the top of the Jefferson tower at Harvard and measured the frequency shift. The frequency shift was tiny but in agreement with the theoretical prediction. Consider a light beam that is travelling away from a gravitational field. Its frequency should shift to lower values. This is known as the gravitational red shift of light." https://courses.physics.illinois.edu/phys419/sp2011/lectures/Lecture13/L13r.html

Albert Einstein Institute: "One of the three classical tests for general relativity is the gravitational redshift of light or other forms of electromagnetic radiation. However, in contrast to the other two tests - the gravitational deflection of light and the relativistic perihelion shift -, you do not need general relativity to derive the correct prediction for the gravitational redshift. A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices. [...] The gravitational redshift was first measured on earth in 1960-65 by Pound, Rebka, and Snider at Harvard University..." http://www.einstein-online.info/spotlights/redshift_white_dwarfs

R. V. Pound and J. L. Snider, Effect of Gravity on Gamma Radiation: "It is not our purpose here to enter into the many-sided discussion of the relationship between the effect under study and general relativity or energy conservation. It is to be noted that no strictly relativistic concepts are involved and the description of the effect as an "apparent weight" of photons is suggestive. The velocity difference predicted is identical to that which a material object would acquire in free fall for a time equal to the time of flight." http://virgo.lal.in2p3.fr/NPAC/relativite_fichiers/pound.pdf

In general relativity measurements of the gravitational redshift should confirm the miraculous gravitational time dilation (fabricated by Einstein in 1911), not the variation of the speed of light. This automatically converts the variation of the speed of light into a fudge factor - irrespectively of the physical plausibility, the variation formula will be anything that makes the gravitational redshift and the gravitational time dilation compatible.

The gravitational time dilation and the gravitational redshift are only compatible if light in a gravitational field behaves in an idiotic way: Its speed DECREASES as the light falls towards the source of gravity - the acceleration of falling photons is NEGATIVE (in the gravitational field of the Earth it is -2g). The idiotic negative acceleration of photons, -2g, was the fudge factor Einstein and his mathematical friends had to introduce in 1915:

Albert Einstein: "Second, this consequence shows that the law of the constancy of the speed of light no longer holds, according to the general theory of relativity, in spaces that have gravitational fields. As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable." https://archive.is/wn4PV

"The change in speed of light with change in height is dc/dh=g/c."

"Contrary to intuition, the speed of light (properly defined) decreases as the black hole is approached." http://www.physlink.com/Education/AskExperts/ae13.cfm

"Einstein wrote this paper in 1911 in German. [...] ...you will find in section 3 of that paper Einstein's derivation of the variable speed of light in a gravitational potential, eqn (3). The result is: c'=c0(1+φ/c^2) where φ is the gravitational potential relative to the point where the speed of light c0 is measured. Simply put: Light appears to travel slower in stronger gravitational fields (near bigger mass). [...] You can find a more sophisticated derivation later by Einstein (1955) from the full theory of general relativity in the weak field approximation. [...] Namely the 1955 approximation shows a variation in km/sec twice as much as first predicted in 1911." http://www.speed-light.info/speed_of_light_variable.htm

Pentcho Valev
Pentcho Valev
2017-11-28 07:50:29 UTC
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Einstein's general relativity was not deduced from postulates. It is a not-even-wrong empirical concoction - a malleable combination of ad hoc 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]

General relativity had not predicted that the gravitational waves travel at the speed of light but was tweaked to make that prediction:

Arthur Eddington: "The statement that in the relativity theory gravitational waves are propagated with the speed of light has, I believe, been based entirely upon the foregoing investigation; but it will be seen that it is only true in a very conventional sense. 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 https://www.amazon.com/Mathematical-Theory-Relativity-S-Eddington/dp/0521091659

In order to be consistent with dark matter, general relativity needs four fudge factors:

"Verlinde's calculations fit the new study's observations without resorting to free parameters – essentially values that can be tweaked at will to make theory and observation match. By contrast, says Brouwer, conventional dark matter models need four free parameters to be adjusted to explain the data." https://www.newscientist.com/article/2116446-first-test-of-rival-to-einsteins-gravity-kills-off-dark-matter/

How many fudge factors LIGO conspirators needed to model the nonexistent gravitational waves is a deep mystery:

"Cornell professors Saul Teukolsky, astrophysics, and Larry Kidder, astronomy, played an instrumental role in the first detection of gravitational waves, a century after Albert Einstein predicted their existence in his theory of general relativity. [...] The LIGO and Virgo group confirmed that these gravitational waves had come from the collision of black holes by comparing their data with a theoretical model developed at Cornell. Teukolsky and the Cornell-founded Simulation of eXtreme Spacetimes collaboration group have been developing this model since 2000, according to the University." http://cornellsun.com/2016/02/10/cornell-scientists-validate-einsteins-theory-of-relativity/

Pentcho Valev
Pentcho Valev
2017-11-28 18:34:10 UTC
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In order for the gravitational time dilation (fabricated by Einstein in 1911) and the gravitational redshift to be compatible, light in a gravitational field must behave in an idiotic way: Its speed must DECREASE as the light falls towards the source of gravity. That is, the acceleration of falling photons is NEGATIVE - in the gravitational field of the Earth it must be -2g. This idiotic negative acceleration of photons, -2g, was essentially a fudge factor Einstein and his mathematical friends had to introduce in 1915 (otherwise general relativity would not have been able to "predict" the gravitational redshift originally predicted by Newton's emission theory of light):

"Specifically, Einstein wrote in 1911 that the speed of light at a place with the gravitational potential j would be c0(1 + j/c0^2), where c0 is the nominal speed of light in the absence of gravity. In geometrical units we define c0 = 1, so Einstein's 1911 formula can be written simply as c = 1 + j. However, this formula for the speed of light - indeed, this whole approach to gravity - turned out to be incorrect. [...] ...the circumferential speed of light differs from the radial speed. The former is given by the same formula as in Einstein's 1911 paper, but the latter differs from the 1911 formula by a factor of 2 on the "potential" term. [...] ...we have c_r = 1 + 2j, which corresponds to Einstein's 1911 equation, except that we have a factor of 2 instead of 1 on the potential term. Thus, as j becomes increasingly negative (i.e., as the magnitude of the potential increases), the radial "speed of light" c_r defined in terms of the Schwarzschild parameters t and r is reduced to less than the nominal value of c." http://www.mathpages.com/rr/s6-01/6-01.htm

Nothing in general relativity is deduced from postulates. The "theory" is a malleable combination of ad hoc equations and fudge factors able to "predict" anything.

Pentcho Valev
Pentcho Valev
2017-12-05 20:56:48 UTC
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A physics theory is either a not-even-wrong empirical concoction or a deductive 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 rigorously) 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."x http://dillydust.com/The%20Character%20of%20Physical%20Law~tqw~_darksiderg.pdf

Pentcho Valev