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GENERAL RELATIVITY: DEDUCTIVE OR EMPIRICAL?



 
 
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  #1  
Old August 9th 15, 12:12 PM posted to sci.astro
Pentcho Valev
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Default GENERAL RELATIVITY: DEDUCTIVE OR EMPIRICAL?

https://www.youtube.com/watch?v=bj8rZnOUjWU
Jürgen Renn: The Genesis and Renaissance of General Relativity

Three comments to the video:

1. Pentcho Valev
Unlike the rest of physics which is deductive, Einstein's general relativity is an empirical model. This means that Einstein and his mathematical friends had to change and fudge the equations countless times until agreement with known in advance results and pet assumptions was reached. In other words, the making of general relativity was analogous to "curve fitting" as defined he

http://collum.chem.cornell.edu/docum...ve_Fitting.pdf
"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."

2. shomolya
All physical theory has to agree with and is motivated by experiment . By your argument all of physics is "curve fitting" and theories "fudged" to fit the data.

3. Pentcho Valev
Not all of physics. Empirical theories (like Einstein's general relativity) have an unlimited capacity to adapt to (new) data or assumptions. In contrast, deductive theories (like Einstein's special relativity) are fixed - once the axioms (postulates) are officially announced, all the conclusions are in a sense predetermined.

Pentcho Valev
  #2  
Old August 9th 15, 01:12 PM posted to sci.astro
Pentcho Valev
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Default GENERAL RELATIVITY: DEDUCTIVE OR EMPIRICAL?

https://www.marxists.org/reference/a...ative/ap03.htm
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."

Special relativity was indeed "built up logically from a small number of fundamental assumptions" but, as the following references clearly show, general relativity was "a purely empirical enterprise" - Einstein's mathematical friends helped him to compile "a classified catalogue" where known in advance results and pet assumptions (e.g. that of gravitational time dilation) coexisted in an apparently consistent manner:

http://www.weylmann.com/besso.pdf
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 équations 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://www.lemonde.fr/planete/articl...1703_3244.html
"C'est à ce moment de l'histoire que commence celle, méconnue, du manuscrit Einstein-Besso. Le physicien convoque son ami et confident suisse pour l'aider à mener les calculs et tester son ébauche de relativité générale sur un problème bien connu des astronomes : l'anomalie de l'orbite de Mercure. "Depuis la fin du XIXe siècle, on sait de manière de plus en plus précise que le périhélie de cette planète (le point de son orbite le plus proche du Soleil) avance un peu plus que le prévoient les équations de Newton : l'excédent est de 43 secondes d'arc par siècle, c'est-à-dire l'angle sous lequel on voit un cheveu à une distance d'un mètre... Einstein se dit simplement que sa théorie sera validée si elle prédit correctement cette "anomalie" de l'avance du périhélie de Mercure." Une part du manuscrit Einstein-Besso est consacrée à ce test crucial. Aux pages d'Einstein, des lignes d'équations, sans ratures, presque vierges de tout texte, succèdent celles de Besso, un peu plus hésitantes et annotées de nombreuses explications. Le résultat est calamiteux. Au lieu d'expliquer le petit décalage de 43 secondes d'arc par siècle, la nouvelle théorie propose une avance de plus de 1 800 secondes d'arc par siècle. Très loin de la réalité des observations astronomiques ! "Mais, un peu plus loin dans le manuscrit, les deux hommes se rendent compte qu'ils se sont trompés sur la masse du Soleil"... Une erreur d'un facteur 10, qu'ils corrigent finalement, pour parvenir à un résultat moins absurde, mais toujours décevant : 18 secondes d'arc par siècle... Echec complet ? Un peu plus loin, en conclusion d'un tout autre calcul, Einstein écrit : "Stimmt" ("Correct"). "En dépit de l'échec de sa théorie à expliquer l'avance du périhélie de Mercure, Einstein croit avoir démontré autre chose, au détour d'une équation... En mai 1907, il avait eu l'intuition qu'une chute libre peut "annuler" un champ de gravitation. Ici, il pense avoir démontré qu'un mouvement de rotation peut, lui aussi, être considéré comme équivalent à un champ de gravitation. Il croit avoir généralisé son principe d'équivalence." Mais, plus de deux ans plus tard, Einstein comprend que son calcul était faux : il n'a rien généralisé du tout. C'est alors qu'il accepte d'utiliser dans sa théorie le premier tenseur, jugé trop complexe, que lui avait proposé Grossmann. Et en 1915, il teste ce nouveau tenseur sur l'avance du périhélie de Mercure. Cette fois, le résultat est le bon !"

Pentcho Valev
  #3  
Old August 10th 15, 07:03 AM posted to sci.astro
Pentcho Valev
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Default GENERAL RELATIVITY: DEDUCTIVE OR EMPIRICAL?

https://en.wikipedia.org/wiki/Fudge_factor
"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, dark energy, dark matter and inflation. (...) In theoretical physics, when Einstein originally tried to produce a general theory of relativity, he found that the theory seemed to predict the gravitational collapse of the universe: it seemed that the universe should either be expanding or collapsing, and to produce a model in which the universe was static and stable (which seemed to Einstein at the time to be the "proper" result), he introduced an expansionist variable (called the Cosmological Constant), whose sole purpose was to cancel out the cumulative effects of gravitation."

The introduction of a fudge factor is only safe in empirical theories. If the theory is deductive, the introduction of a fudge factor would mean that some conclusion from the axioms, deduced in the absence of the fudge factor, is false, and that accordingly at least one of the axioms is false as well.

Pentcho Valev
  #4  
Old August 12th 15, 06:31 PM posted to sci.astro
Pentcho Valev
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Default GENERAL RELATIVITY: DEDUCTIVE OR EMPIRICAL?

Einstein's equations were a hypothesis, which is tantamount to saying that general relativity was an empirical model. Einstein and his mathematical friends did not build up the theory "logically from a small number of fundamental assumptions" - rather, they changed and fudged equations (hypotheses) countless times until the best fit with known in advance results and pet assumptions was found:

http://www.phys.ens.fr/spip.php?article1723&lang=en
Gilles Esposito-Farèse: "General relativity is a relativistic theory of gravity. It is based on two independent hypotheses: the equivalence principle, which allows us to describe the motion of matter in a curved spacetime; and Einstein's equations, which predict how such a curvature is generated by material sources."

Pentcho Valev
 




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