Theoretical Physics' Method: Deduction (Nothing Else)
W. H. Newton-Smith, THE RATIONALITY OF SCIENCE, Routledge, London, 1981, p.. 199: "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."
If the theory is not deductive, then it is an "empirical enterprise", that is, no physical theory at all:
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."
Einstein's special relativity was deductive (although using a false axiom and invalid arguments) but his general relativity was an "empirical enterprise".
Theoretical Physics' Method: Deduction (Nothing Else)
Steven Weinberg: "People suspect that if you have a known fact, the theorist will be able to jiggle his theory to get it into agreement. If you know anything about the way Einstein developed General Relativity, that's not true. He did not design his theory to explain that extra little motion of Mercury."
On the contrary, 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 (a typical empirical approach):
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 exipression he found and the result was 43", in excellent agreement with observation."
"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 !"
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