EINSTEIN'S EMPIRICAL "THEORY"

http://www.quora.com/Is-it-true-that...complex-theory
"Is it true that Einstein used a thought experiment about weightlessness from falling to derive general relativity? How can such a simple concept spawn such a complex theory?"

Here is the answer. Unlike special relativity, general relativity was not deduced from simple concepts, or, to use Einstein's words, was not "built up logically from a small number of fundamental assumptions". Rather, it was "a purely empirical enterprise" - Einstein and his mathematical friends changed and fudged equations countless times until "a classified catalogue" was compiled where known in advance results and pet assumptions (such as Mercury's precession, the equivalence principle, gravitational time dilation) coexisted in an apparently consistent manner:

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."

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 !"

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

The making of general relativity was analogous to "curve fitting" ("empirical models") 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."

Einstein and his mathematical friends did find equations that best fitted known in advance results and pet assumptions, but some parameters of their empirical model turned out to be idiotic. So general relativity predicts that the speed of light falling towards the source of gravity DECREASES (in the gravitational field of the Earth the acceleration of falling photons is -2g):

http://www.physlink.com/Education/AskExperts/ae13.cfm
"Contrary to intuition, the speed of light (properly defined) decreases as the black hole is approached. (...) If the photon, the 'particle' of light, is thought of as behaving like a massive object, it would indeed be accelerated to higher speeds as it falls toward a black hole. However, the photon has no mass and so behaves in a manner that is not intuitively obvious. (....) When we say that the speed of light is decreased, we mean from the perspective of an observer fixed relative to the black hole and at an essentially infinite distance. On the contrary, to an observer free falling into the black hole, the speed of light, measured locally, would be unaltered from the standard value of c. Most of us have heard of the result from special relativity that the speed of light is the same for all observers in inertial frames. The result is not the same in general relativity. In general relativity, the statement becomes that the speed of light is the same (i.e., good old 'c') for all observers in local inertial frames. Local inertial frames in general relativity are just those frames of reference in which the observer is in gravitational free fall. (...) So, it is absolutely true that the speed of light is not constant in a gravitational field [which, by the equivalence principle, applies as well to accelerating (non-inertial) frames of reference]. (...) Indeed, this is exactly how Einstein did the calculation in: "On the Influence of Gravitation on the Propagation of Light," Annalen der Physik, 35, 1911, which predated the full formal development of general relativity by about four years. This paper is widely available in English. You can find a copy beginning on page 99 of the Dover book "The Principle of Relativity." 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+V/c^2), where V is the gravitational potential relative to the point where the speed of light c0 is measured. You can find a more sophisticated result derived later by Einstein from the full general theory in the weak field approximation in the book: 'The Meaning of Relativity,' A. Einstein, Princeton University Press (1955). See pp. 92-93, eqn (107)."

http://www.speed-light.info/speed_of_light_variable.htm
"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.mathpages.com/rr/s6-01/6-01.htm
"Specifically, Einstein wrote in 1911 that the speed of light at a place with the gravitational potential φ would be c(1+φ/c^2), where c is the nominal speed of light in the absence of gravity. In geometrical units we define c=1, so Einstein's 1911 formula can be written simply as c'=1+φ. However, this formula for the speed of light (not to mention this whole approach to gravity) turned out to be incorrect, as Einstein realized during the years leading up to 1915 and the completion of the general theory. (...) ...we have c_r =1+2φ, which corresponds to Einstein's 1911 equation, except that we have a factor of 2 instead of 1 on the potential term."

Pentcho Valev

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 the case of empirical models (such as general relativity). In the case of deductive theories (such as special relativity) 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