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Does General Relativity Predict Gravitational Waves?

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Old March 2nd 16, 06:08 PM posted to sci.astro
Pentcho Valev
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Default Does General Relativity Predict Gravitational Waves?

"Around 1936, Einstein wrote to his close friend Max Born telling him that, together with Nathan Rosen, he had arrived at the interesting result that gravitational waves did not exist, though they had been assumed a certainty to the first approximation. He finally had found a mistake in his 1936 paper with Rosen and believed that gravitational waves do exist. However, in 1938, Einstein again obtained the result that there could be no gravitational waves!"

"What is less well known is that Einstein struggled mightily with the theory of gravitational waves. The fact that Einstein was a genius but nevertheless mortal is, by now, somewhat known. After all, it took him five tries to get the field equations of General Relativity right."

Typical empirical approach isn't it? Unlike special relativity, general relativity was not, to use Einstein's words, "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 in which known in advance results and pet assumptions (such as the Mercury's precession, the equivalence principle, gravitational time dilation) coexisted in an apparently consistent manner:

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."

Since general relativity is an empirical model, it can predict anything - e..g. both existence and non-existence of gravitational waves. Or both static and expanding universe. Or both constant and variable speed of light. Anything!

Pentcho Valev
Old March 3rd 16, 08:02 AM posted to sci.astro
Pentcho Valev
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Default Does General Relativity Predict Gravitational Waves?

J.B. Kennedy, Space, Time and Einstein: An Introduction, p. 189: "Even though general relativity predicts black holes, Einstein always denied their existence."

General relativity is an empirical model - it can predict anything. So it can predict both existence and non-existence of black holes. Einstein preferred "non-existence" but LIGO folks disagree. Тhey know general relativity even predicts important features of black holes - LIGO folks were somehow able to extract those features from gravitational waves.

""There are no gravitational waves ... " ... "Plane gravitational waves, traveling along the positive X-axis, can therefore be found ... " ... " ... gravitational waves do not exist ... " ... "Do gravitational waves exist?" .... "It turns out that rigorous solutions exist ... " These are the words of Albert Einstein. For 20 years he equivocated about gravitational waves, unsure whether these undulations in the fabric of space and time were predicted or ruled out by his revolutionary 1915 theory of general relativity. For all the theory's conceptual elegance -- it revealed gravity to be the effect of curves in "space-time" -- its mathematics was enormously complex."

Einstein equivocated but LIGO folks don't. According to them, general relativity not only predicts the existence of gravitational waves - it even gives minute detail about them. And the detailed predictions were gloriously confirmed, LIGO folks honestly and proudly say.

Pentcho Valev
Old March 4th 16, 05:08 PM posted to sci.astro
Pentcho Valev
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Default Does General Relativity Predict Gravitational Waves?

The making of general relativity was analogous to "curve fitting" ("empirical models") as defined he

"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."

Note that the parameters of the empirical model "do not necessarily correspond to a biological, chemical or physical property". So in Einstein's general relativity one of the parameters - the speed of light falling towards the source of gravity - absurdly DECREASES (in the gravitational field of the Earth the acceleration of falling photons is NEGATIVE, -2g):

"Contrary to intuition, the speed of light (properly defined) decreases as the black hole is approached."

"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."

"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."

Here Michel Janssen describes endless empirical 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."

Pentcho Valev

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