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**Physics, Astronomy & Cosmology / Re: Are there different types of gravity?**

« **on:**08/09/2018 20:14:04 »

It's tricky Bill. Einstein didn't consider it a geometry, as far as I get it,. He used calculus and thought of gravity and inertia in those terms. the geometric interpretation was something that came without him, not meaning that he didn't see the implications, just that he found it questionable. " he thought that General Relativity was no more and no less geometrical than Maxwells theory of electromagnetism; and that the important achievement of GR was the advancement of the uniﬁcation programme in direct continuation of special relativistic electrodynamics. Einstein thought that the special theory uniﬁed electricity and magnetism, the general theory inertia and gravity. Yet, we shall see that, unbeknown to most scholars, Einstein was emphatic in his belief that this should not be interpreted as a ‘geometrization’of gravity, especially if ‘geometrization’was seen as a reduction of gravity/inertia to spacetime geometry

.... As early as 1926 Einstein insisted, explicitly, that his work should not be understood as reducing physics to geometry, either his work on GR or his (and Weyl's and Eddington's) work on a uniﬁed ﬁeld theory of gravitation and electromagnetism. Interestingly, what seems to be Einstein's ﬁrst clear statement on the matter was prompted by a letter from Hans Reichenbach. Reichenbach was at the time engaging with Weyl's and Eddington's theories, and wrote Einstein that he thought that seeing electricity as geometrical in Weyl's theory is not more than an illustration (Veranschaulichung), one that, he argued, is equally possible (and equally trivial) in GR. Einstein agreed wholeheartedly, writing ' You are completely right. It is wrong to think that ‘geometrization’ is something essential. It is only a kind of crutch (Eselsbrücke) for the ﬁnding of numerical laws. Whether one links ‘geometrical’ intuitions with a theory is a … private matter. ' "

So when speaking about a geodesic it's not a geometric path in his terms, " Already in the ﬁrst papers in which Einstein starts making use of the metric tensor to give an account of gravitation, he is at pains to establish the status of the geodesic equation as describing the motion of particles as “straight and uniform” (geradlinig und gleichförmig) even when subject to gravity. This would lead him to call the geodesic equation a “generalized law of inertia”; redeﬁning inertial paths such that the category includes motion under the inﬂuence of gravity. ..... Already in a note added in proof to Einstein (1912), Einstein had stated that equation (1) gives the equation of motion of point particles “not subject to external forces”.

Thus, it was clear that already in 1912, before even embarking on a metric theory of gravitation, Einstein thought of (static) gravitational ﬁelds not as invariant force ﬁelds diverting particles from inertial motion. Already, in 1912, he thought of equation (1) as describing inertial motion on one hand, and as describing motion in the presence of (static) gravitational ﬁelds on the other. "

" Einstein effectively states that the very distinction between ‘gravity’ and ‘inertia’ is useful only for relating the theory to its predecessor theories; it is not a distinction from within the theory itself. Put differently, if one just looks at the theory without relating it to predecessor theories, there is no need whatsoever to distinguish ‘inertial terms’ and ‘gravitational terms’ in the geodesic equation. "

By that I understand he meaning that talking about gravity as a force directing the inertia (willingness to keep on indefinitely) of a test particle made little sense to him.

" In Einstein's mind, the uniﬁcation was very similar indeed, as the December 1919/January 1920 text on the development of relativity shows. There, he recalls the magnet-conductor thought experiment described in the ﬁrst paragraph of his 1905 paper on special relativity, from which he concludes. ' The existence of the electric ﬁeld is a relative one, depending on the state of motion of the coordinate system used; only the electric and magnetic ﬁeld together can be attributed a kind of objective reality, independent of the state of motion of the observer, i.e. of the coordinate system. '

Einstein then describes how he worked on a review article of special relativity in 1907, and links the above realisation regarding the electric and magnetic ﬁeld to another thought experiment regarding inertia and gravity: ' Then I had the most fortunate thought of my life in the following form: The gravitational ﬁeld only has a relative existence in a manner similar to the electric ﬁeld generated by electro-magnetic induction. Because for an observer in free fall from the roof of a house, there is during the fall — at least in his immediate vicinity — no gravitational ﬁeld. Namely, if the observer lets go of any bodies, they remain, relative to him, in a state of rest or uniform motion, independent of their special chemical or physical nature '

quotes taken from " Why Einstein did not believe that General Relativity geometrizes gravity " By Dennis Lehmkuhl.

.... As early as 1926 Einstein insisted, explicitly, that his work should not be understood as reducing physics to geometry, either his work on GR or his (and Weyl's and Eddington's) work on a uniﬁed ﬁeld theory of gravitation and electromagnetism. Interestingly, what seems to be Einstein's ﬁrst clear statement on the matter was prompted by a letter from Hans Reichenbach. Reichenbach was at the time engaging with Weyl's and Eddington's theories, and wrote Einstein that he thought that seeing electricity as geometrical in Weyl's theory is not more than an illustration (Veranschaulichung), one that, he argued, is equally possible (and equally trivial) in GR. Einstein agreed wholeheartedly, writing ' You are completely right. It is wrong to think that ‘geometrization’ is something essential. It is only a kind of crutch (Eselsbrücke) for the ﬁnding of numerical laws. Whether one links ‘geometrical’ intuitions with a theory is a … private matter. ' "

So when speaking about a geodesic it's not a geometric path in his terms, " Already in the ﬁrst papers in which Einstein starts making use of the metric tensor to give an account of gravitation, he is at pains to establish the status of the geodesic equation as describing the motion of particles as “straight and uniform” (geradlinig und gleichförmig) even when subject to gravity. This would lead him to call the geodesic equation a “generalized law of inertia”; redeﬁning inertial paths such that the category includes motion under the inﬂuence of gravity. ..... Already in a note added in proof to Einstein (1912), Einstein had stated that equation (1) gives the equation of motion of point particles “not subject to external forces”.

Thus, it was clear that already in 1912, before even embarking on a metric theory of gravitation, Einstein thought of (static) gravitational ﬁelds not as invariant force ﬁelds diverting particles from inertial motion. Already, in 1912, he thought of equation (1) as describing inertial motion on one hand, and as describing motion in the presence of (static) gravitational ﬁelds on the other. "

" Einstein effectively states that the very distinction between ‘gravity’ and ‘inertia’ is useful only for relating the theory to its predecessor theories; it is not a distinction from within the theory itself. Put differently, if one just looks at the theory without relating it to predecessor theories, there is no need whatsoever to distinguish ‘inertial terms’ and ‘gravitational terms’ in the geodesic equation. "

By that I understand he meaning that talking about gravity as a force directing the inertia (willingness to keep on indefinitely) of a test particle made little sense to him.

" In Einstein's mind, the uniﬁcation was very similar indeed, as the December 1919/January 1920 text on the development of relativity shows. There, he recalls the magnet-conductor thought experiment described in the ﬁrst paragraph of his 1905 paper on special relativity, from which he concludes. ' The existence of the electric ﬁeld is a relative one, depending on the state of motion of the coordinate system used; only the electric and magnetic ﬁeld together can be attributed a kind of objective reality, independent of the state of motion of the observer, i.e. of the coordinate system. '

Einstein then describes how he worked on a review article of special relativity in 1907, and links the above realisation regarding the electric and magnetic ﬁeld to another thought experiment regarding inertia and gravity: ' Then I had the most fortunate thought of my life in the following form: The gravitational ﬁeld only has a relative existence in a manner similar to the electric ﬁeld generated by electro-magnetic induction. Because for an observer in free fall from the roof of a house, there is during the fall — at least in his immediate vicinity — no gravitational ﬁeld. Namely, if the observer lets go of any bodies, they remain, relative to him, in a state of rest or uniform motion, independent of their special chemical or physical nature '

quotes taken from " Why Einstein did not believe that General Relativity geometrizes gravity " By Dennis Lehmkuhl.

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