Undergrad Einstein's views on gravity and inertia

[zonde]

I was reading this article Why Einstein did not believe that general relativity geometrizes gravity and it seemed rather interesting. So it would be interesting to hear what others think of it.

It suggests that Einstein's view on GR was that it does not reduce gravity to inertia and geometry but rather that GR describes gravito-inertial field.
So as I understand it physics are determined by gravito-inertial field and on what geometrical background we chose to describe this gravito-inertial field is a mater of (mathematical) convenience (say we chose such a geometry that gravito-inertial field is reduced to inertial field).

 

[PAllen]

I was reading this article Why Einstein did not believe that general relativity geometrizes gravity and it seemed rather interesting. So it would be interesting to hear what others think of it.

It suggests that Einstein's view on GR was that it does not reduce gravity to inertia and geometry but rather that GR describes gravito-inertial field.
So as I understand it physics are determined by gravito-inertial field and on what geometrical background we chose to describe this gravito-inertial field is a mater of (mathematical) convenience (say we chose such a geometry that gravito-inertial field is reduced to inertial field).

One thing not covered at all in a somewhat quick read of this is Einstein's pioneering role in the enterprise of showing the geodesic equation is a consequence of the filed equations, not needed as an additional postulate (and that geodesic motion is ultimately approximate - the field equations rule). This work began at the end of the period covered by this article, and mostly post dated this period (1938 - 1940s). If Einstein was moving to treating the field equations at the full content of GR, then it is not clear to me how the conceptions attributed to him in this article would carry over.

I am familiar with much of Einstein material quoted here, but I have interpreted it mainly that Einstein took the view that treating SR in general coordinates or frames really is part of GR (contrary to modern authors), and, indeed, that inertial forces and gravitational forces are identical (unified), and whether, in a particular case, you can transform away the forces globally, while in another you case you can't, was not of much import; they are still both the same thing.

However you cast your attempt at understanding Einstein's point of view, I thought that his views being idiosyncratic compared to modern presentations was well known and noncontroversial (and ultimately irrelevant to answering any questions about physics).

 

[zonde]

One thing not covered at all in a somewhat quick read of this is Einstein's pioneering role in the enterprise of showing the geodesic equation is a consequence of the filed equations, not needed as an additional postulate (and that geodesic motion is ultimately approximate - the field equations rule). This work began at the end of the period covered by this article, and mostly post dated this period (1938 - 1940s). If Einstein was moving to treating the field equations at the full content of GR, then it is not clear to me how the conceptions attributed to him in this article would carry over.

Why getting rid of primary role of geodesic equation should change what is claimed in this article? Do you see field equations as more "geometrical" than geodesic equation? Not sure I understand you.
And the article gives one quote from 1948:
"An even stronger late statement, which mirrors almost verbatim Einstein's statement in the Meyerson review 23 years earlier, can be found in a letter from Einstein to Lincoln Barnett from June 19, 1948
I do not agree with the idea that the general theory of relativity is geometrizing Physics or the gravitational field. The concepts of Physics have always been geometrical concepts and I cannot see why the g_ik field should be called more geometrical than f.[or] i.[nstance] the electromagnetic field or the distance of bodies in Newtonian Mechanics. The notion comes probably from the fact that the mathematical origin of the g_ik field is the Gauss–Riemann theory of the metrical continuum which we won't look at as a part of geometry. I am convinced, however, that the distinction between geometrical and other kinds of fields is not logically found."

I am familiar with much of Einstein material quoted here, but I have interpreted it mainly that Einstein took the view that treating SR in general coordinates or frames really is part of GR (contrary to modern authors),

But SR describes only inertia. I'm not sure I understand you but I read your statement as saying that adopting SR (inertia) to general coordinates or frames leads (partially?) to GR. But this does not seems like unification (say as in the case of electromagnetic field).

 

[A.T.]

and ultimately irrelevant to answering any questions about physics

All I see is arguing about what "geometrical" means. Am I missing something?

 

[PAllen]

Einstein claimed in quotes here and elsewhere that the affine term in the equation of motion is gravity (and the split is coordinate dependent), and that there is no difference how much can be attributed to curvature. It is clear he held this view in some of his treatments of the twin paradox. In one of these places he explicitly states the irrelevance of whether the connection can be globally transformed away.

I am not sure I’ll have time to track down more quotes, so take it with a grain of salt.

 

[PAllen]

A good part of the discussion in the article was in terms of the equation of motion. I just wondered whether its change of status had any affect on Einstein’s thinking. The 1948 quote @zonde gave indicates it did not.

 

[zonde]

All I see is arguing about what "geometrical" means. Am I missing something?

As I see the question is about split between geometry and physics.
If I understand it correctly Einsten's idea was that there is no geometry independent from physics. But that would mean there can't be unphysical geometries and that does not seem quite right.

I found this paper in references of that article: Eliminative induction as a method of discovery: How Einstein discovered general relativity
As I understand from it, Einsten tried to find theory of gravity on flat geometry and was not exactly satisfied with result. Then it seems he changed approach - instead of looking for description of theory on flat background he looked for physical content constrained geometries that would satisfy his conditions. And got result that satisfied him.

 

[zonde]

One thing not covered at all in a somewhat quick read of this is Einstein's pioneering role in the enterprise of showing the geodesic equation is a consequence of the filed equations, not needed as an additional postulate (and that geodesic motion is ultimately approximate - the field equations rule).

I would like to check my understanding. You say geodesic motion is approximate. Considering that gravity is non-linear any massive object should have non trivial effect on it's own trajectory trough other sources of gravity. Is this the reason why you say geodesic motion is approximate?

 

[PAllen]

I would like to check my understanding. You say geodesic motion is approximate. Considering that gravity is non-linear any massive object should have non trivial effect on it's own trajectory trough other sources of gravity. Is this the reason why you say geodesic motion is approximate?

It is mainly due to gravitational radiation plus that no real body is exactly a test body. Google MiSaTaQuWa equation for modern treatments of what Einstein et. al. began uncovering after 1938.

 

[zonde]

Google MiSaTaQuWa equation for modern treatments

Thanks. Did that.