Category:Advanced General Relativity (AGR)

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GENERAL RELATIVITY

Advanced General Relativity (AGR)

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General Relativity (1916)
General Relativity (1960)
Advanced General Relativity (C21st)

C21st –


Advanced General Relativity (or Acoustic General Relativity, AGR, GR(a), etc.) is a purist reimplementation of the general theory of relativity that avoids the compromises introduced into "textbook GR" from 1960 onwards. It is a “top down” theory – it starts with the General Principle of Relativity (GPoR), and rederives the rest of classical physics to suit, without assuming that all existing “legacy” theories have to live on in the new theory as perfect limiting cases. It can also be considered as an implementation of Einstein’s declaration in 1950 that nothing should be accepted as part of general relativity until it can be shown to conform to the GPoR.

An accidental side-effect of taking this purist approach is that the result appears to be in agreement with quantum mechanics, and would therefore seem to be not just a “more general” general theory, but technically also a theory of quantum gravity.

GR: "Top-down" vs "bottom-up"

... all attempts to obtain a deeper knowledge of the foundations of physics seem doomed to me unless the basic concepts are in accordance with general relativity from the beginning.
— Albert Einstein, Scientific American, April 1950    

We can characterise a "top down" theory as being principle-based, and working from a set of higher rules (which then require underlying mathematical machinery to be constructed to suit), and a "bottom-up" theory as being "constructional", and assembled pragmatically and incrementally from available components.

GR1916:
Einstein's original general theory combined “top-down” and “bottom-up” approaches, with the hope that the two approaches would meet and mesh somewhere in the middle – the “top-down” component was the General Principle of Relativity (GPoR), the “bottom up” component was special relativity. Unfortunately, in 1960 it was realised that the two components did not mesh, and were in fact geometrically incompatible. The theory was logically inconsistent.
GR1960:
After the 1960 crisis, “textbook GR” was modified to make SR-compatibility a fundamental rule of the theory, with the GPoR having secondary importance. Whenever the GPoR and SR were in conflict, the GPoR was to be suspended in favour of SR, converting the “hard crash” of GR1916 into a “soft crash”, with guidance for how users were to proceed. * While the incorporation of a “fail protocol” into the theory imposed a theological consistency, the resulting system was no longer a fully principle-based theory, and … as it no longer treated the GPoR as an unbreakable law … was technically no longer a full, general implementation of the concept of relativity. * It was “more general” than special relativity, but not completely general.
Advanced GR:
A "purist" approach to general relativity is instead “top-heavy” – it is required to make the GPoR inviolable, and while special relativity can still be used as a convenient approximation or engineering theory, SR physics cannot be a perfect subset of a “proper” general theory’s physical predictions. With “Advanced GR” we obtain most of the same experimental proofs and behaviours of SR, but using a different Lorentzlike relationship, and a relativistic acoustic metric. The main divergences from current classical theory relate to horizon behaviour, which under AGR appears to correspond well to the behaviours of quantum mechanics.
I do not see any reason to assume that the heuristic significance of the principle of general relativity is restricted to gravitation and that the rest of physics can be dealt with separately on the basis of special relativity, with the hope that later on the whole may be fitted consistently into a general relativistic scheme. I do not think that such an attitude, although historically understandable, can be objectively justified.
— Albert Einstein, Scientific American, 1950    

Naming

It would seem that if SR and the GPoR cannot both coexist in a single larger logical system[], any theory that includes special relativity as a perfect physical limiting case cannot logically be fully compliant with the GPoR.

Since all gravitational models currently accepted as credible by C20th criteria are currently required to incorporate SR physics as a perfect subset[], it would follow that none of these theories can be truly GPoR-compliant, and that none of these can in principle be considered truly 100% general general theories of relativity.

As a result, although it is practical to refer to the "advanced" general theory with some form of qualifying prefix to distinguish it from GR1960 ("advanced" / "acoustic" / "purist" / Cliffordian / "truly general" , etc.), the technically correct characterisation of the theory would be that it is simply "general relativity".

Notes

  • It has been suggested that perhaps a more accurate name for GR1960 would be "theory of covariance" []

For the time being we have to admit that we do not possess any general theoretical basis for physics, which can be regarded as its logical foundation.
— Albert Einstein, "The Fundaments of Theoretical Physics", Science, 1940    

Subcategories

This category has only the following subcategory.