Reference: Einstein’s 1920 Book
Section XXVIII (Part 2)
Exact Formulation of the General Principle of Relativity
Please see Section XXVIII at the link above.
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Summary
In the general theory of relativity, the rigid reference bodies are replaced by the Gaussian coordinate systems.
In special theory of relativity, we replace the space-time variables of a Galilean reference-body by the space-time variables of a new reference body that makes use of Lorentz transformation. In general theory of relativity, we replace one Gaussian coordinate system by another, while the equations which express the general laws of nature pass over into equations of the same form.
In a way we are replacing the reference systems of material bodies with limited range of flexibility by reference system of gravitational field with infinite range of flexibility. Special kind of gravitational fields may appear as being attached to material bodies.
In gravitational fields there are no such things as rigid bodies with Euclidean properties. The physical sense of space and time also becomes very different from that in the special theory of relativity.
The rigid reference-bodies of the special theory of relativity are replaced by non-rigid reference-bodies of gravitational field in the general theory of relativity. In a gravitational field, the variations in rigidity are continuous without limitation just like the motion. Therefore, the term “reference-body” may be replaced by the term “reference-mollusk.” The “mollusk” gives a certain comprehensibleness is the (really unqualified) formal retention of the separate existence of the space co-ordinate.
The general theory of relativity thus assigns certain rigidity to space coordinates, from almost no rigidity in case of light to a high order of rigidity in case of matter.
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Final Comments
The gravitational field as represented by Gaussian coordinates is like space with some substantiality. In other words, space has a consistency that varies from one location to the next. As the consistency increases, the space becomes more concentrated and it starts to appear as the electromagnetic radiation. Near infinite consistency turns space into matter with the characteristics of inertia. Within an atom, the increasing consistency appears as the electronic and the nuclear regions.
As the concentration of “substantial” space increases, boundaries between spaces of different consistencies become more visible. Thus come about the appearance of discrete particles within the continuous medium of space.
As consistency increases the velocity decreases, and that seems to provide a model of a vortex of decreasing radius. This radius finally becomes so small that the velocity of concentrated space turns into spin of solid particles at the bottom of the vortex.
This Vortex Model may apply to spinning atoms and also to the spinning planets with their gravitational fields.
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