I Architecture & Assumptions of General Relativity Theory

[Ad VanderVen]

TL;DR Summary

Every theory, whether it is a physical, a psychological or a sociological theory, is defined in terms of an assumed architecture and in terms of a number of assumptions that apply within that architecture. An example from physics is the previously widely accepted dome theory to explain the movement of the stars. This theory has since been replaced by the luminous spheres theory. My question now is: what is the architecture of the theory of relativity, in particular of the general theory of rel

Every theory, whether it is a physical, a psychological or a sociological theory, is defined in terms of an assumed architecture and in terms of a number of assumptions that apply within that architecture. An example from physics is the previously widely accepted dome theory to explain the movement of the stars. This theory has since been replaced by the luminous spheres theory.

The most classical and perhaps also the first non-mathematical model to make a phenomenon understandable was the dome model to explain the movement of the stars in the sky. The stars do move, but they do not move relative to each other. They all revolve around one particular star at the same time and that is the North Star. The obvious model was as follows. We look from below at a sphere with holes. The globe slowly revolves around the point where the North Star is. We are inside the sphere and outside the sphere there is light. There are holes in the sphere and the light falls through the holes. So the stars are actually holes. An assumption within this architecture is that the brightness of a star is determined by the size of the hole in question. The modern view is that the stars are luminous spheres that float through space at great speed, but whose movement we cannot see because of the very large distance of the stars from us. An assumption within that architecture is that the brightness of a star is partly determined by the distance of that star from the earth.

Examples of other architectures within physics are the wave and particle theory to explain light phenomena. In the 17th century, Christiaan Huygens was the first to claim that light is a wave phenomenon. The light-perceived phenomena such as interference and bending argued for this. This was contradicted by Isaac Newton, who stated that light consists of a stream of fast particles.

My question now is: what is the architecture of the theory of relativity, in particular of the general theory of relativity, and can I make a list of assumptions that apply within that architecture.

 

[BvU]

Hello Ad, !

You did a lot of digging already (dome, wave/particle duality). I'm surprised you didn't find something to satisfy your curiosity by yourself !

But now that you did post, the 'Related threads' below should be a real treasure trove !
(I know little to nothing about GR, but enjoyed looking around. Found a nice philosophy site that even has a hole story (not dome holes, though).)

 

[.Scott]

In the case of Relativity and General Relativity, it would be the architecture of the space itself - not what you put into that space.

 

[Ad VanderVen]

Scott: Thanks for your beautiful answer.

 

[Ad VanderVen]

BvU: Thank you for your answer. I will certainly look into the 'Related threads' you referred to.

 

[olgerm]

Geomentry of spactime and stress-tensor are intuitevly understandable quantities. Einstein fieldequation is relation postulated between these 2.
Assumation is that Einstein fieldequation is true.

 

[PeroK]

The modern view is that the stars are luminous spheres that float through space at great speed, but whose movement we cannot see because of the very large distance of the stars from us.

I guess you could argue about what exactly "modern" means; but, in terms of language and perception that sounds like something from the 18th century!

That is not any way a modern physicist would describe things.

 

[Nugatory]

In the case of Relativity and General Relativity, it would be the architecture of the space itself - not what you put into that space.

Although it might be better to be speaking of spacetime here, not space?

 

[PeroK]

Although it might be better to be speaking of spacetime here, not space?

That might be a bit too modern!

 

[robphy]

I would suggest that at the deepest level
the Causal Structure [the "set of light cones"] is the architecture of general relativity.

https://en.wikipedia.org/wiki/Causal_structure
Quoting from Ted Jacobson's essay [bolding mine]
http://terpconnect.umd.edu/~jacobson/spacetimeprimer.pdf

p.16 [paraphrasing a comment initially by Finkelstein]
metric = causal cone + scale.
Thus, although we call gµν the “metric”, it is in large part ( 9/10 ) just the causal structure!

• David Finkelstein, Space-Time Code
  Phys. Rev. 184, 1261 – 1271 (1969) https://doi.org/10.1103/PhysRev.184.1261
  

  p.1262
  The causal order C determines the conformal structure of space-time, or nine of the ten components of the metric. The measure on space-time fixes the tenth component.

p. 18 [referencing the papers below]
It turns out that not only does the causal structure determine the metrical structure up to a function, but it determines the differential structure of spacetime as well!

• The class of continuous timelike curves determines the topology of spacetime
  Journal of Mathematical Physics 18, 1399 (1977); https://doi.org/10.1063/1.523436
  David B. Malament
  

  The title assertion is proven, and two corollaries are established. First, the topology of every past and future distinguishing spacetime is determined by its causal structure. Second, in every spacetime the path topology of Hawking, King, and McCarthy codes topological, differential, and conformal structure.

which extends

• A new topology for curved space–time which incorporates the causal, differential, and conformal structures
  S. W. Hawking, A. R. King, and P. J. McCarthy
  J. Math. Phys. 17, 174 (1976); http://dx.doi.org/10.1063/1.522874
  

  A new topology is proposed for strongly causal space–times. Unlike the standard manifold topology (which merely characterizes continuity properties), the new topology determines the causal, differential, and conformal structures of space–time. The topology is more appealing, physical, and manageable than the topology previously proposed by Zeeman for Minkowski space. It thus seems that many calculations involving the above structures may be made purely topological.