Question

In: Physics

Can general relativity be completely described as a field in a flat space? Can it be...

Can general relativity be completely described as a field in a flat space? Can it be done already now or requires advances in quantum gravity?

Solutions

Expert Solution

ADDITION: in the paper by Straumann, N. - Reflections on Gravity (ESA-CERN Workshop on Fundamental Physics in Space and Related Topics, European Space Agency, 5-7 April 2000(2001), SP-469,55), it is shown (similarly to Deser's classical work but in a more expository style) that a spin-2 field theory on a flat Minkowki 4-manifold ends up being totally equivalent to Einstein's curved spacetime where the ab inition Minkowski metric ends up being unobservable whereas the observable and physical metric is dynamical supporting the relational meaning advocated in the rest of this answer which emphasizes the idea that space, time and causal structure are relational notions between dynamical entities and NOT an absolute static stage (be it Newton's or Minwkoski's) where things, including gravity, live.

Conclusion from the long digression below: yes, you can formulate gravity as a field in a flat manifold (e.g. Deser's, Doran-Gull-Lasenby, tele-parallelism...) but no, that manifold (and its additional structure) is not flat space-time. In any equivalent formulation of general relativity, you cannot avoid the coupling between the physical space-time metric and causal structure to the rest of the degrees of freedom (matter, forces...). Therefore, in any formulation, there are fields living on top of each other, and space-time amounts to relational coincidences between them. The underlying manifold serves as a necessary indexing device for the degrees of freedom of fields, but has no physical observable meaning. If the situation is such that the region of interest can be coordinatized by physical observables (e.g. matter fields embodying observers in that region), then we may use these as indexing the fields' coincidences; if moreover the coupling of those observables to gravity can be neglected, then they describe a physical Minkowskian space-time in that region. (But Minkowski's flat space-time is not a solution to Einstein's field equations when there is a non-vanishing cosmological constant! so assuming physical reality to a global flat 'space-time' is meaningless in any equivalent formulation).

For a wonderful discussion and development of all these conceptual issues, you should read Carlo Rovelli's - Quantum Gravity, chapter 2 (in special 2.2, 2.3 and 2.4).

Einstein's general relativity is a theory about the dynamics of space-time; more precisely, it is the realization that the gravitational field 'is' space-time, and that non-relativistic (newtonian and minkowskian) space and time is a particular solution useful as background in regimes of approximately neglectable gravitational effects compared to the other phenomena of interests. As Einstein remarked in his original article,

"... the requirement of general covariance takes away from space and time the last remnant of physical objectivity..."

A. Einstein, Grundlage der allgemeinen Relativit


Related Solutions

Why does Quantum Mechanics not follow Einstein's Theory of General Relativity? If that's completely true, [we...
Why does Quantum Mechanics not follow Einstein's Theory of General Relativity? If that's completely true, [we know that "The Higgs boson does not technically give other particles mass. More precisely, the particle is a quantized manifestation of a field (the Higgsfield) that generates mass through its interaction with other particles." ] will it follow the famous equation E=mc²?
Explain General Relativity. Give examples.
Explain General Relativity. Give examples.
Einstein's Theory of General Relativity can be considered a "good theory." a) What did this theory...
Einstein's Theory of General Relativity can be considered a "good theory." a) What did this theory explain that other theories could also explain? b) What did this theory explain that other theories could not explain? c) What did this theory predict that nobody had expected, but which were found experimentally?
Which statement best describes the difference between special relativity and general relativity? a) Only the theory...
Which statement best describes the difference between special relativity and general relativity? a) Only the theory of general relativity includes gravity. b) The theory of general relativity describes the behavior of subatomic particles. c) The theory of special relativity applies only to very massive objects. d) Only the theory of special relativity includes gravity.
Which statement best describes the difference between special relativity and general relativity? a) Only the theory...
Which statement best describes the difference between special relativity and general relativity? a) Only the theory of general relativity includes gravity. b) The theory of general relativity describes the behavior of subatomic particles. c) The theory of special relativity applies only to very massive objects. d) Only the theory of special relativity includes gravity.
a) Explain Einstein’s theories of special relativity and general relativity. b) Include at least one piece...
a) Explain Einstein’s theories of special relativity and general relativity. b) Include at least one piece of evidence in support of each theory.
Can an electric or a magnetic field, each constant in space and time, be used to...
Can an electric or a magnetic field, each constant in space and time, be used to accomplish the actions described below? Explain your answers. Indicate if the answer is valid for any orientation of the field(s). Must any other condition be satisfied? (a) move a charged particle in a circle; (b) exert a force on a piece of dielectric; (c) increase the speed of a charged particle; (d) accelerate a moving charged particle; (e) exert a force on an electron...
Show that the affine connection is not a true tensor (general relativity/cosmology)
Show that the affine connection is not a true tensor (general relativity/cosmology)
In a lot of laymen explanations of general relativity it is implied that the four dimensions...
In a lot of laymen explanations of general relativity it is implied that the four dimensions of the space-time are equivalent, and we perceive time as different only because it is embedded in our human perception to do so. My question is: is that really how general relativity treats the 4 dimensions? If so - what are the implications (if any) this has on causality? If no - can the theory support more than one time dimension?
In general, teams can be described three ways. Name and define each.
In general, teams can be described three ways. Name and define each.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT