Is Spacetime a Field in General Relativity?

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Discussion Overview

The discussion revolves around whether spacetime can be considered a field within the framework of General Relativity. Participants explore the nature of spacetime, its relationship to fields, and the mathematical structures involved, including the metric tensor and Riemannian manifold.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants propose that spacetime itself could be viewed as a field.
  • Others argue that spacetime is merely a mathematical model or environment where physical phenomena occur, rather than a field in its own right.
  • One participant suggests that in General Relativity, spacetime is better associated with the entire Riemannian manifold rather than just the metric.
  • Another viewpoint emphasizes that while spacetime is described by a metric tensor, it is fundamentally a quality of the gravitational field and not a field itself.
  • A later reply reiterates that spacetime can be represented as a pair (M,g), where M is a smooth manifold and g is a tensor field, suggesting that the metric can be considered a field on spacetime.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the characterization of spacetime, indicating that the discussion remains unresolved.

Contextual Notes

There are limitations in the definitions used, particularly regarding the terminology of spacetime and its components, which may affect the clarity of the discussion.

brianhurren
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Could spacetime itself be a field?
 
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No, according to the current understanding acquired since the beginning of the 20th physics, spacetime is a mathematical model/environment where all physics takes place, in particular where particles and field 'live'.
 
Yes, in General Relativity, spacetime is a field described by a metric tensor.
 
I think that in GR I would associate spacetime with the whole Riemannian manifold, not just the metric.
 
No, it is a quality of the gravitational field but is not a field in it's own sense.
 
O10infinity said:
Yes, in General Relativity, spacetime is a field described by a metric tensor.
Spacetime is not a field. A spacetime is a pair (M,g) where M is a smooth manifold and g (the metric) is a tensor field on M. It's considered OK to refer to M as "spacetime", even though it would be more accurate to call it something like "spacetime's underlying manifold". If we use this terminology, we can say that the metric is a field on spacetime.
 

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