Is Spacetime a Field in General Relativity?

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Spacetime is primarily viewed as a mathematical model or environment for physical phenomena rather than a field itself. In General Relativity, spacetime is represented by a pair consisting of a smooth manifold and a metric tensor, where the manifold is often referred to as "spacetime." While the metric tensor can be considered a field on this manifold, spacetime itself is not classified as a field. The discussion emphasizes the distinction between spacetime as a structure and the gravitational field it describes. Overall, spacetime serves as a foundational framework for understanding gravitational interactions in physics.
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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.
 

Thread 'EPR revisited'

In an inertial frame of reference (IFR), there are two fixed points, A and B, which share an entangled state $$ \frac{1}{\sqrt{2}}(|0>_A|1>_B+|1>_A|0>_B) $$ At point A, a measurement is made. The state then collapses to $$ |a>_A|b>_B, \{a,b\}=\{0,1\} $$ We assume that A has the state ##|a>_A## and B has ##|b>_B## simultaneously, i.e., when their synchronized clocks both read time T However, in other inertial frames, due to the relativity of simultaneity, the moment when B has ##|b>_B##...
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