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Space Time Curvature

Spacetime curvature is a change in the observer's frame of reference.
It is not a curvature of space. Sometimes there might be confusion between the frame of reference or the physical space.
from Wikipedia.
'
In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams can be used to visualize relativistic effects such as why different observers perceive where and when events occur.

Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its spatial expression in terms of coordinates, distances, and directions) was independent of one-dimensional time. However, in 1905, Albert Einstein based his seminal work on special relativity on two postulates: (1) The laws of physics are invariant (i.e., identical) in all inertial systems (i.e., non-accelerating frames of reference); (2) The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.
'

My interpretation of the above:
Spacetime is a model - or a geometry - of 3 linear dimensions of space (usually XYZ or WHD) and a 4th dimension for time. It describes our frame of reference.

Note: Relativity applies only to an accelerating frame of reference. Normal laws of physics apply when not accelerating.



In the observer's frame of reference using this geometry the linear coordinates are always relative. The zero references for XYZ coordinates are whatever are convenient for the observer. If I wish to move my frame of reference I can change that axis coordinate so its value relative to an actual position is  as desired. Given the universe has no fixed zero reference points for X0,Y0,Z0, absolute positions can never be used in a frame of reference.
If a physical object moves a specific distance the object's coordinates will update with the new relative position in my frame of reference.

here is a long excerpt from the link (the end is noted)
'
By stretching our minds, some of us can even form a vague mental image of what four-dimensional curvature would be like if it did exist. Nevertheless, saying that the gravitational field equations are equivalent to curvature is not the same as saying that there is curvature. In QFT, the gravitational field is just another force field, like the EM, strong and weak fields, albeit with a greater complexity that is reflected in its higher spin value of 2.

While QFT resolves these paradoxical statements, I don't want to leave you with the impression that the theory of quantum gravity is problem-free. While computational problems involving the EM field were overcome by the process known as renormalization, similar problems involving the quantum gravitational field have not been overcome. Fortunately they do not interfere with macroscopic calculations, for which the QFT equations become identical to Einstein's.

Your choice. Once again you the reader have a choice, as you did in regard to the two approaches to special relativity. The choice is not about the equations, it is about their interpretation. Einstein's equations can be interpreted as indicating a curvature of space-time, unpicturable as it may be, or as describing a quantum field in three-dimensional space, similar to the other quantum force fields. To the physicist, it really doesn't make much difference. Physicists are more concerned with solving their equations than with interpreting them. If you will allow me one more Weinberg quote:

weinberg"The important thing is to be able to make predictions about images on the astronomers photographic plates, frequencies of spectral lines, and so on, and it simply doesn't matter whether we ascribe these predictions to the physical effects of gravitational fields on the motion of planets and photons or to a curvature of space and time."  – Steven Weinberg

So if you want, you can believe that gravitational effects are due to a curvature of space-time (even if you can't picture it). Or, like Weinberg (and me), you can view gravity as a force field that, like the other force fields in QFT, exists in three-dimensional space and evolves in time according to the field equations.

'
By stretching our minds, some of us can even form a vague mental image of what four-dimensional curvature would be like if it did exist. Nevertheless, saying that the gravitational field equations are equivalent to curvature is not the same as saying that there is curvature. In QFT, the gravitational field is just another force field, like the EM, strong and weak fields, albeit with a greater complexity that is reflected in its higher spin value of 2.

While QFT resolves these paradoxical statements, I don't want to leave you with the impression that the theory of quantum gravity is problem-free. While computational problems involving the EM field were overcome by the process known as renormalization, similar problems involving the quantum gravitational field have not been overcome. Fortunately they do not interfere with macroscopic calculations, for which the QFT equations become identical to Einstein's.

Your choice. Once again you the reader have a choice, as you did in regard to the two approaches to special relativity. The choice is not about the equations, it is about their interpretation. Einstein's equations can be interpreted as indicating a curvature of space-time, unpicturable as it may be, or as describing a quantum field in three-dimensional space, similar to the other quantum force fields. To the physicist, it really doesn't make much difference. Physicists are more concerned with solving their equations than with interpreting them. If you will allow me one more Weinberg quote:

weinberg "The important thing is to be able to make predictions about images on the astronomers photographic plates, frequencies of spectral lines, and so on, and it simply doesn't matter whether we ascribe these predictions to the physical effects of gravitational fields on the motion of planets and photons or to a curvature of space and time."  – Steven Weinberg

So if you want, you can believe that gravitational effects are due to a curvature of space-time (even if you can't picture it). Or, like Weinberg (and me), you can view gravity as a force field that, like the other force fields in QFT, exists in three-dimensional space and evolves in time according to the field equations.

' - end of the excerpt

 
Spacetime curvature is only in the (accelerating) observer's frame of reference, not with the physical objects. For example time dilation affects only the observer's local time.

link

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