[sjastro]

Interesting Mark including the links.

Originally Posted by Nesti

“In this way, Einstein’s gravity can easily be looked upon as a fictitious force; in that the force itself is applied to spacetime and not the objects within spacetime. Whereas Newtonian gravity states that objects apply the force of gravitation between masses; which is direct. In this simple way, we can now see that gravitation is not the force itself, but the outcome of mass applying an influence on spacetime.

Spacetime is an extension of Newtonian gravitational potental which defines the gravitational field.

Both concepts relate to how a particle (object) interacts with a gravitational field.
The force is applied to the particle, the outcome is spacetime or gravitational potential.

..........a change observed from a separate frame of reference, brought about from the presence of matter and the subsequent warping (negative divergence) of spacetime - then what does the warping, where does the energy come from?

In a gravitational field the particles travel on geodesic paths which define the equation of motion. Since the particles move in inertial frames where the sum of the external forces equals zero, why is energy required for warping?

The question has much more relevance for spacetime expansion. Before it was discovered the Universe was expanding at an accelerating rate, expansion was considered an inertia effect requiring no external forces or energy.

Now that expansion is found to be accelerating the "where is the energy coming from" is pertinent.

I’ll give you an example; Einstein’s formulas for relativity consist of many parts, each representing different functions, such as the Christoffel symbols (Elwin Bruno Christoffel’s work on tensors), these provide a means of inserting forces into spacetime, without being affected by any changing curvature, and the derivatives, which calculate how the curvature must change according to the metric.

The equation of motion of a particle on a geodesic path involves the sum of real and fictitious forces. Since the frame is inertial the sum equals zero. The real force contributes to accelerating the particle through the field, the "fictitious" forces are the terms which contain the Christoffel symbols.

If you change the curvature, you change the metric which in turn changes the equation of motion.

These are all amazing mathematical structures, but they are no more gravity than these words are your understanding of them; mathematics is a descriptive language, it is not a physical act.

The scientists who mathematically developed Quantum Mechanics would be turning over in their graves.

Regards

Steven