Please help review my pre-print paper
Preprint N-body Gravity Simulation by Curvature of Wave Propagation
Specifically, please take a look at:
Page 1 - The introduction and the typical way that is given to represent Mercury’s precession.
Page 2 - The section on “Gravity N-body simulation challenges.”
Page 6 - Figure 3 (illustrates comparison with general relativity).
Page 12 - Figure 8: N-Body simulation of Mercury’s orbital precession and solution convergence.
Examples 1 through 6.
Page 30: Appendix A. Observational Data - Keplerian Elements to Orbital Precession Calculation Method.
Closing Remarks on page 26.
I would appreciate any comments or suggestions you may have regarding the paper. You may contact me directly if desired.
You have make much work, However I can't help you because the matter is not my expertise.
The rules for the calculation aren't at all clear. The equations are written in a particular frame and the claim is made they are frame independent-which isn't by any means obvious.
N-body dynamics means that there are N bodies; much of the presentation is about one-body dynamics. The precession of the perihelion of Mercury is the result of a two-body problem, not an N-body problem.
There's a claim about wave propagation, but there doesn't seem to be a wave equation anywhere. The equations appear in an ad hoc manner and the symmetries-the transformations that leave the equations of motion invariant-are not spelled out.
In general relativity it is known how to describe the way in which gravitational waves affect spacetime curvature and how to describe the motion of a particle in a gravitational wave-and this problem has had recent interest in the context of so-called ``gravitational memory'', where a wave pulse striking a particle can confer on it, either a particular relative displacement or a particular relative velocity with respect to its state before the wave pulse strikes the particle.
However the wave which is referred to here seems to be defined by the trajectory of the particle itself, which is something that must be shown; or, at least the rules for doing the calculations need to be spelled out, before presenting any application.
So the first question the paper ought to address is what is achieved by the present formulation that cannot be achieved by the known formulations, namely general relativity; and, once that issue has been resolved, what is something new that can be obtained by the new formalism that can't be obtained (either at all, or as easily, by some measure) by the known formulations. N-body simulations, after all, are known. cf. Preprint General relativistic weak-field limit and Newtonian N-body simulations
, https://nbody.sourceforge.net/, https://developer.nvidia.com/gpugems/gpugems3/part-v-physics-simulation/chapter-31-fast-n-body-simulation-cuda, https://github.com/MarcVivas/N-body
Dr. Stam Nicolis,
I appreciate your time and valuable comments on my paper. I’ve addressed each one as follows:
Your comment :
The rules for the calculation aren't at all clear. The equations are written in a particular frame and the claim is made they are frame independent-which isn't by any means obvious.
My response:
This paper aims to demonstrate the method, not the derivation. I will clarify that. The complete derivation is presented in the book titled “Time, Matter, and Gravity.” For a copy of this book, please refer to the following link: https://vixra.org/pdf/2102.0123v1.pdf
As mentioned in my paper “Though not yet proven mathematically, the results presented in this paper indicate the curvature of wave propagation method is reference frame independent.” as illustrated in Figure 4 of Example 1.
Your comment :
N-body dynamics means that there are N bodies; much of the presentation is about one-body dynamics. The precession of the perihelion of Mercury is the result of a two-body problem, not an N-body problem.
My response:
All the examples presented in this paper are calculated using n-body simulations, and none of them are for a one-body dynamic interaction. You can verify this by looking at the MATLAB script files. Regarding Mercury, most of its perihelion precession is caused by the planets in our solar system. This is documented in the references I’ve provided in my paper. I do present the special case of a two-body solution for a hypothetical Sun-Mercury system for comparison with published values for General Relativity.
Your comment :
There's a claim about wave propagation, but there doesn't seem to be a wave equation anywhere. The equations appear in an ad hoc manner and the symmetries-the transformations that leave the equations of motion invariant-are not spelled out.
In general relativity it is known how to describe the way in which gravitational waves affect spacetime curvature and how to describe the motion of a particle in a gravitational wave-and this problem has had recent interest in the context of so-called ``gravitational memory'', where a wave pulse striking a particle can confer on it, either a particular relative displacement or a particular relative velocity with respect to its state before the wave pulse strikes the particle.
However the wave which is referred to here seems to be defined by the trajectory of the particle itself, which is something that must be shown; or, at least the rules for doing the calculations need to be spelled out, before presenting any application.
My response:
Thank you. I’ll clarify that the derivation is provided in the book titled “Time, Matter, and Gravity.” (See https://vixra.org/pdf/2102.0123v1.pdf) In Chapter 7 of this book, I demonstrate how the curvature of a body’s motion in a gravitational field is derived from its wave characteristics.
As mentioned in my paper “Though not yet proven mathematically, the results presented in this paper indicate the curvature of wave propagation method is reference frame independent.” as illustrated in Figure 4 of Example 1.
Your comment :
So the first question the paper ought to address is what is achieved by the present formulation that cannot be achieved by the known formulations, namely general relativity; and, once that issue has been resolved, what is something new that can be obtained by the new formalism that can't be obtained (either at all, or as easily, by some measure) by the known formulations. N-body simulations, after all, are known. cf.
Preprint General relativistic weak-field limit and Newtonian N-body simulations
, https://nbody.sourceforge.net/, https://developer.nvidia.com/gpugems/gpugems3/part-v-physics-simulation/chapter-31-fast-n-body-simulation-cuda, https://github.com/MarcVivas/N-body
My response:
As pointed out in my paper, “An N-body gravity simulation that calculates motion based on the local properties of space or the curved spacetime described by general relativity is not found.” See also
https://www.researchgate.net/post/Is_there_a_General_Relativity_based_n-body_simulation_that_can_calculate_Mercurys_total_perihelion_advance_or_precession
However, the method presented in my paper “N-body Gravity Simulation by Curvature of Wave Propagation” offers a straightforward and accurate approach (for both weak and strong gravitational fields) to calculate motion based on the local properties of space. It is also significantly simpler to implement compared to the alternative parametrized post-Newtonian [PPN] approach.
Thank you for the links to your papers and code! I will take time to study them.
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