Derivational Approach
The distinction between "4.0" physics and SR-based relativity theory is apparent when deriving the basic equations of motion that would be required to meet the demands of a "curvature-based" relativistic model.- It is important that certain "relativistic" concepts and results are preserved within inertial physics (such as momenergy and the E=mc2 result for rest mass). These results aren't unique to special relativity's particular equation-set unless we also impose the condition of flat spacetime – which isn't part of the 4.0 design.
- Without the assumption of flat spacetime, an infinite number of other potential relativistic solutions are available that meet the remaining essential criteria for a relativistic theory.
- These potential solutions form a continuum, with each solution related to the others by a "Lorentzlike" transform, [1 - vv/cc]x (a "conventional" Lorentz transform except that the exponent value is unspecified). Provided that we apply the transform correctly, we can move between the predictions of any two potential solutions by knowing how far apart they are placed on the continuum line, and using this separation to set an appropriate value for x.
- The relationships of special relativity appear at one point on this line. The relationships of Newtonian Optics appear at another. Since 4.0's predictions will be compared to those of special relativity, it's useful to take the known, well-documented properties of SR as a reference point for all the other potential solutions.
- Special relativity marks the unique solution in which spacetime geometry remains "flat" irrespective of relative velocity between bodies.
- The difference between other potential solutions can be described in terms of the different strengths of gravitomagnetic effects in associated models. Solutions over to one side of SR's point on the continuum are increasingly "bluer" than SR (by a Lorentzlike factor), solutions over to the other side are increasingly "redder" than SR (by a Lorentzlike factor).
- The "bluer" solutions are discarded as unphysical, since they associate a negative curvature effect with positive relative velocity and positive kinetic energy. For a curvature-based system, we require positive curvature within systems having positive recoverable kinetic energy.
- This leaves potential solutions that are redder than SR, by an (unspecified) Lorentzlike factor whose exponent relates to the (unspecified) strength of velocity-dependent gravitomagnetic effects in the model.
- Solutions more than one Lorentz-factor "step" redder than SR are provisionally rejected as unphysical, since they can describe objects approaching at sufficiently high subluminal velocities as being redshifted. This would be a difficult result to implement.
- The remaining available range for 4.0 is therefore a range terminated by at one end by special relativity, and at the other by a second solution that is one standard Lorentz factor "click" redder than special relativity.
- These two extremal solutions are special cases:
- The first (SR) represents the special case for flat spacetime, where v-gm effect are entirely absent.
- The second represents the special case where v-gm effects produce total light-dragging at a particle's surface, analogous to the total dragging currently predicted by GR1915 at a moving black hole event horizon.
- The second solution also arguably represents the simplest mathematical solution, and gives the simplest reduction to Newtonian mechanics.
- The second solution also represents the only point in our defined range that allows indirect radiation through gravitational horizons.
- "Variable" solutions (where the strength of v-gm effects is a function of surface gravitation) are provisionally rejected as unworkable, since they would generate different equations of motion for different types of body. They would seem to require a collapsing object to change it's state of motion in order to maintain energy conservation as its EoMs changed. This would not seem to be workable.
- A "single", fixed intermediate solution would also not seem to be adequate, since we require the system to work for moving event horizon-bounded bodies, (whose total gravitomagnetic surface dragging requires the second extremal solution). There's no obvious advantage to picking an intermediate (arbitrary) solution that would compensate for the extra introduced complexity and the inability to model moving horizons.
A single solution for 4.0
The previous arguments leave us with just two possible solutions for the basis of a relativistic theory:
... the first solution, which represents zero curvature and special relativity, and which then requires GR1915 (or a similar SR-compatible theory) as a second layer to deal with curvature effects required by the general principle of relativity ...
... and the second solution, which is "redder and shorter" than SR by an additional Lorentz factor, represents the "fully-curved" solution in which gravitomagnetic effects operate at full strength, and which also appears to be the only solution in our continuum that could apply for objects with arbitrarily-strong gravitation.
The SR-based solution isn't appropriate for 4.0, since it appears to break various principles associated with the general principle of relativity (it allows inertial mass to be modeled in the absence of gravitational mass). It's also assumed that relativistic models based on special relativity's equations of motion have already been thoroughly examined by and scrutinised by existing research, and don't need to be rederived.
This leaves us with just one unique remaining solution for the equations required by the 4.0 project – an equation-set that's redder than the predictions of special relativity by exactly one additional Lorentz factor, which can be visualised (naively) as the result of a gravitomagnetic effect missing from the "flat" SR description.
if 4.0 is correct, the existence of this additional gravitomagnetic redshift should be verifiable with current experimental equipment.
www.fourpointzero.org/4.0_derivation.html