4.0 Concepts

Concepts

4.0 modifies some existing concepts and principles, and introduces a few new ones:

Principle of Relativity: In its most general form, that there is no absolute externally-imposed privileged reference state of motion for inertial physics. 4.0 incorporates the special principle of relativity in the sense that it incorporates Newtonian mechanics, and (like SR) applies the same principle to the behaviour of light. The method of achiving this is different.
4.0 doesn't make a sharp distinction between inertial and noninertial physics, inertial physics is treated as a special case of curved spacetime geometry in which certain effects cancel.
4.0 is arguably a more purist, more general general theory of relativity, in that the General Principle of Relativity (in its broadest sense) is applied universally. Unlike GR1915's implementation of the GPoR, 4.0 has no forced reduction to the flat spacetime physics of special relativity, and no assumed "nongravitational" limit.
Observerspace: Observerspace is a term that appears in multiple disciplines, and refers to a visible or sensory environment. It's reality according to direct, uninterpreted instrumentation (see also optical metrics, optical geometry).
Observerspace is deliberately-naive physics, and its arguments break down when we start dealing with horizons. But it's a good way of starting to describe local physics before committing to particular rules. How two bodies "see" and "feel" each other defines their direct interactions.
Doppler Mass Shift (DMS): The result of a strict observerspace interpretation of the physical visible effects associated with relative motion. A photograph of a moving body appears to demonstrate all the effects associated with the presence of a gravitational field.; Within observerspace, that apparent gravitational field is "real". Under 4.0, if a body described in the time domain has a velocity of v, when described in an instantaneous snapshot, will show an apparent gravitomagnetic differential along its viewing path, again of velocity v. The conventional Doppler shift that we'd calculate in the time domain appears in a Δt=0 snapshot as a spacetime curvature effect. since both effects have to explain the same visible shift, gravitational and velocity effects have to obey the same velocity/shift law.
This lets us start to calculate the gravitomagnetic effects (and the change in a body's apparent inertial mass) that ought to be associated with relative motion.
Shift Equivalence Principle (or Single Equivalence Principle), SEP, Universal Shift Equivalence (USE): Occam's Razor asks that descriptions of functionally-equivalent effects should be as interchangeable as possible, even if the usual interpretations of those effects are different. Under 1990's theory, cosmological shifts, gravitational shifts and velocity shifts are all different, and obey two or three different sets of laws (depending on who you talk to). A receding star has three separate shift components due to (a) recession velocity redshift, (b) cosmological recession redshift (Hubble shift) and (c) gravitational redshift. The relationship between effective recession velocity and redshift for cosmology isn't the same as the one for standard recession velocity, or for gravitational redshift (calculated from terminal velocity of a gradient).; Under 4.0, a single law for the dependency between nominal relative velocity and resulting spectral shift has to apply to all three situations.
Gravitomagnetism (gm) Velocity-dependent gravitomagnetism (vgm): Gravitomagnetism refers to gravitational-field effects associated with the relative motion of masses. Existing theory agrees that "gm" effects appear when bodies accelerate or rotate, but the requirement that vgm effects not invalidate special relativity normally prevents us from applying the principle in its most general form.; DMS and SEP require that gravitomagnetic effects are also associated with simple relative motion between physical masses ("vgm").
In 4.0, vgm effects create and regulate local lightspeed constancy for signals passed between relatively-moving bodies, and special relativity is not required.
Nonlinearity, and acoustic metrics: Nonlinearity is a feature of models in which the properties of a signal alter the notional signal-carrying properties of the background metric.
Under 4.0, the moving massenergy of bodies are taken as "gravitational" signals, and the resulting nonlinearity shows up as associated gravitomagnetic distortions.; The natural form of a metric in which signals distort the shape of the metric is an acoustic metric. acoustic metrics have some of the properties of Minkowski metric, but also some key differences (acoustic metrics support Hawking radiation, the Minkowski metric doesn't).; Acoustic metrics appear to be irreconcilable with the flat Minkowski spacetime of special relativity.
Principle of Equivalence (EP): The principle that the physics within an explicit gravitational fields reduces over small regions to inertial physics, where the larger field's effects tend to zero. Physics performed in a small free-falling laboratory will be unaware of the larger field. The EP is used to argue that the concepts of acceleration and gravitation are interchangeable, and that inertial and gravitational mass must be different aspects of the same underlying property. This seems to be necessary for the functioning of (Eotvos' Principle).
v4.0 and GR1915 are both EP-based, but where GR1915 specifies that the inertial physics being reduced to must be that of special relativity by definition, V4.0 refuses to impose a particular format for inertial physics via the EP. the format that emerges naturally is curvature-based.; Under v4.0 it's legitimate to treat acceleration shifts on circling bodies as gravitational shifts, even though this appears to eliminate SR ... under existing theory, we defend SR by applying the clock hypothesis, even though this contradicts a GPoR/EP result ... and then we redefine the EP so that we can say that the EP requires us to do this.; With 4.0 , basic definitions are not corrupted in order to prop up any preexisting theory, and fundamental principles are not suspended when they are inconvenient (such as to allow inertia without gravitation in the case of special relativity). The resulting uncompromised equivalence-principle formulation is arguably cleaner, broader, and more fundamental. than the GR1915 version

Discussion

The SEP ("Equivalence Principle on steroids") locks down various parameters that are more of less set according to historical reasons under GR.

GR1915 agrees that we can calculate gravitational shifts from their associated terminal velocities, DMS requires the same calculations to work backwards, and allow us to calculate the strength of a gravitomagnetic effect from the strength of the associated Doppler shift. With DMS, the motions shifts appear as gravitomagnetic shifts when described outside the time domain.

The SEP then takes things even further. According to the SEP, the curvature-related effects due to cosmological and gravitational curvature also have to operate according to the same shift law for the maximum applicability of Occam's Razor. The SEP tells us that since cosmological horizons have to emit indirect radiation, gravitational horizons have to as well. Our motion-shift relationships then have to be in a form that allows acoustic metrics in the cosmological case, and that also allows indirect radiation through gravitational horizons in the gravitational case. this condition rules out the SR equations of motion and forces the "second solution" referred to on the derivations page. Existing SR-based general theory can't reproduce the QM Hawking radiation result, but the SEP gives us the result, with almost no math, immediately, independently of quantum mechanics. With the SEP and 4.0, Hawking radiation under QM becomes becomes a statistical description of the transmission characteristics of an acoustic metric.

A limited form of "v-gm" effects already appears in GR1915 for moving gravitational bodies – we can describe conventional gravitational slingshotting as a vgm momentum-exchange process, and the Lens-Thirring effect has an explicitly velocity-dependent component. We also know that analogous short-range dragging effects appear in everyday physics.
Current implementation of general relativity can't treat vgm effects consistently as a default behaviour, because this would give an acoustic metric and invalidate the geometry of special relativity. So there's a level of inconsistency in the approach used by the GR1915 system that doesn't appear to be present under 4.0 .