GR without SR: A gravitational-domain description of first-order Doppler effects

3.1. Observed timeflow

If we judge "apparent mass" by watching the object's reaction to a test force calibrated in its own frame, or to a force applied by the observer, then this property has a higher value when an object recedes and a lower one when the object approaches [23].

3.2. Observed ruler-changes.

3.3. Aberration as the result of bipolar gravitational lensing

Figure 1 (a): velocity aberration, (b): lensing aberration, (c): gravitational aberration

Taken together, these two descriptions appear to describe lightspeed constancy as a proximity effect, with light "thrown" forward close to the moving emitter, but taking up a speed of c relative to the background as it leaves the emitter's influence (see section 4.1).

Frame-invariance is discussed in section 4.2.

3.4. Gravitational lensing as a consequence of aberration

If the object's "mass" is wholly a function of its fields, and these fields are redistributed by relative motion, then we would also expect this field redistribution to produce a gravitational frequency-shift. The strength of this shift effect (in the forward and rearward directions) appears to match the frequency-shift law associated with whichever propagation is model being used. Rather than predicting that a moving object appears doubly Doppler shifted, DMS says that the "gravitational" shift calculated from aberration arguments actually is the motion-shift, described within the gravitational domain instead of the time domain.

4.1. Local lightspeed constancy

If we attempted to measure an intermediate speed in this region by introducing a physical probe with a new velocity, the presence of the probe would alter the surrounding geometry so that we would again get a local measurement of c relative to the probe. DMS models include a feature of quantum mechanics in that the act of measurement cannot be isolated from the system that is being examined.

4.2. Recreating frame invariance and Newton's Third Law

1. DMS and gravitational braking. If DMS predicts that a moving object sees rearward environmental matter to be mass-dilated and forward environmental matter to be mass-reduced, then we might expect the object to experience a rearward gravitational attraction that would slow its motion through its environment with respect to a local preferred frame.

2. Aberration and gravitational acceleration. If conventional aberration makes a moving object "see" more environmental matter to be in front of it than behind it (see published maps [29] ), then we might expect the object to experience a forward gravitational attraction towards the region where matter appears to be most concentrated, further increasing the object's speed relative to its environment. Such a universe would be deeply unstable.

Proof of complete cancellation is more difficult and might depend on the choice of shift equations, so for now we shall restrict ourselves to noting that the two effects that might be expected to destroy frame invariance (forward acceleration and rearward acceleration) act against one another in a homogenous universe [30] (although a moving object can still lose momentum to nearby passing particles by dragging and gravitational braking in an inhomogenous universe [31] ).

5.1. Shift formulae

The distinction between "flat" and "curved" models is a critical one, as it dictates our choice of non-transverse shift equation. If we take the three usual non-transverse Doppler equations [32],

	. . . (1)
	. . . (2)
	. . . (3)

we find that the assumption of a particular flat reference-frame leads to a combination of (1) and (3), a situation that SR then "relativises" by using the root product of both equations, (2). SR's chosen shift formula is related to (1) and (3) by the ubiquitous Lorentz term.

Once we lose the assumption of flat space, we no longer have to include both (1) and (3) in the description - we might instead choose to try to apply just (1) throughout. This first equation does look promising as the basis of a relativistic model and can be used to generate many of the usual "relativistic" results, including the E=mc² relationship [33], Einstein's 1905 aberration formula [34], and the usual r=2M Schwarzchild event horizon radius. However, (1) is generally supposed to be inferior because of its basic incompatibility with models based on the idea of flat space [35].

5.2. Comparison

Similarly, we find that (1) predicts that an object trying to hover at the r=2M surface of a superdense object only sees the outside universe to have a doubled frequency rather than an infinite rate of timeflow, so that escape can be attempted in finite time (as with indirect "dark star" radiation) [13]. In such a model, we can follow Einstein's comments to Heisenberg about quantum mechanics and say that it is no longer the "observables" that define the theory, but rather, that "it is the theory which decides what can be observed." [36].

5.3. Energy conservation

6.1. SR and Lorentz contraction

Figure 2(a) shows the internal wavelength-distances according to Einstein's 1905 electrodynamics paper. This ellipsoid has constant width and can be turned back into a constant-size sphere by a simple Lorentz-contraction along the motion axis. Although SR would have us believe that the object's wavefront is a sphere with fixed radius as mapped from all frames, we find that if the region inside the wavefront is mapped using wavelength distances, the internal dimensions of the wavefront are increased by the motion of the central object [34].

Figure 2: Light-distance ellipses according to (a): SR, and (b): DMS models

Figure 2(b) shows the equivalent wavelength diagram for equation (1). This ellipsoid has a further overall Lorentz magnification, and a constant-width cross-section through each focus. With DMS, we can try to preserve the internal wavelength-distances as geodesics to produce a "tilted gravitational well" around the moving mass that represents the additional curvature components of its kinetic energy. However, with DMS, we also have to remember that the act of filling the region with physical sensors that are stationary in the observer's own frame can affect the behavior of the wavefront, so the act of measurement cannot be isolated from the measurement process.

6.2. DMS and "tilted" gravitational wells

Figure 3 (a): "conventional" and (b): "tilted" gravitational wells

This approach only works if gravitation is a fundamental property of the particle. We cannot easily get to this description by constructing a gravitation-free model of inertia and then "retrofitting" gravitational terms later, since our model does not reduce to SR geometry over small regions in the usual way - here, two bodies with relative motion are always separated by a gravitational gradient, no matter how close they are to one another [39].

This description of tilted geometry and redistributed gravitation can be compared with the diagrams produced by Alcubierre [40] [41], and Will [42]. The Will and Alcubierre pieces discuss the use of (hypothetical, negatively-gravitating) exotic matter to generate a mass-imbalance around an object to produce freefall acceleration, and would also produce (undiscussed) gravitational lensing effects to deflect lightbeams along the acceleration axis and mimic conventional aberration effects. In this example, though, we are applying the description to mundane, everyday phenomena - Alcubierre-style distortions are presented here as an intrinsic property of any system with relatively-moving masses, and as the underlying mechanism that allows frame-invariance and Newton's Third Law to operate.

Again, if we place sensors in the region to confirm its geometry, any relative motion of the sensors will produce additional distortions that will alter the readings taken [43].

6.3. Mass-reduction limits

A very crude form of field-strength reduction also occurs in standard models due to observation timelags - when an object is approaching at a particular distance (in flat spacetime), its observed signals and fields correspond those that were emitted when it was further away than this, so the observed fields for the object at its "true" position are weaker than we would expect if the object was at that same position but stationary. Put simply, a distant object created traveling towards the observer at c_SR within a supposedly flat propagation model has no detectable fields, because the object's "new" field-signal (traveling at c) cannot be sensed until the object has already reached the observer's own position. This description becomes more involved in a DMS model.

8.1. Rotating and orbiting masses

The same principle should apply if these two sections of horizon are not connected, but belong to a pair of holes in a mutual circular orbit - a receding hole in a black hole binary should "pull" light more strongly than its approaching twin. Since partial dragging also occurs at a distance from these surfaces where their gravitational influence is weaker, this same partial dragging ought to happen at the idealised surfaces of a conventional double-star system that has a similarly weaker gravitational influence. Although DeSitter [45] [46] and Brecher [47] have both used double-star observations to argue that the speed of light is wholly unaffected by the motion of the emitter, these calculations have been based on the assumption of flat space, and have assumed that any initial lightspeed differences between approaching and receding stars will produce a flight-time offset that multiplies linearly with the distance of the star, over astronomically-large distances. In our revised model, the initial supposed lightspeed difference only really applies to the regions of space where each emitter's own gravitational influence dominates the metric.

As a signal leaves the double-star system, not only does the influence of the emitter on the signal's speed become less significant, but the motion field-effects from both stars become progressively more merged. If the binary system is far enough to treat as a point-source, the root-product superimposition of the "approach" and "recession" field-components gives us an overall gravitational redshifting of the system due to velocity of [(c­v)/c × (c+v)/c]^1/2, or just (1­v²/c²)^1/2 . In other words, if we treat mass as a field effect and allow field strength to be altered by velocity according to equation (1) the crude superimposition of these two fields gives us the Lorentz relationship used by special relativity.

This argument ignores higher-order effects due to the slight difference in effective pathlength to the two stars. The associated timelags can make the system appear to be unbalanced around its true center of gravity, with the timing-discrepancy being more obvious when the two stars are at different distances to the observer. If the two velocity field-components add differently (due to timelags) at different parts of the orbital cycle, the system can show a periodic imbalance in observed mass (for a single observer). Mapping these observed-mass oscillations by observer-position leads to a map of gravitational waves thrown off by the double-star.

8.2. Spectral lines and atomic velocities within stars

Another objection to older emitter-theory models was that if individual emitting atoms in the stellar atmosphere showed complete dragging, their thermal motion would give rise to photons being thrown off with different speeds, giving rise to different transit times for Doppler-redshifted and Doppler-blueshifted light from the star. This would then cause a star moving across our field of view to have a rather "streaky" appearance, with a blueshifted leading edge (faster photons) and a redshifted tail (slower photons).

The reported absence of this effect (and the sharpness of spectral lines) has been taken as additional evidence against equation (1). However, the DMS model says that the photon's velocity is only dictated by its emitting atom at extremely small distances, and that a photon leaving a star quickly takes up a speed of c relative the averaged field of the star (the photon leaves the atom at c relative to the atom, but leaves the star at c relative to the star). Again, the motion field-components of the star's atoms merge to produce an overall (thermal) redshift component that relates to the star's internal kinetic energy.

8.3. Dark stars and Hawking radiation

Although emissions at r=2M cannot reach a remote stationary observer directly, some models based on equation (1) can allow signals to reach the observer indirectly, by interacting with particles outside the r=2M surface. Until recently, the notion of a super-dense object showing "dark-star"-like behaviour and emitting indirect radiation would have been considered to be quite misguided. However, in the early 1970's Hawking [49], Bekenstein [50] and others produced a quantum mechanical prediction of a similar-sounding form of indirect radiation, although the conflict with GR has led to this effect ("Hawking radiation") being described as a separate quantum effect with no classical counterpart. It may be significant that mis-application of GR to an "obsolete" dark star model can result in a similar description of pair-production outside the horizon [14].

We can now consider the "naive" question, "Does an object traveling at high speed turn into a black hole?". With GR, the answer must be "no", because the acquisition of a gravitational event horizon is associated with a real physical collapse that cannot be "undone" by a later change in the observer's relative velocity (this is one reason why modern physics tends to take "mass" to mean "rest mass"). In a DMS model, the object can appear to gain or lose an event horizon depending on whether the object is receding or approaching, but total collapse does not occur - total collapse is averted in a dark star model by indirect radiation-pressure, which under QM would have to be modeled as the pressure due to Hawking radiation within the r=2M surface. Whether a change of shift equation might really allow the complete equivalence of classical and quantum descriptions remains to be seen, since the initial enthusiasm for the black hole model championed by Wheeler (e.g. MTW [15], ch.33) appears to have discouraged work on alternatives. Although DMS allows a comparatively mundane explanation of Hawking radiation, the high cost of this explanation (replacement of a critical shift equation) means that this explanation is not likely to be well received unless experimental data demonstrates that equation (1) is more accurate than its SR counterpart.

9.1. Direct verification of the non-transverse velocity shift law

Direct verifications of the supposed superiority of (2) to (1) still seem to be missing from the literature, even though we would expect this difference to have testable consequences.

9.2. Direct verification of the gravity-shift relationship

9.3. Deflection of light-rays by a moving medium

Transverse dragging by a particulate medium appears to have been verified with spinning transparent disks [53], and circularly polarized light has been shown to exert a torque as it passes through a transparent plate [54].

9.4. Deflection of light by a moving mirrored surface

9.5. Two-stage non-transverse redshift