Henry H. Lindner
Abstract
Relativity, by its axioms, attempts only to
describe motion and the laws of motion as relative to any chosen
frame or observer. It is subjectivistic and limited to the
modeling of measurements. As a program it has had some utility. However, to explain Cosmic
phenomena, we must relate all motion to the space and matter of
this Cosmos. The phenomena imply that all matter affects space by
creating a field of sink or source flow in its surrounding space,
a field that is entrained with matter into its own inertial
motion. This hypothesis exposes a new equivalence
of gravitational and inertial velocity. The consumption and/or
production space by matter is the simplest explanation of the
interaction of matter and space. It fits the known evidence,
produces no paradoxes, unifies our understanding of the effects
of motion and of gravity, and makes new and significant
predictions.
Key words: aberration, absolute space, atomic clocks, black holes, Einstein, entrainment, escape velocity, ether, gravity, inertia, light, matter, motion, Newton, principle of equivalence, Relativity, space, space-time, time
1. Cosmology and Relativity
Albert Einstein's General Relativity (GR) is the basis of modern Cosmology. Is it an appropriate foundation for this science? Cosmology, by it nature, models the physical Cosmos and attempts to understand its fundamental physical entities and processes. Relativity, on the other hand, does neither of these. Relativity incorporated the subjectivism, empiricism and positivism of Berkeley, Hume, and Mach, respectively. Einstein adopted their limitation of science to "methodical thinking directed toward finding regulative connections between our sensual experiences."1 He sought only to comprehend "the connection between sense experiences...by the use of a minimum of primary concepts and relations."2
This limited view of science is evident in the axiomatic structure of Relativity. Einstein chose Galileo's principle of relativity as the foundation of his approach to physics. This principle encompassed the fact that the rules of ballistics were similar for any observer moving parallel to the Earth's surface at (subluminal) constant velocity relative to the Earth's center. Einstein seized upon this ballistic phenomenon because it could be related to observers. He removed it from its physical context and made it the foundation of his program for all physics. His Special Relativity (SR) was defined by:
General Relativity (GR) broadened the scope of this program by attempting to relate the "laws of nature" to any frame, even that of a rotating, randomly accelerating reference "mollusc".4 Einstein's general principle of relativity asserted that: "All Gaussian co-ordinate systems are essentially equivalent for the formulation of the general laws of Nature." 5 GR retained SR's absolute c for every coordinate system (CS) or observer and the Lorentz transformations.
These axioms define a program for physics that has important limitations:
Now consider the use of
Relativity's space-time in Cosmology. Space-time in GR, as in SR,
is only a geometric model of the subjects' experiences and
measurements. It is incorrigibly anthropocentric. It does not
model an objective, observer-independent Cosmos, nor is it itself
a physical entity. It is an imaginary geometric solid composed of
the one thing that different observers can agree upon in
Relativity's measurement scheme--their own measured space-time
intervals between observed events. The interval is created by
each observer using his own "proper" rods and clocks, supposedly
unaffected by any velocity in any physical Cosmos, and each
assuming that light moves at c relative to himself. Time,
the observer's clock-reading, is represented by an imaginary
fourth spatial axis. What is the physical meaning of this
"interval" of which the space-time of modern Cosmology
is constructed? What physical entity or process does it
represent? Einstein admitted that the chronotropic interval, 
, had no physical meaning or significance.7 While the space-time model may
have some utility for the prediction of the some of the
observer's measurements, it is not a proper foundation for
Cosmological theory. (From the standpoint of any physical theory
of space, the space-time model works as well as it does because
the observer's proper time acts as a surrogate measure of his
velocity in the physical space of this Cosmos--the greater his
velocity in space, the slower his clock and the shorter his
rods.)
One cannot reconstruct a physical Cosmos from uninterpreted measurements. The Cosmologists' use of this subjectivistic science to model and explain Cosmic phenomena creates only confusion. Cosmologists use subjectivistic space-time objectivistically--attaching it only to the celestial bodies (the distribution of mass) of this Cosmos, not to any chosen observer. They treat space-time as a kind of physical substance that can be inflated, warped, waved, wormholed, and whirled. They explain gravity as "caused" by the warping of space-time, when this is, at best, merely a description of gravity's effects on the observer's measurements. They dismiss the existence of physical space (ether), but in order to explain the phenomena they are forced to posit dark matter, dark energy, virtual particles, strings, hidden dimensions, quintessence, etc.--all of which ascribe physical properties to "empty" space.
Einstein himself never resolved the incompatibility of his method with his instinctive belief in a physical Cosmos and physical causation. As soon as turned his attention from SR to the modeling of real motion in real gravitational space, he realized that the facts of mechanics and electromagnetism required the hypothesis that space was a physical substance; that there was an ether.8,9 With this belated admission, he contradicted his previous denial of same and contradicted the conceptual foundation of his Relativity program. Clearly, if space is a physical substance that affects inertial, gravitational, and electromagnetic phenomena, then all motion including the velocity of light will be most simply related to it. If light travels at c in Cosmic space, then absolute c for every frame or observer must be interpreted as an illusion produced by a physical alteration of the observer's rods and clocks, as per Lorentz. If space is some substance, then the first task of theoretical physics is model it and investigate its role in all fundamental physical processes. Immobilized by the contradiction between his method and reality, Einstein simply evaded the entire issue. Not only did he refuse to theorize about space, he actually prohibited anyone from doing so, saying that we must not attempt to attribute parts or motion to the ether.10
Cosmology requires a working physical theory of Cosmic space and matter. It needs a truly theoretical physics, one that creates and criticizes theories about what exists and what causes the phenomena that we are able to observe and measure; one that relates motion to the space and matter in this Cosmos, not to any observer. In order to create such a foundation, let us begin by assuming the obvious: that the Cosmos is an evolving physical entity, that its space is a hitherto unknown substance, that time is the pace of Cosmic evolution, and that light moves at c in space, not in every observer's frame. Let us recall the lesson of the Copernican revolution: the frame that yields the simplest treatment of phenomena has unique physical reality until proven otherwise. Let us use all the data available to create a consistently objective theory of Cosmic matter, space, and motion.
2. Flowing Space
Isaac Newton speculated
that gravity was caused by a flow of ether, or space, into
celestial bodies. He discussed this theory in letters to
Oldenburg, Halley, and Boyle.11 For various reasons, he declined
to present this hypothesis in the Principia. He instead
posited the existence of a universal, isotropic, immobile,
"absolute space" that resisted matter's acceleration
but was not itself affected by matter. He asserted that all
matter had some definite velocity in
this space, even if it could not be determined.12 Newton did not know, of course,
that an atom's velocity relative to, and its proximity to a
celestial body produced a spectral red-shift. Newton also did not
know that light had a fixed velocity in space that was
independent of its source's velocity or that matter's velocity
was limited to < c. Had he known these things, he might
have been able to develop the flowing space hypothesis as we
shall do here.
As it happened, Newton produced an inadequate model of Cosmic space. For one thing, it did not explain free-fall in a gravitational field. Newton's gravity was an occult force acting in absolute space. If gravity were like any other impressed force, then an object in free-fall, forced to accelerate toward a gravitational attractor, should "feel" its acceleration relative to absolute space, its accelerometer should record an acceleration. This is not the case. In free fall toward any gravitational attractor, an accelerometer reads "zero". This deficiency in Newton's theory can be easily removed if we allow matter to create gravity by affecting its surrounding inertial space in a certain way.
2.1 The Equivalence of Gravitational and Inertial Acceleration
Einstein removed this deficiency in Newton's theory, but only by modeling what falling and accelerating observers would experience. He realized that being held stationary in a gravitational field (as on the Earth's surface) had similar effects on one's sensations and measurements as being accelerated in deep space by a rocket (at 9.8 m/s2). He reached the conclusion that gravity is an accelerational field, not a force. Thus he formulated his principle of the equivalence of gravitational and inertial acceleration (EGIA). Using his subjectivistic method, Einstein was able to predict other effects of gravity, but failed to draw the objective and physical implications of the EGIA.
We shall assume that
gravity is a physical process caused by matter's interaction with
its surrounding space. If we treat inertial space as a physical
entity and presume that like physical effects result from like
physical causes, we can get beyond the observer's experiences to
the physical reality. We can relate Einstein's EGIA to physical
space with a simple conjecture: A frame is inertial if it is
not accelerating relative to its surrounding inertial space.
We thus infer that the accelerating space ship and the
Earth-surface observer are not inertial frames because both
are in a state of acceleration relative to their surrounding
inertial space; neither being free to return to the natural
state of non-acceleration relative to space. It thus appears that
in a gravitational field, inertial space itself is
accelerating towards the gravitational attractor. Indeed, an
inertial space that accelerates radially towards all matter at 
explains the ballistic and mechanical aspects
of gravity. We have used Einstein's subjectivistic insights to
improve Newton's objectivistic theory--transforming his absolute
space from a uniform solid into a fluid that everywhere flows
into matter as into a sink. (I relate spatial flow only to matter
because we have no convincing evidence that light,
electromagnetic charge, pressure, or any other form of motion
causes gravity.) Can this simple hypothesis explain the other
effects of gravity that Einstein modeled--the red-shift of atomic
spectra, black holes, and the curvature of light? If so, can it
possibly be mere coincidence?
2.3 The Equivalence of Gravitational and Inertial Velocity
If inertial space flows
into the Earth, and all matter, as a fluid into a sink, then it
must have not only an acceleration at any given radial distance, r,
but also a determinate velocity. Its velocity at the Earth's
surface ought to be the sum of its total acceleration from rest
at infinite distance to the Earth's surface. This velocity must
be identical to Newton's escape velocity--the initial velocity
that allows any object on the surface of a large mass to escape
the mass's entire accelerational field. Thus at the Earth's
surface, space should be moving radially Earthward at 
, or 11.2km/s. The velocity of this inflowing space
at any r, outside any mass, M, should be:
.
(Interestingly, these equations of spatial flow indicate that space is not an ideal fluid but appears to be compressible.13 Its flow towards matter is accompanied by a partial compression or collapse. Note also that spatial outflow from matter, with an accompanying spatial expansion, could produce identical velocity and acceleration gradients and therefore could be the cause of the gravity of some or all celestial bodies.)
If, as the evidence suggests, it is velocity in a physical space related to nearby matter, not merely relative velocity, that red-shifts atomic spectra and slows atomic clocks, then an atomic clock held stationary at any given height in a gravitational field should be affected by the velocity of the inflowing space and should slow just as if it were moving at the escape velocity for that height. This is indeed the case. The experimentally confirmed formula for the gravitational slowing of atomic clocks is:
.
Since 
in our model of the velocity of the gravitational
space flow, the gravitational red-shift formula is identical to
that for the 2o or transverse Doppler shift
produced by velocity:
.
Thus the expected velocity of space at any given height in a gravitational field correctly predicts the slowing of atomic clocks at that height. We have thus derived the formula for the gravitational red-shift from the simplest possible physical hypothesis and produced a physical link between the mechanical effects of gravity and its effects on atomic spectra--the former is due to the acceleration of space, the latter to its velocity. The Lorentz transformations and the EGIA are hereby related to an objective matter-influenced Cosmic space instead of to arbitrary coordinate systems. We have unified 2o Doppler shifting by velocity and by gravity; revealing that both are caused by the velocity of the atom relative to its surrounding space. This simple physical model is consistent with all the clock-slowing evidence. We have thus exposed a new principle of the equivalence of gravitational and inertial velocity (EGIV). This principle was not exposed by, and cannot explained within Relativity. (Appendix A) Combining the two equivalence principles yields a new principle of the equivalence of gravitational and inertial acceleration and velocity (EGIAV). This principle reflects our finding that a body's acceleration and velocity relative to its surrounding space produce their respective physical effects, whether the body's motion in space results from a radial gravitational space flow or from its tangential movement in that flow, or from a combination of the two.
Consider the simplicity
with which this theory predicts and explains the existence of
black holes. If the space velocity into the surface of a massive
body is 
c, and if light propagates
through space at c, then light cannot escape the body. The
Schwarzschild radius14, 
, is produced by solving the
escape velocity formula (1) for r, and setting the
space inflow velocity equal to c:
.
This derivation is far
simpler than Schwarzschild's, follows from a simple physical
postulate, and produces predictions not found in Relativity (see
below). It does not require four-dimensional space-time. It
implies no mathematical singularities, nor loss of information,
nor wormholes, nor other universes; only a conglomeration of
matter so massive and compact that light cannot propagate out
through the space that is flowing inward at 
c. The more massive and compact the black
hole, the greater the inflow velocity at its surface; it could be
2c or more. Whether or not such a superluminal black hole
would be stable is another matter.
Can this theory reproduce the other successful predictions of Einstein's General Relativity? After I had formulated this theory independently and attempted to publish it several times, I was informed by a colleague15 that Herbert Ives and Robert Kirkwood had published advanced mathematical treatments of the flowing space hypothesis in mainstream, peer-reviewed journals between 1939 and 1954. Herbert Ives demonstrated that if an object in a gravitational field were affected as if it had the escape velocity for that height--if its frequency were red-shifted, if it were shortened in the vertical direction, and if its effective mass were increased--then the successful predictions of GR were produced with greater simplicity, including gravitational lensing, the gravitational red-shift, and the advance of Mercury's perihelion.16,17 Whereas Ives considered these effects to occur in an isotropic Newtonian and Lorentzian space, Robert Kirkwood posited a physical space that actually flowed towards matter.18,19
Recently, Tom Martin has
demonstrated that, for an isolated gravitational attractor, a
Galilean frame with a spatial inflow or outflow of speed w =
gives all of the correct General Relativistic
physical effects usually associated with the static and curved
space-time Schwarzschild solution. He has also suggested tests
which would easily distinguish between the usual curved
space-time solution of Schwarzschild and the
General-Relativistically-valid flowing space solution in the
region of the gravitational saddle point of the Sun and Earth and
at other parts of the boundary between the solar and terrestrial
flows.20,21,22
This paper adds to the above works by presenting the flowing space theory as a program which is philosophically superior to Relativity, by discussing the entrainment of space which it implies, and by suggesting several other tests that could further distinguish it from Relativity and from other objectivistic theories of space, time, and gravity.
2.3 The Entrainment of Space by Matter
If indeed matter is a space sink, how would it affect the motion of its surrounding space as it moved through it? We would expect that a large, powerful sink, like the Earth, would create a large field of uniform sink flow in its surrounding space. This effect would be all the more pronounced if space were a massless and frictionless fluid, as seems most likely given the minimal resistance it poses to matter at subluminal velocities. Were the Earth's field of flow not uniform, then the inflow velocity into the leading surface of the Earth might be greater by 30km/s than the inflow velocity at the trailing surface--there would be an "ether wind". Such a diurnal/locational variation in the behavior of spectra, light, and atomic clock rates has not been observed. Sink flow is a sufficient explanation for the space-drag first propounded by Stokes23 to explain the null Michelson-Morley experiment. Indeed, the data from all sources, including our extensive experience with satellites, can be most simply interpreted as indicating that our Earth completely determines the motion of its surrounding space for many hundreds of kilometers out, sweeping it along with it into its 30km/s freefall motion through the larger volume of space that is entrained by our Sun and Solar system. An Earth satellite thus is moving through an Earth-centered radially-oriented field of sink flow. It accelerates toward the Earth with this flow, and its atomic clock is slowed by its tangential and radial space velocities. This entrainment must diminish with increasing distance from the Earth in a manner which is susceptible to mathematical modeling.
While the Earth sweeps its surrounding gravitating space into its inertial motion about the Sun, it clearly does not sweep space into its own rotation to any significant degree. There is irrefutable evidence of several kinds that the inflowing space is not significantly dragged into rotation with the Earth: the Coriolis effect, the rotation of the Foucault pendulum, the Cosmic-directional stability of gyroscopes, the Michelson-Gale experiment,24 and the east-west asymmetry in the slowing of moving atomic clocks.25 Therefore, for an Earth-surface observer, light travels at c-vrot in the easterly direction, and at c+vrot in the westerly direction. This rotational space drift (464m/s at the equator) was apparently detected by the Brillet and Hall interferometer,26, 27 casting doubt on the physical reality of the Fitzgerald length contraction. Experiments in which light signals take different times to travel around the Earth in opposite directions28 are also consistent with this rotational space wind.
Why would the Earth entrain space into its inertial motion but not into its rotation? Inflow requires only a medium under pressure so that it moves into any region of lower pressure--as where the medium is losing volume or being removed. For the rotation of the Earth-sink to cause a rotation of the surrounding space, space would also require significant internal friction and sheer strength. Space, however, appears to be essentially frictionless, as matter can move through it with very little resistance--at least at subluminal velocities. Thus only the position and relative motion of celestial bodies should affect the motion of their surrounding space; their rotation should have little, if any effect.
Because of entrainment, the Earth appears to be stationary but rotating to us and to our instruments. It and its surrounding field of sink flow are moving within the larger sink or source-flow field of our Sun. Our Solar system's entrained field flow is moving within that of the Milky Way, and the Milky Way with its entrained space is moving in the entrained space of the surrounding galaxies. Entrainment thus explains how all the matter in the Cosmos influences both the Cosmic and the local inertial and luminiferous "frame", it provides a physical explanation for Mach's Principle. It is because of entrainment that all motion is most simply treated in the frame of the nearby celestial mass or masses and not in any observer's frame whatsoever. It is because of entrainment that the twin who remains at rest relative to the nearby celestial body(ies) has a lesser space velocity and faster clock than the twin who is in tangential motion relative to same. It is because of entrainment that the clocks aboard Earth satellites are slowed by their orbital motion and not the Earth-surface clocks, even though the clocks' motions, like the twins' motions, are symmetrical in each others' frames. A physical space that flows toward or away from matter and is entrained by matter correctly "breaks the symmetry" of any two frames' merely relative motion; it explains the phenomena and eliminates Relativity's paradoxes.
The entrainment of space offers a solution to a vexing problem in astrophysics. Galaxies are spinning much faster than they should, given their visible matter. As Cosmologists must work with Relativity and Quantum Theory, and therefore lack any coherent theory of Cosmic space, they have had to posit the existence of invisible particles to provide the missing mass that keeps the galaxy's stars from flying apart. However, with entrainment of a large region of space by each star, much of the space of the galaxy must be dragged into rotation about the galaxial center. Thus, relative to the surrounding galaxies, a galaxy's local inertial "frame" should rotate in the direction of its stars' motion, at a net angular velocity that is less than that of the stars themselves. The result is that the actual velocity of the stars in their own local inertial space is less than it appears. Galaxies are spatial vortices; their spiral shapes could be explained by the presence of a black hole or other immense gravitational attractor in the center of the stellar vortex.
Some have argued that the Earth cannot be entraining its surrounding space as that would eliminate stellar aberration for the Earth observer. Such arguments have never addressed the radially inflowing and entrained space of this theory. As for aberration, it is Relativity which is inconsistent with the facts. (Appendix B)
3. Testing Flowing Space
I have demonstrated that Relativity is only an observer-based measurement scheme, it does not model the Cosmos nor can it theorize about the causes of physical phenomena. Relativity is not a direct competitor to this or to any other objective and physical theory of Cosmic phenomena, it is an altogether different program. The flowing space theory offered by Ives, Kirkwood, Martin, and myself can only be tested against other objective theories of Cosmic space and motion. In addition, Relativity has become essentially non-falsifiable as Relativists have shown a willingness to "save the appearances" by applying the Lorentz transformations in ways that contradict Relativity's axioms, i.e. by surreptitiously invoking a third (Cosmic) frame to "break the symmetry" of the twins' motions in each others' frames, by placing observers in specific frames that yield the correct answer, etc.
With the entrainment of space that it implies, this theory constitutes a working objective model of space and motion encompassing the entire Cosmos. It specifies the velocity and acceleration of space at any point near any celestial body, and thus at any location or in any chosen frame anywhere in the Cosmos. Assuming that light is propagated at c in space, and that atomic clocks and atomic spectra are red-shifted by their motion in space, this theory specifies the behavior of light and atomic clocks at any point, and in any state of motion near a gravitating body. It specifies the actual spatial velocity of any atomic clock. It is both rich in predictions and falsifiable.
3.1 Testing Flowing Space vs. Static Space(-time)
Flowing Space makes many predictions not found in any static-space model, such as Newton's absolute space, Lorentz's luminiferous space, or Einstein's static space-time. Consider the many immediate implications of spatial flow into or out of matter:
1. Light rising away from the Earth's surface, against an Earthward spatial flow, will move at approximately c-11.2km/s relative to the Earth's surface. Likewise, light falling downwards towards the Earth will move at c+11.2km/s. All celestial bodies should produce a corresponding anisotropy that Relativity does not predict. This effect is difficult to measure locally using atomic clocks due to the well-known problem of synchronizing clocks using the very signal whose velocity one is trying to determine. This fact does not imply, however, that it is a priori impossible to detect any light velocity anisotropy. The use of astronomical data might circumvent the clock-synchronization problem. We might find evidence of this anisotropy in the behavior of light or particles moving towards or away from a celestial body.
2. Matter may be
observed falling into celestial bodies at velocities greater than
c (relative to the sink). In the case of a black hole, the
velocity may exceed 2c. Tom Martin has demonstrated that
spatial sources would produce gravitational effects that are
identical to those of spatial sinks.29 It is thus possible that stars
and even entire galaxies are spatial sources. Astronomical
observations may detect light or matter moving away from space
sources at velocities 
c. Relativity
excludes velocities > or < c in any frame.
3. A one-way light speedometer30, if feasible, could directly detect the gravitational 11.2km/s space wind, and all other velocity relative to space.
4. This theory with its Earth-entrained space does not require the Fitzgerald length contraction to explain the null Michelson-Morley experiment. If the length contraction is not a physical reality, then an interferometer mounted vertically on the Earth's surface will produce a fringe-shift consistent with the gravitational 11.2km/s space wind. Likewise, an interferometer orbiting the Earth will produce a fringe-shift consistent with its velocity in Earth-entrained space.
5. Actual light round-trip travel time experiments between any two points on the Earth's surface in vacuo will show light moving slower than true space-c due to its propagation through the vertical 11.2km/s space flow. Perhaps this small discrepancy is already apparent in the different values of c produced by Earth-surface vs. astronomical methods.
6. A spreading sphere of
light from an Earth-surface source will be displaced Earthward by
the 11.2km/s flow. On the Earth's surface, any light emitted
should drop 0.112m over a 3km distance (11.2km/s space velocity 
3
105 km/s light velocity in space). This local
velocity effect is not a curvature but only linear
displacement--as in the downstream displacement of the waves
produced when a pebble is tossed into a flowing stream. To detect
this effect will require ingenuity as both source and observer on
the Earth's surface have identical velocities in the space flow.
For the observer, the propagating light's downward displacement
is countered by upward aberration due his own upward velocity in
the medium, so the apparent vertical position of the source is
not altered. Neither will lasers work to expose this effect. A
horizontally-mounted laser, because of its construction, can only
emit a beam of light that does travel horizontally. In the frame
of an inflowing space, the same beam is directed upwards at an
angle of 3.73
10-5 radians. Perhaps the displacement may be
detected on Earth if one places two light detectors in a vertical
line at some distance above and below the horizontal level of a
light source. As light propagates spherically from the source,
its downward displacement will cause it to reach the lower
detector first. The matter-ward displacement of light may be
evident astronomically, but such an analysis requires also
sorting out the various spatial flow and/or compression effects
which combine to produce gravitational lensing.
7. In Relativity, the rate of an atomic clock in motion in the Earth's gravitational field is produced by calculating the gravitational red-shift at that height, and adding a "time dilation" factor for the clock's velocity relative to the Earth-observer. The flowing space theory produces the same predictions as Relativity for clocks orbiting the Earth or rising against the space flow, as the gravitational red-shift and the time-dilation red-shift are additive. However, it predicts that radially falling clocks will run faster than predicted by Relativity as they are moving in the same direction as space itself. Time-dilation will be replaced by time contraction. An atomic clock falling radially towards the Earth with the same velocity as space at that r, the escape velocity, will be at rest in space and will run at the fastest rate. The Vessot rocket experiment31 involved a rising and falling clock, but it was not designed to distinguish between Relativity and flowing space. It was a complex experiment using radio signals and was based entirely on Relativistic assumptions. Its results should be thoroughly reevaluated in the light of this theory. It may be necessary to perform simpler experiments, such as firing a clock downward from a high altitude and recovering it at sea. Its elapsed time will be greater than predicted by Relativity.
8. Muons rising against the space inflow with at near-c relative to the Earth will persist longer than muons falling with the same Earth-velocity since the rising muons' space velocity is actually v+11.2km/s compared with v-11.2km/s for the falling muons.
9. At the boundary between the space-flows of two bodies, such as that between the Earth and Sun, there will be anomalous atomic clock-slowing and accelerational effects which are not predicted by the static solutions of the field equations of General Relativity.32,33,34 These can be detected by observing the motion and atomic-clock rate of a satellite which passes through the boundary.
3.2 Testing Entrainment vs. Non-entrainment
Entrainment not only explains the phenomena without paradoxes, it also provides additional tests to distinguish this theory from others. Relativity cannot include entrainment since it treats all motion as only relative to any chosen coordinate system. To admit entrainment is to admit a physical space that is swept into motion by nearby matter thus creating a unique local environment or frame. Clear evidence for entrainment ought to be sufficient to cause even Relativists to doubt the utility of their program.
1. With entrainment of space by all large celestial bodies, the relative slowing of atomic clocks or atomic spectra on their different surfaces will be predicted by their individual spatial inflow velocities only. The relative motion of celestial bodies will not produce any additional 2o Doppler slowing as such motion will produce no space-wind for clocks on either surface. For instance, a clock on the Earth's surface is slowed by an 11.2km/s gravitational space flow and a clock on the Sun's surface by a 617km/s space flow. With entrainment, the observed spectra will reflect this difference only (having factored out the 1o Doppler effect). With entrainment, waves emitted by identical sources on the surfaces of the Sun and Earth should have periods differing by
,
where v is the spatial inflow velocity. This is indeed what the data appear to show35 and, surprisingly, this is how the data are treated in the Relativists' own textbooks.36, 37
However, this treatment
is incompatible with Relativity. Relativity, which must include
all relative motions, must assert that the Earth-surface clock is
slowed not only by the Earth's gravitational red-shift but also
by its 30km/s orbital velocity relative to the Sun-surface clock,
and by the Sun's own gravitational red-shift at the Earth's
distance (a 42km/s space wind). In Relativity, without
entrainment of space by the Earth, the Earth clock should show
the same additional slowing that one would see in an atomic clock
on a man-made satellite orbiting the Sun at the Earth's distance.
A Relativistic treatment, where 
is the
gravitational potential, 
, with units 
, corresponding to ½
, half of the
square of the space velocity in this theory, should predict:
.
Relativity, and physical theories without entrainment, must predict a larger Earth-clock red-shift, and therefore a smaller difference between the periods of the two clocks than does this entrained-space theory. Unfortunately, the Sun's spectral red-shift is too difficult to determine with sufficient accuracy due to the rising and falling of emitters on the Sun's surface. Hopefully, other tests will be possible using spectra or clocks on other planets or on probes in orbit about other planets. To support entrainment, one need only to find that the relative velocity of the star, planet, or galaxy and Earth is not reflected in the observed spectral shift of their atoms. As a galaxy should entrain a large region of surrounding space, its motion away from the Earth should produce only a 1o Doppler red-shift of its spectra and not a 2o Doppler red-shift (there should be no galaxial time-dilation).
2. The existence of galaxial vortices due to entrainment of space by stars can be tested. For instance, we may be able, on Earth, to detect whether our local galaxial inertial frame, the Milky Way, is indeed rotating with respect to the surrounding galaxies in the direction of stellar motion.
4. Conclusion
Relativity did not eliminate the ether or physical space from physics, it only forbade us to think about it. It is time for us to return to studying space and motion objectively, as related to and affected by the distribution of matter in the Cosmos. This flowing space theory is a step in this direction and is firmly grounded in the evidence and in the successful insights of Newton and Einstein. It explains the phenomena in the simplest possible manner and produces no paradoxes. It provides a physical theory of gravity's effects and unifies our understanding of 2o Doppler red-shifting by gravity and by velocity. It produces the successful predictions of General Relativity with greater simplicity, and also makes many other predictions that can be tested.
Of course, any theory of physical space and motion raises innumerable difficult questions, as it goes beyond the mere mathematical description of measurements and attempts to explain the causes of all physical phenomena. It reopens a book of nature that has been closed for 96 years. I have found that flowing space theory invites many fascinating and fruitful conjectures on the physical causes of many phenomena that are currently unexplained, including the nuclear "strong force", the 2o Doppler shift, Cosmic inflation, galaxial recession, atomic blasts, geothermal heat, gravity waves, electrons, neutrinos, and light.38 Even if some aspects of this theory prove incorrect, we must not again default to merely modeling our measurements. We must persist in our attempts to model Cosmic space and motion and to explain the causes of all phenomena.
Appendix A:
Relativity and the Equivalence of Gravitational and Inertial
Velocity
Can Relativists "explain" the equivalence of
gravitational and inertial and velocity (EGIV) within their own
system, without the flowing space hypothesis? They cannot. Some
Relativists have, in fact, simply dismissed the evidence for this
equivalence as a fortuitous coincidence;39 against which assertion the
theory here presented is sufficient argument. A previous reviewer
claimed that the EGIV is merely a consequence of the
observer-based equivalence of gravitational and inertial
acceleration (EGIA) and does not require the flowing space
hypothesis. He argued that an observer falling toward the Earth
from an infinite distance (in vacuo) would accelerate to a
velocity of 11.2km/s at the Earth's surface; and thus to him a
clock on the Earth's surface would appear slowed when he passed
by it. This is the typical Relativist's technique of ignoring the
physical reality of any local spatial frame by placing an
observer in that frame and modeling what that observer measures.
I will show that this observer-based rationalization does not
follow from Einstein's EGIA, contradicts SR, and again exposes
the ambiguity of Relativity. The EGIV has not been noticed or
seriously discussed until this time precisely because it cannot
be understood within Relativity. Consider that:
1. The Relativists must assert that the physical effect of the mass of the Earth on the rate of an atomic clock is "explained" by inventing an observer, letting him fall towards the Earth, and speculating on what he would "see". This is their subjectivistic method. On the contrary, atomic clock-slowing on the Earth's surface is, in fact, evident to the Earth-surface observer, even though he is not in free-fall and has no velocity relative to the clock. He can put a clock on a high tower for some time, bring it back down, and find that it ran faster than his Earth-surface clock; even though both clocks remained at rest relative to himself. This fact alone demonstrates the objective and physical nature of this effect and exposes the complete artificiality of trying to "explain" gravitational clock-slowing using falling observers.
2. Is this "falling observer" rationalization legitimate within Relativity? The EGIA only applies to frames in which an accelerometer detects acceleration. The EGIA asserts only that inertial and gravitational acceleration "feel" the same and produce the same effects on the observer's local experiments. But the observer to which the Relativists appeal here is in free-fall. His accelerometer measures no acceleration, he is not in an accelerated "frame". The fact that the free-fall observer is accelerating relative to the clocks and the Earth even though he feels no acceleration is an objective effect of the Earth's gravity and must be explained as such, as it is in this theory.
3. We know that inertial acceleration does not slow atomic clocks, whereas gravity and velocity do. The EGIA alone thus cannot explain gravitational clock-slowing. Since any velocity can be associated with any acceleration, the association of this particular velocity with this free-fall observer requires an additional assumption that stipulates the velocity and thus violates the strong version of the EGIA. Flowing space predicts this velocity on the basis of a physical model of gravity. The Relativists, as is their wont, simply create an observer whose observations will fit the data at hand, without proper regard to the causes of things.
4. Relativists apply the Lorentz transformations to this observer's velocity to explain the slowing of the clocks. But SR, the subjectivistic (observer/frame-based) interpretation of the Lorentz transformations, does not provide the needed velocity assumption. SR does not treat gravity or acceleration and thus did not predict and cannot explain why gravity produces this apparent velocity. The only link that Einstein made between SR, acceleration, and velocity in his presentations of GR was his thought experiment involving the slowing of clocks due to their velocity on the periphery of a rotating disc,40 and this has no relevance to the relationship between gravity and velocity discussed here.
5. The appeal to SR creates another problem for the Relativists. According to SR, the Earth-surface clock would appear to be slowed to the required rate only for the observer who falls from infinity. The same clock should appear to be slowed less for an observer who falls from a lower height and has a lesser velocity. To invoke SR here is to abandon the equivalence principle of SR: the doctrine that SR is valid in every freely falling frame. Relativists would need to posit that SR is actually valid only in the unique frame that falls from infinity and whose velocity at every point outside a mass equals the escape velocity--which is indeed an implication of the theory presented here.
I conclude that the EGIV
that was predicted and explained by this theory was not predicted
and cannot be explained within Relativity by appeal to observers
using the EGIA and/or SR. Atomic clock-slowing by gravity is a
physical reality that must be related to space as it is affected
by nearby mass. How Einstein predicted the escape velocity
formula for the gravitational red-shift using his subjectivistic
method I do not know, this is a matter for mathematicians and
historians. I have demonstrated that the simplest explanation for
this phenomenon is that mass causes its surrounding space to flow
towards it, attaining a velocity of 
relative to any
stationary atomic clock at any given r.
Appendix B:
Aberration, Flowing Space, and Relativity
In Relativity, aberration must be due only to the relative
motion of source and observer. Stark's experiment refutes this
claim.41 In this experiment, the direction of
light arriving from stationary and high-velocity moving atoms at
the same location was identical. The data from the aberration of
individual stars in a binary system is also refutes Relativity.42, 43 The stars' aberration does not
vary with the stars' velocity relative to the Earth, i.e. when
they're moving with or against the Earth's motion. These data
instead support the theory that space is the physical medium of
light transmission. In such a space, aberration is produced only
by the observer's velocity in the luminiferous medium; not by the
source's velocity in the medium. Specifically, in this
entrained-space theory, annual stellar aberration is caused by
the Earth and its entrained space's nearly circular motion within
the larger entrained space of the Sun and surrounding stars. Some
have argued that an Earth-entrained space would eliminate stellar
aberration. I cannot see how the kinematic effect of the motion
of the Earth on the apparent position of a distant star can be
eliminated by a radially flowing entrained space unless the
Earth's entrained space were to rotate in the precise direction
needed to eliminate the aberration. In fact, all the evidence
indicates that the Earth's space does not rotate relative to the
space of our Sun and surrounding stars. In aberration, the
difference between an unentrained vs. an entrained physical space
is that with entrainment the change in the apparent direction of
the starlight is produced not at the Earth-surface observer, as
in an absolute or unentrained-space theory, but at the interface
of the inflowing Earth-entrained space with the Sun-entrained
space. An observer at great distance would see the starlight bend
as it propagates from the interstellar and Solar space into the
(moving) entrained space of the Earth. This matter certainly
bears further investigation both in the laboratory and
astronomically.
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