Flowing Space

Henry H. Lindner

Example HR

Abstract
A simple theory of Cosmic space and motion explains the experimental results, unifies our understanding of the effects of motion and of gravity, produces no paradoxes, and makes more predictions than Relativity.

Key words: absolute space, atomic clocks, black holes, entrainment, gravity, inertia, light, mass, motion, paradoxes, principle of equivalence, Relativity, space, time

For an analytical/mathematical discussion of the Flowing Space theory, see Tom Martin's General Relativity and Spatial Flows

For additional articles about this theory and about the Relativity and Quantum Theory in general, see the links on my Home page.

1. Flowing Space

1.1 The Equivalence of Gravitational and Inertial Acceleration

Newton did not adequately explain gravity. He posited that it was an occult force acting in an isotropic, immobile, inertial space. This space constituted a single, unique Cosmic frame which resisted any acceleration of matter, and was not affected by the presence of matter. However, if gravity were like any other impressed force, then an object in free-fall, forced to accelerate toward a gravitational attractor, would "feel" its acceleration relative to absolute space. This is not the case. A body in free-fall feels no acceleration, and therefore cannot be accelerating relative to the surrounding inertial space. In a gravitational field, it appears that inertial space itself is accelerating towards the gravitational attractor.

Einstein developed this insight, treating gravity as an accelerational field. He realized that being held stationary in a gravitational field (as on the Earth's surface) had the same effects on one's measurements as being accelerated in deep space by a rocket (at 9.8 m/s²). Thus he formulated his principle of equivalence of gravitational and inertial acceleration (EGIA). However, Einstein analyzed gravity and its effects subjectivistically, placing observers in accelerated states or in free fall relative to other observers and considering how their measurements would differ. He thus failed to see the objective and physical implications of the EGIA. Let us instead treat space as a physical entity and presume that like effects result from like causes. Let us presume that the accelerating space ship and the Earth-surface observer are both 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. We therefore find that the EGIA implies 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, mechanical aspects of gravity. Thus we find that we can improve Newton's theory by transforming his absolute space from a solid to a liquid; allowing it to flow into matter like a fluid into a sink. Can such a "flowing" space also explain the other effects of gravity--such as the red shift of atomic spectra and the curvature of light? If so, can it be mere coincidence?

1.2 The Equivalence of Gravitational and Inertial Velocity

If inertial space flows into the Earth 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 velocityshould be identical to Newton's escape velocity--the initial velocity that allows any object on the surface of a large mass to escape that mass's gravitational field. Thus at the Earth's surface, space should be moving radially Earthward at , or 112km/s. The velocity of this inflowing space at any r, outside any mass, M, should be:

If, as the evidence suggests, it is velocity in physical space, 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 slow just as if it were moving at the escape velocity for that height. This is indeed the case. The accepted formula for the gravitational slowing of atomic clocks is:

Since in our model of gravitational space flow, the gravitational red shift formula is identical to that for the 2^o or transverse Doppler shift:

Thus the expected velocity of space at a 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 a simple physical hypothesis and produced a physical link between the mechanical effects of gravity and its effects on atomic spectra. We have unified 2^o Doppler shifting by velocity and by gravity; it always and only results from the velocity of the atom relative to its surrounding space. The Lorentz transformations and the EGIA are hereby related to an objective matter-influenced Cosmic space instead of to arbitrary coordinate systems. We have thus exposed a new principle of equivalence of gravitational and inertial velocity (EGIV). This principle was not exposed, and cannot explained by Relativity. (Appendix) Combining the two equivalence principles yields the new principle of the equivalence of gravitational and inertial acceleration and velocity (EGIAV). Gravity thus appears to be the flow of space itself towards matter.

This theory provides a physical model for black "holes". If the space velocity into the surface of a massive body is equal to or greater than c, and if light propagates through space at c, then light cannot escape the body. Thus the Schwarzschild radius,
, is produced by solving the escape velocity formula (1) for r,and setting the space inflow velocity equal to c:

This solution does not require a four-dimensional space-time. It implies no mathematical singularities, nor wormholes, nor other universes, nor time travel; only a conglomeration of matter so massive and compact that light cannot propagate out through the space that is flowing inward at velocities c. This derivation has the advantages of producing no absurdities, being far simpler than Schwarzschild's, and of following from a simple physical postulate.

Can this theory reproduce the other successful predictions of Einstein's General Relativity? Having formulated this theory independently and having thrice failed to publish it, I was informed by a colleague ¹ that Herbert Ives²^,³ and Robert Kirkwood⁴^,⁵ had published advanced mathematical aspects of the theory in mainstream, peer-reviewed journals from 1939 through 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 mass were increased--then the successful predictions of General Relativity would be reproduced with greater simplicity--including gravitational lensing, the gravitational red shift, and Mercury's perihelion. While Ives considered these effects to occur in an isotropic Newtonian/Lorentzian space, Robert Kirkwood posited an actual flowing ether. I am unable to judge whether their mathematical treatments are correct; but I know of no refutations of their work. Unfortunately, neither Ives nor Kirkwood offered any tests to distinguish their flowing space model from Special or General Relativity, nor did they investigate any further implications of the existence of such a physical space.

More recently, Tom Martin demonstrated that, for an isolated gravitational attractor, a Galilean frame with spatial inflow or outflow of w =gives all of the correct General Relativistic physical effects usually associated with the static and curved-space Schwarzschild solution. He also has suggested tests which would distinguish between usual curved space-time solution of Schwarzschild and the General Relativistically-valid flowing space solution in the region of the gravitational saddle point between the solar and terrestrial flows.⁶^,⁷

This paper adds to the above works by presenting the flowing space concept 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 distinguish it from Relativity.

1.3 The Entrainment of Space by Matter

If indeed matter is a space sink, how does matter affect the motion of surrounding space as it moves through it? If space is massless fluid, essentially frictionless at subluminal velocities, we would expect that the Earth, as a powerful sink, would create a large uniform field of sink flow in its surrounding space. The data indicate that this is the case. Otherwise, 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 a revolutionary "ether wind". Such a diurnal/locational variation in the behavior of spectra, light, or atomic clock rates has not been observed. The Earth indeed appears to entrain or drag its surrounding, inflowing space into its revolutionary motion. (Here we incorporate the space-drag propounded by Stokes ⁸ to explain the null Michelson-Morley experiment.) 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 the surrounding space for many kilometers out, sweeping it along with it into its 30km/s uniform motion through the larger volume of space that is entrained by our Sun and Solar system. Our galaxy, being a larger collection of matter, entrains a larger body of space. Thus the motion of space in any location in this Cosmos is determined by the distribution and motion of both nearby and distant matter.

While the Earth sweeps its gravitating space into its revolutionary inertial motion, 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,⁹ and the east-west asymmetry in the slowing of moving atomic clocks.¹⁰ Therefore, for an Earth-surface observer, light travels at c-v_rot in the easterly direction, and at c+v_rot in the westerly direction. This rotational space drift (464m/s at the equator) was directly measured by the Brillet and Hall interferometer,¹¹^,¹² casting doubt on the reality of the Fitzgerald length contraction. Various experiments in which light signals take different times to travel around the Earth in opposite directions¹³ are also consistent with a 464m/s rotational space wind at the Earth's equator.

Because of entrainment, the Earth appears to be stationary but rotating to us and to our instruments--even though it is moving in the entrained space of the Sun and the rest of the Cosmos. Entrainment explains how all the matter in the Cosmos influences the local inertial "frame", it provides the missing physical explanation of Mach's Principle. Entrainment explains the phenomena and eliminates the paradoxes of Relativity. The twin who remains at rest relative to the nearby celestial body(ies) has a lesser space velocity than the twin who is in motion relative to same; therefore the moving twin's clock runs slow.

2. Flowing Space vs. Relativity

This flowing space theory, with the entrainment of space which it implies, specifies the velocity of space at any point near a celestial body. 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 space velocity of any atomic clock. It can thus be compared to all known data and produces many predictions that are absent from current models.

2.1 Flowing space vs. General Relativity

Significantly, the EGIAV contradicts the strong version of Einstein's EGIA. It predicts that light does not move at c in any inertial frame--all free-falling laboratories will not produce the same experimental results since the results will be determined by the laboratory's velocity relative to the surrounding space, not merely by the state of free-fall as such. Flowing space with its EGIAV has greater predictive value than General Relativity.

1. Light rising away from the Earth's surface, against the space flow, should move at approximately c-11.2km/s relative to the Earth's surface. Likewise, light falling downwards towards the Earth should move at c+11.2km/s. Relativity does not predict this anistropy.

2. A one-way light speedometer ¹⁴ could directly detect the gravitational 11.2km/s space wind, and all other motion relative to space, which would concretely contradict Relativity.

3. This theory of an 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 should produce a fringe-shift consistent with the gravitational 11.2km/s space wind. An interferometer orbiting the Earth would produce a fringe-shift consistent with its velocity in Earth-entrained space.

4. Actual light round-trip travel time experiments between any two points on the Earth's surface in vacuo should show light moving slower than true space-c due to its propagation through the vertical 11.2km/s space flow. This is analogous to the transverse Doppler effect. Perhaps this discrepancy is already apparent in the different values of c produced by Earth-surface vs. astronomical methods.

5. A spreading sphere of light from an Earth-surface source should be displaced downwards 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 X 3x10⁵ km/s light velocity in space). This local 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 instance, the apparent vertical position of an Earth-surface light source to an Earth-surface observer is not altered since the light's downward displacement is countered by upward aberration due to the observer's upward velocity in the medium. 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 the inflowing space, the same beam is directed upwards at an angle of 3.73x10^-5 radians.

6. Matter may be observed astronomically falling into gravitators at velocities greater than c (relative to the sink). In the case of a black hole, the velocity may exceed 2c. Likewise, matter may be seen moving away from any space sources at velocities >c.Relativity excludes velocities > or < c in any frame.

7. In Relativity, the rate of an atomic clock in motion in the Earth's gravitational field is produced by calculating the gravitational redshift at that height, and adding a "time dilation" factor for the clock's velocity relative to the Earth. The flowing space theory produces the same predictions as Relativity for clocks rising against the space flow, but predicts that falling clocks will run faster than predicted by Relativity as they are moving in the same direction as space itself. 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 thus run at the fastest rate. The Vessot rocket experiment ¹⁵ appears to contradict this claim--it is the only experiment of which I am aware that appears to contradict any aspect of this theory. However, this experiment was not designed to test this theory vs. Relativity. It was very complex, and its design and interpretation were based entirely on Relativistic assumptions. Its results should be thoroughly reevaluated in the light of this theory. I also suggest that simpler experiments be performed, such as firing a clock downward from a high altitude and recovering it at sea. Its elapsed time should be greater than predicted by Relativity. The closer its velocity matches the velocity of the Earth's inflowing space, the faster it will run, and the greater will be the difference between this theory's and Relativity's predictions.

8. Muons rising against the space inflow with at near-c relative to the Earth should 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. Relativity predicts no such anisotropy.

9. In the boundary regions where there is interaction between the space-flows of two bodies, such as between the Earth and Sun, and at distances from bodies where entrained and non-entrained space interact, 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.¹⁶^,¹⁷ These could be detected by studying the motion and atomic-clock rate of a satellite which passes through the Earth-Sun gravitational saddle point.

2.2 Entrainment vs. Relativity

Entrainment provides an additional test to distinguish this theory from General Relativity (GR). Entrainment follows naturally from the basic postulates of this theory, but is incompatible with any Relativistic model which treats all motion as only relative to any chosen coordinate system. To admit entrainment is to admit a physical space which pulled into motion by nearby matter; one cannot do so and still claim to be a Relativist.

1. With entrainment of space by all large celestial bodies, the relative slowing of atomic clocks or atomic spectra on their different surfaces should be predicted by their individual space inflow velocities only. The relative motion of these bodies should not produce any additional slowing. For instance, a clock on the Earth's surface is slowed by an 11.2km/s space flow and a clock on the Sun's surface by a 617km/s space flow. With entrainment, the observed spectra should reflect this difference only. This is indeed what the data appear to show ¹⁸ and this is how the data are treated in textbooks.¹⁹^,²⁰ With entrainment, waves emitted by identical sources on the surfaces of the Sun and Earth would have periods differing by

However, this data and its treatment are incompatible with Relativity. Since Relativity treats only relative motion without entrainment, it must assert that the Earth-surface clock should be slowed not only by the gravitational red shift but also by its 30km/s orbital velocity relative to the Sun-surface clock, and by the Sun's own gravitational potential (flow velocity) at the Earth's distance (a 42km/s space wind). 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 truly Relativistic treatment, where is the gravitational potential with units , corresponding to half of the square of the space velocity in this theory, should predict:

Relativity thus must produce a larger prediction for the Earth-clock red shift, and therefore a smaller difference between the periods of the two clocks than does this entrained-space theory. The Sun's spectral red shift is difficult to determine with sufficient accuracy due to the rising and falling of emitters on the Sun's surface. Other tests may be possible using spectra or clocks on other planets or probes in orbit about other planets. We need only to find situations in which the relative velocity of the star or planet and Earth can be calculated and see if that velocity is reflected or not in the observed spectral shift of surface atoms.

3. Conclusion

Relativity is a philosophically flawed approach to physics. To make any sense of motion in this Cosmos we must admit that space is physical, and relate all motion to this space. We must remove the observer from the center of physics. I have demonstrated that a physical space which flows into matter is the simplest way to explain the phenomena. It provides a physical model of gravity and it unifies our understanding of the 2^o Doppler effect. It reproduces all the successful predictions of General Relativity and makes many other predictions that can be tested. That space is a substance is undeniable, but whether it flows into matter or not, only observation and experiment will tell. I am well aware that this theory raises innumerable questions, as it goes beyond the mere description of measurements and attempts to explain everything. I say that we should tackle these questions after we have tested the inflow hypothesis and found it to work. Regardless of the fate of this particular theory, the future of theoretical physics lies in creating and criticizing theories of what Cosmic space is and how it interacts with light and matter to produce the phenomena that we observe and measure.

Appendix: Relativity and the Equivalence of Gravitational and Inertial Velocity

Is it possible for Relativists to explain the equivalence of gravitational and inertial and velocity (EGIV) within their own system? Some Relativists have, in fact, simply dismissed the evidence for this equivalence as a fortuitous coincidence;²¹ against which assertion the theory here presented is sufficient argument. A previous reviewer instead 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 by this amount when he passed by it. I will show that this observer-based rationalization does not follow from Einstein's EGIA, contradicts SR, and exposes the subjectivistic, aphysical nature of Relativity. I will demonstrate that it is impossible to explain the EGIV from within Relativity; which is why it has remained unnoticed and undiscussed. Consider that:

1. The Relativists believe 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 the subjectivistic method. In contradiction to their method, 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, bring it back down, and find that it had been running faster than his Earth-surface clock; even though both clocks remained at rest relative to himself throughout the test period. This fact alone exposes the complete artificiality of trying to "explain" gravitational clock-slowing using falling observers.

2. Does this Relativistic rationalization "work" at all? 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 in order to explain the EGIV is in free-fall. He feels no acceleration and is thus not in an accelerated "frame". The EGIA only applies to accelerated frames. 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 in this theory.

3. We know that inertial acceleration does not slow atomic clocks, whereas gravity and velocity do. The EGIA is thus inadequate to 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 does so 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 their own ideology or 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 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 at any given r, neither does the EGIA provide this 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,²² 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 concede that SR is actually valid only in the unique frame which 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 produced the escape velocity formula for the gravitational red shift using his subjectivistic method I do not know. 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.

References

1 George Marklin in sci.physics.relativity
2 Herbert Ives, J. Opt. Soc. Am., 29, 183 (1939).
3 Herbert Ives, J. Opt. Soc. Am., 38, 413 (1947).
4 Robert Kirkwood, Phys. Rev., 92, 1557 (1953).
5 Robert Kirkwood, Phys. Rev., 95, 1051 (1954).
6 Tom Martin, Testing the Boundary Conditions of General Relativity Near the Earth-Sun Saddle Point, http://xxx.lanl.gov/abs/gr-qc/9806033.
7 Tom Martin, On the Motion of Free Material Test Particles in Arbitrary Spatial Flows, http://xxx.lanl.gov/abs/gr-qc/9807006.
8 Stokes, Phil. Mag, 27, p.9 (1845), 28, p. 76 (1846), 29, p.6 (1846).
9 A.A. Michelson, Astrophys. J. 61, 137; H.G. Gale, Astrophys. J. 61, 140 (1925)
10J.C. Hafele and R.F. Keating, Science 177, p. 166 (1972).
11 A. Brillet and J.L. Hall, Phys. Rev. Lett. 42, 549 (1979).
12 Harold Aspden, Physics Letters, 85A, 411 (1981).
13 W. Allan, M.A. Weiss, and N. Ashby, Science 228, 69 (1985).
14 Dale Means, Physics Essays, 5, 347 (1992).
15 R.F.C. Vessot, M.W. Levine, E.M Mattison, E.L. Blomberg, T.E. Hoffman, G.U. Nystrom, B.F. Farrel, R. Decher, P.B. Eby, C.R. Baugher, J.W. Watts, D.L. Teuber, and F.D.Wills, Phys. Rev. Lett., 45, 2081 (1980).
16 cf. 20.
17 cf. 21.
18 J. Brault, Bull. Am. Phys. Soc., 8, 28 (1963).
19 V. Fock, The Theory of Space, Time, and Gravitation (The Macmillan Co., New York, 1964) p. 187.
20 Steven Weinberg, Gravitation and Cosmology (John Wiley & Sons, Inc., New York, 1972) p.80.
21 Peter G. Bergmann, The Riddle of Gravitation (Dover Publications, Inc., New York, 1992) p.195.
22 cf. 14., p. 81.

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I have been motivated and encouraged in this effort by the philosophical ideas of Thales, Democritus, Aristotle, Epicurus, Francis Bacon, Karl Popper, and Ayn Rand.

Other Aether Theorists

There are a surprising number of people working on alternatives to Relativity, including many that have developed aether theories similar to this one. The WWW has allowed us to find each other and share our ideas with each other and the world. Among them are:

I have participated in discussions of Relativity and aether theories in sci.physics.relativity.

Let me know what you think.