4.0 A Physical Interpretation of the Results.
The purpose of this section is to augment the discussions in Section 2, and
the mathematical derivations in Section 3, with a further interpretation of
the results in a physical sense. This, it is hoped, will assist in the
understanding of the process of generation of the gravitational effect
presented here, within the Relativistic Domain D1. However, it is again
emphasised that because of the lack of observational evidence, this
interpretation must also be considered as somewhat speculative.
All points in space, including any material bodies that occupy them, exist
within a Relativistic Domain according to one simple criterion. The vector
sum of their velocities along all four Domain axes must always be equal to a
specific value. In previous papers this was termed the Existence Velocity of
the Domain. In the Domain D0, Pseudo-Euclidean Space-Time, the
magnitude of Existence Velocity is the constant velocity parameter c. In
general, the greater part of Existence Velocity will be along the temporal
axis, and the passage of time in the spatial part of the Domain is then
given by the ratio of the distance travelled along the temporal axis, to the
velocity along that axis. When a material body is present in D0, it
interacts with the Domain thereby changing it to produce the gravitational
Domain D1. It is proposed that this occurs in the following manner.
As the motion of the gravitational source along the temporal axis proceeds,
a transition takes place from the temporal dimension to the three spatial
dimensions such that, an expansion of the three spatial dimensions takes
place along all radius vectors from the centre of the source. The transition
enters the spatial part of the Domain at the very centre of the source, and
expands outwards with the linear expansion velocity vis. The
initial value of the linear expansion velocity at the centre of the source
is given by the constant term in (3.30). As the expansion moves away from
the centre in an infinitely close series of wavefronts, the linear expansion
velocity is subjected to a measure of attenuation. Firstly, a degree of
spatial re-absorption appears to take place within the source, causing a
deceleration of vis as represented by the second, variable term in
(3.30). This re-absorption, being a function of distance from the centre of
the source, increases as the expansion proceeds.
Upon reaching the outer periphery of the source, the re-absorption stops and
the linear expansion velocity at this point, and beyond, simplifies to that
given by (3.19). The only attenuation after this point is that resulting
from the inverse distance dependency. The expansion continues on in this
manner into the space surrounding the source.
It should be noted that in the derivation of the spatial linear expansion
velocities, vs and vis in (3.19) and (3.30), the positive
roots have been taken. If the negative roots are taken, negative
gravitational results would be obtained and therefore both positive and
negative values of these parameters provide acceptable solutions. The main
difference of course is that in the case of negative roots, the terms,
vs and vis then represent contraction velocities because
in this case, the source would be generating a contraction of space. The
importance of this will become evident in a future paper on the cosmological
application of Relativistic Domain Theory.
Returning to the solution detailed here, using the positive roots of (3.19)
and (3.30) to produce normal gravitation, the two principle consequences,
applicable both inside and outside the source, are due to the spatial
variability of the linear expansion velocity. The first is that this
variability is the direct cause of gravitational acceleration in the form of
the Acceleration Potential of the Domain. The second consequence concerns
the criterion of existence within the Domain. The linear expansion velocity
of all points both inside and outside the source, causes a corresponding
reduction in their temporal velocity resulting in the basic time dilatation
effect. Also, because the linear expansion velocity is a function of radial
distance, so then is the temporal velocities of all spatial points, and thus
via (3.1), the rate of the passage of time is also a function of radial
distance, thereby constituting the radial variability of the time dilatation
effect.
Finally, it is necessary to comment on other effects this spatial expansion
might have on other material bodies in the vicinity. The Acceleration
Potential and time dilatation discussed above have an additional combined
effect. The combination produces the net acceleration experienced by a
gravitating body as shown in [1] Eq(3.18), the equation of gravitational
planar orbital motion. The Acceleration Potential causes the primary
negative acceleration towards the source, while the spatial variability of
time dilatation causes a velocity dependent positive acceleration. In normal
astronomical situations the first of these terms is predominant. This is the
only additional effect that would be experienced by other material bodies
close to a gravitational source. In particular, the expansion of space
itself would not have any further effect. This is because the expansion does
not involve the dissipation of energy, and therefore cannot impose a
mechanical force on other material bodies. The spatial expansion would
simply flow past and through such bodies, and consequently their states of
motion would not be altered by this part of the process.
It is possible however, that some absorbtion may take place as the spatial
expansion from one source flowed through another close by, just as it does
in the interior of the generating body. The result would be that the
combined gravitational effect behind both bodies in line, would be very
slightly less than the sum of their individual gravitational potentials.
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P.G.Bass, August 2009
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