A QUANTUM APPROACH
                 TO RELATIVISTIC COSMOLOGY


     Cosmology is the branch of astrophysics concerned with
the large-scale structure of the cosmos and (in the current
interpretation) the origin of the universe. Yet the
scientific method employed in other branches of physics
consists in equating the origins of the constituents of the
physical world - the particles and fields that appear in it
- to the ends of other elements: science seeks to explain
the world from a principle of conservation.
     It thus appears incongruous that an explanation of the
large-scale structure of the universe should require the
addition of another "origin", that of the universe as a
whole. If the universe had a beginning, then matter and
motion, space and time, had to be created. This point of
view is obviously incompatible with a principle of
conservation. A model that is consistent with the
conservation principle, and therefore requires no cosmic
beginning, can be investigated by examining the current
conception of the large-scale structure of space and time
in the light of physical theory. Analysis reveals that the
conservation-violating universe model contradicts other
theoretical principles which have received confirmation
from empirical measurement. An alternative model is
proposed to circumvent these difficulties, and an extension
of general relativity theory is posited.
===========================================================
=============
     Cosmology in the twentieth century has been dominated
by two major advances: one observational, the other
theoretical. The former - the discovery that the spectral
lines of light emitted by external galaxies were shifted
toward the red in proportion to distance - constitutes the
primary empirical foundation for a cosmological model. How
this correspondence between redshift and distance is
interpreted in the light of theory determines the model.
     Astronomers presently acknowledge that a universe
model must be predicated upon the analytical framework
established by the second scientific advance - the general
theory of relativity. But unlike the present model for
cosmology, relativity unambiguously retains a conservation
theorem for momentum and energy. If the accepted universe
model is found to exhibit further inconsistencies with
relativity, then it is necessary to abandon this model in
favour of one that concurs rigorously with theoretical
principles.



Standard cosmology

     The existence of galaxies lying outside the "Milky
Way" was not confirmed until early in the twentieth
century, with the advent of telescopes possessing adequate
resolving power. First Slipher, and later, Hubble, noted
that spectra obtained from light emitted by external
galaxies exhibited a shift toward the longer wavelength end
of the electromagnetic spectrum. By the late twenties
Hubble and Humason had accumulated enough observational
data to establish a correspondence between the distance of
a "nebula" from our galaxy, determined by conventional
means, and the degree of redshift of its light spectrum.
     The fractional spectral shift, z, of light received
from a galaxy is defined by
                             
                   z = Dl = (lo - le)/le
where lo  is the wavelength of radiation as measured by the
observer and le is the wavelength at the point of emission,
determined from a laboratory spectrum, assuming local laws
of physics hold in the reference frame of the emitter.
     Since the value of z, interpreted as a Doppler effect
arising from radial motion between galaxies, was observed
to be consistently greater than zero for galaxies beyond
our local group, Hubble concluded that, for small values of
z,
                             
                          Vr = cz
i.e., radial velocity is equal to the product of spectral
shift and the speed of light. He therefore proposed that a
velocity of recession of a galaxy located at distance r
from the observer could be calculated using
                             
                          V = Hr
where H is an empirically derived constant. This formula,
which is interpreted as evidence of the expansion of the
universe, is referred to as Hubble's law.
     The Doppler interpretation of the observed
redshift/distance relation has constituted the fundamental
proposition of all orthodox cosmology since the twenties,
though Hubble long regarded it as only tentative. Combined
with non-static solutions to the field equations of general
relativity obtained in the early twenties by Friedmann and
LeMaitre, the expansion hypothesis has given rise to the
Big Bang cosmological model. According to this model, the
universe was created out of a "cosmic egg", a point-like
spacetime singularity of infinite density, in a primordial
explosion that marked the beginning of time and the origin
of space. Most debate within contemporary astrophysics is
concerned with the age of the universe since its alleged
birth at T = 0, and with the possibility that the cosmic
expansion will either continue indefinitely or reverse
itself in a gravitational contraction culminating in a "big
crunch".



Heterodox models

     The only other cosmological model to receive serious
consideration in the past several decades is the steady-
state theory devised by Bondi, Gold and Hoyle in the
fifties. This model is predicated upon a modification of
the cosmological principle underlying the Friedmann models.
Thus, in addition to being spatially isotropic and
homogeneous (Hubble confirmed this characteristic with his
observations), the universe is also homogeneous in time. To
accommodate the hypothesis of galactic recession, this
"perfect cosmological principle" requires that matter be
continuously created in the interstices of galaxies; this
new matter would fill the void left by the general
expansion. This theory is not regarded as tenable today
because of its inability to account for certain phenomena,
most notably the 3o K. microwave background radiation.
     An alternative to the Big Bang theory was proposed in
the last decade by Hoyle. Hoyle's "whimper cosmology"
emerges from a curious equivalence. In the expansionary
universe scenario, particle masses are regarded as
constant, on the assumption that physical laws are
invariant. However, Hoyle concluded that it was possible to
dispense with expansion by assuming that particles (i.e
atoms) in distant galaxies are lighter, and therefore
larger than those in the local environment. The "old"
electromagnetic radiation emitted by atoms from our past
would therefore exhibit longer wavelengths than that
radiated by contemporary atoms. By requiring particle
masses to be inversely proportional to distance, the Hoyle
theory can yield comparable redshift predictions to the Big
Bang model.
     The Hoyle cosmology incorporates a principle of
delayed action at a distance, whereby inertial mass is
understood as an effect of interactions with other
particles in the universe. A variation of atomic masses
with time is hypothesized to explain a time-correlated
shrinkage of atomic radii and, by extension, the redshift-
distance relation. Hence the larger atoms in distant
galaxies are less massive because local atoms have
"received" more mass through interactions with earlier
matter in the universe. What appeared in the expanding
universe model as a time-origin is now transformed into a
zero-mass surface separating positive and negative mass
aggregates (T = 0 is replaced by m = 0), while the universe
ceases to be limited to a finite spatial and temporal
frame. Though it obviates the arbitrary interpolation of a
spacetime singularity at an absolute temporal origin, the
whimper cosmology abandons both the cosmological and
perfect cosmological principles.



Paradigm and paradox

     Little consideration has been given to Hoyle's whimper
cosmology in the past decade, while the Big Bang paradigm
is now regarded as virtually unassailable. Yet the former
was devised in a conscious effort to avoid a temporal
origin and violation of the conservation principle.
Furthermore, it provides a quantum framework for
understanding mass as a derivative of the structure of the
universe. This was one of Einstein's objectives in
developing the general theory. But because the final
formulation of relativity divides reality into separate
electromagnetic and gravitational components, it assumes
mass to be autonomous and fixed for each particle.
     Cosmology therefore faces the following paradox: the
redshift phenomenon would seem to be explained with equal
cogency by the Doppler-shift/expansion paradigm and the
larger-atom/lower-mass hypothesis. The former
interpretation, however, is plagued by a mathematical
singularity at an absolute T = 0, while the latter posits a
time-dependent zero-mass surface in a universe divided into
discrete positive and negative mass aggregates. Both models
lead to perplexing apriorisms.
     A novel and physically promising component in the
Hoyle cosmology is the direct particle mass interaction,
which necessitates a quantum reformulation of gravitation.1
Yet, as we have seen this model circumvents the
cosmological principle altogether by hypothesizing special
conditions (m = 0) that are incompatible with spatial
isotropy.
     To overcome this theoretical antinomy we must seek an
alternate cause for the redshift phenomenon which is non-
velocity and does not lead to global metric singularities.
In order to avoid a time asymmetry, this explanation must
retain the Hoyle/Narlikar mass interaction, but freed of
the Newtonian condition that mass density must fall to
zero. What is required is a cosmology that adheres to
relativistic principles and embodies a finite distance
parameter derived from the quantum domain.



Redshift and cosmology

     Einstein finalized the general theory of relativity
and formulated the field equations defining the curvature
of spacetime due to energy density in 1916. In the
following year he proposed a cosmological solution for a
quasi-static universe. Assuming spatial isotropy and
galactic motions negligible in comparison to the speed of
light, he modified the gravitational field equations by
adding a constant of integration - the L -term - to
represent a negative pressure. The effect of the
cosmological constant was to establish the mean density of
matter that could remain in equilibrium, as well as the
radius of the spherical, quasi-static space. But by the mid-
twenties, after Friedmann had derived non-static solutions
to the field equations, Einstein abandoned the search for a
static model and acceded to the velocity interpretation of
redshifts.
     Meanwhile, reluctant to reject non-velocity
explanations prematurely, Hubble continued to examine the
implications of a static universe in relation to
observational cosmology. In 1935, he and Tolman contrasted
the Doppler mechanism with the hypothesis that galactic
redshifts could be explained without recession.
Specifically, they proposed that the observational results
might be accounted for on
the assumption that photons emitted by a nebula lose energy
on their journey to the observer by some unknown effect,
which is linear with distance and which leads to a decrease
in frequency without appreciable transverse deflection and,
in particular, without any decrease in rate of arrival at
the observer.2
     Adopting an Einstein universe model with no systematic
galactic motion as a limiting case of a quasi-static world,
they used an infinitesimal line element to compute redshift
as a function of the distance to each galaxy:
                             
               Dl/l = k # dr/(1 - r2/R2)1/2
In the following year, Hubble reviewed the non-velocity
formulation of the redshift law, this time invoking a
gravitational loss of energy proportional to distance as a
possible explanation of the law in a static universe. But
he concluded that the mechanism of the energy loss had yet
to be found:
There must be a gravitational field through which the light-
quanta travel for many millions of years before they reach
the observer, and there may be some interaction between the
quanta and the surrounding medium... Light may lose energy
during its journey through space, but if so, we do not yet
know how the loss can be explained.3
     A similar hypothesis, based on quantum considerations,
was advanced in 1954 by Finlay-Freundlich, who suggested
the possibility that
the cosmological redshift is not due to an expanding
universe, but to a loss of energy which light suffers in
the immense lengths of space it has to traverse in coming
from the most distant star systems.4
     This notion, motivated by observations of anomalous
reddening in radiation from large, hot stars, was supported
by the supposition that light suffers loss of energy in a
radiation field, perhaps due to photon-photon interactions
which could occur in intergalactic space. Pecker, Roberts
and Vigier have since returned to this problem.5 They
determined that an interpretation of the redshift based on
photon-photon interactions could be reconciled with the
problematic 3 o K. background radiation, when temperature t
is calculated by
                             
                        t 3 = H/cA,
with A obtained from
                             
                     z = Dn/n = -At 4L
where L is length of path through a radiation field.
     A more recent attempt at a non-velocity explanation of
the redshift phenomenon, the tired light theory -
originated by Nottale, Pecker, Roberts, Vigier and Yourgau6
- invokes an interaction between photons and a hypothetical
scalar deBroglie f -particle with a mass of less than 10-48
grams and no electric charge. In encounters with this
particle a photon would lose the requisite amount of energy
to yield the observed redshift. Abnormal redshifts
associated with objects such as quasars, and irregularities
produced by the passage of light from distant sources
through or close to galactic clusters and large galaxies,
are explained by a larger number of such collisions, and
consequently a greater density of f -particles. Though the
particles have not been identified, their density, sf, is
presumed to be proportional to the density of matter.
Redshift produced over a small wavelength dL is thus
expressed by
                             
                     z = Dl/l = asf/dW
where a is a constant.



Relativity and the quantum

     Hubble's investigation of redshifts generated by a
static universe model, conducted at a time when
relativistic quantum theory was still in its infancy,
remained incomplete essentially because it could offer no
explanation for photon energy loss. A quantum mechanism is
suggested by the more recent hypotheses that redshift-
related energy attrition may be produced by either photon-
photon (C-C) or photon-scalar particle (C-f) interactions.
We therefore consider the possibility that the field
approach of general relativity may be combined with quantum
particle interaction in a way that will provide a plausible
elucidation of the cosmological problem.
     Hoyle and Narlikar have proposed a quasiclassical
quantum approximation to account for the mass interaction,
and Born has indicated that generalized relativistic
gravitation equations should set a finite length q
satisfying the formula for Planck's constant h/2p = qp
(where p = momentum) 7. We would thus expect to achieve an
understanding of the cosmological redshift by replacing the
infinitesimal line element of the non-static models with a
finite length scale. With a distance parameter defined in
this way, z could be reformulated in terms of a Newtonian
approximation to relativistic quantum dynamics.
     The Schwarzschild solution to the field equations does
provide the appropriate finite length,
                             
                       rs = 2GM/c 2
which is the Schwarzschild radius for a black hole, i.e.
extreme spacetime curvature.
     One prediction of the general theory of relativity is
that a photon climbing through a gravitational field will
experience a loss of energy that manifests itself as a
spectral reddening. This effect has been verified in
terrestrial laboratory experiments 8, as has the
gravitational bending of starlight by a massive object
(observations of this phenomenon provided the first
confirmation of Einstein's gravitation theory in 1919).
Where ne is the emission frequency of a photon leaving an
object of radius r and mass M, and the frequency observed
at a great distance is no, energy loss is given by:

                    dE = h(ne - no)
                       = GM/r X ("mass of photon")
                       = GMhne/rc2
If l = c/n, redshift is just:
                             
                z = (ne - no)/no = GM/rc 2.



Cosmological Einstein redshift

     A gravitational explanation for cosmological redshifts
has been invoked only with reference to massive objects.
These may be either the emission sources themselves, or
interposed galaxies and clusters. Given the analogous
effect - a redshift resulting from loss of energy - it is
logical to posit an identity between the f -particle of the
tired light theory (also the mechanism underlying the
hypothetical photon-photon interactions) and the quantum of
gravity required by gravitational redshift. The formula for
local gravitational energy loss could then be referred to a
broader field of application, namely the observable
universe, while cosmological redshift would be furnished
with a quantum foundation.
     Moreover, there is no reason to restrict the cause of
the redshift to a local object. Although spacetime on the
cosmic scale is punctuated by gravitational warping
associated with galaxies and clusters, in cosmology it is
customary to ignore any local inhomogeneities and assume a
uniform model universe composed of a kind of cosmic fluid
or dust. Point sources within this fluid emit radiation
which traverses a gravitational field that may also be
regarded as uniform.
     We must therefore generalize the gravitational energy
loss formula
                             
                      dE = GMhne /rc2
to account for phenomena on a cosmic scale. In this new
interpretation, observed frequency no is related to the
energy density and radius of a determinate spherical
section of the universe to yield the energy reduction at
the observer due to gravitation. Assuming that the energy
loss is carried off by the f -particle, and that this
particle is associated with a gravitational field, we may
posit a generalized field that incorporates
electromagnetism. In the extreme case of maximum energy
loss, the finite separation formula assumes the simplified
form of the Schwarzschild cosmological radius, R s,
expressed as:
                             
                      R s = 2GM u/c2
     In one of Einstein's first efforts to integrate
special relativity with gravitation - prior to the complete
formulation of general relativity - he deduced a
gravitational time dilation associated with any form of
field, even a homogeneous one. The unification of mass and
spacetime achieved by general relativity encompasses matter
as a special case, i.e. potentially as a singularity of the
field. Gravitation is understood as an expression of the
metric field, while every form of energy produces a
gravitational effect. The local source of the field is not
crucial to the theoretical result for the general case. As
Einstein recalled in addressing the problem of space:
This train of ideas is based essentially on the field as an
independent concept. For the conditions prevailing with
respect to (any uniformly accelerated reference system) are
interpreted as a gravitational field, without the question
of the existence of masses which produce this field being
raised.1
     A local Einstein redshift can in fact be obtained from
a generalization of the gravitational energy loss formula
given in the previous section. If we set c = 1, that
formula takes the form
                             
                       dE = GMhne/r
which suggests an infinitesimal derivation of gravitational
time dilation from the special theory of relativity. A
clock moving at a uniform velocity v relative to an
observer will be seen to run at a frequency no, given by
                             
                         no = gne
where g is the Lorentz factor
                             
                      g = (1 - v2)1/2
Observed frequency is lower than ne, the frequency of the
clock when at rest10.
     To replicate the infinitesimal conditions of the
energy loss formula, we take the derivatives of both sides
                             
                        dno % gdne
and since we restrict ourselves to low velocities, we
substitute an approximation to the full Lorentz factor,
which gives
                             
                    dno % exp (-v2).dne
     If the clock is non-inertial (rotating around the
observer on a disk, for example), rather than in uniform
motion, then it is subject to a constant acceleration a,
and its velocity is determined by
                             
                          v2 = ar
where r is the distance of the clock from the observer at
the centre.
     Integrating both sides to restore relativistic
conditions and substituting for v2, we have the following
approximation to the Einsteinian formula:
                             
                     no % exp (-ar) ne
To convert to gravitational conditions, we invoke Kepler's
Third Law, which relates period of rotation P to the radius
of an orbit by
                             
                         r3 = AP2
Substituting for P we have
                             
                     r3 = A (2pr/v) 2
and finally, we obtain:
                             
                       v2r = A(2p)2
But by Newton's gravitational laws we know that
                             
                        A(2p)2 = GM
and hence, with M the mass of the local object,
                             
                      v2 = GM/r = ar
The local redshift formula therefore becomes:
                             
              z % 1 - no/ne % 1 - exp (-GM/r)
     Furth has arrived at a generalized result11 by
hypothesizing that a photon guided along a curved
trajectory in a gravitational field (i.e. in accelerated
motion) would lose energy in the form of gravitational
waves, or gravitons. He proposed that the energy of photons
travelling from remote galaxies would be dependent upon
distance, since the trajectories of these photons would in
fact be curved paths. Assuming energy proportional to
frequency, and taking M u as the Schwarzschild universe
mass, Furth's formula can be written:
                             
                   z = 1 - exp (-kr/GMu)
where k is a constant or order of magnitude unity.
     To investigate the uniform gravitational field present
in the observable universe, we adopt the simplest condition
for matter: that of a homogeneous incompressible fluid or
energy-continuum. This quasi-static space will possess a
Schwarzschild radius representing the limit of
electromagnetic transmission by the cosmic fluid, which can
be considered to be in equilibrium. Within this "radius of
the universe", the effect of the cosmic gravitational field
will be to reduce the energy (and therefore frequency) of
each photon in proportion to distance, i.e. in the case of
small distances, by
                             
                          z = Hr.
Light emitted from the Schwarzschild universe radius, or
electromagnetic boundary, is redshifted to a maximum value.



Particle mass and the principle of equivalence

     The immediate implication of this result is that the
photon has a nonzero rest mass, since this component
appears in the quantized energy loss formula. If mC is
photon mass, then the theoretical frequency at which the
wavelength becomes reaches a maximum, the photon's
DeBroglie wavelength, occurs at
                             
                     n min = mC c2/h,
by Proca's equations12. At this value, electromagnetic flux
falls to a minimum.
     Experimental measurements have yielded an upper limit
on the photon's "rest mass" at 10 -49 gram. We can
calculate a cosmological radius to a good approximation by
setting wavelength equal to the Schwarzschild world radius.
Accordingly we write:
                             
                         Rs = lmax
Hence:
                             
                       Rs = h/mC c.
For the experimentally measured upper limit on the photon
rest mass, the electromagnetic radius of the universe would
be on the order of 1020 cm. Conversely, assuming the
electromagnetically observable universe to have a radius of
10 26 cm, we arrive at a theoretical photon mass of 10 -71
gm.
     The version of the equivalence principle applied
throughout this analysis is the strong one. Since we
encountered a photon mass in our approximation to quantum
relativistic gravitation, it was necessary to transcend the
restricted formulation of the weak principle, according to
which the mass of the point particle plays no role in
physical effects produced by a gravitational field. With
the strong equivalence principle, we are permitted to
introduce quantum mass values and equate accelerated
systems with gravitational fields. The validity of the
equivalence principle for the quantum realm has been
confirmed by experiments involving neutron
interferometers.13
     When we introduce a photon mass into Maxwell's
equations, and subsequently into the redshift formula, we
therefore adhere strictly to a quantum relativistic
approximation. The approximation obtained is more
comprehensive than the short gravitational field equation,
since it incorporates a length constant of integration
representing electromagnetic repulsion. Einstein's
objection to the loss of economy implied by the
introduction of the cosmological constant is overridden by
the fact that the mathematically more complete formula
encompasses the very electromagnetic phenomena which serve
as tests for the theory of relativity, but which the
original field equations did not embrace.
     The time symmetry established by the application of
the strong form of the equivalence principle to the
cosmological problem constitutes a higher-order distinction
between accelerated motion (as in the Friedmann expanding
model) and gravitational field (Schwarzschild metric). But
in terms of observable effects, the two models will yield
nearly identical predictions.



Luminosity and the velocity of light

     Hubble felt that an expanding model corresponded
better to observed effects because of an important
oversight14: the apparent magnitude-redshift relation used
in his heuristic non-velocity model retains Euclidean
geometry, i.e., flat spacetime. The postulate of a
cosmological gravitational redshift necessitates an
alteration of the redshift-luminosity equation adopted by
Hubble and Tolman for a static universe. Relativity
requires a departure from linearity to reflect spatial
curvature.
     Observational astronomy yields an empirical redshift-
luminosity relation
                             
               m = 5 log (1+z) + a constant,
where m is apparent magnitude and (1+z) is flux. This
relation is the one predicted by the velocity-shift
interpretation. The corresponding relation in flat
spacetime is less than that obtained from observation by a
factor of (1+z):
                             
              m = 2.5 log (1+z) + a constant.
     In the velocity-shift formula, which accords with the
empirical z - m relation, "curvature" is only an illusion
introduced by Hubble acceleration. Spacetime actually
remains flat, while the acceleration of reference frames
creates the redshift and flux dilution effects that add up
to (1+z)2. Naturally, we also find a departure from the
linear picture of flat spacetime with the Schwarzschild
metric, since the gravitational field reduces energy
(redshift) and diminishes photon arrival rate. The apparent
magnitude formula for the gravitational redshift
interpretation therefore replicates the empirical relation,
and it has the advantage of not introducing an arbitrary
mechanical motion. Luminosity declines exponentially with
distance and appears to "switch off" at R s, exactly as in
the case of the nonzero mass photon at the electromagnetic
propagation limit.
     Einstein had already accounted for the non-linear
redshift effect in his 1911 article - alluded to above - in
which he deduced a gravitational redshift. In this article,
the dependency of the speed of light on gravitational
potential, given by
                             
                    c = c'(1 + GM/c2r)
is equivalent to a relativistic dilution of flux. It is
interesting to note that this effect - variable speed of
light - is commonly thought to have been overlooked by
relativity. After Einstein's original treatment, it was not
investigated again until 1964, and when a slowing down of
light was observed by means of radar echo experiments15
conducted within the solar system in 1968, it was regarded
as a new confirmation of relativity.
     In 1945, Einstein reaffirmed his rejection of the
static universe model, arguing that the speed of light
reflected between two distant points should not be affected
by distance travelled. But light propagating through space
also travels through a gravitational field, and hence must
undergo a change of velocity that can be detected. We have
just seen that differences in travel time have in fact been
noted for radar signals reflected within the solar system:
the influence of the sun's gravitational field was found to
increase travel time for a light signal. With the
confirmation of this effect, no further objection to the
quasistatic universe model can be sustained. The principle
of equivalence decides unambiguously in favour of an
Einstein cosmological redshift.



Gravitation and electromagnetism

     To demonstrate gravitational redshift, we equate the
"inertial mass" of the photon to its gravitational mass.
This step enables us to express the redshift phenomenon as
a quantum effect, and is consistent with the strong
principle of equivalence. Rather than resort to a
mechanical Doppler explanation of the galactic redshifts,
we first extend the local gravitational field of our freely
falling inertial frame to the distant galaxies. Then, using
the conclusions of general relativity, we interpret the
observed spectral shifts as a gravitational time-dilation.
The distant galaxies are thus no longer receding as a
result of the expansion of a finite universe; they are
instead the foci of events in a cosmic fluid, which may be
regarded as a spacetime-energy continuum, infinite but
bounded. The portion of the universe visible from any
galaxy appears as if it were the interior of a black hole
with an electromagnetic horizon. Space is only apparently
finite.
     Unlike the classical general theory, this dual-field
description does not assume mass to be intrinsic to each
particle; instead, it regards the gravitational attraction
of any two particles as an effect of the aggregate mass of
the observable "universe".
     The defect of the cosmology developed by Hoyle on the
hypothesis of a variation of particle masses with time lies
in its treatment of cosmic spacetime as equivalent to the
local Euclidean environment16. Its mass variation and zero-
mass state of matter mean essentially that distant clocks -
the radiating atoms in external galaxies - are actually
running slower, whereas Einstein demonstrated that this
apparent slowing-down of time was due not to the intrinsic
construction of the clocks, but to the curvature of
spacetime induced by the density of energy, and
consequently the strength of the gravitational field.
Radiation emitted by distant atoms has merely lost energy
to, and therefore been reddened by the cosmic gravitational
field.
     In this view, the cosmological redshift acquires a new
significance. It can no longer be ascribed to an expansion
of the universe, since the theoretical foundations and
mathematical treatment of the expanding Friedmann models
are unnecessarily truncated. The inclusion of the L -term
in Einstein's field equations yields a mathematically and
physically more complete treatment of spacetime, while the
resulting quasistatic model obviates the time asymmetry of
the expanding Friedmann solutions to the field equations.
     Combining a generalized mass-response (attraction)
with the complementary electromagnetic-response
(repulsion), we achieve a cosmology that resolves the
artificial time-origin of the Big Bang model and the zero-
mass surface of the whimper cosmology into a Schwarzschild
universe horizon.
     The Friedmann solutions on which the Big Bang models
are based admit no electromagnetic response condition17,
and consequently place an absolute edge on the universe at
an arbitrary T = 0. It is because of their treatment of
time as an independent variable that expanding models lead
to a metric singularity and infinite density at an absolute
temporal origin. This peculiarity is analogous to the a
priori interpolation of mass in general relativity. An
extension of relativity to remove this autonomy makes both
mass and proper time dependent upon the large-scale
structure of space. Einstein was aware of this limitation
in his theory:
The present theory of relativity is based on a division of
physical reality into a metric field (gravitation) on the
one hand, and into an electromagnetic field and matter on
the other hand. In reality space will probably be of a
uniform character and the present theory be valid only as a
limiting case.18
     Since it eliminates the asymmetries inherent in the
Friedmann solutions, the introduction of the cosmological
constant into the field equations thus constitutes a
framework for approaching a more general theory, of which
the standard field equations are a locally valid or
limiting case, and achieves a more consistent explanation
of the observed effects, i.e., one not requiring violation
of conservation laws or recourse to mechanical motion.



Redshift and the arrow of time

     Hoyle and Narlikar developed their mass interaction
theory out of a hypothesis of electromagnetic action at a
distance in a static universe put forward by Feynman and
Wheeler in the forties19. Reasoning from the time-symmetry
of Maxwell's equations for electromagnetism and classical
gravitation theory, Feynman and Wheeler deduced that it
would be possible to couple electromagnetism to matter by
assuming a response from all electric charges in the
universe to local field disturbances. Their calculation led
them to the conclusion that, for classical physics, the
response of the universe would cancel local advanced
radiation - waves that go backward in time - leaving a
local asymmetry in favour of retarded response - i.e. waves
that radiate into the future. This is the foundation of the
local "arrow of time". Hoyle and Narlikar subsequently
confirmed these results for quantum theory, using the
quasiclassical approximation alluded to above. In their
approach, retarded wave response was shown to correspond to
a non-zero probability of electron transitions to lower
energy states accompanied by radiative energy loss. They
therefore provide a global context for understanding the
time-asymmetry encountered in local phenomena of
electromagnetism, normally regarded as a manifestation of
"vacuum" fluctuations. According to Hoyle and Narlikar,
...quantum phenomena which are usually taken to arise from
zero-point fluctuations of the quantized electromagnetic
field can also be explained in a fully time-symmetric
theory in terms of the response of the universe... ... time-
symmetric solutions to the electromagnetic equations can
yield all the observed effects, provided local problems are
properly related to the universe and provided the universe
has an appropriate large-scale structure.20
     The correct universe structure for global
electromagnetic symmetry is one that absorbs retarded waves
fully and advanced waves partially, so that advanced waves
will cancel. Expanding Friedmann universes do not have the
requisite perfect future absorber and imperfect past
absorber, and consequently must introduce a universal time
asymmetry - the cosmic clock.
     Hoyle and Narlikar have argued that only a steady
state expanding model possesses the correct combination of
absorbers, since the density of matter remains constant
with expansion when the perfect cosmological principle is
invoked, whereas the Big Bang universe with decreasing
density either cannot absorb retarded radiation fully, or
swallows up all advanced waves in its infinitely dense
singular origin.
     However, a relativistic quasistatic universe such as
the one proposed here also incorporates a perfect
cosmological principle. It thus possesses constant matter
density and absorbs advanced responses fully: its perfect
future absorber is a corollary of gravitational energy loss
- the cosmological redshift - which results in maximum
energy depletion at the Schwarzschild universe boundary.



Quasistatic field equations

     A model that derives local asymmetries of
electromagnetism and time from symmetrical laws describing
the large scale structure of the universe points to the
need for a new mathematical formalism, and introduces a
radically different orientation in physical research. The
symmetry underlying this new paradigm may be stated as
follows: the strength of local gravitational attraction
between particles (or the value of Newton's constant G)
depends on the rest of the mass in the electromagnetically
observable universe, just as electromagnetic repulsion is
determined by the aggregate of electrical charges in the
gravitationally bounded universe.
     Under this paradigm, the first requirement of physical
research is a unified equation in which electromagnetism
and gravitation appear naturally. Classical general
relativity and Maxwellian electromagnetism would be deduced
from this extended theory as special cases. This
investigation of a static particle-coupled model represents
no more than a crude approximation, corresponding to a
pseudo-quantization of the cosmological constant in the
relativistic field equations. In other words, we replace of
the original field equation of gravitation expressing the
relationship between energy density and the curvature of
spacetime with the static equation containing the
electromagnetic repulsion term, where the cosmological
constant defines the radius of a spherically homogeneous
space by an inverse square law:
                             
                         L = 1/Rs2
But if this Schwarzschild gravitational world radius is
also defined by Proca's equation, then we have
                             
                       L = (mC c/h)2
or
                             
                   L = mC2 x a constant
Hence we define the cosmological term as proportional to
the square of the mass of the photon.
     Objections to the introduction of the cosmological
term may be countered by the observation that there is a
very strong precedent for the extension of the field
equations. In the last century, Maxwell, also motivated by
considerations of symmetry, added an extra term to his
field equations for electricity and magnetism, and found
that the additional term accounted for a new, unsuspected
phenomenon: magnetic induction. We should not be surprised
if the "repulsive" force of the cosmological term, like
gravitation itself, is revealed to be a an inductive effect
of aggregate charges, and hence masses, as Weyl has
suggested21. Einstein's "greatest mistake" may ultimately
prove to be his most seminal intuition.



Symmetry and mass

     For each world-point (our terrestrial observatory, for
example) we may envision a surrounding spacetime-mass
aggregate bounded by a horizon that defines the extent of
electromagnetic visibility and "shields" the central point
(in effect a singularity) from electromagnetic interactions
originating outside the horizon. The wavelength of
radiation emitted from the limit is "dilated" to a maximum
value - time stands still - since radiation emitted from
that point must travel through an equivalent Schwarzschild
gravitational potential to reach the electromagnetic
horizon corresponding to its emission point; at the
horizon, all its electromagnetic energy has been converted
into gravitational energy through mass interactions. The
modification of relativity obtained by inserting the mass
interaction makes it possible to explain the phenomenon of
mass within the observable universe by deriving the
universe horizon from the symmetry of the electromagnetic
and gravitational interactions.
     As Hoyle has pointed out, one consequence of time-
dependent cosmologies (i.e. the Friedmann models) has been
to raise a metaphysical barrier at T = 0. What lurks behind
the temporal singularity is regarded as unknowable, and is
ultimately equated with a Creator: the Big Bang is commonly
referred to as the "creation". Relativity unified mass and
spacetime, yet by failing to incorporate direct particle
action, it required an autonomous mass as the explanation
for the properties of a spacetime. Modern standard
cosmology makes the anti-relativistic mistake of
interpolating this autonomy of mass to back to spacetime.
The Big Bang model reverts to an absolute cosmic time and
space, tenuously united with mass in the artifice of an
"origin", in reality a witches' brew of mathematical
delusion. In the relativistic direct particle model, mass
disappears as an independent magnitude, to be replaced by a
gravitational-electromagnetic response symmetry which
accounts for rest mass and the structure of spacetime in a
unified action continuum without absolutes of time, mass or
space.
     The central component of a relativistic cosmology is
the Schwarzschild solution to Einstein's field equations.
The anomalous phenomena associated with the Schwarzschild
solution, such as the singularity and event horizon, have
been interpreted primarily in local contexts. Indeed, only
local confirmations of the theory were feasible at the time
relativity was developed, but this physical constraint
should not be perceived as an insurmountable theoretical
barrier.
     Our approach has entailed generalizing the inferences
of extreme spacetime "curvature" or redshift from the
special cases proposed for the evolutionary sequence of
supermassive stars and galactic centres to a form that
explains the cosmological redshift and the "edge" of the
observable cosmos. In the course of our work we were
obliged to recognize the limitations of relativity theory,
and we have attempted to overcome them by hypothesizing a
quantum description of gravitation predicated on a
unification of gravity and electromagnetism. This step
enabled us to derive a photon mass from the structure of
the universe through direct particle interactions.






Infinite spacetime

     The religious implications of the cosmic egg and Big
Bang did not fail to cause some trepidation among
physicists when the new theory first took shape. The very
hypothesis of an expanding universe prompted Einstein to
write: "This circumstance irritates me." Many astronomers
finally decided that it would be more economical to create
matter than activate inert matter into expansion. For
example, British physicist Edmund Whittaker wrote that "it
is simpler to postulate creation ex nihilo - Divine will
constituting Nature from nothingness." And Edward Milne has
stated bluntly: "our picture is incomplete without Him".
Having accepted an origin, many astronomers have thus been
constrained to embrace a Creator. But the voices of
scepticism were legion, at least in the first half of the
century. Many instinctively rejected the hypothesis of an
origin. Eddington exclaimed: "The notion of a beginning is
repugnant to me... I simply do not believe that the present
order of things started off with a bang... the expanding
Universe is preposterous... incredible... it leaves me
cold."
     For Hubble, the expansion theory always remained
largely a hypothesis, and we saw that he envisioned
(prophetically) the possibility that an explanation of the
redshift might emerge from a quantization of the
gravitational field. This expectation would now appear to
be confirmed. Similarly, Hubble's collaborator, Tolman, was
loathe to accept the "creation" theory. In a posthumously
published note22, Tolman expressed his doubts about the
implications of the expansionary interpretation:
... I think we have to begin by putting the phrase "age of
the universe" in quotation marks, since I see at present no
evidence against the assumption that the material universe
has always existed. For me all that such a phrase could
mean is the estimated time back to some important large-
scale event, for which we have evidence...
     Now the voices of dissent are almost extinguished.
Hoyle and Narlikar have done interesting work on particle
interaction, and we have incorporated their premises, but
not their cosmological conclusion that clocks (in other
words, atoms) in distant galaxies actually "tick" at a
slower rate than those on earth. To do so would have been
tantamount to repudiating general relativity. Pecker has
suggested that our observable universe may be akin to a
black hole, but the quantum problem has never been resolved
satisfactorily, and consequently the possibility of a quasi-
static universe has never been investigated seriously.
Indeed, the Big Bang theory is now almost unanimously
heralded as the obligatory paradigm for all future
cosmology. As we have indicated, the root of the matter
lies in a half-digestion of relativity.
     That Einstein's theory introduced a complete
revolution in the conception of space and time is contested
by no one. It would be more accurate to state that
relativity provides the materials for such a revolution,
but that the impact of the new view has been nullified by
the persistence of a mechanical mode of reasoning. In
cosmology, the effect is utterly negated by the prejudices
of a spatially finite universe, a Newtonian universal,
absolute time, and a metaphysical separation between matter
(singularity) and field (energy).
     For relativity theory the totality of matter, motion,
space and time constitutes a unified reality: they are
united in the concept of the field. Space and time do not
exist independently of the field, as in the pre-
relativistic view, but are determined by the field.
Consequently "there is no such thing as an empty space,
i.e. a space without field". The field is fundamental and
primary, and determines all dynamic effects. The cosmos can
be thought of as a continuum of spacetime and the energy-
field. Time or space as such, as an absolute, with a
beginning and a finite extent, cannot be said to exist.
This continuum is the site of dynamical phenomena which are
compounded to form motion and evolution within a physically
real space and time.



Summary

     A cosmology erected on apriorisms (origin at T = 0,
global time asymmetry, non-conservation of momentum,
systematic expansion) is at variance with relativity theory
and represents a retrograde paradigm, since the essential
conditions of any spacetime description are the
conservation principle, symmetry laws and the principle of
equivalence. Indeed, the evolution of physics suggests that
the very notion of a cosmology, understood as a model for a
closed system, arises from an erroneous projection of local
asymmetrical, decoupled and mechanical relations to the
cosmic scale.
     The present trend toward theorizing the limitations of
relativity theory (e.g., its arbitrary treatment of mass)
as the absolute bounds of human knowledge and the
exhaustion of physical nature is utterly irreconcilable
with the dynamic character of scientific theory, as defined
by Einstein:
However we select from nature a complex (of phenomena)
using the criteria of simplicity, in no case will its
theoretical treatment turn out to be forever appropriate
(sufficient). Newton's theory, for example, represents the
gravitational field in a seemingly complete way by means of
the potential... This description proves to be wanting;
(general relativity) takes its place. But I do not doubt
that the day will come when that description, too, will
have to yield to another one, for reasons which at present
we do not surmise. I believe that the process of deepening
the theory has no limits.23
     Tolman too was keenly aware of the approximate nature
of all physical theories, and equally sensitive to the
shortcomings of the expansionary model. Recognizing that
the problems of empirical fit might lie with relativity
theory, he enumerated a number of speculations that could
be considered as alternate solutions:
(a) that the nebulae actually stay put in space and the red
shifts result not from recession but from some unknown and
doubtless extremely important physical principle in
accordance with which the frequency of a photon would
change with time (Zwicky), (b) that the actually correct
laws of gravity could themselves be derived from the
homogeneity of the universe (Milne), (c) that there are two
mysterious kinds of time, a "kinematical time" and a
"dynamical time" which are logarithmically interconnected
(Milne), and (d) that the constants of nature are not
really constant but have values which change with time
(Dirac). Some of these possibilities must be regarded as
interesting. Furthermore, it is reasonable to regard
general relativity as a development which like others
before it will sometime find its place in some broader
theoretical structure.24
     It can readily be seen that speculations (a) and (b)
are those explicitly adopted in this study, while (c) and
(d) - without time-dependence of the constant - imply that
the preceding hypotheses may be accommodated within a model
that represents macro-micro relations by means of an
invariant cosmic time tied to a comoving reference frame,
or ether, and a local time and coupling constant which are
dependent on the number of mass quanta that make up each
individual particle system.

                            ***
     I wish to express my gratitude to Dr. Jean-Claude
Pecker for his generous comments, criticisms and
encouragement, to Jacques Trempe for valuable discussions
and technical assistance, and especially to Francois Reeves
for his untiring help and decisive contributions during the
completion of this study.

_______________________________

1     Fred Hoyle, Cosmology: a modern course, 1975, pp. 637
ff.

2     Edwin Hubble, Richard C. Tolman, Two methods of inves
tigating  the nature of the nebular red-shift, in Astrophys
ical  Journal, vol. 82, 1935, p. 304. cf. also  Richard  C.
Tolman, Relativity, thermodynamics and cosmology, 1934, pp.
331-419.

3     Edwin  Hubble, Observational approach  to  cosmology,
1938, p. 30

4     E. Finlay-Freundlich, Red shifts in the spectra of ce
lestial  bodies, in Philosophical Magazine, vol. 45,  1954,
pp. 317-318.

5     J.  C. Pecker, A. P. Roberts, J. P. Vigier, Non-veloc
ity  redshifts and photon-photon interactions,  in  Nature,
vol. 237, 1972, pp. 227-229.

6     L. Nottale, J.C. Pecker, J.P. Vigier, W. Yourgau,  La
constante de Hubble mise en question, in La Recherche, Vol.
68, June 1976.

7     Max  Born,  Natural philosophy of cause  and  chance,
1964, pp. 142-3

8      Michael   Berry,   Principles   of   cosmology   and
gravitation, 1976, p. 45.

9     Albert Einstein, Relativity: the special and  general
theory, 1961, p. 153.

10   Sam Lilley, Discovering relativity for yourself, 1981.

11    R.  Furth, A new hypothesis to account for  the  red-
shift  in the spectra of distant stars, in Physics Letters,
Vol. 13, No. 3 (1964), pp. 221-223.

12   Alfred S. Goldhaber, Michael M. Nieto, The mass of the
photon, in Scientific American, May 1976.

13    Daniel M. Greenberger, Albert W. Overhauser, The role
of  gravity in quantum theory, in Scientific American,  May
1980.

14   Edwin Hubble and Richard C. Tolman, op. cit., pp. 334-
335.

15   Michael Berry, op. cit., pp. 88-91.

16   Fred Hoyle, op. cit., pp. 657-658, 661.

17    Fred  Hoyle, Jayant V. Narlikar, Action at a distance
in physics and cosmology, 1974, pp. 173-4, 200-202.

18    Albert Einstein, The meaning of relativity,  5th  edi
tion, 1956, p. 129.

19    Jayant  V.  Narlikar, The structure of the  universe,
1977, pp. 190 ff.

20   Fred Hoyle, Jayant V. Narlikar, op. cit., pp. 4-5.

21    Hermann  Weyl, Philosophy of Mathematics and  Natural
Science, 1963, p. 289.

22   Richard C. Tolman, The Age of the Universe, in Reviews
of Modern Physics, Vol. 21, No. 3, 1949, pp. 374-378.

23    Albert  Einstein, Letter to Felix Klein,  in  Abraham
Pais, Subtle is the Lord, 1982, p. 325.

24   Richard C. Tolman, op. cit., p. 377.