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Relativity and the Physical Universe
FORWARD THINKING IN ASTRONOMY
[A series of eight lectures specially prepared for Compu-
Serve Information Systems (CIS), for presentation in ASTROFORUM.
Copyright 1990 by Tom Van Flandern of Washington, DC [CIS ID code
71107,2320]. Please seek the author's permission before
reprinting more than two paragraphs. If redistributed in
electronic form, must include this statement of source and
copyright.]
CHAPTER IV. RELATIVITY, AND THE PHYSICAL UNIVERSE
A. Waves
One cannot study the nature of things for very long before
an understanding of waves and their properties becomes an
essential tool. When substance is disturbed, individual
particles may scatter or behave "randomly"; but the surrounding
medium communicates the effects of the disturbance outward by
means of organized motions of its own constituent particles.
These organized motions in a medium are called "waves".
Waves are pulses, sometimes in the same direction as the
wave motion (called "longitudinal" waves; e.g. sound waves in
air); and sometimes perpendicular to the direction of the wave
motion (called "transverse" waves; e.g. water waves, also light).
Dissimilar waves from different sources pass through one another
without lasting effects -- i.e. they do not exhibit the property
of collision, as particles do (although a barrier can be made to
reflect them).
When water is the medium of transmission, individual
molecules of water merely move up and down as the wave passes;
they do not themselves advance with the wave. When air is the
medium, individual molecules move at extremely high velocities,
much faster than the wave itself, colliding with other molecules
frequently. The passing wave is merely a statistical tendency
for the molecules to collide more frequently in certain locations
("condensations"), and less frequently in others
("rarefactions"). Information about the time and place of some
source disturbance is transmitted by the wave, although the
molecules comprising it do not themselves share that information.
The propagation velocity of the wave is a function of the density
of the medium and the speed and mean distance between collisions
of the individual particles comprising it.
The hypothetical "sea of entitiararae have postulated in
earlier discussions, pervading the entire universe, can likewise
transmit information by means of waves -- information not shared
by individual entities. Although waves in this entity sea are
not exactly analogous to any of the other kinds of waves we have
mentioned, their behavior will bear many similaritias. Since
known waves such as light which can exist purely in this entity
sea propagate with the speed of light, we conclude that this is a
natural wave velocity of the medium. By analogy with air,
however, the velocitias of the individual particles are many
orders of magnitude greater than the speed of light, c.
B. General Relativity
In the case of a wave already traveling at the velocity c
approaching a massive body, the gravitational force of the
massive body tries to make the wave travel faster than c.
However the effect of the imbalance in the number of "gravitons"
on the two sides of the approaching wave must be to shorten the
wavelength of the wave (increasing its energy), since its
velocity is not free to change. We may apply this result
immediately to light waves traveling away from a massive body.
The light will experience a "redshift" (an increase in
wavelength, which represents a loss of energy), instead of a
slowing in velocity. This is the so-called "gravitational
redshift" of light, one of the three tests of Einstein's General
Relativity Theory.
Now imagine that the light wave passes close by the massive
body. The same constraints apply, since the velocity of the wave
cannot itself be either accelerated or decelerated by the massive
body. However the wave can be bent by "refraction" in exact
analogy to what happens when a light wave passes from a thinner
medium into a denser one. It has been shown by many authors that
the famous "light-bending" test of Einstein's General Relativity
theory can be derived exactly in a model which assumes a flat
space-time with refraction in a medium whose wave velocity is c.
It even gives correctly the time delay of radar waves in the
solar system as a consequence of the slight slowing of the speed
of light when traveling in a denser medium near a massive body.
We were already aware that light slows down when traveling in
denser media, such as water. Although this refraction analogy
has been known almost since the General Relativity theory was
first published, the "curved space-time" model has received wide
acceptance over the "refraction" model for these phenomena
because of the failure of experiments to detect the presence of a
medium within which light propagates. This has to do with the
"Special Relativity" theory, which we will examine in a moment.
The third test of General Relativity is the excess rotation
of Mercury's elliptical orbit, which has been accurately
verified. This, too, may be seen as merely a consequence of the
behavior of bodies becoming more "wave-like", including the
bending of their paths by refraction rather than by acceleration
as they approach the speed of light. Specifically, the
contraction of space and time, which are consequences of Special
Relativity (to be discussed next), will result in a greater force
from the Sun when Mercury is at perihelion (closest point to the
Sun) than at aphelion (farthest from the Sun). As is well known
in Celestial Mechanics, applying a radial perturbation to an
orbit which augments the central force at perihelion, and
decrements it at aphelion, has the effect of rotating the
direction of perihelion in the forward direction.
C. Special Relativity
Why do clocks slow down when the speed of a body approaches
the speed of light? Clocks, change, aging, and all measurements
of time ultimately depend upon the structure of the matter they
are made out of. To focus on just one aspect of this, consider
the revolution of electrons around atomic nuclei. Suppose every
electron in every orbit around every atom took twice as long to
complete a revolution (or any motion). Then clocks, aging, and
indeed time itself for observers made of such "slow atoms" would
slow to half the usual rate.
A reason that electrons might "slow down" while moving at
high velocities is that it takes longer for them to complete a
revolution when their atoms are moving near the speed of light
than when their atoms are stationary. This is true of any body
traveling in a moving medium.
******** Consider a canoe moving upstream and back downstream to
its starting point against a current. Show that the faster the
current, the longer the round trip takes.
The essence of Special Relativity is that all motion is
relative. It is supposed that there is no measurement which can
decide that one body is "really moving" and another is not, since
the opposite point of view is equally valid. The theory then
goes on to propose that moving bodies undergo an apparent
contraction of space and time, as seen from a stationary frame:
distances seem to be compressed in the direction of motion of the
body, and clocks traveling with the body seem to tick more
slowly.
Although the contraction of space and time is negligible at
ordinary velocities, it becomes indefinitely great as the
velocity of the observer approaches c. This is often dramatized
with an example of two newly-born twins. It is supposed that one
of the twins remains on Earth, while the other is placed on a
spacecraft moving toward a nearby star (Alpha Centauri) with a
speed of 99% of the speed of light, c. We further suppose that
the nearby star is about four lightyears away, so that the one
way journey takes just a little over four years, as measured by
Earth clocks. We then imagine that the traveling twin turns
around and returns to Earth. According to Special Relativity
theory, the twin who stayed on Earth will be over eight years old
when the two are re-united; whereas the traveling twin will have
aged only a little over one year, and will still be a baby,
because of slowing of the rate of progress of time for any body
traveling with a velocity of 99% of c. Traveling atomic clocks
have been successful in showing that such effects really do
occur, and that traveling bodies age more slowly.
We have always known that we could use the average position
and velocity of all bodies in a given vicinity as a reference
frame for both position and motion. And if some velocity greatly
exceeds the motion of any individual body in the vicinity, such a
velocity is both detectable and has physical consequences. Only
in that sense can it be called an "absolute" velocity. In the
universe as a whole, there would be asymmetries in the amount of
visible matter in the forward and aft directions; and the cosmic
microwave background radiation would be red-shifted in the
direction of motion and blue-shifted in the opposite direction.
These likewise enable us to detect a sort of "absolute" motion,
but only in a statistical sense.
With these concepts in mind, let us examine by analogy
exactly how and why space and time contract in our model as
velocities approach the speed of light; and most importantly, how
it is possible for substance to travel faster than the speed of
light without violating Special Relativity, and without moving
backwards in time, thereby violating causality. ["Violating
causality" from traveling backwards in time means, for example,
preventing your own grandfather from being born. Since you would
then never come to exist, you couldn't do what you just did.]
D. The "Sound" Analogy
Consider an alternate universe containing "atoms" of
unspecified size and mass, each consisting of a "nucleus"
exerting some attractive force, and "electrons" in orbit around
that nucleus, similar to the Bohr model for the Hydrogen atom.
Now let the universe be filled with a continuous medium having
the properties of air, and let the electrons of our hypothetical
atom propagate through this medium in their orbits around their
nucleus just as sound propagates through air. Let the Bohr
radius of an imitation "Hydrogen atom" in this universe provide
the unit of length; and let the elapsed interval needed for the
corresponding electron to circle its nucleus provide a unit of
time in this universe.
The essential difference between this model and the real
universe is that all motion in this model is via wave propagation
through a medium in which the limiting propagation velocity is
the speed of sound. We will find the implications of this
variation familiar.
Suppose that an airplane composed of these alternate atoms
flies through the air-like medium (assuming no gravity) by means
of propellers. Since its means of propulsion is by pushing
against the medium (rather than action-reaction, as in jets or
rockets), the speed of the airplane is limited to the speed of
sound. (The speed of sound is the maximum speed at which waves
or pressure can propagate in a medium.) As ever more energy is
applied to make the propellers spin faster, the airplane's speed
will approach the speed of sound ever closer; but it can never
quite reach it, except with infinite energy and infinite
propeller speed.
To a physicist in this alternate universe, it appears as if
the airplane's inertial mass is increasing as its velocity
increases. The airplane seems to resist further acceleration as
the energy applied approaches infinity because the airplane's
inertial mass seems to approach infinity. This is PRECISELY
analogous to the way in which the inertial mass of a body in the
real universe seems to approach infinity as its velocity
approaches the speed of light.
As the airplane's velocity approaches the speed of sound,
the sound waves emanating from it in the direction of motion get
bunched up closer and closer together, because their velocity
relative to the airplane gets less and less. For precisely the
same reason, the orbits of the electrons in the airplane get
compressed in the direction of motion, because they, too,
propagate like sound waves in our special universe. But since
the dimensions of the electron orbits provide the unit of length
in this universe, a physicist in this universe would conclude
that distances contract in the direction of motion as bodies
approach the speed of sound. Indeed, he would derive precisely
the well-known "Lorentz contraction" formula to represent the
amount of this contraction. In the real universe, distances seem
to be contracted in the direction of motion in accord with the
Lorentz formula as bodies approach the speed of light.
Moreover, if the matter is judged by a stationary observer,
the electrons will take more time to complete their orbits,
because the round trip time for any particle moving upstream and
downstream in a moving current is greater than the round trip
time in a stationary medium. This "time dilation" for the moving
electrons of the airplane also follows the Lorentz formula,
because the revolution time for the electron approaches infinity
as the velocity of the airplane approaches the speed of sound.
In the real universe, the clocks of moving observers seem to slow
down with respect to those of stationary observers as their
relative velocity approaches the speed of light.
The contractions of the units of length and time are exactly
analogous in the alternate universe with respect to the speed of
sound, to what they are in the real universe with respect to the
speed of light. So it follows that all observers in the
alternate universe performing "Michelson-Morley" experiments, or
trying to measure the speed of sound, will get the same constant
answer regardless of their state of motion with respect to the
air medium, just as that happens for light in the real universe.
In fact, all experiments performed in the two universes would be
analogous. Even a moving biological twin being made of such
hypothetical "sound" atoms would age more slowly than his non-
moving identical brother, because the "sound" atoms of which he
is comprised slow down in all respects.
E. Causality
Now because the situation is reciprocal for "moving" and
"stationary" observers (i.e. each "sees" the clocks of the other
slow down and distances contract, but via waves traveling at the
speed of sound, not light), it has been concluded that no
experiment can tell which observer is really moving and which is
stationary. But we have just described how the same experimental
results may be achieved within a medium which provides a
"preferred" reference frame. So the conclusion that "no
experiment can tell ..." is incorrect. It is possible in
principle to measure the average motion of all air molecules in a
given volume, and to adopt that average as a standard of rest.
Of course there might be a "breeze" blowing through our entire
adopted volume, so that it does not provide an "absolute"
standard of rest for the alternate universe. But it would
provide a preferred frame for any volume of arbitrary size. In
the real universe, we propose to make the same remark about the
sea of agents, the presumed medium for the propagation of light.
Any experiment which could measure its statistical properties
could determine a preferred frame.
There is one more important point to consider. In the real
universe it is concluded that faster-than-light communications
would violate causality because they would propagate backwards in
time. In our alternate universe we may see a similar line of
reasoning if all communications were limited to the speed of
sound. The fact that atoms and clocks would slow down as they
approached the speed of sound, and that the electrons would
reverse direction if the speed of sound were exceeded, does not
alter the forward flow of "meta time" as kept by clocks fixed in
the preferred frame. Indeed, the phenomenon of "slowed time" may
be seen as a consequence of using imperfect clocks which depend
upon the speed of propagation of waves through a medium. An
observer could choose to use "meta-clocks" which do not depend
upon the speed of sound or the properties of the medium they
reside in. Against such meta-clocks the observer could measure
the slowing of his own imperfect clocks and of his own biological
processes as his velocity increased.
If a physicist in the alternate universe could devise a way
to construct an enclosure out of matter from our real universe,
it would not be subject to the speed of sound limitations in his
universe. Such an enclosure could fly through his air medium at
any speed whatever, shielding occupants within (still composed of
"sound" atoms) from experiencing space and time contractions. By
analogy, if real physicists could find a way to construct an
enclosure out of substance which was not subject to the
limitations of ordinary matter (all electromagnetic forces
propagate at the speed of light), then they too could move
through the universe faster than light without suffering space-
time contractions -- or violating causality!
If the reader accepts this analogy, then we have
demonstrated that wondrous things are possible. Although it may
be that our starting point is incorrect, nonetheless if it is
not, then faster-than-light travel is possible. And if there
truly is a "sea of entities", then there will be no such thing as
"black holes" in the usual sense, nor singularitias in nature.
Dense masses will be capable of shielding some of the matter in
their interiors from acting on the external universe (a violation
of the "Universal" Law of Gravitation), which would prevent
escape velocities for such dense masses from ever reaching or
exceeding the speed of light. There may come a day when we
master the utilization of the entities through which light
propagates, using them for communications as easily as we have
now mastered the use of light itself.
F. The Big Bang Universe
Our examination of the large scale structure of the universe
would not be complete without adding some obvious corollaries of
the assumption that it is infinite in extent, time, and scale.
At SOME level of scale, whether that be "super-bubble-clusters"
or well beyond, the structure may become non-uniform in the
extreme. It may appear at first that there are limits to the
matter in the universe; but we will eventually discover that
other such super-super structures exist at vast distances. It
will be analogous to finding the limits of stars within our own
galaxies, later to discover that there are entire other galaxies
at vast distances beyond ours.
Related problems for the Big Bang theory are that the
distribution of matter on the largest scales is supposed to be
uniform; and the highest redshift galaxies should consist of only
very young stars. The highest redshift quasar to date, 4.73, has
an ordinary spectrum, implying roughly the same materials and
evolution as later galaxies. And the smoothness of the cosmic
background radiation ("the heat left over from the creation of
the universe") contrasts with the lumpiness of matter in
galaxies, clusters, super-clusters, and bubbles.
If the universe is infinite in extent, duration, and mass,
how can such an idea be reconciled with the Big Bang theory, or
with the observed "expansion of the universe", or with the
universe's "observed" age?
All of modern cosmology is based ultimately upon a very
small number of observed facts, the chief of which is that the
further away a galaxy is, the more its light is redshifted. For
lack of any better explanation, the redshift of galaxies has been
assumed to be due to a velocity of recession. Hence, the further
away a galaxy is, the faster it is receding from us (and from all
other galaxies). A traceback of these fleeing galaxies with
their "observed velocities" tells us the "age of the universe" --
the time when this expansion began. The theory which explains
the beginning of the expansion of the universe in an explosive
event is called the Big Bang theory.
We also observe a cosmic microwave background radiation
nearly uniformly around the sky, with a peak temperature of 2.78
degrees Kelvin, which is interpreted as the remnants of the
"fireball" from the Big Bang explosion.
A third observation useful to cosmologists is that, if
redshift (z, the ratio of cosmological wavelength to local
wavelength for known spectral features) is interpreted as a
velocity indicator, and if velocity is a distance indicator, then
the space density of radio galaxies increases at one goes further
out into the universe.
The redshifts and the microwave background radiation are
observed facts. It is easy to forget that their interpretation
as velocities and fireball remnants, respectively, is theory.
There is nothing compelling about these interpretations; they
were merely the best available explanations at the time they were
thought of. We must continually evaluate whether or not these
theories continue to be of value (i.e. make useful predictions),
and whether they continue to be supported by newer observational
data.
Arp's book, "Quasars, Redshifts, and Controversies", offers
compelling evidence from many different sources that at least
some galactic and quasar redshifts are not due to velocity. But
if some are not, then we must question whether any large
redshifts are due exclusively to velocity. Indeed, we must
question whether it is reasonable to continue assuming that the
universe is expanding at all. Even if Arp were wrong about all
of the evidence he presents, it would still be reasonable to
question the velocity interpretation of redshifts. There is,
after all, next to nothing in the way of evidence that the
redshifts ARE due to velocities. It is merely the case that
objections have been raised to all other possibilitias proposed
to date.
G. The Weak Light Universe
It has been proposed by many authors that redshifts of
distant objects may be in part due to a loss of energy of photons
which have traveled very great distances. The objections to this
idea, called the "tired light" theory, are twofold: (1) If the
energy losses are due to interaction with particles in space, the
resulting "scattering" effect on the photons would prevent images
of distant objects from being sharp in our telescopes. (2) Type
I supernovas from extragalactic sources have their lightcurves
stretched out in time as expected if the galaxies are truly
receding from us at their redshift velocities, but not as
expected if their relative velocities are much lower.
However we can readily visualize that a sea of gravitons
traveling many orders of magnitude faster than light would not
necessarily be subject to these objections, because the energy
losses would be slow, gradual, and continuous. Let us describe
this new variation of the "tired light" theory by the
description: the "weak light" model for cosmological redshifts.
It has the immediate advantage that the same mechanism, the
cumulative energy loss effect of the passage of photons through
gravitational fields, could also explain anomalous redshifts for
seemingly nearby quasars, since quasars are also associated with
intense gravitational fields.
More specifically, in the Weak Light model, we propose that
the redshift of starlight from distant galaxies is produced by
the same mechanism as that which produces gravitational
redshifts. But it is the continuous background of a sea of
gravitons which serves as a medium for light to propagate in, as
well as giving rise to the force we call gravity in the vicinity
of masses, which produces the redshift. So the properties of the
Weak Light redshift include propagation delay, just as is true of
gravitational redshifts, or of any wave propagating through a
medium (i.e. refraction slows propagation).
Indeed, in an infinite universe, there must be some such
loss of energy by photons, forcing them out of the range of
visible light. If there were not, then Olbers' Paradox would
come into play: in an infinite universe, a line drawn in any
direction would eventually intersect a star from which photons
are emerging; hence the sky would be everywhere bright. The
shift of photons out of the visible range through this
"frictional" energy loss with the graviton sea can explain why
the sky is dark; and it causes a redshift of the light of
galaxies even without any expansion of the universe!
It will eventually be possible to distinguish between the
two possible causes of redshift: high velocity, in the Big Bang
theory; or energy loss by passage through a refracting medium, in
the Weak Light model. In the Big Bang theory, matter does not
form into galaxies for about a billion years after the
originating explosion, so there is a maximum possible redshift
for the youngest galaxies we can ever observe. This maximum
should occur at redshifts of about 50 or so. At longer
wavelengths there should be few photons from the relatively cold
gas which has not had time to form into stars and galaxies.
Finally, the background spectral feature in the microwave region
is the fireball remnant, with nothing observable except neutrinos
expected beyond that.
In the Weak Light model, there will be no such limit to the
redshift of ordinary galaxies, which will be ever more abundant
as one observes fainter and fainter, perhaps without limit.
Galaxies with redshifts of 100 will eventually be found, then
1000, etc.
H. The Microwave Blackbody Spectrum
The spectrum of the cosmic microwave radiation has been
determined to be quite close to that of a "blackbody", which is a
type of spectrum requiring a fairly narrow source, such as the
"surface" of a fireball remnant. So if the microwave radiation
is indeed "background", i.e. coming from beyond the remotest
galaxies, then it surely is what the Big Bang theoreticians have
hypothesized: the remnant of a gigantic explosion involving much
or all of the visible universe.
But there is another possibility. Really, any fireball
remnant which surrounds us would produce almost exactly the same
type of spectrum. For example, if a supernova in our part of the
galaxy exploded in the past, its fireball would eventually
encompass us. Once inside of it, we would see a blackbody
spectrum coming uniformly from all directions on the sky, which
would inevitably cool to 2.78 degrees Kelvin at some time in its
history. We would be virtually unable to tell the difference.
The reason for the uniform appearance for an observer not
near the center of the remnant may need some explanation. It is
well known in physics that any inverse square field emanating
from a spherical shell will produce a uniform effect everywhere
inside the shell. (For example, the gravitational potential
inside of a massive spherical shell is constant.) To see why,
consider the radiation into a certain solid angle arriving at an
observer at some distance inside the shell. The flux seen by the
observer will vary inversely with the square of the distance; but
the area of the shell emitting into that solid angle will
increase with distance squared. The two effects exactly
compensate, keeping the flux at the observer constant regardless
of the distance to the shell wall. It follows that observers
inside a fireball remnant would continue to be irradiated by it
at some constant flux level no matter how large the fireball
expanded, but for the fact that the fireball cools and gradually
emits less flux with time.
The distance of the microwave radiation is difficult to
determine. But perhaps our new "COsmic Background Explorer"
(COBE) satellite will find some evidence in mapping the microwave
emissions from over the entire sky. For example, gravitational
lensing effects might tend to brighten a background source in
that direction. So if COBE sky maps trace outlines of bubbles
and walls and other large scale features of the universe, the
source must be more distant than those. On the other hand, if
the maps have asymmetries similar to our own galaxy, that would
argue strongly for a source related to our galaxy.
Another good test of cosmologies is provided by the radio
galaxies, whose space density seems to increase with distance.
In the Weak Light model, distance is proportional to redshift,
not to velocity. For example, at redshift z = 1, velocity = 0.6
c, and the distance is about 9 billion light years in the Big
Bang theory; but the distance would be 15 billion light years
(the Hubble radius) in the Weak Light model, which implies nearly
five times the volume of space out to that distance. There is
more volume in the Weak Light model corresponding to any given
redshift, so the inferred densitias are less.
As soon as we can observe and count the number of galaxies
at large redshifts, we will be immediately able to distinguish
between the two theories. We do have to be careful, though, that
we use only cosmological redshifts in making such a comparison.
Much evidence has accumulated in recent years that many quasars
are not at the distances indicated by their redshifts. For
example, many high-redshift quasars are associated with low-
redshift galaxies.
If the Weak Light model does not seem probable to the
reader, he should at least appreciate how amazingly fragile is
all of modern cosmological theory, based as it is on an
assumption (that redshifts are due to velocities) whose rationale
has since been severely undercut (some redshifts apparently are
not due to velocities).
The Big Bang theory, the physical limitation of the speed of
light, the existence of "black holes" -- three fundamental tenets
of present day cosmological research. There are reasons to
believe that none of them is correct as customarily interpreted.
We have also examined an alternative model which, at worst, has a
comparable number of objections to it as the Big Bang theory, and
perhaps fewer. But this model is deductive, not inductive. So
it can be invalidated only by faulty reasoning or an incorrect
starting point or assumptions. If it explains existing
observations, provides insight and understanding, and predicts
new things not previously known, I argue that is sufficient for
it to be worthy of consideration AS A HYPOTHESIS in the field of
astronomy.
It should not be ignored that the model we have presented
also offers an explanation of the how and why of the fundamental
behavior of large scale processes in the universe, all in a
single, coherent model. Separate AD HOC explanations are needed
for many phenomena in the conventional models.
******** Clearly the same model could be extended to small scale
phenomena as well. For example, why do photons and electrons
behave as if they are particles when observed individually, and
waves when observed collectively? The model suggests that they
are pure transverse waves in a continuum; and that, when they
encounter other substance, they THEN give the appearance of being
particles. But that may be an illusion produced by interaction
with the substance they encounter. The model provides such a new
view of phenomena that all of quantum physics must be re-thought
in this light. Since quantum physics already has reality
paradoxes, a new way of interpreting its phenomena is at least
timely, even if beyond the scope of this on-line course.
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