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Gravity, Light, and Force
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 III. GRAVITY, LIGHT, AND FORCE
******** This week and next we will complete our alternative
cosmology from our new starting point. This week we will speak
of the nature of force in general and gravitation in particular.
Next week we will cover applications and implications. In the
following week, we'll switch to the solar system.
A. The Nature of Gravitation
"Every particle of matter in the universe attracts every
other particle of matter with a force which is directly
proportional to the product of the masses, and inversely
proportional to the square of the distance between them."
(Newton's Law of Universal Gravitation)
Why! Physics has come to understand something of the nature
of light and sound, of matter and energy, of force and motion.
We know that heat is a phenomenon caused by the motion of
molecules. Matter is composed of molecules, which are composed
of atoms, which are composed of baryons, etc. Forces are
understood as something pushing against something else, or as
action and reaction. But our understanding of gravity is at a
far more primitive level. We can describe operationally HOW
gravity acts, and the gravitational laws of motion must be the
most exactly measured and confirmed in physics. But we really
know very little about the WHY of gravity. This is primarily
because of its remarkable properties, which seem to defy all
understanding.
"Every particle of matter in the universe" -- regardless of
chemical composition, regardless of atomic makeup, regardless of
charge or spin or any other property -- surely a remarkable
thing. "Attracts" -- other forces of nature have both attractive
and repulsive manifestations, but gravity always attracts -- why?
"Inversely proportional to the square of the distance" --
this is perhaps the easiest property of gravity to understand,
since it is true of so many other physical manifestations. As
something (light, sound, energy) propagates, it spreads out in
two dimensions as it moves forward in a third dimension and in
time. This causes an inverse square weakening, simply because
the "area" of the propagating something increases with the square
of distance, so its "density" (substance per unit area) must
decrease with the square of distance.
Although not spelled out explicitly in the universal law of
gravitation, there are two other remarkable properties which need
elaboration before we can begin any contemplation about why there
is universal gravity. The first is the question of "action at a
distance". (We will save the second, the "instantaneous" nature
of the action, for a bit later in this discussion.) Can one
object act upon another at a distance without some agent passing
between them? In the case of atomic forces, there certainly are
such agents, said to be photons travelling at the speed of light.
However in the case of gravity, it is commonly supposed that
there is no agent.
B. Action at a Distance
Isaac Newton is credited as the first to make a remark which
I personally find to be compelling: it is surely impossible for
one body to influence another at a distance without the action of
some agent passing between them. Forces, such as gravity or
magnetism, which appear to act at a distance must actually
consist of SOMETHING which passes between the source body and the
affected body. In other words, "action at a distance" in its
purest form, where something far away is affected by something
locally without any causative agent passing between the two, must
logically be impossible. In the cases of gravity and magnetism,
this postulate is reinforced by the observation that the field of
force exists continuously at every distance from the source,
suggesting an outward propagation from that source.
Sometimes physicists talk about the "curvature of space-
time" near a massive body, predicted by Einstein's Relativity
Theory, as an example of action at a distance. But SOMETHING
must act to maintain the so-called "curvature of space-time" at a
distance. Moreover, if the massive body is suddenly accelerated,
it must take a finite time (however small) for the accompanying
"curvature of space-time" to respond and begin accelerating too.
If the massive body were to cease to exist, there must likewise
be a finite time before the "curvature" also ceased to exist.
This is merely restating the first principle, that there must
exist some agent which passes between to accomplish any action;
and this agent cannot act instantaneously, because its velocity
must be finite. (Note, however, that there is nothing in the
field of logic which compels us to set any upper limit on the
speed of such hypothetical agents; it particular, logic alone
does not place any requirement that they travel at the velocity
of light or slower.)
The agents which produce forces must exist; therefore they
must be tangible in some way. Everything existing is classified
as either matter or energy; and ultimately, all matter and energy
are interchangeable (matter can be converted completely into
energy, and vice versa), according to modern-day physics. For
purposes of this discussion, it is unimportant whether the
"agents" which give rise to forces are matter or energy, or
"something else"; but it will be convenient to think of them as
having "substance", at least on some infinitesimal scale.
Therefore I suppose, and feel no doubt in my supposition,
that gravity acts by means of some sort of agents making contact
with matter, despite no such agents being as yet known to
physicists. Conceptually, the only way that "agents" have to act
on bodies is by means of collisions. If an agent does not come
into contact with a body to influence it, then we have another
"action at a distance" dilemma, once removed. "Collisions" which
lead to sticking, or to destruction of the target body, may be
thought of as consisting of numerous elastic, non-destructive
collisions occurring at a more microscopic level. It is also
intrinsic to any collision that it requires a finite time
interval; it cannot occur instantaneously.
C. The Sea of Agents
We might then imagine two possibilities: the agents come
from within the matter which attracts; or the agents originate
outside the matter. Our first impulse is to assume an origin
from within; but it is not easy to see intuitively how agents
coming from within one body, then travelling to and making
contact with a second body, can give rise to a force of
attraction between the two bodies. Such a force would logically
be "pushing", or repulsive. On the other hand, a sea of rapidly
moving agents everywhere outside a body would tend to push down
on the surface of the body, giving rise to an apparent force of
attraction toward the center of the body. Moreover, two bodies
would shadow each other from some of the agents, giving rise to
an apparent force of attraction between the bodies (since fewer
agents would be available to "push" from the shadowed side than
from the opposite side of each body).
Such a force would be always attractive, as gravity is. If
the universe is filled with these "agents", the force would be
universal. The force would be inverse square, as would any force
from agents which diverge in two dimensions while moving in a
third.
And lastly, assume that the agents are sufficiently small
that most of them can easily pass entirely through large solid
bodies without contact. (Recall that, at the atomic level,
ordinary matter is mostly empty space anyway.) Then every atom
of matter, even the ones near the center of the body, will
contribute its share to the net "gravity" force exerted by the
body, because the occasional collision between an agent and an
atom of matter in the body would be equally likely to occur for
every unit of mass. (The agents which pass through without
contact contribute no force at all. Matter which deflects agents
then shields matter behind it from the possibility of collision
with the same agents, which results in an imbalance of collisions
on one side.)
To summarize, consider a spherical body of ponderable mass.
Although the hypothetical agents are flying through it all the
time, some of them are always colliding with the atomic particles
making up the body, producing push-like forces. When a collision
occurs, the agent rebounds, and therefore is not available to
collide with other atomic particles deeper in the spherical body.
This means that more agents strike every atom from above than
from below, because of the shielding effect of the nearby matter.
The resultant of all such collisions must therefore be that every
particle of the spherical body is "pushed" in the net direction
toward the center of the mass, where the most shielding from
push-collisions occurs.
If the picture is not yet clear, take it to the logical
extreme: suppose the matter in the spherical body was so dense
that no agent could penetrate, and every agent reflected off the
surface of the body. Then all collisions of agents with the
spherical body would serve to cause a downward force at the
surface of the body pushing toward the center. The body seems to
have "gravity", and would be held together, even though its atoms
do not, in this concept, actually attract one another.
Now suppose we have two spherical bodies of ponderable mass
some distance apart. Each shields the other from some collisions
by the omni-present agents. The result is that each body
experiences more "pushes" from one side than from the side toward
the other body. It is just as if the two bodies somehow
magically attracted one another from a distance -- but all of the
action is produced by the pushing collisional forces of the
supposed universal agents.
Since the spherical bodies are nearly transparent to the
rapidly-moving agents, every particle of matter within them helps
contribute to the "force" experienced by the remote body.
Moreover, since the angle subtended by the remote body decreases
with the square of the distance from the shielding body, the
force it experiences is inversely proportional to the square of
the distance between the bodies. In other words, the
hypothetical force we have just constructed exactly mimics
Newton's Universal Law of Gravitation.
D. The Role of Time Delay
If the basic model is clear, let me now turn to a potential
problem with it. The objection has been raised that the
hypothetical "sea of agents" should act like a "perfect gas".
This means that it should apply pressures equally on all sides of
every particle. There should then be no more of a tendency for
two bodies in space to attract each other because of collisions
with agents, than there is for two bodies in air to be pushed
together by collisions from air molecules.
To see this point from a different perspective suggested by
Hal Finney of CIS's ASTROFORUM, consider an infinite wall of
infinite density, through which no agents can pass. If an
ordinary body approaches the wall, agents strike it from the
outside, producing a force toward the wall. However those agents
which get through fill the space between the body and the wall,
eventually to the same density as those outside; and provide an
equal number of strikes from the inside, which should produce an
equal force away from the wall. So the body should experience no
net force.
Since the objection is important, let me provide one last
example of it. Consider a linear chain of simple particles. At
first glance it appears that the particle on the end of the chain
will be struck by agents more often from above than below, and so
will experience a force toward the rest of the chain. But on
further inspection it may be seen that each of the other
particles in the chain reflects some agents back toward the first
particle, exactly compensating for the agent collisions which
were otherwise missing from below. Again, there would be no net
force.
This objection must be answered to preserve our starting
assumption that some such agents must exist to produce the action
of gravity over finite distances. If the agents were absorbed
instead of reflected, a net force would occur; but all bodies
would be continually increasing the total amount of their
substance. If agents were absorbed from one direction and re-
emitted in a completely random direction, they would still behave
like a perfect gas, producing no net force.
But even a perfect gas produces pressure. The resolution of
the dilemma appears to be that the compensating forces occur
after a transmission time delay, so that they do not balance.
For example, in the chain of particles, those reflected back from
inside the chain arrive later than those which strike the first
particle from the outside, resulting in a net force toward the
center of the chain. For the infinite wall, the agents between
the body and the wall apply their back pressure slightly later
than the agents striking from the front. These agents differ
from the perfect gas because they penetrate matter, and because
the back-scattered agents apply their back force slightly later
than the arriving agents apply the forward force.
It might seem that, after a time, the number of "old" agents
applying back forces would equal the number of "new" agents
applying forward forces, giving no net force. But the imbalance
my be seen to be present for any single agent. So no matter how
many agents are present, the imbalance cannot be nullified;
rather, it is multiplied agent-by-agent.
It might also seem that this time-delay property was invoked
to save the model: always a risky proposition. But on reflection
it may be seen that the delay property for the sea of agents is
required, not arbitrary. Moreover, it expands the model in some
additional, remarkable ways. We reasoned earlier that, at the
most minute levels, space-time must be everywhere filled densely
with substance. In order to change the motion state of a body
(for example, to give it a small impulse, so that it moves
slightly faster), it is necessary to push the substance
immediately in front of the body out of the way, which in turn
pushes other substance, and so on. In other words, a wave is
sent out from the body through the substance which fills space.
And the body itself feels resistance to this change in its state
of motion; that is, it exhibits "inertia" (resistance to changes
of motion).
At the same time, the impulse tends to create a vacuum
behind the body. But as already noted, the substance of the
universe will immediately rush in to fill any vacuum, followed by
other substance further out, and so on. So we have a wave
propagating outward behind the body, also. The velocity of
propagation of waves in this medium is the speed of light.
Once the state of the body's motion has been altered, and
the substance of the universe has adjusted to accommodate that
change, the body will feel no further resistance to motion (of
the sort it would feel if it moved relative to a medium) because
the state of the entire medium has changed to accommodate the
body. Only if the body tried to move faster than the speed of
light would the medium be unable to adjust fast enough to
accommodate the change of the body's speed.
To elaborate this point a bit, in air the molecules are
widely-spaced; and there is plenty of room to accommodate
molecules with get pushed out of the way. But the substance of
the universe is supposed to be a continuum, with entities filling
all space at all times on all scales. So in order for a body to
accelerate it must displace a potentially infinite column of such
entities. In practice, the pressure of the displacement is a
wave, and propagates away at the velocity of light. So only a
finite number of entities appear to resist the acceleration.
Then once the body has attained a new velocity, the entities
establish an accommodating flow condition on both sides such that
only a new acceleration (or deceleration) would be resisted, but
not the body's velocity. Just as ocean currents do not damp out
from resistance, neither would these presumably frictionless
entity currents.
In addition to giving us an understanding of the origin of
inertia, our sea of agents go one step further. They show us WHY
a uniform acceleration of a body is just like immersing that body
in a gravitational field: in either case, agents pile up on one
side of the body, producing a net force on it. This property is
Einstein's famous "Equivalence Principle". A uniform
acceleration and a gravitational field are indistinguishable
observationally. And so they must be, in this model.
We conclude that such a force produced by the action of a
sea of agents would have all the properties which gravity has.
Since the existence of some such agents seems required to avoid
"action at a distance" paradoxes, we conclude that this is an
operational description of the "how" and "why" of gravity. It
requires the existence of a universal sea of minute substances,
so small that large solid bodies are virtually transparent to
them.
The advantages of the underlying concept we have just
described, which has been discussed by numerous authors since the
eighteenth century, is that it provides an intuitively
understandable construct to explain why there is universal
gravitation, how bodies can act on one another at a distance, why
the force is always attractive, why there is resistance to
acceleration, and why accelerations are equivalent to
gravitational fields. The equality of inertial and gravitational
masses for bodies also follows in a natural way from the model.
E. The Speed of Gravity
The other remarkable property of gravity not explicitly
stated in Newton's Law of Universal Gravitation is that gravity
is assumed to act instantaneously over all distances. In the
equations of motion of Celestial Mechanics, for example, each
body in the solar system affects each other body from its
instantaneous true position. By contrast, solar system bodies
are not SEEN to be in their instantaneous true positions; but
rather, they appear in the positions they occupied when the light
just reaching the observer left them.
Take as an example the case of the Sun and Earth. It takes
light nearly 500 seconds, or 8.3 minutes, to travel the
150,000,000 kilometers between the two bodies. When we look at
the Sun in the sky, we do not see it where it is now, but rather
where it was 8.3 minutes ago. This amounts to a displacement of
about 20 arc seconds on average -- an astronomically large angle,
impossible to mistake. Despite the almost unimaginably fast
speed of light, it is not fast enough to allow the Sun, planets,
or stars to appear in their present locations. In the case of
some distant stars, we see them where they were thousands of
years ago.
Astronomical observations are accurate enough to permit us
to measure the direction of the force acting on the Earth caused
by the Sun. Do you suppose that direction corresponds with the
Sun's apparent position in the sky (which it really occupied 8.3
minutes ago, and is the position from which light now appears to
come), or with the Sun's true instantaneous position now (which
we won't be able to see until 8.3 minutes in the future)? While
the astronomers who calculate the motions of solar system bodies
use equations which assume instantaneous action of gravity, NOT
gravity acting at the speed of light, what would be the
observable consequences of assuming a finite propagation speed
for gravity?
In fact, the Sun's gravity emanates from its instantaneous
true position, as opposed to the direction from which its light
seems to come. If gravity propagated at the speed of light, it
would act to accelerate the orbital speed of bodies. By
observation, no such acceleration exists down to the level of
about one arc second per century squared. The absence of the
acceleration implies that the gravitational lines of force
arriving at the Earth from the Sun are not parallel to the paths
of its arriving photons, but rather have directions which differ
by about 20 arc seconds.
[Understanding why the Sun would accelerate the Earth if
gravity propagated at the speed of light is of no importance to
our discussion. But for those who would like to develop a feel
for this, consider the analogy of a vertically-falling rain
encountered by a rapidly-moving train. The faster the train
moves, the more slanted from the forward direction the rainfall
appears. The faster the Earth's motion, the more slanted in the
forward direction the sunlight (and by extension, its gravity, if
it travelled at light speed) would appear to be. The Sun would
then always have a forward-pulling component to its force which
would accelerate the Earth.]
Relativists have postulated that the speed of light is the
upper limit for the speed of anything with substance in nature.
There are a variety of supporting arguments for this postulate,
some of which seem quite strong. We will consider these
arguments next week. For now, it is enough that the existence of
the postulate should not hinder us from looking at the evidence
objectively.
The absence of an observed orbital acceleration of the Earth
about the Sun places a lower limit to the speed of propagation of
hypothetical gravitational agents between the Sun and Earth.
This lower limit is about 1E8 times the speed of light!
Relativists argue that the existence of the Sun's mass
produces a curve in space-time which bends the motion of bodies
near it, producing what appears to be a gravitational force.
Since the space-time field at the Earth's distance is already
pre-curved by the Sun's mass, the Earth simply encounters the
already curved field and responds to it instantaneously. In this
view, the gravitational force is produced by the Earth's
encounter with the space-time curvature, not by its encounter
with gravitational agents from the Sun which produce the
curvature; so the propagation velocity of the agents, which is
assumed to be the speed of light, is said to be irrelevant.
In point of fact, I believe the reasoning in such a
construction is defective. If the agents maintaining the field
propagate with the velocity of light, then the directions of
lines of force in the field must still suffer "aberration", just
as light does. If the Earth moves through the field with a
velocity of 30 km/s or 1E-4 the speed of light, then the field
lines must seem to stream somewhat toward the Earth, bent by 1E-4
radians (about 20 arc seconds). Just as for light, this effect
arises from the RELATIVE velocity of the Sun and Earth, and is
not dependent upon which is thought to be "moving", and which
"stationary". So the ratio of the speed of a moving body to the
speed of regeneration of the local space-time curvature
determines the resultant direction of the force lines.
To visualize aberration at work, consider the flight of an
arrow from a source (analogous to the Sun) toward a train passing
in a perpendicular direction (analogous to the Earth). The arrow
at all instants moves radially away from the Sun, both before,
during, and after its encounter with the moving train. Now
visualize the path of the arrow as it passes through an open
window, through the train, and out another window on the other
side, without meeting any obstruction. As seen by passengers on
the train, the flight path through the passenger cabin has a
rearward component due to the forward motion of the train.
Indeed, if the arrow interacted with the train by striking it, it
would apply a slight decelerating force to the train. (A pulling
force like gravity would have a slight accelerating component
acting on the Earth.)
The same point may be extended to the mutual interactions of
three or more bodies. Consider the Sun-Earth-Moon system. The
Moon's orbit around the Earth is approximately an ellipse, but
one which is quite distorted by the Sun's gravitation. I myself
have analyzed observations of the two bodies to solve for the
direction of the force exerted by the Sun on the Moon's orbit.
The solution showed that the Sun's force comes from its true,
instantaneous position rather than its apparent, aberrated
position, to a precision of one arc second. (The two positions
differ by 20 arc seconds). This solution alone constrains the
speed of propagation of the Sun's force to be at least 20 times
that of light. No relativist has yet, to my knowledge, devised a
theory to explain how it can be that the direction of the Sun's
gravitational force on the Earth and the direction of the photons
arriving from the Sun are not parallel.
Perhaps contact binary star systems place the tightest
constraints on a lower limit to the speed of propagation of
gravity. Unless the speed of gravity exceeds 1E10 times the
speed of light, such systems would fly apart within a few hundred
years. Moreover, since the centers of mass of the two nearby
massive bodies are accelerating, not merely moving linearly at
high speed, one could show by such examples that even the
response of a gravitational field to an ACCELERATION (not merely
a motion) of its source body must propagate faster than light.
The conclusion of the preceding considerations is that
whatever agents propagate the force of gravity from the source
body to its field must travel at least 1E10 times faster than
light. It might seem that the thrust of the argument is that the
action must be instantaneous. But this would be another form of
action at a distance: action which propagates at infinite speed.
I do not at all propose that the velocity of propagation is
infinite; far from it. A velocity of a MERE 1E10 times light
speed, or across the observable universe in 1.5 years, is a very
far cry indeed from infinite velocity if the universe is truly
infinite.
This disbelief was manifested when the velocity of light was
itself first measured. It took a very long time to accept that a
velocity of 300,000 km/s, or seven times around the Earth in one
second, was real; it had always been assumed up to that time that
light propagated instantaneously throughout the universe. It was
likewise very difficult to accept the initial discovery that
stars were, after all, at a finite distance, although the nearest
of them was 25 trillion miles away! Later it was difficult to
accept the dimensions of our galaxy, or the Hubble age of the
universe. Each time our knowledge of the size and age of the
universe was extended, the initial reaction was disbelief. Then,
when these new limits were finally accepted, each time there was
a tendency to believe that the new limits were truly LIMITS, not
merely the latest extension of our growing knowledge of the
universe.
So the picture of gravity we have arrived at here demands a
universe filled with gravitational agents moving at velocities
much faster than light, in order to explain the nearly
instantaneous action of gravity on the local scale.
F. Some Corollaries
It is logical to ask if the other three fundamental forces
in nature can be modeled in similar ways to gravity. Our
knowledge about the structure of matter below the atomic level is
evolving rapidly, and in my opinion suffers from a lack of
structured models with which to interpret new results. What is
badly needed is a collection of experimental results which must
be adhered to in forming new models. What is made available
instead is the interpretation of those experimental results
("spin", "mass", "charge", etc.).
How can it be possible for protons to repel protons,
electrons to repel electrons, and yet protons and electrons to
attract? We can construct an analog in the meta world of light
and gravity to illustrate one way in which such a thing can
happen. We can make a balloon satellite large enough that the
repulsive force of light from the Sun would be greater than the
gravitational force of attraction between the two. Consider,
then, a set of such balloon satellites and a set of Sun-like
stars. All balloon satellites would gravitationally attract one
another, because they emit no light. All stars gravitationally
attract one another because light pressure is negligible in
comparison with their gravitation. And yet all stars would repel
all balloon satellites because light pressure exceeds
gravitation. Light, because it originates from within, produces
repulsion; gravity is attractive because it results from the
shadowing of external agents.
If matter exhibits gravitation because of the shadowing of
other matter from the action of a sea of agents, it follows that
at some density, the shielding is complete, and no gravitational
agents can penetrate at all. If a sphere of matter were to
collapse to such a high density that no gravitational agents
could penetrate, then only the surface layers would reflect the
gravitational agents. None of the matter in the interior of the
body would make any contribution to the strength of its
gravitational field. It follows that mathematical black holes
would not exist in physics, since the gravitational force exerted
by a finite body cannot become indefinitely large at its surface
as the body collapses. Escape velocities could never exceed the
velocity of light, since that is the limiting velocity of
propagation in the sea of agents which produce gravity.
Direct observational tests for the existence of shielded
mass within large bodies would not be easy, because large bodies
reveal their mass only through their gravitation. The easiest
method would seem to arise in a three-body case. For example,
suppose the Earth were massive enough so as to block some
gravitons from passing through its core regions. Then at the
times of a total eclipse of the Moon, some of the Sun's
gravitation should also be blocked from reaching the Moon. For a
brief period, the net gravitational force on the Moon would
decrease, allowing the Moon to move slightly farther away, and
lengthen its period of revolution around the Earth. Such an
effect is observed, but it is attributed entirely to the effects
of tidal friction. Perhaps observational accuracy will
eventually improve to the point where we can learn if some of the
"tidal acceleration" in fact occurs in discrete increments at
times of lunar eclipse, rather than continuously, as presently
assumed. In any event, a similar test involving more massive
bodies, such as any third body in orbit around a binary pulsar,
could provide the opportunity for a definitive test of this idea.
******** Before we can put this model into proper perspective,
we must complete it; and that requires us to deal with Einstein's
General and Special Theories of Relativity, and the nature of
waves, which we will do next week. We will also see how this
model compares to the real universe, and how it contrasts with
the "Big Bang" theory of the universe.
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