The Density Gradient in White Dwarf Stars

Dewey B. Larson

In connection with assembling the material for a new edition of the 1959 book in which I introduced
the theory of a universe composed entirely of motion, I am reviewing the progress that has been made
in the intervening 22 years, both in the development of the details of the theory itself and in the fields
of observation and experiment, to make certain that the new work has the benefit of these advances.
One item that came to my attention during this review is particularly important because it supplies a
positive verification of the theoretical findings as to the structure and density of the white dwarf stars, a
result that has far-reaching implications.

In order to appreciate the significance of the observed facts in relation to the theory, it is necessary to
understand the general nature of the motion of which the theoretical universe of motion is composed.
The most important direct consequence of the postulates that define this universe is the existence of a
general reciprocal relation of a scalar nature between space and time. By reason of this reciprocal
relationship, motion in such a universe can take place either on the basis of a space-time ratio of 1/n, a
speed less than unity (which we can identify as the speed of light), in which case the change of position
takes place in space, or on the basis of a space-time ratio of n/1, a speed greater than unity, in which
case the change of position takes place in time. The first of these alternatives is the prevailing motion in
our immediate environment. What I have shown in my previous publications is that the extremely
compact astronomical objects discovered in recent years—white dwarf stars, pulsars, quasars, etc.—are
aggregates whose components are moving at greater-than-unit speeds.

Of course, the idea of speeds in excess of the speed of light conflicts with Einstein’s dictum that such
speeds are impossible, but to err is human, and Einstein is no exception. As usually happens in such
cases, the error stems from the use of an invalid assumption. In his book, The Character of Physical
Law, Richard Feynman points out that when we put all of our presumed knowledge together, “we get
inconsistency, because we get infinity for various things when we calculate them, and if we get infinity
how can we ever say that this agrees with nature?” Feynman attributes this inconsistency to the use of
”*a number of tacit assumptions... about which we are too prejudiced to understand the real
significance.” What Einstein apparently did not realize is that one of the assumptions on which he
based his conclusions violates a universal law: the Law of Diminishing Returns.

Strangely enough, this law, generally recognized in most other fields of thought, is practically ignored
in science. But we cannot repeal a law of nature by ignoring it. This is the law that prohibits the
infinities that Feynman deplores. It tells us that the ratio of the output of any physical process (such as
the acceleration of a mass) to the input (in this case, the applied force) does not remain constant
indefinitely, but eventually decreases, and ultimately reaches zero.

So the relation expressed in Newton’s Second Law of Motion, F=ma, cannot remain constant.
Recognition of this fact leads to an interpretation of the experimental results that is quite different from
Einstein’s. Instead of his conclusion that it is impossible to exceed the speed of light (which follows if,
as he assumed, the relation F=ma remains constant), the correct interpretation is that it is impossible to
accelerate a mass to a speed greater than that of light by means of an electrical force. In other words,
the limitation is not on the speed, but on the capabilities of the process. The significance of this is that it
does not preclude acceleration to higher speeds by other means, such as the sudden release of large
quantities of energy in violent explosions.

Copyright ©1974 by Dewey B. Larson. All rights reserved. Rev. 6

2 The Density Gradient in White Dwarf Stars

One of the reasons why Einstein’s interpretation of the observed facts has been so widely accepted in
spite of its unsound foundation, involves another of the “tacit assumptions” mentioned by Feynman. It
has been assumed that a speed in excess of that of light would result in a corresponding increase in the
rate of change of spatial position. The absence of any observed changes of position at higher rates
(except for some observations of quasar components, whose true significance is still in doubt) has
therefore been regarded as a confirmation of Einstein’s conclusion. But here again, the conclusion that
has been drawn goes beyond the evidence, which applies only to the rate of change of position in space,
and has relevance to the speed only insofar as the change of position due to the motion takes place in
space. In the universe of motion, the change of position is in space if the space-time ratio (speed) is 1/n.
It is thus impossible for a change of position in space to take place at a rate (speed) in excess of unity
(the speed of light), because the limiting value of the quantity 1/n is 1/1. But this does not mean that
higher speeds are impossible; it merely means that motion at higher speeds, with space-time ratio n/1,
is motion in time rather than motion in space.

According to the theory of a universe of motion, the neutral condition is motion at unit speed, and the
motions of the universe as a whole are symmetrical around this level, the true speed magnitude in each
case being the deviation from unity. As a result of the space-time symmetry, the effect of any motion in
time is the inverse of the effect of the corresponding motion in space. The particular motion with which
we are concerned at the moment is the motion imparted to the products of the explosion of a star: a
supernova. Some of the products of such an explosion are ejected at speeds less than that of light, and
they take the form of a cloud of particles moving outward in space from the site of the explosion, but
remaining in the original location (the moving location indicated by a clock) in time. Another portion
of the explosion products is accelerated to speeds greater than that of light. These products take the
form of a cloud of particles expanding into three-dimensional time, but remaining in the original
location in space. This cloud of particles is the white dwarf star.

As I have shown in my publications, a development of the details of the properties and the evolutionary
course of the white dwarfs on this theoretical basis leads to results that are in full accord with the
observations. For present purposes, however, we are concerned only with the density relations. The
expansion of the (relatively) slow-moving explosion products into space results in a large decrease in
the density of the expanding aggregate. Because of the reciprocal relation between space and time, the
expansion of the fast-moving product into time results in a large increase in the density of this
aggregate. The white dwarf star is therefore an object of abnormally high density, compared to a
normal star. Furthermore, the density gradient is the inverse of that which prevails in the normal stars;
that is, the center of the white dwarf is the region of greatest compression in time (equivalent to
expansion in space), and it is therefore the region of minimum density.

This picture of the white dwarf derived from the theory of a universe of motion is, of course, quite
different from the currently popular view, and it is possible that many individuals will find it little short
of outrageous. But the reason for writing this article is that in the course of my review of the progress
in the white dwarf field that has taken place in recent years, it became evident that some of the
information about these objects that is now available supplies a positive confirmation of the upside
down nature of the white dwarf structure.

As pointed out by James Liebert in a review article in the 1980 Annual Review of Astronomy and
Astrophysics, it is generally conceded that the apparently normal matter in the outside layers
(atmosphere) of the white dwarf stars must have been accreted from the environment. (The
development of the theory of a universe of motion arrives at this same conclusion.) This matter, then, is
mainly a mixture of hydrogen and helium, with hydrogen as the major constituent. If conventional

The Density Gradient in White Dwarf Stars 3

theory is correct, the heavier element, helium, will preferentially move downward, leaving the outer
layers of the star enriched in hydrogen. On the other hand, if the inverse density gradient required by
the theory of a universe of motion actually exists, the hydrogen will preferentially move downward,
and the outer layers will be enriched in helium. The verdict from observation is unequivocally in favor
of the universe of motion. Liebert reports that the “cooler heltum-rich stars” are “the most numerous
kind of white dwarf,” and that some have almost pure helium atmospheres. “The existence of nearly
pure helium atmosphere degenerates over a wide range of temperatures has long been a puzzle,” he
says. But it need not continue to be a puzzle. The helium accumulates in the outer layers because these
are the regions of greatest density in the white dwarf.

This theoretical conclusion, strange as it may seem in the light of current thought, is further confirmed
by an examination of the behavior of the elements heavier than helium, commonly lumped together as
“metals” in discussions of stellar composition. The metals, too, should preferentially accumulate in the
regions of greatest density: the center of the star, according to current astronomical theory; the outer
layers, according to the theory of a universe of motion. Liebert describes the observed situation in this
manner:

The metals in the accreted material should diffuse downward, while hydrogen should
remain in the convection layer. Thus, the predicted metals-to-hydrogen ratio would be at or
below solar (interstellar) values, yet real DF-DG-DK stars have calcium-to-hydrogen
abundance ratios ranging from about solar to well above solar.

Here again, as in the helium distribution, the verdict is unequivocal. The larger concentration of the
heavier elements in the outer regions definitely identifies these as the regions of greatest density, a
result that is inexplicable on the basis of conventional theory, but is specifically required by the theory
of a universe of motion. Liebert admits that no plausible explanation on the basis of current
astronomical theory is known. The only suggestion that he mentions is that the accretion of hydrogen
must be blocked by some kind of a mechanism, a far-fetched idea without the least support from
observation.

When it is viewed in conjunction with the gradual decrease in component speeds that takes place as
energy is lost to the environment, the inverse density relation also supplies an explanation of the
occurrence of novae. The continued energy losses eventually result in the speeds of some of the
constituent particles dropping below the unit level, and into the region of motion in space. These
particles then occupy more space because of their spatial speed, and they form “bubbles” that move to
the region of least density, the center of the star. Accumulation of this material with high spatial speeds
builds up a gas pressure. Eventually the pressure reaches a level at which it breaks through the
overlying matter, resulting in a flare-up of the star, as the hot material from the interior is exposed
briefly. The outburst relieves the internal pressure, the star resumes its normal condition, and a new
pressure build-up begins.

The explanation of the origin, the extreme density, the novae, and other properties of the white dwarfs
that I derived originally by deduction from the properties of space and time as they exist in a universe
composed entirely of motion requires some significant conceptual reorientation, and most astronomers
have been reluctant to entertain the possibility that current ideas may have to be altered to such an
extent. However, more and more of those who examine the existing problems carefully are recognizing
that something will have to undergo a drastic change, and are assessing the situation in a manner
similar to the following from Martin Harwit:

The fundamental nature of astrophysical discoveries being made—or remaining to be made

4 The Density Gradient in White Dwarf Stars

—leaves little room for doubt but that a large part of current theory will have to be
drastically revised over the next decades. Much of what is known today must be regarded
as tentative and all parts of the field have to be viewed with healthy skepticism.
(Astrophysical Concepts, Wiley, New York, 1973, page 9)

The big problem, of course, is to determine just what has to be changed, and what has to be put in its
place. The inverse density gradient that we find in the white dwarfs now identifies one of the
requirements that must be met by the “drastically revised” theory. It must provide a new explanation of
the white dwarf structure that incorporates this upside down density relation. Perhaps there are
alternative ways in which this requirement can be met, but it seems rather obvious that the first step in
exploring the situation ought to be to take a good look at the theory already in existence that
anticipated this requirement.