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The Dark Side of the Force of Gravity

by John G. Cramer

Alternate View Column AV-05
Keywords: dark matter, axions, space drive
Published in the February-1985 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 8/1/84 and is copyrighted ©1984, John G. Cramer. All rights reserved.
No part may be reproduced in any form without the explicit permission of the author.


    This column is devoted to a scientific mystery story. As we shall see, most of the mass of our universe seems to be in some mysterious and unknown form which we do not presently understand. This puzzle has gradually emerged from the work of physicists, cosmologists and astronomers who are trying in various ways to determine and account for all the mass in the universe.

    The mass-to-volume ratio of the universe is of cosmic importance. It determines whether the universe will expand (as it is presently doing) forever or whether it will eventually recontract to a Big Gnab (the time-reverse of the Big Bang). The Big Bang is somewhat like a cannonball fired from a large Jules-Vern-style cannon on the surface of an airless planet. There is a "magic" cannonball speed called the escape velocity which measures whether its velocity "bank balance" exceeds the gravitational "debt" which must be paid to escape the planet's gravity well. If the cannonball leaves the cannon barrel with a speed greater than escape velocity it will escape the planet's pull; with less than escape velocity it will fall back; with exactly escape velocity it will move ever more slowly away from the planet, requiring an infinite time to escape completely.

    The analog of this cannon is the Big Bang which three or so billion years ago sent all objects in the universe hurtling away from each other, as they continue to do today. There is, however, no "planet" from which these objects (gas molecules, stars, galaxies, clusters) may escape; rather, they seek to escape each other. There is a particular mass-to-volume ratio for the universe which is the analog of escape velocity. It is called the critical density and is about the density produced if 6 pounds of matter were smeared out inside a sphere that enclosed the orbit of the moon.

    Cosmologists use the symbol W to represent the fraction of this critical density which is actually present in the universe. If W is greater than 1.0 the universe is overweight, and its expansion velocity is not enough to overcome the gravity pull of its mass; the universe is "closed" like a black hole and will ultimately collapse to the Big Gnab (bang spelled backwards). If W is less than or equal to 1.0 the pull of gravity is too weak to cause collapse, and the universe is "open" and will continue to expand forever. The question of the ultimate fate of the universe reduces to a single issue: How big is W?

    The simplest way to get at W is to count stars per galaxy, galaxies per cluster, and galactic clusters in an average volume of space. With this information and the average mass of various types of stars W is calculated to be about .05% of critical density. But this mass-census misses any "dark" matter, including interstellar gas and dust, non-luminous planet-size objects, dead stars, black holes, etc. This could represent a considerable fraction of the total mass of the universe, and is a serious error in the method.

    Astronomers can measure the orbital velocities of bright stars at the extreme edges or "haloes" of nearby galaxies, which gives the amount of galactic mass which lies within the orbit of the star. This method has led to a remarkable discovery: there is about 300 times more mass in an average galaxy than can be accounted for by counting stars. Only about 0.3% of a galaxy is in the form of visible stars, so the remaining 99.7% must be something else. This mysterious extra mass gives us an W which is about 15% of critical density.

    This result is confirmed in another way. Shortly after the Big Bang the universe was a sort of nuclear pressure cooker, squashing together protons and neutrons to form most of the deuterium, helium and lithium atoms which we find around us today. The present fractions of these elements tell us a great deal about conditions inside the pressure cooker. To explain the nuclear isotope populations of today a value of W near 0.15 is required. Therefore, two independent methods, the orbits of stars in galactic haloes and nuclear production in the early universe, indicate that the universe has about 15% of critical density. It must be so ... or must it?

    There is a compelling chain of logic indicating that W is exactly 1.0000... and that the universe has exactly critical density. It appears very unlikely that today the universe could be within 15% of critical density by accident. Returning to the cannonball analogy, our "cannonball" (the universe itself) has been "rising" against the pull of gravity for about 3 billion years. In the process both the expansion velocity of the components and the strength with which they pull on each other have been reduced to tiny fractions of their original values. Two exceedingly large energy values (positive kinetic energy and negative gravitational energy) have almost cancelled one another, and the very small remaining fractions of these energies are still within 15% of one another. To accomplish this the original energy values at one second after the Big Bang must have matched to one part in 1015. At the time of "inflation" they must have matched to one part in 1049. That two independent variables should match to such unimaginably high precision seems unlikely; there must be a mechanism. And although theologians tell is that God is good, could He be that good? Cosmologists prefer another mechanism to solve this "flatness" problem: according to the new inflationary scenario our universe has precipitated like a bubble from the energy-saturated H-space medium of the Big Bang. [See my September, 1984, Alternate View column.] The dynamics of the bubble itself produced both the expansion speed of the bubble walls and for the quantity of matter inside, "regulating" the value of W to precisely 1, both today and in the early universe.

    And thus it emerges that we have two dark-matter problems:
(a) "What is the dark matter (DM1) that makes up 99.7% of the mass of galaxies?", and
(b) "What is the other dark matter (DM2) which raises W from 0.15 to 1.00?"
DM1 must be clumped around the galaxies while DM2 must be uniformly distributed. Cosmologists distinguish between "hot" dark matter which arose from the extremely high temperatures present in the early universe, and "cold" dark matter which arose from tangles in the geometry of space itself in the early universe. Examples of "hot" dark matter would be any of several types of massive neutrinos possibly produced in the Big Bang. Examples of "cold" dark matter are such curiosities as "strings" and the "axions" discussed below.

    The current opinion (as of 8/84) among cosmologists is that DM1of the galactic haloes is of the "cold" variety, while the more generally distributed DM2 is of the "hot" type. This conclusion is supported by computer simulations that start from an early universe of smoothly distributed matter beginning to congeal from gravitational attraction and follow the formation of galaxies and clusters, seeking to explain the galaxy-size clumpiness that we now observe. In these simulations different dark-matter prescriptions can be tried and the result observed. If dark matter is omitted there is not enough gravitational attraction to form galaxies. If "hot" dark matter added there is too much attraction and the resulting universe looks nothing like ours. But when "cold" dark matter is added to the recipe the familiar galactic lumpiness emerges in the universe contained in the computer cook-pot.

    Is our universe really permeated with two distinctly different types of invisible stuff which account for most of its mass? That sounds very much like science fiction, doesn't it? OK, so maybe we should explore its science fiction implications. The leading candidate for the mysterious cold dark matter is a hypothetical particle called the axion. Axions have never been observed and (like magnetic monopoles) may be only a part of the mythology of particle physics. They are alleged to be tiny uncharged sloshings back and forth of space itself, sloshings which have both mass and energy but not much of either. It is estimated that the axion has a mass about 1/400,000,000 of an electron mass, and that there should be about half a trillion of them in each cubic centimeter of space in the vicinity of the earth, more per cc near the galactic center, but only 200,000 per cc in intergalactic space.

    Axions have a geometrical resemblance to an electric and a magnetic field oriented parallel to each other. In theory, this property can be exploited to convert axions into photons (radio/light/gamma-rays) through the use of intense electric and/or magnetic fields. If cosmic axions were converted to photons, their estimated mass-energy would make electromagnetic microwaves like those used in home microwave ovens. It has been suggested that the axion-saturated space in our vicinity constitutes a "population inversion" of the sort exploited for lasers, and that under the proper circumstances it might be possible to make an axion-maser which converts this hidden energy embedded in space itself into a coherent beam of microwaves. Zap!! However, before getting serious about building a pocket size axion-maser for barbecuing the opposition it should be realized that the available microwave power would at best be only about 3 milliwatts/cm2 (about 2% of the energy content of sunshine on the equator at noon). This would make for a rather slow barbecue, but might be a useful energy source for other purposes.

    However, the axion energy calculated depends on how rapidly axions enter the converion apparatus. I used a velocity of 0.1% c (light-speed), about the rate of motion of our solar system through the galaxy. If this speed goes up the available energy goes up accordingly. At near-light speeds the available axion-power would be about 3 watts/cm2 times b × g2, where b=(v/c) is the velocity relative to light, and g2=1/[1-b2] is the square of the relativistic mass-increase factor. At a velocity of 99.9% c the available power from axions would be about 1500 watts/cm2, enough power for a modest energy-efficient space drive. And the faster you go, the more such power becomes available.

    The conversion of axions to photons has another interesting property: it makes momentum (or recoil thrust). Every axion which is converted to a photon with the same total energy and going in the same direction produces a momentum kick of Dp = mc × g(1-b) where m is the axion rest mass. This would seem to make possible a fuel-less "axion ramjet" which takes axions in the front and shoots photons out the back, pushing us through the universe in the process. However, there are several "engineering details" to be worked out. The solar system is not an ideal place to use such a drive because the local axion density is so small that a plausible engine would only have a thrust measured in micro-pounds. An axion drive would work best near the galactic center where the axion density should be high and would work worst in the voids between galaxies. We seem to need an "axion concentrator" to make the idea work (space-drive inventors please note). At high velocities one might think that the axion drive efficiency might be much better because the rate of axion intake is increased and because g is larger. However, the push per axion goes down because the crucial momentum kick is obtained from speeding up the axion mass-energy packets to light speed, and as their incoming velocities begin to approaches c the kick gets smaller, reducing the effectiveness of the drive at high velocities.

    So there you are, Dear Readers and Authors: the raw material for almost unlimited free energy, for energy beam weapons, and for fuel-less (but flawed) space drives, all powered by the dark matter of the universe. Maybe Luke and Obi-wan shouldn't have been so down on the Dark Side of the Force.

John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available online as a hardcover or eBook at: or

SF Novels by John Cramer: Printed editions of John's hard SF novels Twistor and Einstein's Bridge are available from Amazon at and His new novel, Fermi's Question may be coming soon.

Alternate View Columns Online: Electronic reprints of 212 or more "The Alternate View" columns by John G. Cramer published in Analog between 1984 and the present are currently available online at: .


Critical Density:
D. N. Schramm, Physics Today 36 #4, 27 (April, 1983).

Inflationary Universe:
A. H. Guth and P. J. Steinhart, Scientific American 250 #5, 116 (May, 1984).

Axion Conversion:
P. Sikivie, Physical Review Letters 51, 1415 (1983).

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