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Antigravity II: A Fifth Force?

by John G. Cramer

Alternate View Column AV-15
Keywords: hypercharge, 5th force, Eötvös experiment
Published in the September-1986 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 2/1/86 and is copyrighted ©1986, John G. Cramer. All rights reserved.
No part may be reproduced in any form without the explicit permission of the author.


    Sometimes physics moves surprisingly fast, sometimes dismayingly slowly. In mid-December, I wrote my AV column (Analog, 7/86) on antigravity, a familiar SF concept. That column was based on a 1957 paper by Bondi on negative mass. Almost nothing had been published on gravitational repulsion in the almost 30 years since the appearance of Bondi's paper. The scientific "field" of antigravity research was essentially non-existent.

    Then, as soon as my column was safely submitted, hot new results on antigravity appeared. The lead article in the January 6, 1986 issue of Physical Review Letters had the unassuming title: "A Reanalysis of the Eötvös Experiment" by E. Fischbach, et al. Two days later the New York Times ran an article with the headline: "Hints of Fifth Force in Universe Challenge Galileo's Findings" describing the importance of Fischbach's work. Peculiar experimental results from terrestrial gravity measurements and from the behavior of "strange" K-mesons (kaons) had been explained by a new theory proposing a "hypercharge" force, a new fifth force of nature which is gravity-like but which repels rather than attracting nearby masses. This new antigravity force is the subject of this AV column.

    The first thread of this story goes back two centuries to Sir Isaac Newton. Newton discovered the famous gravitational "inverse square-law" relation, F12 = Gm1m2/r2, which proved equally useful in predicting the orbit of the Moon and the force of gravity at the surface of the Earth. In Newton's equation G is a fundamental quantity called the universal gravitational constant. Among the physical constants of nature, G stands out as being the most uncertain. Fundamental constants (the velocity of light, the electron charge) are usually known to a few parts per million, but G, with a value of 6.673 × 10-11 m3/kg-s2, is known to only about 1 part in 2000.

    In a way, it is surprising that G is so poorly known. The orbits of planets in our solar system depend directly on G and are both observed and calculated to parts per billion. The problem is that to obtain G from these data we must have a completely independent knowledge of the masses involved in the gravitational attraction. Unfortunately, we have no way, independent of orbital dynamics, of measuring the masses of the Earth, Moon, Sun, Jupiter, etc. Therefore, our imprecise knowledge of G must come from the very weak force of gravitational attraction observed in the laboratory between two masses, for example two large lead spheres placed close together.

    But there is another way of measuring G. The oil industry has developed extremely precise devices for measuring g, the acceleration due to gravity, both on and beneath the Earth's surface. The dependence of the acceleration g on depth can be used to determine the gravity constant G. When the densities of the rock strata have been well mapped, this determination has an accuracy comparable to laboratory measurements of G. One would expect both methods to give the same value of the "constant". It is a big surprise, therefore, that the geological technique gives a value of 6.734 × 10-11 m3/kg-s2 (instead of 6.673 × 10-11). It would appear that this "universal constant" has significantly different values below the Earth's surface and in a surface laboratory.

    The second thread of the story comes from modern particle physics. The species of particles called K-mesons or kaons are unusual among mesons in having a characteristic called hypercharge, a conserved property of certain particles. The neutral "matter" kaon is the Ko theoretically a system composed of a "down" quark and an "anti-strange" quark, has a hypercharge of +1. Its antimatter twin, the Kõ, a strange quark and an anti-down quark, has a hypercharge of -1. Both Ko's have the same electrical charge (Q=0), the same spin (s=0), and the same mass (about half that of a proton). From all external clues these two theoretical particles are indistinguishable except in their hypercharge, which is not directly observable.

    In this situation where two states of matter cannot be distinguished externally, quantum mechanics tells us that a very interesting thing happens. The two indistinguishable states are "mixed" to make two new states of matter which are distinguishable. This mixing produces from the combination (Ko-Kõ) the particle KS which decays in about 10-10 seconds (and so is called K-short). And it produces from the combination (Ko+ Kõ) the particle KL which decays 581 times more slowly (and therefore is called K-long). The KL particle has been found to be very peculiar in its decay into other particles, showing a favoritism for one direction of time over another and for matter over antimatter. These violations of symmetry principles of nature (time-reversal and charge invariance) are not understood in any fundamental way.

    But more recently another peculiarity of the kaon system has been discovered which is even more of a puzzle. Detailed studies of the KL and KS mesons have been made at a number of accelerator laboratories under a variety of experimental circumstances. When these experiments are reduced to the few basic "constants" of the kaon system, for example the KL-KS mass difference and the KS half-life, these "constants" are found to depend on the velocity of the kaons with respect to the laboratory frame of reference. This is not a special relativity effect; those are already included in the data analysis. In fact, this velocity dependence cannot be readily accounted for by any of the four known forces or by any known physical effects.

    Prof. Ephriam Fischbach and his colleagues, in the paper mentioned above, have sought to explain both of these curious results, the variation of G and the velocity dependence of the kaon system, with a single theory. They start with the fact that kaons, neutrons, and protons all have hypercharge. Perhaps, the paper speculates, there is new and very weak force associated with hypercharge which is responsible for the anomalies in both the gravitational and the kaon measurements. Starting from this point, they calculate the properties which such a "fifth" force must have to be consistent with these observations. They conclude that this new force would be very much like gravity, but with four important differences: (1) it depends on hypercharge rather than mass; (2) it is a repulsive force, in that objects with the same hypercharge are repelled from each other; (3) it has a strength only 0.7% that of gravity; and (4) it is a "short range" force which cuts off exponentially at distances on the order of 200 meters.

    This last point requires some explanation. Two of the four known forces of nature, gravity and electromagnetism, are "long range" forces which fall off as 1/r2 with the distance from a massive or charged object but otherwise extend to infinity. The other two known forces, the weak and strong interactions, are "short range" and cut off to zero at distances on the order of the size of a nucleus. These differences in range are attributed to the masses of the "mediating particles" which produce the forces. Electromagnetism is mediated by the photon and gravity by the graviton, both particles with zero rest-mass which give their corresponding forces infinite range. The strong interaction is mediated by the gluon and the weak interaction by the Z and W particles, all of which have masses on the order of that of the proton and give their corresponding forces very short ranges. According to the "fifth force" hypothesis, the range of the force which would account for the G measurements and the kaon anomalies would have to be about 200 meters. This corresponds to a very light mediating particle (the "hyper-photon") with a mass about 10-14 that of the electron.

    This hypothesis can explain the G difference. Gravitating objects within a few hundred meters of each other, for example, the lead spheres in a laboratory measurement of G, feel a 0.7% repulsion from the hypercharge force which reduces the attraction slightly and leads to a slightly low measured value for G. The geological measurements of g, however, record the gravitational attraction of masses which are typically much more distant than a few hundred meters and give a value of G unmodified by hypercharge repulsion.

    The hypothesis can also explain the kaon energy dependence. The Ko and Kõ, with opposite hypercharges, are mixed in slightly different proportions at different velocities because the extra hypercharge force from the nearby neutrons and protons of nuclei in the laboratory acts oppositely on them. Thus their invariant properties become variables. The "true" properties of the kaons, according to the hypercharge theory, would be obtained if measurements were made in empty space with no hypercharge field from nearby matter to modify the Ko+ Kõ mixing.

    Like any theory, this one need testing. And one "test" has already been done and seems to agree with the predictions of the theory. This test was not a new experiment but a re-analysis of the Eötvös Experiment, the famous experimental comparison of inertial and gravitational mass performed by a Hungarian count in the early decades of this century and published only after his death in 1922. Fischbach and his collaborators realized that Eötvös should have seen some evidence for the hypercharge force. The reason is that the hypercharge of a nucleus depends strictly on the number of neutrons and protons in the nucleus, while the mass of a nucleus depends also on the binding energy of the system. Thus an iron nucleus with large binding energy has a larger hypercharge-to-mass ratio than does a hydrogen nucleus. To put it another way, a kilogram sphere of water contains fewer neutrons and protons and has a smaller hypercharge than a kilogram sphere of iron. Therefore the sphere of water should fall slightly faster in vacuum than the iron sphere because there would be a smaller hypercharge force acting on the water than on the iron. The Eötvös experiment should have shown the effects of these small modifications of the force of gravity. And Fischbach's re-examination of the Eötvös data reveals that indeed the predicted effect does seem to be present in the old data.

    This new theory has had its first experimental confirmation. Much more work in testing for the hypercharge force needs to be done, of course, before it can be considered as established. This is a "hot" topic and many experimental groups, including one in my own laboratory, are swinging into action to do the testing.

    But in the nature of this column, let's assume for the moment that the hypercharge force is real and consider its science fiction implications. First, by damn, we have antigravity! But no dancing in the streets just yet, please! For use in the "normal" antigravity way in science fiction, the hypercharge force does have a few problems: (1) it's too weak, and (2) it only works over a few hundred meters of distance. So we need some hypercharge "amplifier", some way for getting more hypercharge without getting more mass. That might be possible if there were massless particles (maybe hyper-photons or neutrinos), that had hypercharge without having a proton-size mass, but none-such are known. Or perhaps there are "hyper-magnetic" effects when a hypercharged object is moved at a goodly velocity.

    Anyhow, suppose we can overcome this obstacle and produce vehicles using hyper-repulsion. How might they work? Well, first of all the range is a problem. At 600 meters above the ground, the range effect will cut down the hyper-repulsion to only 5% of what it is at the surface. So the vehicle would be most effective at distances of 50 meters or less above the surface. It would resemble the "floaters" and "grav sleds" which are common SF techno-props, but it would not be directly useful in space travel or propulsion.

    It's worth considering also that in the process of repelling the ground, the hyper-force on our hypothetical floater would also tend to repel the passengers. This unpleasant side effect might be avoided by placing the repulsion sources for minimum effect on the passengers, perhaps at many points which lie on the same spherical surface. But passenger-repulsion might also be turned into an advantage by using it to reduce or nullify the forces of acceleration. With a suitable hyperfield system high-performance spacecraft or aircraft might might, by balancing inertial forces with hyper-repulsion, be able to accelerate at many g's without squashing pilot and passengers. Free-fall space habitats might produce simulated gravity with hyperfield units mounted in the ceilings, with hyper-repulsion pushing the occupants toward the floor.

    Anyhow, stay tuned to this column for further developments on the hypercharge force. The definitive tests of the theory will be well in progress by the time you read this column.

Followup Note (01/31/2021): Subsequent ultra-sensitive experiments with torsion balances and other work showed no evidence of a 5th force related to hypercharge or other variables.


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: .


G Measurement Anomaly:
S. C. Holding and G. J. Tuck, Nature 307, 714 (1984).

Kaon Anomaly:
S. H. Aronson, G. J. Bock, H. Y. Cheng, and E. Fischbach, Physical Review D28, 476 (1983).

Fifth Force Theory:
E. Fischbach, D. Sudarsky, A. Szafer, C. Talmage, and S. H. Aronson, Physical Review Letters 56, 3 (1986).

Eötvös Experiment:
R. von Eötvös, D. Pekár, and E. Fekete, Ann. Phys. (Leipzig) 68, 11 (1922).

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