Abstract
In 1986 Ephraim Fischbach, Sam Aronson, and Carrick Talmadge proposed a modification of Newton’s law of universal gravitation. This modification changed the gravitational potential from V = −Gm 1m 2∕r to V = (−Gm 1m 2∕r)[1 + αe −r∕λ] where α, the strength of the interaction, was approximately one percent and the range of the force λ was approximately 100 meters. This additional term was known as the Fifth Force. This suggestion was based on tantalizing evidence provided by a reanalysis of the Eötvös experiment, an early test of the equivalence principle, a difference between the measured value of G, the gravitational constant, as determined by laboratory measurements and those performed in mineshafts, and a small energy dependence in the CP-violating parameters in K 0-meson decay. The two initial measurements of the Fifth Force disagreed. One supported its existence and the other did not. How this discrepancy was resolved and the subsequent history of experiments on the Fifth Force will be discussed. By 1990 the consensus was that such a Fifth Force did not exist. Despite that judgment, work continued, and the more recent history of the Fifth Force is also discussed. The consensus remains that there is no Fifth Force.
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Notes
- 1.
Physicists, at the time, spoke of four forces: 1) the strong or nuclear force, which holds the atomic nucleus together; 2) the electromagnetic force, which holds the atom together; 3) the weak force responsible for radioactive decay; and 4) gravity. Although the Fifth Force was a proposed modification of gravity, it involved the exchange of a different particle, a massive scalar particle, and so was considered as another force.
- 2.
This was a reference to the fact that the proposed Fifth Force, unlike gravity, was composition dependent. The Fifth Force between two lead masses would be different than the Fifth Force between a lead mass and a copper mass. The Fifth Force, as discussed below, also differed from the force of gravity in its dependence on the distance between the masses.
- 3.
The Moriond Workshops, devoted to“new and exotic phenomena,” were very important in the history of the Fifth Force. Not only were new results presented, but there was rigorous criticism of the new work, both formal and informal.
- 4.
For a more complete and detailed history, see Franklin (1993).
- 5.
CP symmetry allows the \(K^0_S\) meson, the short-lived neutral K meson, but not the \(K^0_L\) meson, its long-lived counterpart, to decay into two pions. In 1964 Fitch and Cronin and their collaborators (Christenson et al. 1964) found evidence for the two-pion decay for the \(K^0_L\) meson and thus for CP violation.
- 6.
The K mesons, along with the Λ hyperon, had rather peculiar properties. They were copiously produced in strong interactions but decayed rather slowly by means of the weak interaction. No other particles, at the time, behaved in this manner. This led Gell-Mann and Nishijima to suggest that the K mesons possessed a property called strangeness, which was conserved in the strong, but not in the weak, interactions. This would explain the odd properties of the K mesons. The K 0 and its antiparticle the anti-K 0 had strangeness 1 and − 1, respectively. At the time of the Fifth Force, the conservation of strangeness was an established conservation law. When physicists spoke of the strong interactions, they spoke of the K 0 the anti-K 0 mesons. In discussing the weak interaction, they spoke of the \(K^0_S\) and \(K^0_L\) mesons, which were different linear combinations of the K 0 the anti-K 0 mesons.
- 7.
The K 0 mesons would be stable if the range of the force was of the order of the radius of the Earth, something Weinberg regarded as unlikely.
- 8.
The phenomenon of regeneration was one of the very unusual properties of the K 0 mesons. An accelerator-produced beam of K 0 mesons contains \(50\% K_S^0\) mesons and \(50\% K_L^0\) mesons. If one waited until all of the \(K_S^0\) mesons decayed and then allowed the remaining \(K_L^0\) mesons to interact with matter, one found that the beam once again contained \(K_S^0\) mesons. They had been regenerated.
- 9.
These energy dependences later disappeared, but at the time, they were “tantalizing” effects.
- 10.
Ephraim Fischbach gave me a copy of the referee’s report.
- 11.
- 12.
Although a varying constant seems like an oxymoron, it is useful shorthand.
- 13.
Later work would show that no effect existed.
- 14.
Fischbach has stated that Fujii’s work had no direct influence on this work. He keeps detailed chronological notes of papers read. He reports that he has notes on Fujii’s work at this time, but does not recall it having any influence on his work.
- 15.
An interesting aspect of this reanalysis was reported in a footnote to this paper. Rather than reporting the observed values of Δκ for the different substances directly, Eötvös and his colleagues had presented their results relative to platinum as a standard.“The effect of this combining say Δκ(H 2O − Cu) and Δκ(Cu − Pt) to infer Δκ(H 2O − Pt) is to reduce the observed effect (for water and platinum) from 5σ to 2σ” (Fischbach et al. 1986a). Δκ(H 2O − Cu) = (−10 ± 2) × 10−9 and Δκ(Cu − Pt) = (+4 ± 2) × 10−9, respectively. Adding them to obtain Δκ(H 2O − Pt) yields (−6 ± 3) × 10−9. Fischbach and colleagues chose to use copper as their standard which minimized the need for such additions.
- 16.
A skeptic might remark that the effect is seen only when the data are plotted as a function of Δ(B∕μ), a theoretically suggested quantity. As Alvaro De Rujula remarked,“In that case, Eötvös and collaborators would have carried their secret to their graves: how to gather ponderous evidence from something like baryon number decades before the neutron was discovered” (De Rujula 1986a, p. 761). Although one may be surprised, along with De Rujula, that data taken for one purpose takes on new significance in the light of later experimental and theoretical work, it is not unprecedented.
- 17.
There is some question as to whether Galileo ever performed this experiment. See Cooper (1935).
- 18.
De Rujula’s analysis was important because it answered the question of whether one should use reduced mass. In several measurements Eötvös used a brass vial to hold the sample of the material. In reporting the final results, he multiplied the measured value Δκ by a factor (M Sample + M Container )∕M Sample . This assumed that the container had no effect on the measurement. This was a reasonable procedure if one was interested only in setting an upper limit but might overestimate the effect. Fischbach and collaborators had used the“composite” value, whereas De Rujula used the reduced value (vials not included). The agreement of the two slopes showed that the analysis was independent of which one used, as long as one remained consistent.
- 19.
Boynton had initially found a 3.5 standard-deviation positive effect. His later, more accurate experiments found no effect.
- 20.
With apologies to George Lucas.
- 21.
I will not discuss several fascinating proposed experiments, which were never performed. For details of these proposals and for a more detailed history, see (Franklin and Fischbach 2016).
- 22.
This was similar to Bennett’s experiment at the lock on the Snake River, discussed earlier.
- 23.
These were discussed earlier.
- 24.
The group also included Fischbach and Talmadge, two of the initial proposers of the Fifth Force hypothesis.
- 25.
As we shall see below, this is not quite accurate.
- 26.
The title of the paper was, “New tests of the universality of free fall.”
- 27.
The group also stated that, “We also test Weber’s claim that solar neutrinos scatter coherently from single crystals with cross sections ∼ 1023 times larger than the generally accepted value and rule out the existence of such cross sections” (Su et al. 1994, p. 3614). For a more detailed history of this episode, see Franklin (2010).
- 28.
The major purpose of the experiment, as the title of the paper reveals, was to measure G, the gravitational constant.
- 29.
- 30.
The Eöt-Wash group continued its whimsy with the naming of their new apparatus.
- 31.
Focardi’s paper was presented at a conference in 2000, but the conference proceedings were not published until 2002.
- 32.
For various personal reasons, Bennett did not publish these results until 2001.
- 33.
The title of their paper is “Testing the equivalence principle on a trampoline.”
- 34.
This was the approximate range suggested in the initial paper, based on the (later withdrawn) results of Stacey and his collaborators. The data of the Eötvös and his collaborators is consistent with ranges up to 1 AU.
- 35.
- 36.
As we saw in Section 7.2 and in the history presented above, this is not accurate.
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Franklin, A. (2018). The Rise and Fall of the Fifth Force. In: Rowe, D., Sauer, T., Walter, S. (eds) Beyond Einstein. Einstein Studies, vol 14. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-7708-6_7
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