A fifth force farce

On Evidence for a Third Force in the Two New Sciences: A Reanalysis of Experiments by Galilei and Salviati

Abstract: We have carefully reexamined the experiments described by Salviati on the acceleration of objects at the Earth’s surface and find evidence for the existence of a new force. An archival search indicates that this result is supported by earlier work of Aristotle.

Submitted to: Physical Review Letters (and the New York Times)

It is commonly assumed that the work of Galileo Galilei and collaborators ¹ established the basis for the Newtonian theory of universal gravitation, later refined by Einstein. However, we note here that a careful examination of their published results indicates a potential anomaly, which could represent evidence for a new self-coupling resulting in a velocity-dependent force for baryonic matter. Confirmation of this result could help explain earlier anomalous results reported by Aristotle. ² It is possible that other anomalous results ^3–5 may also be explained in terms of this new effect.

In the absence of relativistic effects, and other external nongravitational perturbations, Einstein’s theory predicts a coupling of the form $$V\left(r\right)=\hspace{0.17em}-G_N{m}_1{m}_2/r$$ (1) between two masses m _1,2. Here G _N is Newton’s constant, and r is the distance separating the objects in question.

The experiments of Salviati et al. are reported to have involved in one instance observation of acceleration at the Earth’s surface over a distance of 12 cubits. ¹ Based on information obtained by us, ⁶ we estimate this to be approximately 8 meters. The experiments were performed using “a very round polished bronze ball” of undetermined alloy content and size, and a wooden channel, lined with parchment. Since no lubrication was reported, we may assume a coefficient of kinetic friction in the region 0.07–0.1. We will also assume a drag coefficient of 8 × 10⁻⁵ Ns/m, appropriate for a ball of radius 1 m in air at room temperature.

The results of interest involved observation of distances traversed in consecutive time intervals as the bronze ball rolled down the wooden channel. As reported by Salviati ¹ the ratios of these distances were given by the ratio of consecutive odd integers. It was also reported that no two measurements disagreed by more than $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$10$}\right.$ of a pulse beat and that each set of measurements was performed 100 times. From this, assuming a standard pulse rate of 90 beats per minute based on an exhaustive analysis of medical records from that time, ⁷ we therefore expect a timing accuracy of about 6 × 10⁻³ seconds. For small inclinations, the time required to traverse one tenth of the distance along the wooden ramp could be in excess of 6 seconds. Thus the expected accuracy of the Galilei results is one part in 10⁻⁴.

For experiments of the type described by the authors, several other effective forces in addition to that described in equation ((1)) must be taken into account. These may not be conservative and therefore cannot be derived from a potential. Two that will interest us here are of this type, including a frictional force of the form F = μF _N, where F _N is the normal force of one object on another and μ the coefficient of kinetic friction, and the drag force F = kν, where k is the drag coefficient in air and ν the velocity.

The first effect that could alter the result from the quoted one expected for a constant force is the fact that the actual gravitational potential over the length of the 8 meter channel is slowly varying, as given in (1). Expanding to first order in this length over the Earth’s radius we find δa/a ≈ 3 × 10⁻⁶ for the change in the acceleration from the top to the bottom of the channel. This is below the measurement accuracy derived earlier. Similarly, the frictional force, while non-negligible, is constant and hence, while it would change the absolute value of the measured acceleration due to gravity at the Earth’s surface, it would not change the ratio of consecutive distances traversed in equal time intervals.

The drag force of air on the ball is however both relatively large, and time varying. For small inclinations we expect ν _final in the range of 2–3 meters per second, implying a drag force in the range of 2 × 10⁻⁴ newtons. For inclinations of 10°–20°, the gravitational force is about 1 newton for a 1 kg ball. Thus the expected deviation in acceleration from top to bottom of the channel is about $$\delta a/a\approx 2\times {10}^{-4}.$$ (2) This level is clearly above the quoted limits.

We interpret this result as suggestive of the presence of a new velocity-dependent force which operates on a distance scale of meters which can counteract the effects of the drag force described above. Such an intermediate-range force may in fact have escaped detection in experiments testing Newtonian gravity and its subsequent revisions, although it is not clear to us why the space shuttle is not affected upon reentry. This latter concern might justify a wide range of new experiments performable by NASA. ⁸

Spurred on by this, we have made an exhaustive search of the literature to see if this effect has been previously measured. Such a force seems to have been measured earlier by Aristotle, ² who observed a velocity dependent force resulting in changes in acceleration of order $$\delta a/a\approx 1.$$ (3)

The agreement between equations ((2)) and ((3)) is surprisingly good. Rare K-decay experiments are also suggestive. ⁹

We have also discovered evidence in the work of Galilei and Salviati, and the earlier work of Aristotle, for variations in acceleration at the Earth’s surface depending on composition of the material used. We do not consider this here, however, since the later results of Eötvös et al. ¹⁰ demonstrate convincingly with great accuracy that there is no such effect.

While a repeat of the experiments of Galilei et al. with better sensitivity may be possible with modern techniques, we have not performed such an experiment. While such an effort was being considered, recent results ¹¹ led to it being abandoned. In the meantime, however, Monte-Carlo studies of this effect in a unified gauge field theory are being carried out by A. Chodos et al. ¹² Also, R. Shankar ¹³ is presently reanalyzing several of Einstein’s gedanken experiments. We are hopeful that in the near future some new results will appear.

Since this velocity-dependent force appears to have first appeared in the work of Galilei and Aristotle, we suggest that if our analysis is confirmed by later work, the force should be entitled the “third” force, since it was discovered before the strong and weak interactions, and after gravitation and magnetism. We personally find this possibility extremely exciting.