Roland Eötvös' classic experiment concerning the proportionality of inertial and gravitating masses, performed at first in 1889, has again become the focus of scientific interest in the 1980's, due to the possibility of the existence of a Fifth Force, as proposed by Fischbach and coworkers. The publication of Eötvös, Pekár and Fekete omitted various details of their experiment which may be relevant for the re-interpretation of their results. The aim of this report is to fill in some of these details, and to discuss the impact of the Eötvös experiment on modern research.

"Ars longa, vita brevis"

Inspired by the beauty of the Newtonian system, Baron Roland von Eötvös experimentally investigated the proportionality of inertial and gravitating masses in 1889, and reported his results in the Proceedings of the Hungarian Academy in 1890^[1]. In this work he improved Bessel's accuracy 1/60 000 to 1/20 000 000. This was a short report of 3 pages. Inspired by this achievement, the Royal Scientific Society of Göttingen in 1906 offered a prize (see Appendix I) for the following task:

"A very sensitive method was given by Eötvös to make a comparison between the inertia and gravity of matter. Considering this and the new development of electrodynamics as well as the discovery of radioactive substances, Newton's law concerning the proportionality of inertia and gravitation is to be proved as extensively as possible."

Eötvös began a series of investigations with his co-workers Pekár and Fekete in the years 1906-1909. This included data taking through approximately 4000 hours. Eötvös personally reported his results at the l6th International Geodesic Conference in London in 1909^[2], quoting an achieved accuracy of 1/100 000 000. The complete work of Eötvös, Pekár, Fekete was submitted to the Beneke Foundation in 1909^[3]. Its motto was "Ars longa, vita brevis" (the art lasts long, life lasts short), which is indeed a true characterization of the fate of Eötvös' work. The evaluation of C. Runge, Dean of the Faculty of Science in Göttingen^[4] says that Eötvös has quoted an accuracy of 1/200 000 000, but since the submitted text does not include the real theoretical discussion of the observational data, the Faculty recommends only a reduced prize for this work (3400 German Marks instead of 4500 Marks). In Appendix I we reprint the text of this evaluation.

Shortly thereafter the First World War came. Roland Eötvös died in 1919, and the detailed description of the experiments performed in 1906-1909 was published by his assistants Pekár and Fekete only in 1922^[5]. This is the text known, cited, and translated by the international scientific community worldwide. When the collected works of Roland Eötvös were published by the Hungarian Academy of Sciences^[6], the editor (Eötvös' former student P. Selényi) included some additions in parentheses [...] in the reprinted Eötvös-Pekár-Fekete paper^[5], taken from the original manuscript^[3]. The original Beneke-prize manuscript was lost somewhere in the hands of the heirs to Pekár and Selényi. The more complete text taken from the Volume^[6] has been reprinted in English in Budapest in 1963^[5].

The Eötvös experiment was repeated by J. Renner (a former student of Eötvös, and a physics teacher in the famous Lutheran High School in Budapest where among others J. von Neumann and E. P. Wigner studied). The results of Renner's experiment were published in Hungarian^[7] (with a German abstract, reprinted in Appendix II). Renner claimed an empirical accuracy of 1/2 000 000 000 to 1/5 000 000 000.

Acknowledging the basic role played by the connection between inertial mass and gravitating mass in General Relativity, P. G. Roll, R. Krotkov and R. H. Dicke carried out a new experiment, using modern technology, and achieved an accuracy of 1/100 000 000 000^[8]. Dicke and co-workers were able to increase the sensitivity compared to Eötvös in part by measuring the accelerations of their test masses to the Sun, rather than to the Earth as Eötvös had done. In such an experiment any signal arising from the difference between gravitational and inertial mass would have the same 24-hour periodicity as the Earth's rotation. The advantage of such an approach from an experimental point of view is that it allows such a signal to be discriminated from background perturbations, without disturbing the torsion fibre. Of course, one must be careful to exclude other perturbations which will have the same 24-hour period. In fact Eötvös, Pekár and Fekete were the first to compare the accelerations of different materials to the Sun, and for platinum versus mangalium they quote a fractional difference of 6 x 10^-9. However, since no error is quoted and few other details of their analysis are presented, it is difficult to know precisely how the sensitivity of this part of their experiment compared with that of their more extensive work measuring accelerations to the Earth.

Fig. 1. Torsion balance used in Eötvös' measurements

Fig. 2. Sketch of the torsion balance

In analyzing the Eötvös results, Dicke expressed his polite doubts about the accuracy claimed by Eötvös' assistants. Among his concerns were the following:

1. Dicke was suspicious about the perturbation of air motion created by temperature differences. The present authors think that Eötvös' team was quite careful in this respect. The observations were performed in a shaded closed room, in a double-walled tent (the space between the two walls was stuffed with sea-weed), with a torsion balance protected by triple copper coating with air space between (Figs 1,2 and the letter of J. Renner to R. H. Dicke, due to the encouragement of one of us (G.M.) as reprinted in Appendix III.) Further evidence for the concern of Eötvös and co-workers over thermal effects is reflected in the fact that they affixed thermometers to the torsion balance at various locations. (The double-arm balance, used in their third method, had three thermometers: One along each arm, and one near the torsion fibre.) The question of possible thermal effects was raised by Dicke as an alternative to the Fifth Force to explain the correlations in the Eötvös data noted by Fischbach and co-workers. This question has been discussed in detail in^[12], where it is noted that the main objection to such an explanation of the Eötvös results is that the thermal effects would have to be of constant sign and magnitude during approximately 4000 hours of data taking, spread out over several years, which seems unlikely.

2. Dicke was also concerned about the poorly defined gravitational perturbation, caused by the observer himself. This potential source of error was well known to Eötvös. While the vibrations of the torsion pendulum were damped, the observer was far away. When the balance had come to rest, the observer came running and made the reading, before the pendulum (of period of 40 minutes) had time to swing out^[9].

Fig. 3. Data sheet from the R. Eötvös bequest

3. Unfortunately, the statistical evaluation of the empirical data cannot be fully reconstructed in the case of the Eötvös-Pekár-Fekete experiment, as the details are not given in any of their publications. (In the bequest of Eötvös, kept in the Library of the Hungarian Academy of Sciences, sheets with laboratory data readings can be found, e.g.Fig. 3, but they do not contain sufficient information to allow the statistical evaluation to be repeated.) In the Hungarian publication of J. Renner^[7] more details can be found. It can be seen, as pointed out by Dicke^[8], that Renner tried to eliminate the influence of environmental changes by interpolation in time. The numbers obtained by interpolation are not statistically independent, but Renner treated them as if they were. For this reason the statistical errors might be larger by a factor of 3 than claimed by Renner. It should be noted that this factor is 2.4 as shown by Király^[19]. Taking this source of error into account, Renner's data lay suspiciously near to zero, concerning the difference of the two masses. Therefore Dicke and others have suggested that Renner's conclusions cannot be relied upon. Renner learned this statistical technique from Eötvös' team. The inaccuracy quoted by Pekár in his paper^[5] originated from observational errors and statistical errors in a ratio unknown to us; it could be that the accuracy of 10^-8[2], given by Eötvös personally is the reliable one. This is in any case a marvellous achievement, and the curious trends, noted by Fischbach and co-workers seem to survive. (See the next Section.)

It should be emphasized that the analyses of both Dicke and Fischbach agree that the errors quoted by Eötvös, Pekár and Fekete are consistent with the statistical scatter of their data. Moreover, the confidence level of the best fit of Fischbach et al to the Eötvös data, viewed as suggesting a Fifth Force, is 86%, which is perfectly reasonable.

Let us quote Eötvös himself^[5]: "Ars longa, vita brevis. The admonition of this old saying motivates the authors of this paper to compile the results of their investigation and to submit them to the judgement of a high scientific Aeropag. Methods of observation refine and improve naturally in the course of observation, and hence no mortal could close his work if without cease would follow the otherwise laudable impetus to replace the useful by the even better."

Eötvös' experiment is one of the last pearls of the grand epoch of classical physics. At the end of their investigations^[5] Eötvös, Pekár, and Fekete studied how far the proportionality of inertia and gravity is valid in case of radioactive materials. (This was already in the era of E = mc².) The proportionality was verified for a 0.1 g sample of RaBr₂ with an accuracy of 1/2 000 000.

In the following decades, the investigation of the structure of matter called attention to other possible forces of Nature beyond the long-ranged gravity and electricity, and beyond the short-ranged nuclear and weak interactions. According to the quantum theory the range of the force (r) is related to the mass (m) of the quanta of the transmitting field by the quantum law r = h / mc, where h is Planck's constant and c is the speed of light.

The infinite length of the gravitational and electric field lines is logically connected to the absolute conservation laws of mass (energy) and charge. If there is any further exact or approximate conservation law (e.g. the conservation of the baryonic charge B, discovered by E. P. Wigner^[10]), it may be that a further unknown field exists which may transmit a Fifth Force. But if the rest mass of the field quanta were exactly zero (as in the case of photons), hot bodies would radiate these quanta as well, in contradiction to thermodynamical experience. Thus one may hypothesize that the field quanta should have a small but nonvanishing rest mass (m), consequently the transmitted Fifth Force would have a long but finite range (x₀  = h / mc). This gives rise to a composition-dependent "action at a distance" between two massive bodies, where the interaction energy is the sum of the gravity and the Fifth Force contributions:

For astronomical distances only Newtonian gravity contributes,

For laboratory distances, however, one may experience an "effective gravity"

with an effective gravitational constant

which may differ from the (astronomical) Newtonian gravitational constant G. If B is the baryon number (protons plus neutrons) in the atom, and if M is the mass of the atom in hydrogen atom mass units m_H, that is M = m / m_H, then

with a = F / Gm_H². In the case of hydrogen B/M  1, whereas for carbon B/M = 1.00782, for copper B/M = 1.00895, and for lead B/M = 1.00794. Hence the effective gravitational constant, manifesting itself over laboratory scales may be composition dependent. This idea can be checked by comparing the empirical value of G on astronomical and laboratory scale, and by testing its composition-dependence. Eötvös' experiments contributed to both. The torsion balance was used to measure any small difference between gravitational accelerations of two substances. Any significant difference would imply a composition-dependent inertial mass / gravitational mass ratio. Plotting ( / g) (where g is the gravitational acceleration) for the results published by Eötvös-Pekár-Fekete^[5] as a function of (B/M) (see Fig. 4. based on the work of P. Király^[19]), a linear relationship may be suspected. Fischbach and co-workers concluded that the slope of the resulting line was (5.65±0.7) x 10^-6, which differs from the expected value of zero by several standard deviations^[11]. If the Fifth Force really exists with a range of 100 m, say, the composition-dependence must be due to the action of nearby mass distribution.

The Fifth Force hypothesis has had a double effect: It has encouraged a series of modern experiments, and it has increased the interest in details of the original Eötvös-Pekár-Fekete experiment^[5] (which seemed to indicate a positive effect). Full lines inFig. 4; represent error bars given by the original authors, while dashed lines give increased statistical errors suggested by P. Király. Results obtained in the environment of the Renner experiment^[7] apparently suggest a zero result.

Fig. 4. Plot of ( / g) as a function of (B/M)^[19]. In the EPF measurement: 1. tallow - Cu; 2. water - Cu; 3. CuSO₄ solution - Cu; 4. CuSO crystals - Cu; 5. Asbestos - Cu; 6. snakewood -Pt; 7. AgSO₄ and FeSO₄ (before and after the reaction); 8. mangalium - Pt; 9. Cu - Pt. In Renner's measurement: a) paraffin - brass; b) NH₄F - Cu; c) Bi - brass; d) Pt - brass; e) glass - brass; f) Mn-Cu alloy - Cu. (The dashed lines show the increased statistical scatter, as indicated in the text.)

The authors of the present report do not intend to enter the field of controversies related to the Fifth Force, the interested readers may find references in the review papers^{[e.g. 12]}. Our only goal is to supply information about the environments of the two classic Hungarian experiments. But when doing so, let us keep in mind what Nieto, Goldman and Hughes wrote^[13]: "neither the concept of baryon number, nor the mass defect existed at that time. Without these concepts, Eötvös could have spent considerable time and effort in a fruitless attempt to find out why the scatter in his data points was larger than his error estimates. We can easily sympathize and imagine the gnawing feeling that something was wrong, or that something very important was being missed."

The Faculty of Science of the University of Budapest (carrying the name of Roland von Eötvös since 1950) is located in the downtown of Budapest, East of the Danube. The river follows a geological break: Its West shore abounds in steep hills (CaCO₃, MgCO₃), its East shore is flat (mostly wet sand deposit of the river). The East-West asymmetry is the dominating geological feature (Fig. 5).

Fig. 5. Geological cross-section between Gellért Hill and Eötvös University in Budapest

Eötvös designed and built the building of the Physics Institute in the 1880's; his laboratory is now the Department of Atomic Physics (Puskin utca 5). According to the Eötvös-Pekár-Fekete paper^{[6, page 328]} the laboratory room where the Eövö-Pekár-Fekete experiment was carried out looks South with two windows on the ground floor; opposite to it there are tall buildings^{[6, page 328]}. (Recollections made two decades later^[13] contradict this original paper^[5] but are compatible with the site of Renner's experiment, therefore this hint should be probably disregarded). J. Barnóthy joined the Institute 5 years after the departure of Eötvös, and he firmly locates the site of the Eötvös-Pekár-Fekete experiment is a small annex at the SW end of the building^[14] (E on Figs 6 and 7), which now houses neutron generators. At Eötvös' time there was no building to the West. To the SW there was a temporary hole that was dug for future construction, to the East there is the huge complex of the Physics Institute with a strong concrete tower, about 20 meters NE (Fig. 8). Below the experimental room there was no cellar but only soil, above it there was no floor.

Fig. 6. Building of the Physics Institute from the South

In contrast to the highly asymmetric location of the Eötvös-Pekár-Fekete site, the Renner experiment was performed 25 years later, probably in the geophysical laboratory, on the North side, in the middle of the ground floor of the Institute of Physics building (about where the computer room is now). This location of the geophysical laboratory is given by G. Barta^[15] indicated by R inFig. 7. Below this room there was a cellar, above it one additional floor, which means that the Renner site is located rather symmetrically (up-down, E-W) in the building. According to Talmadge et al^[16], the asymmetric location of the Eötvös site may be the source of a Fifth Force, explaining the positive (composition-dependent) outcome(Fig. 8). The symmetric position of the Renner site R (compensated Fifth Force) may explain the zero (composition-independent) outcome (Fig. 8). The explanation works if the Fifth Force exists with a range of 10-50 meters. These conclusions have to be checked by modern experiments by observers who are ready to learn patience from Baron Roland von Eötvös. (G. Barta, who is presently repeating the original Eötvös Experiment, speaks about 2 days of waiting before one single reading of the equilibrium position of the torsion balance^[17]). Eötvös selected the best (most linear and most sensitive) Tungsten wires which hung with weight for several years, to get rid of any distorting internal tension. Eötvös demanded thousands of hours of patient unbiased observations from his assistants. Let us conclude this report from the past with Eötvös' message^[5]: "The authors bow to the fate of human limitations and leave it to future times and future workers to further elaborate those observations which they themselves believe upon mature experience to be able to still improve."

Fig. 7. Ground plan of the building

The recent revival of interest in the possibility of non-Newtonian gravity, which followed the reanalysis of the Eötvös experiment by Fischbach and co-workers^[11,12] owes much to the perception that the experiments of Eötvös, Pekár, and Fekete were carefully done and hence deserve to be taken seriously. The widespread favorable view of this series of experiments is due in part to the detailed description of their experiment contained in the published literature, and in part to other details of their experiment which we know of from personal communications^[9,14,15,17], and from aspects of their methodology that we can infer from various sources. The following are two additional examples of some of the details of their experiment which were not described in their paper. The torsion balances used in the experiment were mounted on stone piers (approximately one meter on a side) which were sunk deep into the ground.

Fig. 8. Campus

The purpose of these piers was to provide a stable shock-free platform for the sensitive balances, and a number of these are still visible today at the Atomic Physics Institute. Another interesting example deals with their comparison of the reactants before and after the chemical reaction

Ag₂SO₄ + 2FeSO₄ =>  2Ag + Fe₂(SO₄)₃.

Since the Ag produced by this reaction precipitates out of the liquid, the center-of-mass of the initial reactants would not coincide with that of the final products. If the difference of the centers of mass were not corrected for, then it would couple to local gravity gradients and produce a large (but spurious) signal which could simulate a violation of Equivalence Principle^[12]. In fact Eötvös and co-workers found that the accelerations of the reactants before and after the chemical reaction were the same, which is what we expect in all theories. This indicates that the authors were evidently careful to correct for this effect, although the details of their methodology are not provided.

It has now been approximately five years since the classic work of Eötvös, Pekár and Fekete stimulated interest in the possibility of a fifth force. During this period numerous experiments have been carried out, and many are still under way. To date these experiments have not confirmed the original suggestion of a fifth force, as inferred from the Eötvös data by Fischbach and co-workers^[12]. However, neither has any group pinpointed an error in the Eötvös experiment which could be the source of their suggestive data. Since all of the recent experiments differ from the original Eötvös experiment in various ways, the possibility remains that there is some theoretical model in which a subtle aspect of the original experiment which we have heretofore overlooked could explain why those authors saw an effect while the more recent ones do not. The significance of the Eötvös experiment is that it will continue to be a stimulus for new ideas, such as the recent suggestion^[18] that spin may have played a role in the original work. However the search for new gravity-like forces turns out, it is clear that the Eötvös experiment has played a fundamental role in shaping our understanding of gravity and other possible forces in Nature.

1. R. v. Eötvös, Mathematische und Naturwissenschaftliche Berichte aus Ungarn, 8, 65, 1890.

2. R. v. Eötvös, in Verhandlungen der 16 Allgemeinen Konferenz der Internationalen Erdmessung (London-Cambridge, 21-29 September 1909). G. Reiner, Berlin, 319,1910.

3. R. v. Eötvös, D. Pekár, E. Fekete: Beiträge zum Gesetz der Proportionalität von Trägheit and Gravität, with the motto "Ars longa, vita brevis", submitted to the Beneke Foundation in Göttingen (1909). This text is now unknown.

4. C. Runge, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, No. 1, 37-41. Weidmann, Berlin, 1909.

5. R. v. Eötvös, D. Pekár, E. Fekete, Annalen der Physik (Leipzig) 68, 11, 1922. English translation for the U. S. Department of Energy by J. Achzenter, M. Bickeböller, K. Bräuer, P. Buck, E. Fischbach, G. Lubeck, C. Talmadge, University of Washington preprint 40048-13-N6. - More complete English text reprinted earlier in Annales Universitatis Scientiarium Budapestiensis de Rolando Eötvös Nominate, Sectio Geologica, 7, 111, 1963.

6. Roland Eötvös Gesammelte Arbeiten, edited by P. Selényi, Hungarian Academic Press, Budapest, 1953, 385 pages.

7. J. Renner, Matematikai és Természettudományi Értesítő, 13, 542, 1935, with abstract in German.

8. P. G. Roll, R. Krotkov, R. H. Dicke, Annals of Physics, New York, 26, 442, 1964.

9. Personal communication by J. Renner to G. M. 1963.

10. E. P. Wigner, Proc. American Philosophical Society, 93, 521, 1949.

11. E. Fischbach et al., Phys. Rev. Letters, 56, 2424, 2426, 1986; E. Fischbach, D. Sudarsky, A. Szafer, C. Talmadge, S. H. Aronson, 57, 1959, 1986.

12. E. Fischbach, D. Sudarsky, A. Szafer, C. Talmadge, S. H. Aronson, Annals of Physics, New York, 182, 60, 1988.

13. D. Pekár, R. v. Eötvös, 50 years anniversary of the torsion balance, Budapest, 1939 (in Hungarian), p. 107.

14. Personal communication of J. Barnóthy to G. M. 1986.

15. Personal communication of G. Barta to G. M. 1987.

16. C. Talmadge, S. H. Aronson and E. Fischbach, in Progress in Electroweak Interactions, ed. by J. Tran Thahn Van (Editions Frontières, Gif sur Yvette, 1986) p. 229.

17. Personal communication of G. Barta to G. M. 1990.

18. A. M. Hall, H. Armbruster, E. Fischbach and C. Talmadge, in Proceedings of the 2^nd International Conference on Medium and High Energy Nuclear Physics, Taipei, May 1990.

19. P. Király, Természet Világa (World of Nature), 5, 154, 1987 (in Hungarian).

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* Dedicated to Prof. J. Csikai on his 60^th birthday