The Eötvös experiment was a famous physics experiment that measured the correlation between inertial mass and gravitational mass, demonstrating that the two were one and the same, something that had long been suspected but never demonstrated with any sort of accuracy. The primary experiment was carried out by Roland von Eötvös starting around 1885, with further improvements in a lengthy run between 1906 and 1909. Eötvös' team followed this with a series of similar but more accurate experiments, as well as experiments with different types of materials and in different locations around the Earth, all of which demonstrated the same equivalence in mass. In turn, these experiments led to the modern understanding of the equivalence principle encoded in general relativity, which essentially states that there is no "gravitational mass" at all, and that inertial mass is all that really exists.

Eötvös' original experimental device consisted of two masses on either end of a rod, hung from a thin fiber. A mirror attached to the rod, or fiber, reflected light into a small telescope. Even tiny changes in the rotation of the rod would cause the light beam to be deflected, which would in turn cause a noticeable change when magnified by the telescope.

Two primary forces act on the balanced masses, gravity and the centripetal force due to the rotation of the Earth. The former is calculated by Newton's law of universal gravitation, which depends on gravitational mass. The later is calculated by Newton's laws of motion, and depends on inertial mass. The experiment was arranged so that if the two types of masses were different, the two forces will not exactly cancel, and over time the rod will rotate.

Initial experiments around 1885 demonstrated that there was no apparent difference, and he improved the experiment to demonstrate this with more accuracy. In 1889 he used the device with different types of sample materials to see if there was any change in gravitational force due to materials. This experiment proved that no such change could be measured, to a claimed accuracy of 1 in 20 million. In 1890 he published these results, as well as a measurement of the mass of Gellért Hill in Budapest.[1]

The next year he started work on a modified version of the device, which he called the "horizontal variometer". This modified the basic layout slightly to place one of the two rest masses hanging from the end of the rod on a fiber of its own, as opposed to being attached directly to the end. This allowed it to measure torsion in two dimensions, and in turn, the local horizontal component of g. It was also much more accurate. Now generally referred to as the Eötvös balance, this device is commonly used today in prospecting by searching for local mass concentrations.

Using the new device a series of experiments taking 4000 hours was carried out with Pekár and Fekete starting in 1906. These were first presented at the 16th International Geodesic Conference in London in 1909, raising the accuracy to 1 in 100 million.[2] Eötvös died in 1919, and the complete measurements were only published in 1922 by Pekár and Fekete.

Eötvös also studied similar experiments being carried out by other teams on moving ships, which led to his development of the Eötvös effect to explain the small differences they measured. These were due to the additional accelerative forces due to the motion of the ships in relation to the Earth, an effect that was demonstrated on an additional run carried out on the Black Sea in 1908.

In the 1930's a former student of Eötvös, J. Renner, further improved the results to between 1 in 2 to 5 billion.[3] Robert H. Dicke with P. G. Roll and R. Krotkov re-ran the experiment much later using improved apparatus and further improved the accuracy to 1 in 100 billion.[4] They also made several observations about the original experiment which suggested that the claimed accuracy was somewhat suspect. Re-examining the data in light of these concerns led to an apparent very slight effect that appeared to suggest that the equivalence principle was not exact, and changed with different types of material.

In the 1980s several new physics theories attempting to combine gravitation and quantum physics suggested that matter and anti-matter would be affected slightly differently by gravity. Combined with Dicke's claims there appeared to be a possibility that such a difference could be measured, and this led to a new series of Eötvös-type experiments (as well as timed falls in evacuated columns) that eventually demonstrated no such effect. A side-effect of these experiments was a re-examination of the original Eötvös data, including detailed studies of the local stratigraphy, the physical layout of the Physics Institute (which Eötvös had personally designed), and even the weather and other effects. The experiment is therefore well recorded.[5]

Loaded Eötvös balance rotor hanging (top) from a tungsten filament 1/4 the diameter of a human hair. All surfaces are gold plated to dissipate static electricity.

Equivalence Principle Tests

Researcher	Year	Method	Difference/Average Sensitivity
John Philoponus	500 AD?	Drop Tower	"small"
Simon Stevin	1585	Drop Tower	5x10-2
Galileo Galilei	1590?	Pendulum, Drop Tower	2x10-2
Isaac Newton	1686	Pendulum	10-3
Friedrich Wilhelm Bessel	1832	Pendulum	2x10-5
Southerns	1910	Pendulum	5x10-6
Zeeman	1918	Torsion Balance	3x10-8
Loránd Eötvös	1922	Torsion Balance	5x10-9
Potter	1923	Pendulum	3x10-6
Renner	1935	Torsion Balance	2x10-9
Dicke, Roll, Krotkov	1964	Torsion Balance	3x10-11
Braginsky, Panov	1972	Torsion Balance	10-12
Shapiro	1976	Lunar Laser Ranging	10-12
Keiser, Faller	1981	Fluid Support	4x10-11
Niebauer, et al.	1987	Drop Tower	10-10
Heckel, et al.	1989	Torsion Balance	10-11
Adelberger, et al.	1990	Torsion Balance	10-12
Baeßler, et al.	1999	Torsion Balance	5x10-13
MiniSTEP, MICROSCOPE, Galileo Galilei	2010?	Satellite Orbit	10-17?

Eötvös experiments are rational inquiries. Noether's theorem: For each continuous symmetry in physics there must be a conserved observable, and vice-versa. A list of symmetries (easy) is then a list of fundamental properties (otherwise difficult to identify) to be tested.

Internal symmetries' observables transform fields amongst themselves leaving physical states (translation, rotation) invariant. Internal symmetries' observables are default null results in any Eötvös experiment.

Parity is unique for being absolutely discontinuous, a mirror reflection along each axis. Parity is not a Noetherian symmetry. Covariance with respect to reflection in space and time is not required by the Poincaré group of Special Relativity or the Einstein group of General Relativity. Parity Eötvös experiment net output may be observed without contradicting orthodox theory or prior observations in any venue at any scale.

Class	Invariance	Conserved quantity
Proper orthochronous Lorentz symmetry	translation in time   (homogeneity)	energy
	translation in space   (homogeneity)	linear momentum
	rotation in space   (isotropy)	angular momentum
Discrete symmetry	P, coordinates' inversion	spatial parity
	C, charge conjugation	charge parity
	T, time reversal	time parity
	CPT	product of parities
Internal symmetry (independent of spacetime coordinates)	U(1) gauge transformation	electric charge
	U(1) gauge transformation	lepton generation number
	U(1) gauge transformation	hypercharge
	U(1)Y gauge transformation	weak hypercharge
	U(2) [U(1)xSU(2)]	electroweak force
	SU(2) gauge transformation	isospin
	SU(2)L gauge transformation	weak isospin
	PxSU(2)	G-parity
	SU(3) "winding number"	baryon number
	SU(3) gauge transformation	quark color
	SU(3) (approximate)	quark flavor
	S((U2)xU(3)) [U(1)xSU(2)xSU(3)]	Standard Model

Beryllium-magnesium and beryllium-titanium test mass contrasts respectively give 0.1919% and 0.2398% difference/average nuclear binding energies. These are among the largest net active mass composition Eötvös experiments possible. 420+ years of Equivalence Principle tests have given zero net output within experimental error. The largest possible amplitude Eötvös experiment is a parity Eötvös experiment - assay of spacetime geometry with test mass geometry.

Test Masses' Divergent Property	Fraction of Rest Mass
rest mass	100%
crystal lattice geometric parity	99.9726%a alpha-Quartz 99.9771%a Cinnabar
nuclear binding energy (low Z)	00.76% (4He)
neutron versus proton mass	00.14%
electrostatic nuclear repulsion	00.06%
electron mass	00.03%
unpaired spin mass	00.005% (55Mnb)
nuclear antiparticle exchange	00.00001%
Weak Force interactions	00.0000001%
Gravitational binding energy, Nordtvedt effect and lunar laser ranging	00.000000046% Earthc 00.0000000019% Moon

^a(nuclear mass)/(atomic mass), corrected for isotopic abundance
_^bglobally aligned undecatiplet
^ciron core rather than homogeneous body

Chemically identical, opposite parity mass distributions have never been tested in an Eötvös experiment. Do metaphoric left and right shoes vacuum free fall along identical trajectories? A parity Eötvös experiment opposes crystallographic opposite parity space groups P3121 (right-handed screw axes) and P2221 (left-handed screw axes) cultured alpha-quartz (average atomic weight = 20.03) or cinnabar (average atomic weight = 116.33) solid single crystal spheres or other solid shapes with all identical moments of inertia (no directional bias).

General relativity (postulated) and string theory (BRST invariance demanded) require parity Eötvös experiment zero net output. Affine (Einstein-Cartan theory), teleparallelism (Weitzenböck), and noncommutative (Connes) gravitation theories predict measurable parity Eötvös experiment output. If the vacuum is reproducibly demonstrated to contain a chiral anisotropic background then angular momentum need not be conserved for opposite parity mass distributions (Noether's theorem). Lorentz invariance would be broken. Somebody should look.

References

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, G. Reiner, Berlin, 319,1910
3. ^ J. Renner, Matematikai és Természettudományi Értesítõ, 13, 542, 1935, with abstract in German
4. ^ P. G. Roll, R. Krotkov, R. H. Dicke, Annals of Physics, 26, 442, 1964.
5. ^ One Hundred Years of the Eötvös Experiment