The Eötvös Experiment: Is Gravity Equal for All Matter?

Does a lump of platinum fall at the same rate as a lump of wood? Every textbook says yes, and every textbook is leaning on a century of increasingly delicate measurements. The first great one was made by the Hungarian physicist Loránd Eötvös, who hung two different materials from the ends of a rod on a thread and looked for a twist that never came. His successors, with better balances, then a Moon landing, then a satellite, have pushed the test to roughly three parts in a quadrillion, and still found no difference.

That result matters well beyond falling objects. The equal fall of all matter is the foundation on which Einstein built general relativity. This article follows the experiments in order: what is being tested, how a torsion balance does it, how the precision grew, and what each step did and did not show.

Two things called mass

Physics uses the word "mass" for two different jobs. Inertial mass measures how strongly an object resists being accelerated: push a shopping cart and the heavier it is, the less it speeds up. Gravitational mass measures how strongly gravity grabs the object, the way electric charge measures how strongly an electric field grabs a particle.

In electricity, these two roles are obviously separate. Two particles with the same mass but different charges accelerate differently in the same electric field, and two particles with the same charge but different masses do too. Gravity could in principle work the same way. A material with a high ratio of gravitational to inertial mass would fall faster than one with a low ratio, and the world would have a rich zoo of falling speeds depending on what things were made of.

It does not. As far as anyone has been able to measure, the ratio of gravitational to inertial mass is identical for every material. That is the weak equivalence principle (WEP), also called the universality of free fall: in a given gravitational field, all test bodies accelerate at the same rate regardless of composition. Physicists express a test of it with the Eötvös ratio, defined in Clifford Will's review in Living Reviews in Relativity as η = 2|a₁ − a₂| / |a₁ + a₂|, the fractional difference between the accelerations of two bodies. If the principle is exact, η is zero. Each experiment in this article is a bound on how large η can be.

This is the place where an analogy earns its keep. Imagine a race in which every competitor carries a different load, wears different shoes, and starts with a different amount of pushing force, and they all finish in the same instant to within a hair. You would suspect that the organizers had rigged the race so that the force scales with the load. Gravity is rigged that way, and the question is how exactly.

For the broader theory, see our explainers on what gravity is and on Einstein's relativity.

Before Eötvös: dropping things and swinging things

The first tests were falling tests. The story that Galileo dropped balls from the Leaning Tower of Pisa traces to a biography by his secretary Vincenzo Viviani, published in 1654, and historians doubt it. Physics World's retelling notes that in his own writing Galileo reports dropping a cannonball and a musket ball and finding that they did not quite fall together. The same article records that scholars as early as the sixth century, and one of Galileo's predecessors as professor at Pisa, had also tested falling bodies. Experiments by the Flemish engineer Simon Stevin in the 1580s, who dropped lead balls from a church tower in Delft, are often cited as an early carefully documented one. Our article on Galileo's inclined plane experiments covers the experiments Galileo reliably did.

Dropping things is a crude instrument. Air resistance spoils the comparison, and the fall is too quick to time well. The better trick was to use a pendulum, which stretches the motion out and lets you compare many swings. Isaac Newton did this in Book III, Proposition VI of the Principia. He filled a hollow pendulum bob with equal weights of gold, silver, lead, glass, sand, salt, wood, water, and wheat and compared the periods. They agreed to within about one part in a thousand, according to the tabulation on Wikipedia's page on the Eötvös experiment. Later, around 1832, Friedrich Bessel repeated the idea with greater care, reaching about two parts in 100,000 by the same tabulation.

The pendulum also exposed the method's limit. The restoring force that makes a pendulum swing is gravity, and its period depends on the ratio of gravitational to inertial mass. A small difference between two materials would show up as a small difference in period, but periods are hard to measure to better than a part in a hundred thousand. To do much better, someone needed a different kind of instrument.

How a torsion balance finds a difference of one part in a billion

A torsion balance is a horizontal rod hung from a thin fiber. A force that pushes one end of the rod in one direction and the other end in the other twists the fiber, and a tiny twist moves a mirror on the rod, which swings a beam of light across a distant scale or into a telescope. The device amplifies a very small torque into a visible shift. It is the same kind of instrument as in the Cavendish experiment, which weighed the Earth with two lead spheres and a wire.

Eötvös's twist on the idea was to hang two masses of different materials at the two ends of the rod and ask whether the rod would turn.

Here is the logic. On a rotating Earth, each mass hangs under two forces: gravity, which depends on the mass's gravitational mass, and the centrifugal force from the Earth's rotation, which depends on its inertial mass. The two forces point in slightly different directions, which is why a plumb line does not point exactly at Earth's center. If the ratio of gravitational to inertial mass were different for the two materials, the balance between those two forces would differ at the two ends of the rod. The result would be a net torque, and the rod would rotate.

Eötvös turned the apparatus around, so that the two masses swapped ends, and watched for the signal to reverse. A real effect should reverse with the instrument. Drafts, temperature, and a sagging fiber will not. According to Will's review, Eötvös used the Earth's rotation to modulate the torque in this way. The null result is a rod that sits there. The entire precision of the measurement comes from how still it sits.

Component	Job
Thin torsion fiber	Weak restoring torque, so that a small force makes a measurable twist
Two test masses of different material	The comparison: do they feel the same ratio of gravity to inertia?
Mirror and light beam (or telescope)	Magnify the rod's rotation into something readable
Rotating the instrument	Reverses the sign of a real signal, separating it from drifts

The four parts of an Eötvös-type measurement.

Eötvös's measurements, 1885 to 1922

Eötvös (1848–1919) was born in Budapest, and the National High Magnetic Field Laboratory's biography credits him with designing the first instrument usable for gravitational gradiometry, a sensitive torsion balance for measuring the Earth's gravitational field. In 1889 he carried out tests with different sample materials and claimed an accuracy of about one part in 20 million, with results published in 1890, a large improvement on the pendulum experiments.

The decisive series ran from 1906 to 1909 with his collaborators Dezső Pekár and Jenő Fekete, about 4,000 hours of measurement with an improved instrument. It reached about one part in 100 million. Eötvös himself reported it at the 16th International Geodesic Conference in London in 1909. He died in 1919, and the full description of the experiments was published by Pekár and Fekete in 1922 in Annalen der Physik. The Wikipedia tabulation puts the 1922 limit on any difference at about five parts in a billion.

Eötvös did not need to wait for a theory to value his result, but one arrived. Einstein referred to Eötvös's experiments in his 1916 paper "The Foundation of the General Theory of Relativity." The equality of inertial and gravitational mass is built into the way general relativity describes gravity as the shape of spacetime: if everything falls the same way regardless of composition, then gravity can be described as a feature of the space rather than a force acting differently on different things.

The instrument had a second life in geophysics. Because a torsion balance responds to how gravity changes from place to place, it became a tool for mapping the underground. The Eötvös correction, which accounts for how a moving vehicle's velocity changes its apparent weight, is still used with gravity meters on ships and aircraft.

A later wrinkle: the fifth-force episode

In 1986, Ephraim Fischbach and collaborators reanalyzed the Eötvös data and suggested it contained a very slight effect, implying that the equivalence principle might not be exact and might depend on material. That claim set off a wave of "fifth force" experiments in the late 1980s, searching for a short-range force beyond gravity, electromagnetism, and the nuclear forces. Their null results also served as tests of WEP.

The fifth force did not survive. In a paper first posted in 2018, Gyula Tóth proposed that the original results could be explained by a classical systematic effect: gradients in the ambient gravity field acting on samples of different shapes. The abstract notes that the fifth-force hypothesis was dropped after later experiments gave negative results. The episode is a good reminder that an old data set can be reread, and that the original experimenters could not have known about every systematic effect.

The precision ladder

The following table collects the tests described in this article, from Newton to the present. The figures are the claimed limits on the fractional difference in acceleration, with the source of each noted in the text.

Year	Experiment	Method	Limit on η
1687	Newton	Pendulums	about 10⁻³
1832	Bessel	Pendulums	about 2 × 10⁻⁵
1889	Eötvös	Torsion balance	about 5 × 10⁻⁸
1906–09 (published 1922)	Eötvös, Pekár, Fekete	Torsion balance	about 10⁻⁸ to 5 × 10⁻⁹
1930s	Renner	Torsion balance	about 10⁻⁹ to 10⁻¹⁰
1964	Roll, Krotkov, Dicke	Torsion balance, Sun as source	about 3 × 10⁻¹¹
1970s	Braginsky, Panov	Torsion balance	about 10⁻¹²
1999	Baeßler et al.	Torsion balance	about 5 × 10⁻¹³
2008	Schlamminger et al.	Torsion balance	about 2 × 10⁻¹³
2012	Williams, Turyshev, Boggs	Lunar laser ranging	(−0.8 ± 1.3) × 10⁻¹³
2022	MICROSCOPE	Satellite	(−1.5 ± 2.3 ± 1.5) × 10⁻¹⁵

Sources are cited in the sections that follow. Figures from Eötvös to Schlamminger follow the tabulation on Wikipedia's page on the Eötvös experiment and Will's review.

From Newton to MICROSCOPE, the precision improved by about 12 orders of magnitude. Hardly any measurement in physics has had such a long and steady climb.

Dicke and the Sun: a better modulator

In the 1960s Robert Dicke and his collaborators Roll and Krotkov in Princeton made the next jump, to about three parts in 10 to the 11th (Will's review and the Wikipedia table give figures of this size). Their key idea was to use the Sun rather than the Earth as the source of the gravitational pull. The Sun's direction stays fixed in space, while the Earth's rotation turns the instrument through a full circle once a day. A real difference in how the two test masses fall toward the Sun would therefore appear as a torque that oscillates with a 24-hour period, a signal that is easy to pick out of slow drifts and local disturbances. Braginsky and Panov in the early 1970s pushed the bound to around one part in 10 to the 12th using the same approach.

This is a pattern worth noticing. Good precision experiments usually owe less to a more sensitive sensor than to a cleverer way to switch the signal on and off at a known frequency. The torsion balance was already extraordinarily sensitive. The trick was to ask the universe a question that repeated every day.

The modern version of this line is the work of the Eöt-Wash group at the University of Washington, whose torsion balances reached about 2 × 10⁻¹³ (Will's review and the Wikipedia table both cite the figure, which the table dates to 2008). These instruments descend from the fifth-force searches of the late 1980s, whose null results doubled as tests of the equivalence principle.

The Moon: a hammer, a feather, and laser pulses

On August 2, 1971, at the end of the last moonwalk of Apollo 15, Commander David Scott held a hammer in one hand and a falcon's feather in the other and let go. The NASA Apollo 15 preliminary science report gives the hammer's mass as 1.32 kilograms, with the objects released from about 1.6 meters. They hit the lunar surface together. Scott's remark afterward was that Mr. Galileo was correct in his findings.

As a demonstration it is unforgettable. As an experiment it was loose, and a Physics World retrospective (published February 4, 2003) is candid about this: the drop height, probably 110 to 160 centimeters, the fall time, and the arm position were not measured. The point was that there is no air on the Moon, so drag does not hide the equality the way it does on Earth. The demonstration belongs with the older vacuum-tube experiments, including those of Robert Boyle, which we cover in our piece on Boyle's air pump experiments.

The Moon contributed a far more precise result without any hand gestures. Apollo crews left mirrors on the lunar surface, and observatories on Earth time laser pulses bounced off them to measure the Earth-Moon distance very accurately. For the equivalence principle, the question is whether the Earth and the Moon fall toward the Sun at the same rate despite their different masses, compositions, and gravitational self-energies, as the paper by Williams, Turyshev, and Boggs puts it. If they did not, the Moon's orbit would be pulled slightly toward or away from the Sun, producing a signal in the ranging data with the Moon's 29.53-day synodic period, the interval between successive full moons.

The result, published in 2012, is a limit of (−0.8 ± 1.3) × 10⁻¹³ on any inequality of the gravitational-to-inertial mass ratios of Earth and Moon. An earlier analysis from 2005 gave (−1.0 ± 1.4) × 10⁻¹³. The Moon, in effect, is a free test body the size of a small planet, and the Earth is another. Our article on the Apollo program's science legacy covers the mirrors and the rest of what those missions left behind.

MICROSCOPE: dropping it from orbit

A torsion balance on the ground fights two problems: the fiber and the floor. The fiber has to be thin enough to twist, but a thin fiber is fragile and noisy, and the floor is never still. A satellite in orbit solves the second one, because everything inside is in continuous free fall.

MICROSCOPE, a microsatellite of the French space agency CNES carrying accelerometers built by ONERA, was launched from Kourou on a Soyuz rocket on April 25, 2016, into a 710-kilometer sun-synchronous orbit. It operated until it was decommissioned in October 2018. The mission produced roughly five months of science free-fall data over about two and a half years. It carried pairs of test masses, one pair of titanium and platinum alloys and a reference pair of platinum masses, and checked whether Earth's gravity accelerated the two materials differently. In each pair, electrostatic forces keep the two masses centered on each other, so any difference in how gravity pulls on them would show up as a difference in the force required to hold them in place.

The final results, published in Physical Review Letters in 2022, give an Eötvös parameter for the titanium-platinum pair of η = [−1.5 ± 2.3 (statistical) ± 1.5 (systematic)] × 10⁻¹⁵. In other words, no violation was found down to about 2.7 parts in 10¹⁵ when the two uncertainties are combined, roughly two orders of magnitude tighter than the best torsion-balance limit of about 2 × 10⁻¹³ from the Eöt-Wash group. The platinum-platinum control pair, which has to give zero by construction, did: the paper reports η = [0.0 ± 1.1 (statistical) ± 2.3 (systematic)] × 10⁻¹⁵. The first results, released in 2017, had much larger uncertainties of about 9 × 10⁻¹⁵ statistical.

A limit of about 10⁻¹⁵ means that if the two metals did fall differently, the difference in their accelerations is smaller than one part in a thousand trillion of the acceleration itself. Newton's pendulums could not have seen anything smaller than a part in a thousand.

Why a violation would matter, and why nobody has found one

The equivalence principle comes in layers. The weak form (WEP) says that the motion of uncharged test bodies in a gravitational field does not depend on their composition. The Einstein equivalence principle (EEP) adds that in a small freely falling laboratory, the results of all non-gravitational experiments are the same as in empty space, regardless of where and when you do them. Will's review notes that Schiff's conjecture would make WEP tests the empirical foundation for the full EEP, although the conjecture has not been rigorously proven, and some counterexamples are known. In plain terms, if WEP failed, the rest of general relativity's foundations would be in question.

That is why the tests keep going. Many proposed extensions of known physics, including attempts to unify gravity with quantum mechanics, predict new long-range forces that would couple differently to different materials. Such forces would show up as a small violation of the universality of free fall. Every null result closes off a part of the space where such theories could live. The MICROSCOPE team had a target of 10⁻¹⁵ in the Eötvös ratio; the result came out at about that sensitivity with no signal.

The other classic tests of general relativity probe different consequences of the same foundation. The 1919 eclipse expedition measured the bending of starlight (see our piece on the 1919 eclipse expedition). The Pound-Rebka experiment measured the gravitational redshift. The Hafele-Keating experiment flew atomic clocks around the world, as our article on the Hafele-Keating experiment describes, and the practical matter of clocks running at different rates in different gravitational potentials is explained in our article on why time moves slower near gravity. All of those results presuppose that gravity treats everything alike, which is the thing the Eötvös-type experiments check directly.

What people get wrong

"The equivalence principle says heavy things fall as fast as light things, so a feather and a bowling ball fall together." In air they do not, because drag hits a feather much harder. The principle is about gravity's own effect, with everything else removed. That is why the Apollo 15 demonstration mattered, and why MICROSCOPE flew in orbit.

"Equal acceleration means equal force." The force of gravity on a hammer is much larger than on a feather. It is the hammer's greater inertia that cancels the bigger force, leaving the same acceleration. The equivalence of the two masses is exactly what makes that cancellation exact.

"Galileo dropped weights from the Tower of Pisa." The story comes from Viviani's later biography. Galileo's own writing describes a cannonball and a musket ball that did not quite land together. What Galileo clearly did was reason, with thought experiments and inclined planes, that falling is independent of weight.

"A null result means nothing happened." Every experiment in this article, from Eötvös to MICROSCOPE, found nothing, and each was a major achievement. A null result with a stated precision is a measurement. It says how big a violation could possibly be.

"The Eötvös experiment proved general relativity." It supports one of its premises to extraordinary accuracy. It does not test curvature, light bending, or gravitational waves, which is why the other experiments in the list above exist.

Questions people ask

Q: What is the Eötvös experiment in simple terms? A: It is a test of whether different materials feel the same gravitational pull relative to their inertia. Loránd Eötvös hung two masses of different materials from the ends of a rod on a thin fiber and looked for a twist. He saw none, to about one part in 100 million in his 1906–1909 series, which means gravity treated both materials alike to that accuracy.

Q: How precisely has the equivalence principle been tested? A: The best laboratory torsion-balance tests reach about two parts in 10 trillion, and lunar laser ranging reaches about one part in 10 trillion for Earth and Moon. In 2022 the MICROSCOPE satellite reported no violation of the principle at about 2.7 parts in a quadrillion for titanium and platinum.

Q: Did the Apollo 15 hammer and feather drop prove the principle? A: It demonstrated it vividly, but it was not a precision test. The drop height and timing were not carefully measured, so it could only show that any difference was small. Its value was showing that without air, a hammer and a feather land together.

Q: What is a torsion balance? A: A horizontal rod suspended from a thin fiber, with a mirror that turns the rod's tiny rotations into a visible shift of a light beam. Because the fiber resists twisting only weakly, a very small force produces a measurable turn. The Cavendish experiment and the Eötvös experiment both rely on it.

Q: Why did the MICROSCOPE team put the experiment in space? A: A satellite is in continuous free fall, so the test masses are not held up by a floor or a fiber, and Earth's gravity acts on them all the time. The mission ran in a 710-kilometer orbit and gathered about five months of science data. The result improved on the best ground test by nearly two orders of magnitude.

Q: Could the equivalence principle still turn out to be wrong? A: It could in principle, and that is why people keep testing it. Many theories that try to unify gravity with other forces predict a small violation. So far every test is consistent with zero, with the limit currently around a few parts in 10¹⁵ for the materials tested. For related experiments, see our complete guide to science experiments and the complete science guide.

What this means

Eötvös built the first instrument that could see whether gravity played favorites, and he found that it did not. Over the following century, the question was never answered once and for all. It was asked again with a longer baseline, a calmer platform, a better modulator, a cleaner orbit, and each time the answer was the same with fewer places left to hide a difference.

What gives these experiments their weight is that nothing in the theory forces the answer. Newtonian physics would work with different ratios for different materials, and several modern theories expect them. Equal fall is a fact about the world that has had to survive every attempt to break it, from a wooden pendulum in 1687 to a satellite in 2022.

Sources

• Will, C. M., "The Confrontation between General Relativity and Experiment," Living Reviews in Relativity (arXiv version): ar5iv.labs.arxiv.org/html/1403.7377.
• Touboul, P. et al., "MICROSCOPE mission: final results of the test of the Equivalence Principle," Phys. Rev. Lett. 129, 121102 (2022): arXiv:2209.15487.
• Williams, J. G., Turyshev, S. G., and Boggs, D. H., "Lunar Laser Ranging Tests of the Equivalence Principle," Class. Quantum Grav. 29, 184004 (2012): arXiv:1203.2150; and the 2005 analysis, arXiv:gr-qc/0507083.
• Wikipedia, "Eötvös experiment" (timeline and tabulated limits): en.wikipedia.org.
• NASA NSSDC, "Apollo 15 Hammer-Feather Drop": nssdc.gsfc.nasa.gov.
• National High Magnetic Field Laboratory, "Roland Eötvös" biography: nationalmaglab.org.
• Tóth, G., "Explanation of the EPF experiment in terms of gravity gradients": arXiv:1803.04720.
• Physics World, "The legend of the leaning tower" (February 4, 2003): physicsworld.com.