Eötvös experiment

Eötvös experiment

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The Eötvös experiment was a famous physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

 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 the same accuracy. The earliest experiments were done by Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

 (1642–1727) and improved upon by Friedrich Wilhelm Bessel (1784–1846). A much more accurate experiment using a torsion balance was carried out by Loránd Eötvös
Loránd Eötvös
Baron Loránd Eötvös de Vásárosnamény , more commonly called Baron Roland von Eötvös in English literature, was a Hungarian physicist. He is remembered today largely for his work on gravitation and surface tension.-Life:...

 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
Equivalence principle
In the physics of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body is actually...

 encoded in general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, which states that the gravitational and inertial masses are the same.

It is sufficient for the inertial mass to be proportional
Proportionality (mathematics)
In mathematics, two variable quantities are proportional if one of them is always the product of the other and a constant quantity, called the coefficient of proportionality or proportionality constant. In other words, are proportional if the ratio \tfrac yx is constant. We also say that one...

 to the gravitational mass. Any multiplicative constant will be absorbed in the definition of the unit of force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...


Eötvös' original experiment

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
A telescope is an instrument that aids in the observation of remote objects by collecting electromagnetic radiation . The first known practical telescopes were invented in the Netherlands at the beginning of the 1600s , using glass lenses...

. 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.

As seen from the Earth's frame of reference (or "lab frame", which is not an inertial frame of reference), the primary forces acting the balanced masses are the string tension, gravity, and the centrifugal force
Centrifugal force
Centrifugal force can generally be any force directed outward relative to some origin. More particularly, in classical mechanics, the centrifugal force is an outward force which arises when describing the motion of objects in a rotating reference frame...

 due to the rotation of the Earth. Gravity is calculated by Newton's law of universal gravitation
Newton's law of universal gravitation
Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them...

, which depends on gravitational mass. The centrifugal force is calculated by Newton's laws of motion
Newton's laws of motion
Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces...

 and depends on inertial mass.

The experiment was arranged so that if the two types of masses were different, the two forces will not act in exactly the same way on the two bodies, and over time the rod will rotate. As seen from the rotating "lab frame", the string tension plus the (much smaller) centrifugal force cancels the weight (as vectors), while as seen from any inertial frame the (vector) sum of the weight and the tension makes the object rotate along with the earth.

For the rod to be at rest in lab frame, the reactions, on the rod, of the tensions acting on each body, must create a zero net torque (the only degree of freedom is rotation on the horizontal plane). Supposing that the system were constantly at rest – this meaning mechanical equilibrium (i.e. net forces and torques zero) – with the two bodies thus hanging also at rest, but having different centrifugal forces upon them and consequently exerting different torques on the rod through the reactions of the tensions, the rod then would spontaneously rotate, in contradiction with our assumption that the system is at rest. So the system cannot exist in this state; any difference between the centrifugal forces on the two bodies will set the rod in rotation.

Further improvements

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
Gellért Hill
Gellért Hill is a high hill overlooking the Danube in Budapest, Hungary. It is part of the 1st and 11th Districts. Gellért Hill was named after Saint Gerard who was thrown to death from the hill. The famous Hotel Gellért and the Gellért Baths can be found in Gellért Square at the foot of the...

 in Budapest
Budapest is the capital of Hungary. As the largest city of Hungary, it is the country's principal political, cultural, commercial, industrial, and transportation centre. In 2011, Budapest had 1,733,685 inhabitants, down from its 1989 peak of 2,113,645 due to suburbanization. The Budapest Commuter...


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
Prospecting is the physical search for minerals, fossils, precious metals or mineral specimens, and is also known as fossicking.Prospecting is a small-scale form of mineral exploration which is an organised, large scale effort undertaken by mineral resource companies to find commercially viable ore...

 by searching for local mass concentrations.

Using the new device a series of experiments taking 4000 hours was carried out with Dezsö Pekár (1873–1953) and Jenő Fekete (1880–1943) 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. Eötvös died in 1919, and the complete measurements were only published in 1922 by Pekár and Fekete.

Related studies

Eötvös also studied similar experiments being carried out by other teams on moving ships, which led to his development of the Eötvös effect
Eötvös effect
The Eötvös effect is the change in perceived gravitational force caused by the change in centrifugal acceleration resulting from eastbound or westbound velocity...

 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
Black Sea
The Black Sea is bounded by Europe, Anatolia and the Caucasus and is ultimately connected to the Atlantic Ocean via the Mediterranean and the Aegean seas and various straits. The Bosphorus strait connects it to the Sea of Marmara, and the strait of the Dardanelles connects that sea to the Aegean...

 in 1908.

In the 1930s a former student of Eötvös, János Renner (1889–1976), further improved the results to between 1 in 2 to 5 billion. Robert H. Dicke
Robert H. Dicke
Robert Henry Dicke was an American physicist who made important contributions to the fields of astrophysics, atomic physics, cosmology and gravity.-Biography:...

 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. 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, 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
Stratigraphy, a branch of geology, studies rock layers and layering . It is primarily used in the study of sedimentary and layered volcanic rocks....

, 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.