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The Eötvös experiment is a classic physics experiment designed to test the equivalence of inertial and gravitational mass, demonstrating that the two masses are proportional. Conducted by Hungarian physicist Loránd Eötvös in the late 19th century, it involved a torsion balance to measure variations in gravitational force on different masses. The experiment's results support the idea that inertial mass and gravitational mass are equivalent, a crucial aspect of understanding gravity in the framework of relativity.

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5 Must Know Facts For Your Next Test

• The Eötvös experiment provided strong evidence supporting the equivalence principle, which states that the effects of gravity are indistinguishable from acceleration.
• Eötvös used a torsion balance with two different materials to show that they experienced the same gravitational acceleration, reinforcing the notion of mass equivalence.
• The precision of the Eötvös experiment was such that it has been fundamental in testing modifications to Newtonian gravity and theories of relativity.
• The experiment's results have implications for modern physics, particularly in general relativity, where the distinction between inertial and gravitational mass becomes negligible.
• Eötvös' work laid groundwork for later experiments and contributed significantly to our understanding of gravity and its role in the universe.

Review Questions

• The Eötvös experiment demonstrated the relationship between inertial and gravitational mass by using a torsion balance to measure the gravitational force acting on two different masses. Eötvös showed that these masses experienced the same gravitational acceleration, regardless of their composition. This finding suggested that inertial mass and gravitational mass are equivalent, supporting the principle that gravitational interactions do not depend on the type or amount of matter.
• Eötvös' findings have significant implications for modern physics, particularly in validating the equivalence principle foundational to general relativity. By showing that inertial and gravitational masses are equivalent, his work supports Einstein's theory that gravity can be described as a curvature of spacetime rather than a force acting at a distance. This insight has led to numerous advancements in cosmology and our understanding of phenomena like black holes and gravitational waves.
• The Eötvös experiment has greatly influenced experimental methods in physics by setting a standard for precision measurements in gravitational studies. Its innovative use of a torsion balance has inspired subsequent experiments to investigate gravitational interactions with higher accuracy. The methods developed from Eötvös' work continue to be applied in contemporary research to test theories beyond general relativity, making it essential for ongoing explorations into fundamental physics questions about gravity and mass.

Related terms

Inertial Mass : Inertial mass is a measure of an object's resistance to acceleration when a force is applied, reflecting how much matter is contained in the object.

Gravitational Mass : Gravitational mass determines the strength of an object's interaction with a gravitational field, influencing how much force it experiences due to gravity.

Torsion Balance : A torsion balance is a sensitive instrument used to measure small forces, particularly in gravitational experiments, by observing the twisting of a wire under applied forces.

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• About the articles
• Coriolis effect
• Centrifugal effect
• Coriolis effect in Meteorology
• Rotational-vibrational coupling
• Oceanography: Inertial oscillations
• Comparison of ballistics and inertial oscillations
• Meteorology: Cyclonic flow
• The Foucault pendulum
• Main article
• Elaboration

The Eötvös effect

• Coriolis flow meter
• Angular momentum of orbiting objects
• Gyroscope Physics
• The Earth's equatorial bulge
• Centrifugal force
• Apparent motion
• Inertial coordinate system
• Inertial space
• Quantity of motion
• Calculus of Variations
• Fermat's stationary time
• Hamilton's stationary action
• Least action (Legacy)
• The Sagnac effect
• Special relativity
• General relativity
• Inertial oscillation
• Great circles.
• Ballistics and orbits
• Circumnavigating pendulum
• Foucault pendulum
• Foucault rod
• Angular acceleration
• Spacestation vertical throw

Physical explanation

The most common design for a gravimeter for field work is a spring-based design; a spring that suspends an internal weight. The suspending force provided by the spring counteracts the gravitational force. A well manufactured spring has the property that the amount of force that the spring exerts is proportional to the amount of stretch. The stronger the effective gravity at a particular location, the more the spring is extended; the spring extends to a length at which the internal weight is sustained. Also, the moving parts of the gravimeter will be dampened, to make it less susceptible to outside influences such as vibration.

For the calculations I'll assume the internal weight in the gravimeter has a mass of 10 kilogram, 10,000 grams. I assume that for surveying a method of transportation is used that gives good speed while moving very smoothly: an airship. Let the cruising velocity of the airship be 25 meters per second (90 km/h, 55 miles/h).

To calculate what it takes for the internal weight to be neutrally suspended when it is stationary with respect to the Earth the fact that the Earth rotates must be taken into account. At the equator the velocity of Earth's surface is about 465 meters per second. The amount of centripetal force required to cause an object to move along a circular path with a radius of 6378 kilometer (the Earth's equatorial radius), at 465 m/s, is about 0.034 newton per kilogram of mass. For the 10,000 gram internal weight that amounts to about 0.34 newtons. The amount of suspension force required is the mass of the internal weight (multiplied with the gravitational acceleration), minus those 0.34 newtons. In other words: any object co-rotating with the Earth at the equator has its measured weight reduced by 0.34 percent, thanks to the Earth's rotation.

When cruising at 25 m/s due east, the total velocity becomes 465 + 25 = 490 m/s, which requires a centripetal force of about 0.375 newtons. Cruising at 25 m/s due West the total velocity is 465 - 25 = 440 m/s, requiring about 0.305 newtons. So if the internal weight is neutrally suspended while cruising due east, it will not be neutrally suspended anymore after a U-turn; after the U-turn, the weight of the 10,000 gram internal weight has increased by about 7 grams; the spring of the gravimeter must extend some more to accommodate the larger weight. On the other hand: on a non-rotating planet, making the same U-turn would not result in a change of gravimetric reading.

Derivation of the formula for motion along the Equator

A convenient coordinate system in this situation is the inertial coordinate system that is co-moving with the center of mass of the Earth. Then the following is valid: objects that are at rest on the surface of the Earth, co-rotating with the Earth, are circling the Earth's axis, so they are in centripetal acceleration with respect to that inertial coordinate system.

What is sought is the difference in centripetal acceleration of the surveying airship between being stationary with respect to the Earth and having a velocity with respect to the Earth. The following derivation is exclusively for motion in east-west or west-east direction.

It can readily be seen that in the case of motion along the equator the formula for any latitude simplifies into the formula above.

The second term represents the required centripetal acceleration for the internal weight to follow the curvature of the earth. It is independent of both the earth's rotation and the direction of motion. For example, when an aeroplane carrying gravimetric reading instruments cruises over one of the poles at constant altitude, the aeroplane's trajectory follows the curvature of the earth. The first term in the formula is zero then, due to the cosine of the angle being zero, and the second term then represents the centripetal acceleration to follow the curvature of the Earth's surface.

Explanation of the cosine in the first term

The mathematical derivation for the Eötvös effect for motion along the Equator explains the factor 2 in the first term of the Eötvös correction formula.

Because of its rotation, the Earth is not spherical in shape, there is an equatorial bulge. The force of gravity is directed towards the center of the Earth. The normal force is perpendicular to the local surface.

On the poles and on the equator the force of gravity and the normal force are exactly in opposite direction. At every other latitude the two are not exactly opposite, so there is a resultant force, that acts towards the Earth's axis. At every latitude there is precisely the amount of centripetal force that is necessary to maintain an even thickness of the atmospheric layer. (The solid Earth is ductile. Whenever the shape of the solid Earth is not entirely in equilibrium with its rate of rotation, then the shear stress deforms the solid Earth over a period of millions of years until the shear stress is resolved.)

Again the example of an airship is convenient for discussing the forces that are at work. When the airship has a velocity relative to the Earth in latitudinal direction then the weight of the airship is not the same as when the airship is stationary with respect to the Earth. If an airship has an eastward velocity, then the airship is in a sense "speeding". The situation is comparable to a racecar on a banked circuit with an extremely slippery road surface. If the racecar is going too fast then the car will tend to drift wide. For an airship in flight that means a reduction of the weight, compared to the weight when stationary with respect to the Earth. If the airship has a westward velocity then the situation is like that of a racecar on a banked circuit going too slow: on a slippery surface the car will slump down. For an airship that means an increase of the weight.

The Eötvös effect is proportional to the component of the required centripetal force perpendicular to the local Earth surface, and is thus described by a cosine law: the closer to the Equator, the stronger the effect.

Motion along 60 degrees latitude

An object located at 60 degrees latitude, co-moving with the Earth, is following a circular trajectory, with a radius of about 3190 kilometer, and a velocity of about 233 m/s. That circular trajectory requires a centripetal force of about 0.017 newton for every kilogram of mass; 0.17 newtons for the 10,000 gram internal weight. At 60 degrees latitude the component that is perpendicular to the local surface (the local vertical) is half the total force. Hence, at 60 degrees latitude, any object co-moving with the Earth has its weight reduced by about 0.08 percent, thanks to the Earth's rotation.

When the surveying airship is cruising at 25 m/s towards the east the total velocity becomes 233 + 25 = 258, which requires a centripetal force of about 0.208 newtons for the gravimeter's internal weight; local vertical component about 0.104 newton. Cruising at 25 m/s towards the west the total velocity becomes 233 - 25 = 208 m/s, which requires a centripetal force of about 0.135 newtons; local vertical component about 0.68 newtons. Hence at 60 degrees latitude the difference before and after the U-turn of the 10,000 gram internal weight is a difference of 4 gram in measured weight.

The diagrams also show the component in the direction parallel to the local surface. In Meteorology and in Oceanography it is customary to refer to the effects of the component parallel to the local surface as the Coriolis effect.

To my knowledge the first scientist who recognized that the Eötvös effect and the meteorological Coriolis effect are interconnected was the meteorologist Anders Persson, who has published about it in several articles, starting around the year 2000.

The information about the Eötvös effect was retrieved from the following source: The Coriolis effect PDF-file. 780 KB 17 pages. A general discussion by the meteorologist Anders Persson of various aspects of geophysics, covering the Coriolis effect as it is taken into account in Meteorology and Oceanography, the Eötvös effect, the Foucault pendulum, and Taylor columns.

Last time this page was modified: June 18 2017

December 1, 1961

The Eötvös Experiment

Around 1900 a Hungarian baron conducted exquisite measurements to demonstrate that all bodies fall at precisely the same rate. His result, crucial to the general theory of relativity, has now been confirmed

By R. H. Dicke

Eötvös effect in rotational dynamics

Understanding the eötvös effect: principles and dynamics.

The Eötvös Effect , named after the Hungarian physicist Loránd Eötvös, is a fascinating phenomenon that occurs in rotational dynamics and plays a crucial role in geophysics and precision measurements. This effect is primarily concerned with the variation in gravitational acceleration on a rotating body, influenced by the rotation of the Earth.

The Mechanics of the Eötvös Effect

E = vωcos(φ)/g

Precision Measurements and Applications

Rotation and its impact.

The rotation of the Earth introduces complexities in the measurement of gravitational forces. Understanding the Eötvös Effect is crucial for compensating these rotational influences, especially in airborne and shipborne gravity surveys. This compensation allows for more accurate data collection and interpretation, leading to better geological and geophysical insights.

Advanced Applications in Modern Science

Challenges and future prospects.

Despite its widespread applications, the Eötvös Effect presents certain challenges. The primary difficulty lies in accurately measuring and compensating for this effect in various scenarios. Advancements in technology, such as improved sensors and computational methods, are continuously being developed to overcome these challenges. Looking forward, the Eötvös Effect holds potential for further breakthroughs in understanding Earth’s dynamic systems and in enhancing the precision of geophysical surveys.

Environmental and Educational Implications

The Eötvös Effect, a phenomenon born from the interplay of Earth’s rotation and gravitational forces, stands as a cornerstone in the field of geophysics. Its applications, ranging from resource exploration to space exploration, highlight its versatility and importance. While challenges in its measurement and interpretation persist, ongoing advancements in technology are paving the way for more precise and comprehensive applications. As we continue to explore and understand our planet and beyond, the Eötvös Effect remains an essential tool, providing insights into the dynamic and intricate nature of Earth’s gravitational system.

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Difference between the Coriolis effect and the Eötvös effect

The coriolis accelaration is $-2\Omega \times u$, where $\Omega$ is the earths rotation and u is the velocity in a basis following the earth.

When something moves east/west, this results in acceleration upwards/downwards. This is also called the eötvös effect, which wikipedia says corresponds to $2\Omega u cos(\phi) + \frac{u^2 + v^2}{R}$, where u is movement in east/west direction and v is movement in north/south direction.

If the eötvös effect is the vertical component of the coriolis effect, then why are the expressions different? The coriolis effect lacks $\frac{u^2 + v^2}{R}$. Without that term, sufficient velocity west would push an object into the ground, instead of generating a centrifugal effect.

Does the derivation of the coriolis effect assume low velocity, or am I missing something else?

• newtonian-mechanics
• reference-frames
• centrifugal-force
• coriolis-effect

• $\begingroup$ Does the derivation of the coriolis effect assume low velocity?: No, it is just the difference between the land speed at that latitude and the a horizontal speed of the air stream. The eötvös effect is due to the increase in centrifugal force when it's speed is added to the earth's spin, forcing it outward towards the equator, or the decrease in centrifugal force when going east to west against the earth's spin, allowing it to fall towards the pole. If it was going east to west at more than double the ground speed, it would be forced towards the equator anyway. $\endgroup$ –  Peter R. McMahon Commented Apr 30, 2023 at 3:55

2 Answers 2

Essentially yes

Take a look at the last expression in this link:

https://hepweb.ucsd.edu/ph110b/110b_notes/node15.html

That's the Coriolis force on a ball that is fired from some lattitude $\lambda$ . The ball is fired with angle $\theta$ to the local zenith and $\phi$ from the east in the local horizontal plane. So, $\phi=0°$ is east and $\phi=180°$ is west.

Now take a look at the last expression in that link, the one with the fully expanded Coriolis force for the situation described above.

The Z-component of the acceleration is:

$\vec{a}=2\omega v\cos\lambda \sin\theta cos\phi\vec{z}$

Now, take the case in which the cannonball is fired horizontally, meaning, $\theta=90°$

The force becomes:

$\vec{a}=2\omega v\cos\lambda cos\phi\vec{z}$

For $\phi = 0°$ , eastward travel is obtained:

$\vec{a}=2\omega v\cos\lambda \vec{z}$

For $\phi = 180°$ , westward travel is obtained:

$\vec{a}=-2\omega v\cos\lambda \vec{z}$

Basically, both cases can be subsummed by assuming positive $v$ for eastern travel and negative $v$ for westward travel.

Which gives you the main component of the Eotvos effect for velocities that are below the local rotational velocity of the earth.

The 2nd term $(u^2+v^2)/r$ , the correction does not appear unless you assume that the travelling object is trying to keep a circular orbit or in case of a ship, just follow the curvature of the earth.

Another answer mentioned that "the coriolis term wouldn't appear on a cylindrical earth"

But it would. The z-component of it would appear. It even appears on earth for objects fired purely westward or eastward. Bullets for example. And that's for an object that doesn't try to maintain a circular orbit, but one that is just fired freely. If an object is trying to follow the curvature of the earth, the 2nd term (the correction applies) because now it will experience an additional centrifugal force due to the fact that it is moving with velocity $u$ relative to earth and is in a circular trajectory relative to already rotating earth.

Whether the whole effect should be called Eotvos effect or just the 2nd term or even just the 1st term, I do not know. But the first term 100% appears just by expanding the Coriolis force. The 2nd term only appears after an orbit is assumed (or in case of a ship, trying to follow the shape of the earth). The 2nd term is nothing but a circular orbit relative to an already rotating system.

For the case of a travelling bullet or a cannonball, the 2nd term does not apply because it does not try to maintain the orbit and the entire Eotvos effect is just due to Coriolis force.

• $\begingroup$ Thanks! A question about this: "The 2nd term (𝑢^2+𝑣^2)/𝑟, the correction does not appear unless you assume that the travelling object is trying to keep a circular orbit" Why not? If you fire a cannonball westward faster than earth's rotation, you are going to see it go upwards, as compared with the earth's surface. Not downwards, as 2𝜔𝑣cos𝜆𝑧 alone would predict. Maybe this is me assuming that it's trying to keep a circular orbit. But if we don't assume that, I don't see why the 2𝜔𝑣cos𝜆𝑧 force would apply (or why it would predict the ball to be pushed downwards!). $\endgroup$ –  fluff Commented Apr 17, 2020 at 19:53
• 1 $\begingroup$ (1/3) Think about an extreme example. Imagine if you were on a very small planet that is rapidly rotating in the same direction as earth, west-to-east. You throw a ball westwards at t=0 in a straight line. You measure height relative to the place where you are standing. There is a tangential plane that touches the planet at the place where you are standing. Whenever you measure height, you measure height relative to that plane. pasteboard.co/J4iRmJn.png $\endgroup$ –  user238194 Commented Apr 18, 2020 at 0:56
• 1 $\begingroup$ (2/3), left picture is situation at t = 0. red plane is your local coordinate system that rotates with you and that's where you see eotvos acceleration. ball is thrown at t = 0, purely westward. after some time deltaT, right picture appears. ball is still moving in straight line relative to an inertial observer but this time, the planet has rotated and now if you were to measure height of the ball, you will see that it went below your feet because to an inertial observer, your reference frame is rotating alongside earth and so your reference point for height changes direction and origin. $\endgroup$ –  user238194 Commented Apr 18, 2020 at 0:59
• 1 $\begingroup$ (3/3) the extra term would only be necessary if ball was trying to maintain a circular orbit around an already rotating earth. u and v are not absolute speeds but speeds relative to rotating observer. $\endgroup$ –  user238194 Commented Apr 18, 2020 at 1:06

fluff, your problem begins with this assertion: "If the eötvös effect is the vertical component of the coriolis effect..."

In many science disciplines, casual versus formal usages become intermixed, and this is certainly one area. Eötvös is not the vertical component of Coriolis.

The earth is both (a) spherical and (b) spinning. This produces a number of phenomena that affect bodies in motion on or near the surface of the Earth. In casual usage these phenomena tend to be lumped together into all being called "Coriolis," but they are actually discrete physical properties that are not related, except for the fact that they are artifacts of (a), (b), or both.

Coriolis is a conservation of angular momentum consideration when objects move north/south across a spinning sphere. As you move away from the equator latitudinally, the same angular rate of rotation around the Earth's C/G results in a different velocity in the east/west component, and the effects of this difference is the Coriolis Effect. Were the Earth a cylinder instead of a sphere, there'd be no Coriolis Force.

Eötvös on the other hand is a centrifugal force/orbital mechanics problem. Eötvös would still occur on a cylinder, where Coriolis would not.

There IS an angular momentum force that acts east/west based on the height of an object's trajectory or orbit, and thus would affect the vertical component of a projectile's trajectory at long distances involving high trajectories... But this isn't Eötvös at all. If I shoot a projectile perfectly vertically a few miles into the air, conservation of angular momentum dictates the projectile will not land back on me, it will land several feet west of me, opposite the direction of the Earth's spin. It may be more correct to think of THIS motion as the vertical component of Coriolis.

Hope this helps.

• $\begingroup$ Sorry but this is wrong. Coriolis force is a force that's needed, together with centrifugal force, to describe motion in a non-inertial reference frame (both are not needed when describing the same motion in an inertial reference frame). See user238194's answer for the correct description. $\endgroup$ –  Roel Schroeven Commented Mar 1, 2020 at 14:43
• $\begingroup$ I agree that my description above has oversimplified Coriolis. user238194's description of Coriolis is correct, and corrects my oversimplification. However, the vertical component of Coriolis is not Eötvös. Coriolis is a virtual force we calculate to correct the linear tangential momentum imposed on a projectile by the eastward (spin-ward) motion of the "shooter." Agreed, this is required when moving between inertia and non inertial frames. Eötvös is not a correction between reference frames. It is a physical phenomenon, not a virtual one, that can be seen in-situ in either frame. $\endgroup$ –  Max R Commented Mar 2, 2020 at 15:54
• $\begingroup$ There are common ballistic scenarios where Coriolis imposes what appears to be a +Z motion on the projectile in the spherical frame, but that Eötvös is actually -Z. (Think about how that could be.) And think about this... If you change the mass of the earth but leave rotation the same, and use the same velocity and mass of projectile... The net deflection caused by Coriolis remains the same, the net displacement resulting from Eötvös is very different. If they were simply the same phenomena using different names this could not be so. $\endgroup$ –  Max R Commented Mar 2, 2020 at 16:17

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Eötvös experiment

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

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.

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.

a (nuclear mass)/(atomic mass), corrected for isotopic abundance b globally aligned undecatiplet c iron 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.

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

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The Eotvos Experiment: Discussion and Analysis

• Thread starter thecoop
• Start date Oct 28, 2012
• Tags Experiment
• Oct 28, 2012
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A PF Universe

I see equations without derivations in textbooks too sometimes.  

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thecoop said: the eotvos experiment consists of two objects of different composition connected by a rod of length l and suspended horizontally by a fine wire . if the gravitational acceleration of the two masses is different then there will be a torque , I saw this equation in the most of texts without derivation , what do you think guys ?

FAQ: The Eotvos Experiment: Discussion and Analysis

1. what is the eotvos experiment.

The Eotvos experiment is a scientific experiment conducted by Hungarian physicist Baron Roland von Eotvos in the late 19th century. It was designed to test the equivalence principle, which states that the acceleration of an object due to gravity is independent of its mass and composition.

2. How was the Eotvos experiment conducted?

The experiment involved suspending two identical masses from a horizontal rod and measuring the difference in their accelerations as the rod was rotated. If the equivalence principle is true, the two masses should experience the same acceleration and therefore remain at the same distance from the center of rotation. Any deviation from this would indicate a violation of the principle.

3. What were the results of the Eotvos experiment?

The Eotvos experiment found that the two masses experienced the same acceleration, providing strong evidence for the equivalence principle. This result has been confirmed by numerous subsequent experiments and is a fundamental principle in modern physics.

4. What is the significance of the Eotvos experiment?

The Eotvos experiment was one of the first tests of the equivalence principle and provided crucial evidence for its validity. This principle is a cornerstone of Einstein's theory of general relativity and has important implications for our understanding of gravity and the structure of the universe.

5. How is the Eotvos experiment relevant today?

The Eotvos experiment continues to be relevant in the field of physics, as it remains one of the most precise tests of the equivalence principle. It is also used in the development of new theories and models that aim to further our understanding of gravity and its effects on the universe.

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One hundred years of the Eötvös experiment

• Atomic and Molecular Physics
• Published: April 1991
• Volume 69 , pages 335–355, ( 1991 )

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• E. Fischbach 2 ,
• G. Marx 1 &
• Maria Náray-Ziegler 3  

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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.

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On the “Forgotten” Euler Inertial Force

Measurements of the gravitational constant using two independent methods

Deducing Newton’s second law from relativity principles: A forgotten history

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

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

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.

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

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 Scientiarum Budapestiensis de Rolando Eötvös Nominate, Sectio Geologica, 7 , 111, 1963.

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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Bod, L., Fischbach, E., Marx, G. et al. One hundred years of the Eötvös experiment. Acta Physica Hungarica 69 , 335–355 (1991). https://doi.org/10.1007/BF03156102

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High Energy Physics - Phenomenology

Title: generalized analysis of the eötvös experiment.

Abstract: We present a generalized phenomenological formalism for analyzing the original Eötvös experiment in the presence of gravity and a generic "5th force." To date no evidence for a 5th force has emerged since its presence was suggested by a 1986 reanalysis of the 1922 publication coauthored by Eötvös, Pekàr, and Fekete (EPF). However, our generalized analysis introduces new mechanisms capable in principle of accounting for the EPF data, while at the same time avoiding detection by most recent experiments carried out to date. As an example, some of these mechanisms raise the possibility that the EPF signal could have arisen from an unexpected direction if it originated from the motion of the Earth through a medium.

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Supplement to Experiment in Physics

Appendix 4: the fall of the fifth force.

In this episode we will examine a case of the refutation of a hypothesis, but only after a disagreement between experimental results was resolved. The “Fifth Force” was a proposed modification of Newton’s Law of Universal Gravitation. The initial experiments gave conflicting results: one supported the existence of the Fifth Force whereas the other regued against it. After numerous repetitions of the experiment, the discord was resolved and a consensus reached that the Fifth Force did not exist. A reanalysis of the original Eötvös experiment [ 1 ] by Fischbach and his collaborators (1986) had shown a suggestive deviation from the law of gravity. The Fifth Force, in contrast to the famous Galileo experiment, depended on the composition of the objects. Thus, the Fifth Force between a copper mass and an aluminum mass would differ from that between a copper mass and a lead mass. Fischbach and collaborators also suggested modifying the gravitational potential between two masses from

where the second term gives the Fifth Force with strength \(\alpha\) and range \(\lambda\). The reanalysis also suggested that \(\alpha\) was approximately 0.01 and \(\lambda\) was approximately 100m. (For details of this episode see (Franklin 1993)).

Figure 8. Schematic diagram of the differential accelerometer used in Thieberger’s experiment. A precisely balanced hollow copper sphere (a) floats in a copper-lined tank (b) filled with distilled water (c). The sphere can be viewed through windows (d) and (e) by means of a television camera (f). The multiple-pane window (e) is provided with a transparent x-y coordinate grid for position determination on top with a fine copper mesh (g) on the bottom. The sphere is illuminated for one second per hour by four lamps (h) provided with infrared filters (i). Constant temperature is maintained by mea ns of a thermostatically controlled copper shield (j) surrounded by a wooden box lined with Styrofoam insulation (m). The Mumetal shield (k) reduces possible effects du e to magnetic field gradients and four circular coils (l) are used for positioning the sphere through forces due to ac-produced eddy currents, and for dc tests. From Thieberger (1987).

Figure 9. Position of the center of the sphere as a function of time. The y axis points away from the cliff. The position of the sphere was reset at points A and B by engaging the coils shown in Figure 21. From Thieberger (1987).

In this episode, we have a hitherto unobserved phenomenon along with discordant experimental results. The first two experiments on the Fifth Force gave contradictory answers. One experiment supported the existence of the Fifth Force, whereas the other found no evidence for it. The first experiment, that of Peter Thieberger (1987a) looked for a composition-dependent force using a new type of experimental apparatus, which measured the differential acceleration between copper and water. The experiment was conducted near the edge of the Palisades cliff in New Jersey to enhance the effect of an intermediate-range force. The experimental apparatus is shown in Figure 8. The horizontal acceleration of the copper sphere relative to the water can be determined by measuring the steady-state velocity of the sphere and applying Stokes’ law for motion in a resistive medium. Thieberger’s results are shown in Figure 9. The sphere clearly has a velocity, indicating the presence of a force. Thieberger concluded, “The present results are compatible with the existence of a medium-range, substance-dependent force” (p. 1068).

Figure 10. Schematic view of the University of Washington torsion pendulum experiment. The Helmholtz coils are not shown. From Stubbs et al. (1987).

Figure 11. Deflection signal as a function of degrees. The theoretical curves correspond to the signal expected for alpha = 0.01 and lambda = 100m. From Raab (1987).

The second experiment, by the whimsically named Eöt-Wash group, was also designed to look for a substance-dependent, intermediate range force (Raab 1987; Stubbs et al. 1987). The apparatus was located on a hillside on the University of Washington campus, in Seattle (Figure 10). If the hill attracted the copper and beryllium bodies differently, then the torsion pendulum would experience a net torque. This torque could be observed by measuring shifts in the equilibrium angle of the torsion pendulum as the pendulum was moved relative to a fixed geophysical point. Their experimental results are shown in Figure 11. The theoretical curves were calculated with the assumed values of 0.01 and 100m, for the Fifth Force parameters \(\alpha\) and \(\lambda\), respectively. These were the best values for the parameters at the time. There is no evidence for such a Fifth Force in this experiment.

The problem was, however, that both experiments appeared to be carefully done, with no apparent mistakes in either experiment. Ultimately, the discord between Thieberger’s result and that of the Eöt-Wash group was resolved by an overwhelming preponderance of evidence in favor of the Eöt-Wash result (The issue was actually more complex. There were also discordant results on the distance dependence of the Fifth Force. For details see Franklin (1993; 1995a)). The subsequent history is an illustration of one way in which the scientific community deals with conflicting experimental evidence. Rather than making an immediate decision as to which were the valid results, this seemed extremely difficult to do on methodological or epistemological grounds, the community chose to await further measurements and analysis before coming to any conclusion about the evidence. The torsion-balance experiments of Eöt-Wash were repeated by others including (Cowsik et al. 1988; Fitch, Isaila and Palmer 1988; Adelberger 1989; Bennett 1989; Newman, Graham and Nelson 1989; Stubbs et al. 1989; Cowsik et al. 1990; Nelson, Graham and Newman 1990). These repetitions, in different locations and using different substances, gave consistently negative results. In addition, Bizzeti and collaborators (1989a; 1989b), using a float apparatus similar to that of Thieberger, also obtained results showing no evidence of a Fifth Force. There is, in fact, no explanation of either Thieberger’s original, presumably incorrect, results. The scientific community has chosen, I believe quite reasonably, to regard the preponderance of negative results as conclusive. [ 2 ] Experiment had shown that there is no Fifth Force.

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The Eötvös experiment, GTR, and differing gravitational and inertial masses Proposition for a crucial test of metric theories

Journal of Physics: Conference Series

The Eötvös experiment has been taken as basis for metric theories of gravity and particularly for the general theory of relativity (GTR), which assumes that gravitational and inertial masses are identical. We highlight the fact that, unlike the long lasting and reigning belief, the setup by Eötvös experiments and its follow-ups serve to demonstrate no more than a mere linear proportionality between said masses, and not ineludibly their exclusive equality. So much so that, as one distinct framework, Yarman–Arik–Kholmetskii (YARK) gravitation theory, where a purely metric approach is not aimed, makes the identity between inertial and gravitational masses no longer imperative while still remaining in full conformance with the result of the Eötvös experiment, as well as that of free fall experiments. It is further shown that Eötvös experiment deprives us of any knowledge concerning the determination of the proportionality coefficient coming into play. Henceforward, the Eötvös experiment...

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Home > ETD > DISSERTATIONS > AAI8807679

Reanalysis of the Eotvos experiment

Carrick L Talmadge , Purdue University

We present here the details for our reanalysis of the experiment of Eotvos, Pekar, and Fekete (EPF). After outlining the original motivation for reexamining the EPF paper, the history of this experiment is reviewed in some detail. A phenomenological framework is developed for describing the EPF and other similar experiments, and this is then applied to analyzing the EPF data. It is shown that these data evidence a strong correlation between the measured fractional acceleration differences of various sample pairs of materials, and the corresponding differences of baryon number-to-mass ratios. Such a correlation can result from a coupling of the test masses to an intermediate-range field whose source is baryon number, and it is shown that the properties of this field which emerge from the geophysical data provide a good description of the EPF results. It is further demonstrated that no other known mechanism, either conventional or otherwise, provides an adequate explanation of these data. Various experiments to check the EPF results are described, and a general overview of the various classes of experiments is given. In Appendix A the effects of local mass inhomogeneities are analyzed, which appear to represent the dominant sources in Eotvos-like experiments, and in the other Appendices more detailed discussions of the various aspects of this analysis are given.

Fischbach, Purdue University.

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Robert Henry Dicke (1916–1997)

Robert H. Dicke, who made fundamental and lasting contributions to radio astronomy, solar physics, gravitational physics, and cosmology, died in Princeton on 4 March 1997. He is survived by his wife, Annie, whom he married in 1942 and three children. Dicke held the Cyrus Fogg Brackett professorship of physics from 1957 to 1975 and the Albert Einstein professorship of science from 1975 to 1984 (emeritus 1984-97).

Though not consistently a member of the American Astronomical Society, he was awarded the Society's Beatrice M. Tinsley Prize in 1992 for his many contributions to our field. In particular, he played a central role in the transformation of cosmology from "a dream of zealots" to a science firmly based on observations (to quote William A. Fowler in his forward to Robertson and Noonan's 1968 book, Relativity and Cosmology ).

Bob Dicke was born in St. Louis on 6 May 1916. He attended both Rochester and Princeton Universities, graduating from the latter in 1939. His doctorate was obtained two years later from Rochester, in nuclear physics, a field he was to leave almost immediately for defense-related work at the "Rad Lab" at MIT.

At the Radiation Laboratory, he worked primarily on the development of radar and on microwave techniques, inventing along the way the Dicke radiometer, in use in radio observatories around the world, and the magic tee, a staple of waveguide circuits. He also improved and made full use of the technique of phase sensitive detection (the "lock-in 'amplifier" as he called it).

During Dicke's years at the "Rad Lab" he posed the question, just how bright is the night sky at microwave frequencies? Using a microwave radiometer of his own design, and a room-temperature calibrator, he and his colleagues showed that the brightness at centimeter wavelengths is less than 20 K. There is a marvelous and by now well-known photograph of Bob, calibrator in hand, making the first measurement of the radio brightness of the sky from an MIT rooftop.

It has often been remarked that this upper limit was set just a few years before Alpher, Herman, and Gamow predicted that a hot Big Bang would leave a relic radiation field of approximately 5 K temperature. Many have wondered why Bob Dicke did not recall his measurement when the papers by Alpher, Follin, Gamow, and Herman appeared. I would suggest one simple answer. In 1946, Bob moved back to Princeton, a university and a town he and Annie came to love, and he changed his research to atomic physics. The microwave work of the war years was succeeded for ten very fruitful years by prize-winning research on quantum physics, superradiance (the overpopulation of an excited state that leads to maser or laser action), and the measurement of fundamental constants like the g-factor of the electron. Indeed, it is easy for those of us who are astronomers to forget how great an impact Bob Dicke had on atomic physics. His National Medal of Science (1971), Comstock Prize (1973), and Cresson Medal of the Franklin Institute (1974) were awarded primarily for work in physics, not astronomy or cosmology. Bob always thought of himself as a physicist , a designer of experiments, not an observer.

By the late 1950's, however, his interest was drawn to astronomical or cosmological questions by his work on Mach's principle and precision tests of gravity, among them his exquisitely sensitive repetition of the Eotvos experiment, which established that gravitational acceleration is independent of the elemental composition of the material accelerated. In this simple but beautiful experiment, carried out in a pit near Princeton's baseball field, he established this basis of the weak equivalence principle to an accuracy of a few parts in 10 11 . Other work with students and colleagues established the equivalence of passive and active gravitational mass. Both results constrained the nature of theories of gravity, including the one Bob and Carl Brans were working on at the same time. Bob realized that modifications to General Relativity could be tested by looking for anomalies in the motion of the moon or in the precession of the perihelon of the orbit of Mercury. The former led to a lunar ranging experiment left on the moon by Apollo 11 astronauts; the latter to attempts that occupied the last two decades of his active life at Princeton to measure the solar oblateness and hence to refine classical values for the perihelion precession.

But the work for which Dicke is best known, at least to astronomers, is the prediction and explanation of the cosmic microwave background. By the mid 1960's, Bob had become intrigued by the possibility of a cyclically expanding and contracting universe. Aware that stars convert hydrogen to helium and on to heavy elements, he asked why a cyclic universe would not be glutted by heavy elements. His answer was to posit a hot Big Crunch, which photo-dissociated the heavy elements, followed each cycle by a hot Big Bang. With characteristic thoroughness, he and his colleagues, especially Jim Peebles, set out to follow up the observational consequences of a hot Big Bang. And with his characteristic physicist's vision, he proposed to Peter Roll and David Wilkinson that they build a radiometer to search for the relic heat of the Big Bang at centimeter wavelengths.

While Bob and his group were making observations at 3 cm, the cosmic background was being independently discovered a few miles away at the Bell Telephone Laboratories by Arno Penzias and Robert W. Wilson. As soon as he heard of the Bell Labs result, Dicke was sure both that the relic heat of the Big Bang had been found and that the Princeton group had been scooped. Bob's interpretation of the measurements of Penzia and Wilson has been triumphantly confirmed over the past 30 years, and the cosmic microwave background is now a cornerstone of modem physical cosmology

In addition to the honors mentioned previously, Dicke received honorary DSc's from the University of Edinburgh, Rochester, Ohio Northern University, and Princeton. He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences (and winner of their Rumford Premium Award in 1967) and served on a very large number of advisory panels and committees for NSF, NASA, NBS, and other organizations. A brief obituary appeared in Nature (386, 448, 1997) and a longer one should appear in the Biographical Memoirs of the National Academy of Sciences . Oral history material from 1983 and 1985 and responses to a questionnaire on the origins of lasers are on file at the Neils Bohr Library of the American Institute of Physics.

Despite Dicke's crucial role in the interpretation of the cosmic background, he published only a few papers on the topic. Instead, he continued his work on solar oblateness and gravity theory. He also gave kind, active, and insightful support to younger scientists in what came to be known as the Gravity Group at Princeton, in which Bob's students and colleagues mingled happily with those of John Wheeler. For a young assistant professor, as I was then, the years in the Gravity Group were an absolutely ideal experience. Bob could always be counted on for gentle and sensible advice, and he bubbled over with clever ideas from adaptive optics ("rubber mirrors" he called them) to radioactive dating to helium abundances in stars, all areas of interest today. I remember Bob Dicke best as an inspiring mentor. History will remember him as a major contributor to both twentienth century physics and modem cosmology.

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Remeasurement of the Eötvös experiment - status and first results

• October 2019
• CC BY-NC-ND 4.0
• Conference: International Conference on Precision Physics and Fundamental Physical Constants

• Budapest University of Technology and Economics

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