Eötvös experiment

The Eötvös experiment was a 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 the same accuracy. The earliest experiments were done by Isaac Newton (1642–1727) and improved upon by Friedrich Wilhelm Bessel (1784–1846).[1] A much more accurate experiment using a torsion balance was carried out by Loránd Eötvös starting around 1885, with further improvements in a lengthy run between 1906 and 1909. Eötvös's 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 states that the gravitational and inertial masses are the same.

It is sufficient for the inertial mass to be proportional to the gravitational mass. Any multiplicative constant will be absorbed in the definition of the unit of force.[2]

Eötvös's original experiment

If the ratio of F1 to F2 differed from the ratio of G1 to G2, the rod would rotate. The mirror is used to monitor the rotation: a scale would be observed in reflection.
Direction of the centrifugal force in relation to gravity on the surface of Earth.

Eötvös's original experimental device consisted of two masses on opposite ends 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.

As seen from the Earth's frame of reference (or "lab frame", which is not an inertial frame of reference), the primary forces acting on the balanced masses are the string tension, gravity, and the centrifugal force due to the rotation of the Earth. Gravity is calculated by Newton's law of universal gravitation, which depends on gravitational mass. The centrifugal force 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 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 the 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 was 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 Eötvös 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.[3]

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 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.[4] 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 1930s a former student of Eötvös, János Renner (1889–1976), further improved the results to between 1 in 2 to 5 billion.[5] 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.[6][7] 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 mechanics 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.[8][9][10][11][12][13]

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.[14]

Table of measurements over time

Tests on the Equivalence principle

Researcher Year Method Average sensitivity
John Philoponus 517 AD Drop Tower "small"
Simon Stevin 1585 Drop Tower 5×10−2
Galileo Galilei 1590? Pendulum, Drop Tower 2×10−2
Isaac Newton 1686 Pendulum 1×10−3
Friedrich Wilhelm Bessel 1832 Pendulum 2×10−5
Southerns 1910 Pendulum 5×10−6
Zeeman 1918 Torsion balance 3×10−8
Loránd Eötvös 1922 Torsion balance 5×10−9
Potter 1923 Pendulum 3×10−6
Renner 1935 Torsion balance 2×10−9
Dicke, Roll, Krotkov 1964 Torsion balance 3×10−11
Braginsky, Panov 1972 Torsion balance 1×10−12
Shapiro 1976 Lunar Laser Ranging 1×10−12
Keiser, Faller 1981 Fluid support 4×10−11
Niebauer, et al. 1987 Drop Tower 1×10−10
Heckel, et al. 1989 Torsion balance 1×10−11
Adelberger, et al. 1990 Torsion balance 1×10−12
Baeßler, et al.[15] 1999 Torsion balance 5×10−13
Adelberger, et al.[16] 2006 Torsion balance 1×10−13
Adelberger, et al.[17] 2008 Torsion balance 3×10−14
MICROSCOPE[18] 2017 Satellite orbit 1×10−15

See also

References

  1. ^ Marco Mamone Capria (2005). Physics Before and After Einstein. Amsterdam: IOS Press. p. 167. ISBN 1-58603-462-6.
  2. ^ Brewer, Jess H. (1998). "The Eötvös Experiment".
  3. ^ R. v. Eötvös, Mathematische und Naturwissenschaftliche Berichte aus Ungarn, 8, 65, 1890
  4. ^ R. v. Eötvös, in Verhandlungen der 16 Allgemeinen Konferenz der Internationalen Erdmessung, G. Reiner, Berlin, 319,1910
  5. ^ Renner, J. (1935). "KÍSÉRLETI VIZSGÁLATOK A TÖMEGVONZÁS ÉS A TEHETETLENSÉG ARÁNYOSSÁGÁRÓL" (PDF). Matematikai és Természettudományi Értesítő (in Hungarian). 53: 542–568., with abstract in German
  6. ^ Roll, P.G; Krotkov, R; Dicke, R.H (1964). "The equivalence of inertial and passive gravitational mass". Annals of Physics. 26 (3). Elsevier BV: 442–517. Bibcode:1964AnPhy..26..442R. doi:10.1016/0003-4916(64)90259-3. ISSN 0003-4916.
  7. ^ Dicke, Robert H. (December 1961). "The Eötvös Experiment". Scientific American. 205 (205, 6): 84–95. doi:10.1038/scientificamerican1261-84.
  8. ^ Fischbach, Ephraim; Sudarsky, Daniel; Szafer, Aaron; Talmadge, Carrick; Aronson, S. H. (31 March 1986). "Reanalysis of the Eötvös Experiment". Physical Review Letters. 56 (13). American Physical Society (APS): 1427. doi:10.1103/physrevlett.56.1427. ISSN 0031-9007.
  9. ^ Thodberg, Hans Henrik (1 August 1986). "Comment on the Sign in the Reanalysis of the Eötvös Experiment". Physical Review Letters. 57 (9). American Physical Society (APS): 1192. doi:10.1103/physrevlett.57.1192.5. ISSN 0031-9007.
  10. ^ Chu, S. Y.; Dicke, R. H. (13 October 1986). "New Force or Thermal Gradient in the Eötvös Experiment?". Physical Review Letters. 57 (15). American Physical Society (APS): 1823–1824. Bibcode:1986PhRvL..57.1823C. doi:10.1103/physrevlett.57.1823. ISSN 0031-9007. PMID 10033558.
  11. ^ Vecsernyés, P. (15 June 1987). "Constraints on a vector coupling to baryon number from the Eötvös experiment". Physical Review D. 35 (12). American Physical Society (APS): 4018–4019. Bibcode:1987PhRvD..35.4018V. doi:10.1103/physrevd.35.4018. ISSN 0556-2821. PMID 9957666.
  12. ^ Nordtvedt, Kenneth (15 February 1988). "Lunar laser ranging and laboratory Eötvös-type experiments". Physical Review D. 37 (4). American Physical Society (APS): 1070–1071. Bibcode:1988PhRvD..37.1070N. doi:10.1103/physrevd.37.1070. ISSN 0556-2821. PMID 9958777.
  13. ^ Bennett, Wm. R. (23 January 1989). "Modulated-Source Eötvös Experiment at Little Goose Lock". Physical Review Letters. 62 (4). American Physical Society (APS): 365–368. Bibcode:1989PhRvL..62..365B. doi:10.1103/physrevlett.62.365. ISSN 0031-9007. PMID 10040214.
  14. ^ Bod, L.; Fischbach, E.; Marx, G.; Náray-Ziegler, Maria (31 Aug 1990). "One Hundred Years of the Eötvös Experiment". Archived from the original on October 22, 2012.
  15. ^ Phys. Rev. Lett. 83(18), 3585 (1999); "Copia archiviata" (PDF). Archived from the original (PDF) on 12 September 2006. Retrieved 26 April 2008.
  16. ^ Phys. Rev. Lett. 97, 021603 (2006); "Copia archiviata" (PDF). Archived from the original (PDF) on 8 December 2006. Retrieved 26 April 2008.
  17. ^ Phys. Rev. Lett. 100, 041101 (2008); "Copia archiviata" (PDF). Archived from the original (PDF) on 2 February 2010. Retrieved 26 April 2008.
  18. ^ Brax, Philippe (September 14, 2022). "Satellite Confirms the Principle of Falling". Physics. 15 (94). American Physical Society (APS): 94. doi:10.1103/Physics.15.94.

Read other articles:

Dua puluh pence (uang logam Irlandia)

Uang logam 20 pence Irlandia Uang logam dua puluh pence (20p) (Irlandia: fiche pingincode: ga is deprecated ) adalah subdivisi pound Irlandia. Uang logam ini diperkenalkan pada 30 Oktober 1986. Koin ini adalah 1/5 dari pound Irlandia. Semua koin dua puluh pence ditarik pada tahun 2002 dengan munculnya euro. Pranala luar Situs web Irish Coinage - katalog - dua puluh pence desimal Coinage (Dimension and Design) Regulations, 1986 New Coinage (Twenty Pence) Order, 1986 lbsMata uang Republik Irlan...

 

Marmaris

MarmarisDistrik Provinsi Muğla1. Pemandangan Marmaris dari jauh; 2. Pantai Marmaris; 3. Kapal kayu; 4. Pusat kota Marmaris; 5. Pantai Marmaris; 6. Dolphinarium di Marmaris; 7. Marina Marmaris; 8. Hotel Mares; 9. Kastil Marmaris.Negara TurkiRegionAegeaProvinsiMuğlaPemerintahan • Wali KotaMuhammet Ali Acar (CHP)Luas[1] • Distrik878,09 km2 (33,903 sq mi)Ketinggian7 m (23 ft)Populasi (2012)[2] • Perkotaan34.0...

 

Allemagne

Pour les articles homonymes, voir Allemagne (homonymie), République fédérale d'Allemagne (homonymie) et BRD. République fédérale d’Allemagne(de) Bundesrepublik Deutschland Drapeau de l'Allemagne Armoiries de l'Allemagne Devise en allemand : Einigkeit und Recht und Freiheit[1] (« Unité et droit et liberté »), non officielle Hymne en allemand : Deutschlandlied (« Chant d'Allemagne ») Fête nationale 3 octobre · Événement c...

January 1926

Month of 1926 1926 January February March April May June July August September October November December << January 1926 >> Su Mo Tu We Th Fr Sa 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31   The following events occurred in January 1926: January 1, 1926 (Friday) Flooding of the Rhine river struck Cologne; 50,000 were forced to evacuate their homes.[1] Ireland's first regular radio service, 2RN (later Radio Éireann), be...

 

Duodenal bulb

Duodenal bulbInterior of the stomach. (There is no label for Duodenal bulb, but the portion of the duodenum labeled at upper left is the duodenal bulb.)DetailsIdentifiersLatinampulla duodeni,[1]bulbus duodeni[1]Anatomical terminology[edit on Wikidata] The duodenal bulb (also ampulla of duodenum, duodenal ampulla, or duodenal cap) is the initial, dilated portion of (the superior part of) the duodenum[1] just distal to the stomach; it begins at the pylorus and ends a...

 

2020年夏季奥林匹克运动会马来西亚代表团

2020年夏季奥林匹克运动会马来西亚代表團马来西亚国旗IOC編碼MASNOC马来西亚奥林匹克理事会網站olympic.org.my（英文）2020年夏季奥林匹克运动会（東京）2021年7月23日至8月8日（受2019冠状病毒病疫情影响推迟，但仍保留原定名称）運動員30參賽項目10个大项旗手开幕式：李梓嘉和吳柳螢（羽毛球）[1][2]閉幕式：潘德莉拉（跳水）[3]獎牌榜排名第74 金牌 銀牌 銅�...

Esfandiar Rahim Mashaei

Esfandiar Rahim MashaeiMashaei pada 2013 Wakil Presiden Tingkat Satu Iran ke-4Masa jabatan17 Juli 2009 – 25 Juli 2009PresidenMahmoud AhmadinejadPendahuluParviz DavoodiPenggantiMohammad-Reza RahimiKepala Jawatan PresidenMasa jabatan25 Juli 2009 – 7 Desember 2012PresidenMahmoud AhmadinejadPendahuluAbdolreza SheykholeslamiPenggantiMir-Hassan MousaviPetinggi Pemerintahan Presidensial IranMasa jabatan19 September 2009 – 9 April 2011PresidenMahmoud AhmadinejadPendah...

 

Środula

This article does not cite any sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Środula – news · newspapers · books · scholar · JSTOR (December 2013) (Learn how and when to remove this message) Środula Środula is a former village in Poland, now the northern district of the town of Sosnowiec, Poland. Edward Gierek, a former leader of Poland (the 4th First...

 

Elton John

British singer, composer and pianist (born 1947) This article is about the musician. For the album, see Elton John (album). For other uses, see Elton John (disambiguation). SirElton JohnCH CBEJohn at the 2024 Gershwin PrizeBornReginald Kenneth Dwight (1947-03-25) 25 March 1947 (age 77)Pinner, Middlesex, EnglandOther namesReggie DwightAlma materRoyal Academy of MusicOccupationsSingersongwritercomposerpianistYears active1962–presentSpouses Renate Blauel ​ ...

Micron Technology

American company producing semiconductor devices For other uses, see Micron (disambiguation). Not to be confused with Mikron Group, the Russian microelectronics company or JMicron, a Taiwanese company. Micron Technology, Inc.Company typePublicTraded asNasdaq: MUNasdaq-100 componentS&P 500 componentIndustrySemiconductorsFoundedOctober 5, 1978;45 years ago (1978-10-05)FoundersWard ParkinsonJoe ParkinsonDennis WilsonDoug PitmanHeadquartersBoise, Idaho, U.S.Area servedWorld...

 

Sinode Dordrecht

Synod of Dordrecht (1729) oleh Bernard Picart Sinode Dordrecht (juga disingkat Dordt atau Dort) berlangsung pada tahun 1618-1619.[1] Pembukaan sinode ini diadakan pada 13 November 1618.[2] Sinode Dordrecht dilatarbelakangi oleh pertikaian mengenai ajaran Jacobus Arminius dengan kelompok-kelompok politik Belanda yang mengarah pada pecahnya perang saudara.[1] Akhirnya, pemerintah mengumpulkan sinode se-Belanda, yang juga dihadiri oleh utusan-utusan sejumlah besar gereja ...

 

Billings, Montana

Peta Montana menunjukkan lokasi Billings Billings merupakan kota yang terletak di sebelah utara Amerika Serikat. Kota ini tepatnya di negara bagian Montana, Amerika Serikat. Pada tahun 2006, kota ini memiliki jumlah penduduk sebanyak 101.721 jiwa dengan memiliki luas wilayah 106 km². Kota ini memiliki angka kepadatan penduduk sebanyak 1.029 jiwa/km². Kota ini merupakan kota terbesar di negara bagian itu. Didirikan tahun 1877. Pranala luar Wikimedia Commons memiliki media mengenai Billi...

History of slavery

Part of a series onForced labour and slavery Contemporary Child Labour Child soldiers Conscription Debt Forced marriage Bride buying Child marriage Wife selling Forced prostitution Human trafficking Peonage Penal labour Contemporary Africa 21st-century jihadism Sexual slavery Wage slavery Historical Antiquity Egypt Babylonia Greece Rome Medieval Europe Ancillae Black Sea slave trade Byzantine Empire Kholop Prague slave trade Serfs History In Russia Emancipation Thrall Genoese slave trade Ven...

 

丘北县

丘北县县椒莲广场、锦屏文笔塔丘北县政府、普者黑湖丘北县（红色）在文山州（粉色）和云南省的位置坐标：24°02′36″N 104°11′26″E / 24.04321°N 104.19052°E / 24.04321; 104.19052国家 中华人民共和国隶属行政区云南省文山壮族苗族自治州面积 • 总计5,038 平方公里（1,945 平方英里） 人口（2020） • 總計468,172人 • 密度92.9人/...

 

義大利—烏克蘭關係

義大利–烏克蘭關係 義大利 烏克蘭 代表機構義大利駐烏克蘭大使館（英语：Embassy of Italy, Kyiv）烏克蘭駐義大利大使館（英语：Embassy of Ukraine, Rome） 義大利－烏克蘭關係是義大利和烏克蘭兩個歐洲國家之間的雙邊關係，意大利於1991年12月28日承認烏克蘭獨立，兩國於1992年1月29日開始外交關係[1]。義大利在基輔設有大使館，烏克蘭在羅馬設有大使館。 2018年，意大利是�...

روبيرتو أنزولين

روبيرتو أنزولين   معلومات شخصية الميلاد 18 أبريل 1938   فالداجنو  الوفاة 6 أكتوبر 2017 (79 سنة) [1]  فالداجنو  الطول 1.76 م (5 قدم 9 1⁄2 بوصة) مركز اللعب حارس مرمى الجنسية إيطاليا (18 يونيو 1946–6 أكتوبر 2017) مملكة إيطاليا (18 أبريل 1938–18 يونيو 1946)  المسيرة الاحتر...

 

Social services

Range of public services The provision of education services is an example of a social service. For more, see Public Education.Part of a series onLiberalism Schools Classical Conservative Cultural Feminist Equity Green Internationalist Muscular National Neo Ordo Radical Religious Christian Catholic Islamic Jewish Secular Social Techno Third Way Principles Consent of the governed Due process Democracy Economic liberalism Economic globalization Equality Gender Legal Federalism Freedom Economic ...

 

Victoria Salmon Kings

This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these messages) This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional sources.Find sources: Victoria Salmon Kings – news · newspapers · books · scholar · JSTOR (September 2015) This article needs ad...

Désinformation

Si ce bandeau n'est plus pertinent, retirez-le. Cliquez ici pour en savoir plus. Cet article doit être recyclé (novembre 2020). Une réorganisation et une clarification du contenu paraissent nécessaires. Améliorez-le, discutez des points à améliorer ou précisez les sections à recycler en utilisant {{section à recycler}}. La désinformation est un ensemble de pratiques et techniques de communication visant à influencer l'opinion publique en diffusant volontairement des informations f...

 

Politics of the Republic of Ireland

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Politics of the Republic of Ireland – news · newspapers · books · scholar · JSTOR (September 2017) (Learn how and when to remove this message) Politics of the Republic of IrelandCoat of armsPolity typeUnitary parliamentary democratic RepublicConstitutionConsti...