A Theory of Inertia Based on Mach’s Principle
A non-relativistic theory of inertia based on Mach’s principle is presented as has been envisaged, but not achieved, by Ernst Mach in 1872. The central feature is a space-dependent, anisotropic, symmetric inert mass tensor. The contribution of a mass element <inline-formula> <math...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-08-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/5/8/188 |
| _version_ | 1798040674791063552 |
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| author | Volkmar Putz |
| author_facet | Volkmar Putz |
| author_sort | Volkmar Putz |
| collection | DOAJ |
| description | A non-relativistic theory of inertia based on Mach’s principle is presented as has been envisaged, but not achieved, by Ernst Mach in 1872. The central feature is a space-dependent, anisotropic, symmetric inert mass tensor. The contribution of a mass element <inline-formula> <math display="inline"> <semantics> <mrow> <mi>d</mi> <mi>m</mi> </mrow> </semantics> </math> </inline-formula> to the inertia of a particle <inline-formula> <math display="inline"> <semantics> <msub> <mi>m</mi> <mn>0</mn> </msub> </semantics> </math> </inline-formula> experiencing an acceleration from rest is proportional to <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mo form="prefix">cos</mo> <mn>2</mn> </msup> <mi>α</mi> </mrow> </semantics> </math> </inline-formula>, where <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula> is the angle between the line connecting <inline-formula> <math display="inline"> <semantics> <msub> <mi>m</mi> <mn>0</mn> </msub> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>d</mi> <mi>m</mi> </mrow> </semantics> </math> </inline-formula> and the direction of the acceleration. Apsidal precession for planets circling around a central star is not a consequence of this theory, thereby avoiding the prediction of an apsidal precession with the wrong sign as is done by Mach-like theories with isotropic inert mass. |
| first_indexed | 2024-04-11T22:10:50Z |
| format | Article |
| id | doaj.art-81c7b12e148244f09fc7c0c10df7343e |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-04-11T22:10:50Z |
| publishDate | 2019-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-81c7b12e148244f09fc7c0c10df7343e2022-12-22T04:00:34ZengMDPI AGUniverse2218-19972019-08-015818810.3390/universe5080188universe5080188A Theory of Inertia Based on Mach’s PrincipleVolkmar Putz0Institute for General Secondary Education, University College of Teacher Education Vienna (PH Wien), 1100 Vienna, AustriaA non-relativistic theory of inertia based on Mach’s principle is presented as has been envisaged, but not achieved, by Ernst Mach in 1872. The central feature is a space-dependent, anisotropic, symmetric inert mass tensor. The contribution of a mass element <inline-formula> <math display="inline"> <semantics> <mrow> <mi>d</mi> <mi>m</mi> </mrow> </semantics> </math> </inline-formula> to the inertia of a particle <inline-formula> <math display="inline"> <semantics> <msub> <mi>m</mi> <mn>0</mn> </msub> </semantics> </math> </inline-formula> experiencing an acceleration from rest is proportional to <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mo form="prefix">cos</mo> <mn>2</mn> </msup> <mi>α</mi> </mrow> </semantics> </math> </inline-formula>, where <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula> is the angle between the line connecting <inline-formula> <math display="inline"> <semantics> <msub> <mi>m</mi> <mn>0</mn> </msub> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>d</mi> <mi>m</mi> </mrow> </semantics> </math> </inline-formula> and the direction of the acceleration. Apsidal precession for planets circling around a central star is not a consequence of this theory, thereby avoiding the prediction of an apsidal precession with the wrong sign as is done by Mach-like theories with isotropic inert mass.https://www.mdpi.com/2218-1997/5/8/188inertiaMach’s principlehistory of physics |
| spellingShingle | Volkmar Putz A Theory of Inertia Based on Mach’s Principle Universe inertia Mach’s principle history of physics |
| title | A Theory of Inertia Based on Mach’s Principle |
| title_full | A Theory of Inertia Based on Mach’s Principle |
| title_fullStr | A Theory of Inertia Based on Mach’s Principle |
| title_full_unstemmed | A Theory of Inertia Based on Mach’s Principle |
| title_short | A Theory of Inertia Based on Mach’s Principle |
| title_sort | theory of inertia based on mach s principle |
| topic | inertia Mach’s principle history of physics |
| url | https://www.mdpi.com/2218-1997/5/8/188 |
| work_keys_str_mv | AT volkmarputz atheoryofinertiabasedonmachsprinciple AT volkmarputz theoryofinertiabasedonmachsprinciple |