Counterexamples to the Maximum Force Conjecture

Dimensional analysis shows that the speed of light and Newton’s constant of gravitation can be combined to define a quantity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>F</mi&g...

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Autores principales:	Aden Jowsey, Matt Visser
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	maximum force maximum tension general relativity Elementary particle physics QC793-793.5
Acceso en línea:	https://doaj.org/article/d791653659fb498caccb3bacdef2cefc
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spelling	oai:doaj.org-article:d791653659fb498caccb3bacdef2cefc2021-11-25T19:09:29ZCounterexamples to the Maximum Force Conjecture10.3390/universe71104032218-1997https://doaj.org/article/d791653659fb498caccb3bacdef2cefc2021-10-01T00:00:00Zhttps://www.mdpi.com/2218-1997/7/11/403https://doaj.org/toc/2218-1997Dimensional analysis shows that the speed of light and Newton’s constant of gravitation can be combined to define a quantity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>F</mi><mo></mo></msub><mo>=</mo><mrow><msup><mi>c</mi><mn>4</mn></msup><mo>/</mo><msub><mi>G</mi><mi>N</mi></msub></mrow></mrow></semantics></math></inline-formula> with the dimensions of force (equivalently, tension). Then in <i>any</i> physical situation we <i>must</i> have <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>F</mi><mi>physical</mi></msub><mo>=</mo><mi>f</mi><mspace width="0.277778em"></mspace><msub><mi>F</mi><mo></mo></msub></mrow></semantics></math></inline-formula>, where the quantity <i>f</i> is some dimensionless function of dimensionless parameters. In many physical situations explicit calculation yields <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>=</mo><mi mathvariant="script">O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>, and quite often <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>≤</mo><mrow><mn>1</mn><mo>/</mo><mn>4</mn></mrow></mrow></semantics></math></inline-formula>. This has led multiple authors to suggest a (weak or strong) maximum force/maximum tension conjecture. Working within the framework of standard general relativity, we will instead focus on idealized <i>counter-examples</i> to this conjecture, paying particular attention to the extent to which the counter-examples are physically reasonable. The various idealized counter-examples we shall explore strongly suggest that one should not put too much credence into any truly universal maximum force/maximum tension conjecture. Specifically, idealized fluid spheres on the verge of gravitational collapse will generically violate the weak (and strong) maximum force conjectures. If one wishes to retain any truly general notion of “maximum force” then one will have to very carefully specify precisely which forces are to be allowed within the domain of discourse.Aden JowseyMatt VisserMDPI AGarticlemaximum forcemaximum tensiongeneral relativityElementary particle physicsQC793-793.5ENUniverse, Vol 7, Iss 403, p 403 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	maximum force maximum tension general relativity Elementary particle physics QC793-793.5
spellingShingle	maximum force maximum tension general relativity Elementary particle physics QC793-793.5 Aden Jowsey Matt Visser Counterexamples to the Maximum Force Conjecture
description	Dimensional analysis shows that the speed of light and Newton’s constant of gravitation can be combined to define a quantity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>F</mi><mo></mo></msub><mo>=</mo><mrow><msup><mi>c</mi><mn>4</mn></msup><mo>/</mo><msub><mi>G</mi><mi>N</mi></msub></mrow></mrow></semantics></math></inline-formula> with the dimensions of force (equivalently, tension). Then in <i>any</i> physical situation we <i>must</i> have <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>F</mi><mi>physical</mi></msub><mo>=</mo><mi>f</mi><mspace width="0.277778em"></mspace><msub><mi>F</mi><mo></mo></msub></mrow></semantics></math></inline-formula>, where the quantity <i>f</i> is some dimensionless function of dimensionless parameters. In many physical situations explicit calculation yields <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>=</mo><mi mathvariant="script">O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>, and quite often <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>≤</mo><mrow><mn>1</mn><mo>/</mo><mn>4</mn></mrow></mrow></semantics></math></inline-formula>. This has led multiple authors to suggest a (weak or strong) maximum force/maximum tension conjecture. Working within the framework of standard general relativity, we will instead focus on idealized <i>counter-examples</i> to this conjecture, paying particular attention to the extent to which the counter-examples are physically reasonable. The various idealized counter-examples we shall explore strongly suggest that one should not put too much credence into any truly universal maximum force/maximum tension conjecture. Specifically, idealized fluid spheres on the verge of gravitational collapse will generically violate the weak (and strong) maximum force conjectures. If one wishes to retain any truly general notion of “maximum force” then one will have to very carefully specify precisely which forces are to be allowed within the domain of discourse.
format	article
author	Aden Jowsey Matt Visser
author_facet	Aden Jowsey Matt Visser
author_sort	Aden Jowsey
title	Counterexamples to the Maximum Force Conjecture
title_short	Counterexamples to the Maximum Force Conjecture
title_full	Counterexamples to the Maximum Force Conjecture
title_fullStr	Counterexamples to the Maximum Force Conjecture
title_full_unstemmed	Counterexamples to the Maximum Force Conjecture
title_sort	counterexamples to the maximum force conjecture
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/d791653659fb498caccb3bacdef2cefc
work_keys_str_mv	AT adenjowsey counterexamplestothemaximumforceconjecture AT mattvisser counterexamplestothemaximumforceconjecture
_version_	1718410247435976704

Counterexamples to the Maximum Force Conjecture

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