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1. • CommentRowNumber1.
   • CommentAuthorFrancky5
   • CommentTimeJul 31st 2024
   • (edited Jul 31st 2024)
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   Author: Francky5
   Format: TextMach’s principle is well presented on Wikipedia. To go further, one reference book is: J.B. Barbour, H. Pfister, eds. (1995). “Mach's principle: from Newton's bucket to quantum gravity”. Volume 6 of Einstein Studies, Birkhäuser, Boston, 1995. The motivation to open this discussion is due to this question: can Mach’s principle explain away dark matter? In 1918, Einstein wrote: “... in a consistent relativity theory there cannot be inertia relative to “space” but only inertia of masses relative to each other”. Later in life, he retracted his support of Mach's principle because he had linked it to general relativity and general relativity was criticised because of that link. From the quote, we should understand that masses determines the inertial reference. In a galaxy, as the stars are rotating, the inertial reference is rotating with the stars. As the inertial reference is rotating, individual stars have no relative speed (relative to the inertial reference), so no centrifugal force, no reason for the stars to escape the galaxy, no need for dark matter.

   Mach’s principle is well presented on Wikipedia. To go further, one reference book is: J.B. Barbour, H. Pfister, eds. (1995). “Mach's principle: from Newton's bucket to quantum gravity”. Volume 6 of Einstein Studies, Birkhäuser, Boston, 1995.
   
   The motivation to open this discussion is due to this question: can Mach’s principle explain away dark matter?
   
   In 1918, Einstein wrote: “... in a consistent relativity theory there cannot be inertia relative to “space” but only inertia of masses relative to each other”. Later in life, he retracted his support of Mach's principle because he had linked it to general relativity and general relativity was criticised because of that link.
   
   From the quote, we should understand that masses determines the inertial reference. In a galaxy, as the stars are rotating, the inertial reference is rotating with the stars. As the inertial reference is rotating, individual stars have no relative speed (relative to the inertial reference), so no centrifugal force, no reason for the stars to escape the galaxy, no need for dark matter.
2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJul 31st 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe issue with informal principles like Mach's is that they appeal to everyday language and as such are less precise than a mathematical theory; because, in Bohr's words: "when it comes to fundamental physics, language can be used only as in poetry". Such (poetic) principles may help with motivating a mathematical theory but can become obsolete or even a conceptual burden once that mathematical theory is present. This is what happend to Mach's principle and Newton's bucket argument once GR was finally conceived. Specifically on your argument: (1.) Dark matter is not needed to explain why stars are gravitationally bound in a galaxy, but is invoked to explain their peculiar observed velocity distribution as a function of their distance from the center. (2.) If it were true that in a reference frame there is "no centrifugal force" then galaxies would collapse under the remaining force of gravitational attraction.

   The issue with informal principles like Mach’s is that they appeal to everyday language and as such are less precise than a mathematical theory; because, in Bohr’s words: “when it comes to fundamental physics, language can be used only as in poetry”.

   Such (poetic) principles may help with motivating a mathematical theory but can become obsolete or even a conceptual burden once that mathematical theory is present. This is what happend to Mach’s principle and Newton’s bucket argument once GR was finally conceived.

   Specifically on your argument: (1.) Dark matter is not needed to explain why stars are gravitationally bound in a galaxy, but is invoked to explain their peculiar observed velocity distribution as a function of their distance from the center. (2.) If it were true that in a reference frame there is “no centrifugal force” then galaxies would collapse under the remaining force of gravitational attraction.