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    Mach's Principle was successfully incorporated into Einst... — Carmelics
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    Mach's Principle was successfully incorporated into Einstein's general theory of relativity

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    1 reason for
    2 reasons against

    Reasons For

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    Reason for
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    • 1.Mach's Principle requires that inertial structure cannot exist in the absence of matter
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    • 2.Einstein's field equations admit no vacuum solutions for a static universe
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    • 3.The non-existence of vacuum solutions shows that the metric cannot be determined without matter
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Einstein's field equations admit vacuum solutions, most notably the Schwarzschild solution and flat Minkowski spacetime.
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    • 2.The existence of well-defined spacetime metric in vacuum directly contradicts the Machian requirement that inertia be determined by matter distribution.
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    • 3.Einstein himself acknowledged by 1918 that GR does not fully satisfy Mach's Principle, coining the term while recognizing the theory's incompleteness on this point.
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    Reason against 2 of 2
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    • 1.Gödel's 1949 rotating universe solution to Einstein's field equations permits closed timelike curves and absolute rotation independent of distant matter.
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    • 2.A theory permitting Gödel spacetime cannot have incorporated Mach's Principle, since that solution restores an absolute rotational standard Mach explicitly rejected.
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    • 3.Dennis Sciama and later Julian Barbour demonstrated that genuine Machian theories require relational mechanics fundamentally distinct from GR's geometric framework.
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    Related

    A theory permitting Gödel spacetime cannot have incorporated Mach's Principle, s...Dennis Sciama and later Julian Barbour demonstrated that genuine Machian theorie...Einstein himself acknowledged by 1918 that GR does not fully satisfy Mach's Prin...Einstein's field equations admit no vacuum solutions for a static universe
    +5 moreShow less
    Einstein's field equations admit vacuum solutions, most notably the Schwarzschil...Gödel's 1949 rotating universe solution to Einstein's field equations permits cl...Mach's Principle requires that inertial structure cannot exist in the absence of...

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    Einstein failed to successfully incorporate Mach's Principle into his ...89%Einstein's general theory of relativity requires Riemann's infinitesim...80%String theory is able to derive general relativity as a low energy fea...79%Einstein's general theory of relativity places Riemannian differential...78%

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    According to Einstein’s Machian convictions, since inertia is determined only by matter, there can be no inertial structure or field in the absence of matter. Consequently, it is impossible, Einstein conjectured, to find a solution to the field equations—that is, to determine the metric \(g_{ij}\)—if the energy-momentum tensor \(T_{ij}\) representing the mass-energy content of the universe is zero. The non-existence of ‘vacuum solutions’ for a static universe demonstrated, Einstein thou
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    Details

    The existence of well-defined spacetime metric in vacuum directly contradicts th...
    The non-existence of vacuum solutions shows that the metric cannot be determined...
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    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit