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It is not the case that Einstein's attempt to incorporate Mach's Principle (version 2) into general relativity and relativistic cosmology is misguided
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Reasons For
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Reason for
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1.
Mach's Principle version 2 is grounded in the Leibnizian-Machian relational conception of motion
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2.
The Leibnizian-Machian relational conception of motion is incoherent within the context of general relativity
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3.
A principle that relies on an incoherent conception should not be incorporated into a physical theory
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Reasons Against
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Reason against 1 of 2
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1.
General relativity admits vacuum solutions (e.g., Minkowski spacetime) where inertial structure exists without any matter distribution.
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2.
Mach's Principle version 2 requires inertial frames to be fully determined by the global matter distribution.
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3.
A principle that is falsified by the theory's own solutions cannot be coherently incorporated into that theory as a foundational constraint.
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Reason against 2 of 2
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1.
Einstein's field equations permit de Sitter spacetime, a matter-free solution with well-defined inertial properties, which Weyl and others recognized as a decisive counterexample.
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2.
If inertia can be defined in the complete absence of matter, then the causal-explanatory role Mach's Principle assigns to matter distribution is rendered otiose within general relativity's formalism.
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