I don't see enough equations in any of your 3 posts in this thread for readers to check. Don't make us guess! Learn enough LaTeX to post your work here, including basic assumptions, equations, and the form of the integral you evaluated numerically by spreadsheet. A diagram of the geometry you're...
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You avoided my request above for a reference, so I request again: please supply a credible published reference that explicitly discusses the possibility, existence and consistency of a path-dependent metric/tetrad in 4D spacetime. Otherwise you waste everyone's time trying to debate an...
Just look at Wikiedia: https://en.wikipedia.org/wiki/Spin_connection!
So for the Levi-Civita connection ##\left\{ _{\mu\nu}^{\alpha}\right\}##, the spin-connection ##\omega## is expressed uniquely and unambiguously in terms of ##e## and its first derivatives. For more general connections...
Congratulations!
But do note that neither IJRAP nor its ISSN: 2201-1056 are listed on Clarivate's Master Journal List. So unfortunately said journal is not considered a valid reference source here on Physics Forums.
I'm curious: how did you make the choice to submit and publish there?
How is this paper relevant to your claim in post #23?
The tetrad ##e## and spin-connection ##\omega## appear nowhere in the Schmidt paper. And your later GitHub reference is not refereed so it's disallowed on Physics Forums.
My citation in post #22 explicitly states that the...
Not according to the reference I posted above. Only the tetrad ##e## and connection ##\Gamma## can be independently and freely selected, from which the spin connection ##\omega## is then derived. Can you quote a credible reference that says otherwise?
Your equation is not an integrability condition that must be satisfied by ##e,\omega,\Gamma##. Instead, it simply defines the spin connection. From page 5 of https://people.physics.illinois.edu/stone/torsion.pdf:
So you are free to select any arbitrary tetrad field ##e## and any connection...
Paul Merriam's arXiv paper reads more like philosophy, with a capital P, not physics. All of its recent references appear in philosophy journals. Is it suitable for posting on PF?
Here's what Mathematica gives for the roots of the equation ##z^3=-2+2\,i##, expressed in both rectangular and polar form. You can use these results to verify your formula:
1) Can you elucidate the criteria by which a fundamental theory is distinguished from an effective one?
2) Can you cite examples of known fundamental theories?
Thanks.
Yes, gravitational fields in vacuum or a medium can be viewed as inducing effective dielectric properties therein. Here's the abstract of a 1980 paper on the subject:
Dielectric tensor and magnetic permeability in the weak field approximation of general relativity
by Pegoraro, F. ; Radicati, L...