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 adj. Not equivalent
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"inequivalent" and the inequivalence of two generic theories can be shown almost instantly.

Hence, mathematical logic suggests that the application of mathematical physics to the universe as a whole can generate two different types of multiverse: classes of nonisomorphic but elementarily equivalent models; and classes of nonisomorphic and elementarily inequivalent models.

In this case, the models of the theory will be mutually nonisomorphic and elementarily inequivalent.

These different vacua are likely to be unitarily inequivalent, similar to what happens with Hawking radiation and the Unruh effect.
Everything You Ever Wanted to Know About Quantum Mechanics, But Were Afraid to Ask

If this works then the perturbative Killing fields are on comoving frames, and the difference between them from region to region might then lead to inequivalent vacua from which some of these types of analyses might be performed.
Everything You Ever Wanted to Know About Quantum Mechanics, But Were Afraid to Ask

If my inequivalent vacua theory is correct then it means the universe admits no global symmetry, including the ColemanMandula theorem on the maximal permissible set of symmetries for the Smatrix.

The observable universe is a process which takes one nothing, the set of unitarily inequivalent vacua, to another nothing which is the Minkowski void at conformal infinity.

In other words two spin fields with multiple topologically inequivalent paths attaching them is equivalent to a brane charge determined by the orbifolding of a string.

This grand path integral is from a set of inequivalent vacua states to the Minkowski spacetime at conformal AdS infinity.

Clifton and Halvorson improve this result by showing that Bohr's idea of position and momentum complementarity can be expressed in terms of inequivalent representations in the C*algebraic formalism of quantum mechanics.
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