Abstract
It was shown by de Broglie and Bohm that the concept of a deterministic particle trajectory is compatible with quantum mechanics. It is demonstrated by explicit construction that there exists another more general deterministic trajectory interpretation. The method exploits an internal angular degree of freedom that is implicit in the Schrödinger equation, in addition to the particle position. The de Broglie-Bohm model is recovered when the new theory is averaged over the internal freedom. The model exhibits a strong form of entanglement which implies a primary role for the wavefunction of the Universe. The conditions of autonomy are examined, and the viability of the theory is established by application to the measurement problem.
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We emphasize that we are simply rewriting the usual complex Hilbert space formalism in terms of real functions. This is not the same as so-called “real” quantum mechanics which uses only the first term on the right-hand side of the scalar product (2.6) and has different physical content. See S. L. Adler, Quaternionic Quantum Mechanics and Quantum Fields (Oxford University Press, Oxford, 1995), p. 44.
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Holland, P.R. New Trajectory Interpretation of Quantum Mechanics. Foundations of Physics 28, 881–911 (1998). https://doi.org/10.1023/A:1018813112648
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DOI: https://doi.org/10.1023/A:1018813112648