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Quantum Mechanics Without Wavefunctions

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Seven years ago, the first paper was published [1] on what has come to be known as the “Many Interacting Worlds” (MIW) interpretation of quantum mechanics (QM) [2,3,4]. MIW is based on a new formulation of QM [1,5,6], in which the wavefunction Ψ(t, x) is discarded entirely. Instead, the quantum state is represented as an ensemble, x(t, C), of quantum trajectories or “worlds.” Each of these worlds has well-defined real-valued particle positions and momenta, and is thereby classical-like. Unlike a classical ensemble, however, nearby trajectories/worlds can interact with each other dynamically, giving rise to quantum effects. In this respect, MIW is very different from the Everett Many-Worlds Interpretation (MWI); another key difference is that no world branching occurs.

The MIW approach offers a direct “realist” description of nature that may be beneficial in interpreting quantum phenomena such as entanglement, measurement, spontaneous decay, etc. It provides a useful analysis of MWI, explaining how the illusion of world branching emerges in that context. Moreover, x(t, C) satisfies a trajectory-based action principle, which allows quantum theory (via the Euler-Lagrange equation and Noether’s theorem) to be placed on the same footing as classical theories. In this manner, a straightforward relativistic generalization can also be obtained [7,8], which offers a notion of global simultaneity even for accelerating observers. Whereas the original MIW theory is fully consistent with Schroedinger wave mechanics, the more recently developed flavors offer the promise of new experimental predictions. These and other developments, e.g. for many dimensions, multiple particles, and spin, may also be discussed.

[1] B. Poirier, Chem. Phys. 370, 4 (2010).
[2] M. J. W. Hall, D.-A. Deckert, and H. Wiseman, Phys. Rev. X 4, 041013 (2014)
[3] B. Poirier, Phys. Rev. X, 4, 040002 (2014).
[4] C. T. Sebens, Phil. Sci. 82, 266 (2015).
[5] P. Holland, Ann. Phys. 315, 505 (2005).
[6] J. Schiff and B. Poirier, J. Chem. Phys. 136, 031102 (2012).
[7] B. Poirier, arXiv:1208.6260 [quant-ph], (2012).
[8] H.-M. Tsai and B. Poirier, EmQM15: Emergent Quantum Mechanics 2015, ed. G. Grössing, (J. Physics, IOP, 2016) 701, 012013.