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arXiv · 1107.1898

An entropic picture of emergent quantum mechanics

D. Acosta·P. Fernandez de Cordoba·J. M. Isidro·J. L. G. Santander
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Abstract

Quantum mechanics emerges a la Verlinde from a foliation of space by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantised in units of Boltzmann's constant k. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on space. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Planck's constant h from Boltzmann's constant k.

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D. Acosta, P. Fernandez de Cordoba, J. M. Isidro, J. L. G. Santander. 2011-07-10. An entropic picture of emergent quantum mechanics. https://arxiv.org/abs/1107.1898

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