## Abstract

Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to an ensemble of subsystems of the universe with identical constituents and similar preparations and environments. A new kind of interaction is posited amongst such similar subsystems which acts to increase their distinctiveness, by extremizing the variety. In the limit of large numbers of similar subsystems this interaction is shown to give rise to Bohm’s quantum potential. As a result the probability distribution for the ensemble is governed by the Schroedinger equation. The measurement problem is naturally and simply solved. Microscopic systems appear statistical because they are members of large ensembles of similar systems which interact non-locally. Macroscopic systems are unique, and are not members of any ensembles of similar systems. Consequently their collective coordinates may evolve deterministically. This proposal could be tested by constructing quantum devices from entangled states of a modest number of quits which, by its combinatorial complexity, can be expected to have no natural copies.

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## Notes

If the ontology posited by the [6–11] papers may seem extravagant, their proposal had the virtue of a simple form for the inter-ensemble interactions. This inspired me to seek to use such a simple dynamics in the real ensemble idea. In particular, an important insight contained in [11] is that if there are

*N*particles on a line with positions, \(x_i\), with \(i =1, \dots , N\), the density at the*k*’th point can be approximated by$$\begin{aligned} \rho (x_k ) \approx \frac{1}{N (x_{k+1} - x_k )} \end{aligned}$$(1)This motivates the choose of a ultraviolet cutoff, in equation (27) below.

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## Acknowledgments

It is a pleasure, first of all, to thank Julian Barbour for our collaboration in the invention of the idea of maximal variety [12, 13], and for many years of conversations and friendship since. This work represents a step in a research program which builds on a critique of the role of time in cosmological theories developed with Roberto Mangabeira Unger [1] and explored with Marina Cortes and, most recently Henrique Gomes. This work develops a specific idea that emerged from that critique, which is that ensembles in quantum theory must refer to real systems, that exist somewhere in the universe [4, 5]. I am grateful to Lucien Hardy, Rob Spekkens and Antony Valentini for criticism of my original real ensemble formulation, as well as to Jim Brown, Ariel Caticha, Marina Cortes, Dirk - Andrei Deckert, Michael Friedman, Laurent Freidel, Henrique Gomes, Michael Hall, Marco Masi, Djorje Minic, Wayne Myrvold, John Norton, Antony Valentini and Elie Wolfe for comments on the present draft or related talks.

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Smolin, L. Quantum Mechanics and the Principle of Maximal Variety.
*Found Phys* **46, **736–758 (2016). https://doi.org/10.1007/s10701-016-9994-x

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DOI: https://doi.org/10.1007/s10701-016-9994-x

### Keywords

- Measurement problem
- Quantum foundations
- Hidden variables