Why the Quantum

To answer John Wheeler's ``Really Big Question,'' ``Why the quantum?'' via quantum information theory according to Bub, one must explain both why the world is quantum rather than classical and why the world is quantum rather than superquantum, i.e., ``Why the Tsirelson bound?'' We propose an answer to these questions based on the assumption that the world is not ``quantum rather than classical'' but is fundamentally both, as constrained by conservation principles from the spacetime symmetry group (``contextuality''). That is, since classical mechanics needs quantum mechanics to explain its fundamental momentum exchanges and quantum mechanics needs classical mechanics to provide the distribution of those momentum exchanges in their classical spacetime context, we would expect conservation principles from the spacetime symmetry group to serve as contextual constraints for a quantum-classical reality. We illustrate this using the spin singlet state and the `Mermin photon state', showing how quantum correlations satisfy conservation of angular momentum for binary (quantum) outcomes. Thus, violations of the Bell inequality up to the Tsirelson bound follow from quantum correlations per conservation of angular momentum for binary outcomes. Accordingly, expecting the Bell inequality to be satisfied for quantum outcomes per classical probability theory means abandoning the conservation of angular momentum in certain experimental configurations. Thus, classical objects interacting per classical probability theory (classical-classical reality) violates conservation of angular momentum for binary outcomes in certain experimental configurations. This is ruled out empirically by violations of the Bell inequality. Likewise, we show how superquantum correlations that satisfy the no-signaling condition and exceed the Tsirelson bound violate the conservation of angular momentum for binary outcomes in certain experimental configurations. Since we have no measurements of the CHSH quantity in excess of the Tsirelson bound, we can empirically rule out classical objects interacting per superquantum correlations (superquantum-classical reality). Accordingly, that experiments have produced violations of the Bell inequality up to the Tsirelson bound and not beyond, can be explained via contextuality, i.e., conservation of angular momentum for quantum outcomes per quantum-classical reality as constrained by the spacetime symmetry group.  

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