Abstract
To answer Wheeler’s 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 show that the quantum correlations and quantum states corresponding to the Bell basis states, which uniquely produce the Tsirelson bound for the Clauser–Horne–Shimony–Holt (CHSH) quantity, can be derived from conservation per no preferred reference frame (NPRF). A reference frame in this context is defined by a measurement configuration, just as with the light postulate of special relativity. We therefore argue that the Tsirelson bound is ultimately based on NPRF just as the postulates of special relativity. This constraint-based/principle answer to Bub’s question addresses Fuchs’ desideratum that we “take the structure of quantum theory and change it from this very overt mathematical speak ... into something like [special relativity].” Thus, the answer to Bub’s question per Fuchs’ desideratum is, “the Tsirelson bound obtains due to conservation per NPRF”.
Highlights
Wheeler’s opening statement in his 1986 paper, “How Come the Quantum?” holds as true today as it did [1]The necessity of the quantum in the construction of existence: out of what deeper requirement does it arise? Behind it all is surely an idea so simple, so beautiful, so compelling that when—in a decade, a century, or a millennium—we grasp it, we will all say to each other, how could it have been otherwise? How could we have been so stupid for so long?The problem is, as Hardy points out, “The standard axioms of [quantum theory] are rather ad hoc.Where does this structure come from?” [2]
It struck me that if we couldn’t take the structure of quantum theory and change it from this very overt mathematical speak—something that didn’t look to have much physical content at all, in a way that anyone could identify with some kind of physical principle—if we couldn’t turn that into something like this, the debate would go on Entropy 2019, 21, 692; doi:10.3390/e21070692
Just as with the light postulate of special relativity, we see that no preferred reference frame requires quantum (+1/−1) outcomes for all measurements and that leads to a constraint-based/principle answer to Bub’s question
Summary
Wheeler’s opening statement in his 1986 paper, “How Come the Quantum?” holds as true today as it did [1]. A measurement configuration constitutes a reference frame, as with the light postulate of special relativity This constraint, conservation per NPRF, reproduces the quantum correlation function for the Bell-basis-states phenomena whence the Tsirelson bound. We concur with the QIT approach to view quantum mechanics in terms of spacetime constraints on par with a principle theory such as special relativity (Figure 5), rather than dynamical laws or processes We feel this constraint-based explanation of the Tsirelson bound does contribute to the desideratum of QIT. Just as with the light postulate of special relativity, we see that no preferred reference frame requires quantum (+1/−1) outcomes for all measurements and that leads to a constraint-based/principle answer to Bub’s question. We can do that using empirically unverifiable hidden variables (Figure 3)
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