Do Spins Have Directions?
Diederik Aerts, Massimiliano Sassoli de Bianchi

TL;DR
This paper extends the Bloch sphere model to explore quantum spin, revealing that spin states are generally non-spatial but can be related to Euclidean directions through higher-dimensional representations, leading to a new realism framework.
Contribution
It introduces the extended Bloch representation to analyze quantum spin, showing spin states are non-spatial and proposing multiplex realism for interpreting quantum and classical elements.
Findings
Spin eigenstates are generally non-spatial and represented in higher-dimensional Blochean space.
Certain vectors in the Bloch space correspond to Euclidean space directions.
A new realism framework, multiplex realism, is proposed for interpreting quantum phenomena.
Abstract
The standard Bloch sphere representation was recently generalized to the 'extended Bloch representation' describing not only systems of arbitrary dimension, but also their measurements. This model solves the measurement problem and is based on the 'hidden-measurement interpretation', according to which the Born rule results from our lack of knowledge about the interaction between measuring apparatus and the measured entity. We present here the extended Bloch model and use it to investigate the nature of quantum spin and its relation to our Euclidean space. We show that spin eigenstates cannot generally be associated with directions in the Euclidean space, but only with generalized directions in the Blochean space, which generally is a space of higher dimension. Hence, spin entities have to be considered as genuine non-spatial entities. We also show, however, that specific vectors can be…
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