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• W2185095381 abstract "The observation of emergent particles in condensed matter physics such as phonons, holes, and recently magnetic monopoles [1] may lead one to speculate that real particles themselves could exist as emergent properties of a space-time lattice. There are many examples in the literature of the Dirac equation being supported by a lattice structure [2,3,4,5], related, for example, to the physics of ice [6] or of graphene [7]. In particular the case of the Dirac equation on the ice lattice is of potential practical interest as ice models can now be realised in a variety of new experimental systems, including spin ice materials [1] and artificial micromagnetic arrays [8]. We noticed that a Reichenbach causal net [9] has the same topology as an ice lattice and hence, if formulated in space-time, might support a version of relativistic quantum mechanics. In this paper we explore this idea at its simplest level. We propose a causal net for the free motion of a particle based on a relational concept of time as an ordered series of possible events that are linked by a principle of common cause. The causal net is 1+1 dimensional but applies along the direction of motion of the particle in three dimensions. It is reminiscent of the Feynman chequerboard [2] and the ice model [6] but differs from both in important respects. The causal net appears to support the 3+1 dimensional Dirac equation [10] for a free fermion and hence the Schrodinger equation in the low velocity limit. The causal net idea gives an intuitive picture of relativistic quantum mechanical motion and the origin of quantization although it is not a complete re-derivation of conventional quantum mechanics, partly because the space-time is discrete, and partly because it does not automatically imply a principle of superposition. If however we identify a causal net as representing a Dirac state vector then superposition of nets allows a development more consistent with conventional quantum mechanics. We therefore suggest that a more detailed study of effective quantum mechanics on causal nets, based on the transparent underlying concepts of causality and probability, might be a fruitful exercise." @default.
• W2185095381 created "2016-06-24" @default.
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• W2185095381 date "2010-01-01" @default.
• W2185095381 modified "2023-09-27" @default.
• W2185095381 title "Effective relativistic quantum mechanics on a causal net" @default.
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