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arXiv:1503.02229 · Foundations of Physics

A Matter of Principle: The Principles of Quantum Theory, Dirac’s Equation, and Quantum Information

Arkady Plotnitsky

Published Jul 13, 2015• 9 citations
arXivHTMLPDF
DOI
10.1007/s10701-015-9928-z

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•May 1, 2015•0 citations
Without using the relativity principle, we show how the Dirac equation in three space dimensions emerges from the large-scale dynamics of the minimal nontrivial quantum cellular automaton satisfying unitarity, locality, homogeneity, and discrete isotropy. The Dirac equation is recovered for small wave vector and inertial mass, whereas Lorentz covariance is distorted in the ultrarelativistic limit. The automaton can thus be regarded as a theory unifying scales from Planck to Fermi. A simple asymptotic approach leads to a dispersive Schr\"odinger equation describing the evolution of narrowband states at all scales.
Following the famous Dirac equation, in which space, time and matter are all connected with spinor, this paper uses the combination of these spinors to express the state of quantum field in a new style - the global state. Thus, the state, state equation and action function of quantum fields are all expressed in an integrated system. Based upon this, it seems that the origin of the principle of least action, the intrinsic connection between classical mechanics and quantum theory can be fully exposed.
One of the reasons for 1933 Nobel Prize for physics is “for the discovery of new productive forms of atomic theory” (namely Schrodinger equation and Dirac equation). While, this paper points out that Schrodinger equation and Dirac equation are improper. According to Neutrosophy, Schrodinger equation and Dirac equation have three situations of truth, falsehood and indeterminacy respectively. Three reasons lead to Schrodinger equation and Dirac equation are improper: firstly, they are not derived by the principle of conservation of energy; secondly, the random (stochastic) concept could lead to absurd results; thirdly, they cannot solve many problems such as gravitation. Applying partial and temporary unified theory of natural science so including all the equations of natural science so far (in which, the theory of everything to express all of natural laws, described by Hawking that a single equation could be written on a T-shirt, is partially and temporarily realized in the form of partial and temporary unified variational principle of natural science so far), this paper presents partial and temporary unified theory of quantum mechanics so far, this unified theory can be used to make Schrodinger equation and Dirac equation tend to be proper (making Schrodinger equation and Dirac equation are restricted (or constrained) by principle of conservation of energy, and thus they can satisfy the principle of conservation of energy; also making they are restricted (or constrained) by a certain gravitational theory, and establish partial and temporary unified theory of quantum-gravitation so far).