1108.5729 (Roman Sverdlov)

Can quantum lattice be generated through several classical ones
superimposed in spacetime continuum?    [PDF]

Roman Sverdlov

This paper has few different, but interrelated, goals. At first, we will propose a version of discretization of quantum field theory (Chapter 3). We will write down Lagrangians for sample bosonic fields (Section 3.1) and also attempt to generalize them to fermionic QFT (Section 3.2). At the same time, we will insist that the elements of our discrete space are embedded into a continuum. This will allow us to embed several different "lattices" into the same continuum and view them as separate "quantum" field configurations. Classical parameters will be used in order to specify "which lattice" each given element "belongs to". Furthermore, another set of "classical" parameters will be proposed in order to define so-called "probability amplitude" of each "field configuration", embodied by a corresponding lattice, "taking place" (Chapter 2). Apart from that, we will propose a set of "classical" signals that propagate throughout continuum, and define their dynamics in such a way that they produce the mathematical information consistent with the desired "quantum" effects within the lattices we are concerned about (Chapter 4). Finally, we will take advantage of the lack of "true" quantum mechanics, and "add" gravity in such a way that avoids the issue of its quantization altogether (Chapter 5). In the process of doing so, we will propose a gravity-based collapse model of a wave function. In particular, we will claim that the collapse of a wave function is merely a result of states that violate Einstein's equation being "thrown away". The mathematical structure of this model (in particular, the appeal to gambler's ruin) will be similar to GRW collapse models.

View original: http://arxiv.org/abs/1108.5729