How perturbing a classical 3-spin chain can lead to quantum features
- URL: http://arxiv.org/abs/2012.15187v2
- Date: Sun, 3 Jan 2021 19:00:54 GMT
- Title: How perturbing a classical 3-spin chain can lead to quantum features
- Authors: Bianca Rizzo
- Abstract summary: We will work under the premises of the Cellular Automata Interpretation of QM, by Gerard 't Hooft.
We will show that quantum phenomena, in particular superposition states, can arise in a deterministic model because of the limited precision of measurements.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In this thesis we will work under the premises of the Cellular Automata
Interpretation of QM, by Gerard 't Hooft, according to whom particles evolve
following the rules of Cellular Automata (CA), a mathematical model consisting
of discrete units that evolve following deterministic laws in discrete space
and time. The states of a Cellular Automaton are, by definition, classical and
thus deterministic and do not form superpositions.
Since it is not possible to know how to demonstrate the underlying classical
deterministic structure and dynamics at the smallest microscopic scales at
present, what we pursue in this thesis, besides summarizing the concept of the
Cellular Automaton Interpretation, is to show that quantum phenomena, in
particular superposition states, can arise in a deterministic model because of
the limited precision of measurements. In order to do that, we follow the path
of a recent article by Elze, considering a triplet of Ising spins and their
dynamics in a CA context, which is possible to formalize using Pauli matrices
and quantum mechanics operators. We will thus observe how the system will shift
from a triplet of Ising spins to a triplet of qubits due to the arising of
superposition after applying some perturbations on the Hamiltonian and the
dynamics operators.
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