Abstract
We investigate a possible reduction mechanism from (bosonic) Quantum Field Theory (QFT) to Quantum Mechanics (QM), in a manner that could explain the apparent loss of degrees of freedom of the original theory in terms of quantum information in the reduced one. This reduction mechanism consists mainly of performing an ansatz on the boson field operator, which takes into account quantum foam and non-commutative geometry. Through the reduction mechanism, QFT reveals its hidden internal structure, which is a quantum network of maximally entangled multipartite states. In the end, a new approach to the quantum simulation of QFT is proposed through the use of QFT’s internal quantum network. Finally, the entropic equilibrium of fully mixed and maximally entangled states in the quantum network seems to suggest that the black hole paradox of information loss might be solved under suitable conditions.
Highlights
Until the 1950s, the common opinion was that quantum field theory (QFT) was just quantum mechanics (QM) plus special relativity.But that is not the whole story, as is described in [1,2]
We investigate a possible reduction mechanism from Quantum Field Theory (QFT) to Quantum Mechanics (QM), in a manner that could explain the apparent loss of degrees of freedom of the original theory in terms of quantum information in the reduced one
A few questions arise: “Is there any quantum information hidden in QFT?” : “How can we reduce QFT to QM in such a way that the hidden informational quantum structure, if it exists, can be revealed?” : “Does that quantum information structure lead to a direct simulation of the original QFT?”
Summary
Until the 1950s, the common opinion was that quantum field theory (QFT) was just quantum mechanics (QM) plus special relativity. The ansatz we perform in this work corresponds to a boson translation in terms of the annihilation operator in momentum space This defines a new vacuum and, in the case of infinite volume, the two representations are unitarily inequivalent. Within the attractor basin it is possible to define a new metric, quantized in Planck units, that undergoes quantum fluctuations, (the quantum foam) [16,17], which induce uncertainties in the position states The latter can be interpreted as maximally entangled qubits on the surfaces of the spheres centred at the attractor point. In QM, i.e., for systems with a finite number of degrees of freedom, the choice of Quantum Rep. 2020, 2, 3 representation is inessential to the physics, since all the irreducible representations of the canonical commutation relations (CCR) are each unitarily equivalent: this is the content of the Stone-von Neumann theorem.
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