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The LorentzDirac equation in complex spacetime
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Quantum Gravity without Spacetime Singularities or Horizons ∗ Abstract
, 2009
"... In an attempt to reestablish spacetime as an essential frame for formulating quantum gravity – rather than an “emergent ” one –, we find that exact invariance under scale transformations is an essential new ingredient for such a theory. Use is made of the principle of “black hole complementarity”, ..."
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In an attempt to reestablish spacetime as an essential frame for formulating quantum gravity – rather than an “emergent ” one –, we find that exact invariance under scale transformations is an essential new ingredient for such a theory. Use is made of the principle of “black hole complementarity”, the notion that observers entering a black hole describe its dynamics in a way that appears to be fundamentally different from the description by an outside observer. These differences can be boiled down to conformal transformations. If we add these to our set of symmetry transformations, black holes, spacetime singularities, and horizons disappear, while causality and locality may survive as important principles for quantum gravity.
The Emergence of Quantum Mechanics internet:
"... It is pointed out that a mathematical relation exists between cellular automata and quantum field theories. Although the proofs are far from perfect, they do suggest a new look at the origin of quantum mechanics: quantum mechanics may be nothing but a natural way to handle the statistical correlatio ..."
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It is pointed out that a mathematical relation exists between cellular automata and quantum field theories. Although the proofs are far from perfect, they do suggest a new look at the origin of quantum mechanics: quantum mechanics may be nothing but a natural way to handle the statistical correlations of a cellular automaton. An essential role for the gravitational force in these considerations is suspected.
Violation of Bell’s inequality in fluid mechanics
, 2013
"... We show that a classical fluid mechanical system can violate Bell’s inequality because the fluid motion is correlated over large distances. The observed violations of Bell’s inequality show that quantum mechanics cannot be modelled using local hidden variables [1–3]. This has led to debate about non ..."
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We show that a classical fluid mechanical system can violate Bell’s inequality because the fluid motion is correlated over large distances. The observed violations of Bell’s inequality show that quantum mechanics cannot be modelled using local hidden variables [1–3]. This has led to debate about nonlocal hidden variables [4, 5] and about ‘locality ’ given that signals do not exceed the speed of light [6]. Some authors suggest, more generally, that the Bell tests rule out models with only local interactions [7]; but ’t Hooft and Vervoort have separately advanced the possibility that Bell’s inequality may be violated in systems such as cellular automata that interact only with their neighbours but have collective states of correlated motion [8,9], while Pusey, Barrett and Rudolf argue that a pure quantum state corresponds directly to reality [10]. In this paper we show that Bell’s inequality can be violated in a completely classical system. In fluid mechanics, nonlocal phenomena arise from local processes. For example, the energy and angular momentum of a vortex are delocalised in the fluid. Here we show that Euler’s equation for a compressible inviscid fluid has quasiparticle solutions that are correlated in precisely the same way as as the quantum mechanical particles discussed in Bell’s original paper. This correlation violates Bell’s inequality. Locality in fluid mechanics Collective phenomena in fluid mechanics behave locally in some respects, and nonlocally in others. To see this, consider a vortex in a compressible inviscid fluid. The local aspects of the motion can be understood by treating the vortex as if it were a point in two dimensions located at its centre. The resulting trajectories can be complex or chaotic [11, 12]. The nonlocal aspects can be understood from the energy and angular momentum. In cylindrical coordinates (r, θ), the flow speed is given by u = C/r where C is the circulation. The kinetic energy is∫