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Register a new userBells Theorem, Non-Computability and Conformal Cyclic Cosmology: A Top-Down Approach to Quantum Gravity
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T.N. Palmer
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This paper draws on a number of Roger Penroses ideas - including the non-Hamiltonian phase-space flow of the Hawking Box, Conformal Cyclic Cosmology, non-computability and gravitationally induced quantum state reduction - in order to propose a radically unconventional approach to quantum gravity: Invariant Set Theory (IST). In IST, the fundamental laws of physics describe the geometry of the phase portrait of the universe as a whole: quantum process are associated with fine-scale fractal geometry, gravitational process with larger-scale heterogeneous geometry. With this, it becomes possible to explain the experimental violation of Bell Inequalities without having to abandon key ingredients of general relativity: determinism and local causality. Ensembles in IST can be described by complex Hilbert states over a finite set $mathbb C_p$ of complex numbers, where $p$ is a large finite integer. The quantum mechanics of finite-dimensional Hilbert spaces is emergent as a singular limit when $p rightarrow infty$. A small modification to the field equations of general relativity is proposed to make it consistent with IST.
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John St. Bell was a physicist working most of his time at CERN and contributing intensively and sustainably to the development of Particle Physics and Collider Physics. As a hobby he worked on so-called foundations of quantum theory, that was that time very unpopular, even considered to be scientifically taboo. His 1964-theorem, showing that predictions of local realistic theories are different to those of quantum theory, initiated a new field in quantum physics: quantum information theory. The violation of Bells theorem, for instance, is a necessary and sufficient criterion for generating a secure key for cryptography at two distant locations. This contribution shows how Bells theorem can be brought to the realm of high energy physics and presents the first conclusive experimental feasible test for weakly decaying neutral mesons on the market. Strong experimental and theoretical limitations make a Bell test in weakly decaying systems such as mesons and hyperons very challenging, however, these systems show an unexpected and puzzling relation to another big open question: why is our Universe dominated by matter, why did the antimatter slip off the map? This long outstanding problem becomes a new perspective via the very idea behind quantum information.
The principles and methods of the Conformal Quantum Geometrodynamics (CQG) based on the Weyls differential geometry are presented. The theory applied to the case of the relativistic single quantum spin 1/2 leads a novel and unconventional derivation of Diracs equation. The further extension of the theory to the case of two spins 1/2 in EPR entangled state and to the related violation of Bells inequalities leads, by an exact albeit non relativistic analysis, to an insightful resolution of all paradoxes implied by quantum nonlocality.
(A) Bells theorem rests on a conjunction of three assumptions: realism, locality and ``free will. A discussion of these assumptions will be presented. It will be also shown that, if one adds to the assumptions the principle or rotational symmetry of physical laws, a stronger version of the theorem emerges. (B) A link between Bells theorem and communication complexity problems will be presented. This also includes experimental realizations, which surprisingly do not involve entanglement. (C) A new sufficient and necessary criterion for entanglement of general (mixed) states is be presented. It is derived using the same geometric starting point as the inclusion of the symmetry in (A). The set of entanglement identifiers (EIs) emerging via this method contains entanglement witnesses (EWs), but they form only a subset of all EIs. Thus the method is more powerful than the one based on EWs.
The problem of simulating complex quantum processes on classical computers gave rise to the field of quantum simulations. Quantum simulators solve problems, such as Boson sampling, where classical counterparts fail. In another field of physics, the unification of general relativity and quantum theory is one of the greatest challenges of our time. One leading approach is Loop Quantum Gravity (LQG). Here, we connect these two fields and design a linear-optical simulator such that the evolution of the optical quantum gates simulates the spinfoam amplitudes of LQG. It has been shown that computing transition amplitudes in simple quantum field theories falls into the class BQP -- which strongly suggests that computing transition amplitudes of LQG are classically intractable. Therefore, these amplitudes are efficiently computable with universal quantum computers which are, alas, possibly decades away. We propose here an alternative special-purpose linear-optical quantum computer, which can be implemented using current technologies. This machine is capable of efficiently computing these quantities. This work opens a new way to relate quantum gravity to quantum information and will expand our understanding of the theory.
Bells inequality is a strong criterion to distinguish classic and quantum mechanical aspects of reality. Its violation is the net effect of the non-locality stored in the Heisenberg uncertainty principle (HUP) generalized by quantum gravity scenarios, called generalized uncertainty principle (GUP). Here, the effects of GUP on Bell-like operators of two, and three outcomes, as well as continuous cases, are studied. The achievements claim that the violation quality of Bells and Bell-like inequalities may be a proper tool to get better understanding of the quantum features of gravity and its effects on reality. Indeed, it is obtained that the current accuracy of Stern-Gerlach experiments implies $beta_0ll10^{23}$.
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