Article

# Emergent Quantum Mechanics

Authors:
• Austrian Institute for Nonlinear Studies
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... The objective of this paper is to explore the origin and function of the phase of wavefunctions in the solutions of Schrödinger's equation, building on and clarifying some previous work [1,2]. As in emergent quantum mechanics [3], the goal is to find an underpinning of Schrödinger's equation, rather than an interpretation. ...
... where a normalization constant α has been inserted. 3 The constant is necessary to allow the filtered paths in the continuum limit to survive diffusive scaling. If we keep α = 1 the parity filtered ensemble is dominated by the full ensemble of diffusive paths and the effect of these paths in relation to all diffusive paths will be lost in the continuum limit. ...
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By associating a binary signal with the relativistic worldline of a particle, a binary form of the phase of non-relativistic wavefunctions is naturally produced by time dilation. An analog of superposition also appears as a Lorentz filtering process, removing paths that are relativistically inequivalent. In a model that includes a stochastic component, the free-particle Schrödinger equation emerges from a completely relativistic context in which its origin and function is known. The result establishes the fact that the phase of wavefunctions in Schrödinger’s equation and the attendant superposition principle may both be considered remnants of time dilation. This strongly argues that quantum mechanics has its origins in special relativity.
... is a distribution meaning that the first term on the right hand side of (15) requires that the integration in k and k be interpreted as Cauchy principle value integrals. It is possible to calculate τ νn (z) in the limit of large z provided that the initial state g mk is regular enough as a function of k; see Appendix B for mathematical details. ...
... is written as the sum of three terms: the first term τ P nm (z) originates from the Cauchy principle value integration based on the first term in (15), the other two terms τ δ± nm (z). come from integration of δ (n) (ω mk ε − ω mkε ) giving contributions at k = ±k that is indicated in the super index δ± . ...
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The paper explores the fundamental physical principles of quantum mechanics (in fact, quantum field theory) that limit the bit rate for long distances and examines the assumption used in this exploration that losses can be ignored. Propagation of photons in optical fibers is modelled using methods of quantum electrodynamics. We define the "photon duration" as the standard deviation of the photon arrival time; we find its asymptotics for long distances and then obtain the main result of the paper: the linear dependence of photon duration on the distance when losses can be ignored. This effect puts the limit to joint increasing of the photon flux and the distance from the source and it has consequences for quantum communication. Once quantum communication develops into a real technology (including essential decrease of losses in optical fibres), it would be appealing to engineers to increase both the photon flux and the distance. And here our "photon flux/distance effect" has to be taken into account. This effect also may set an additional constraint to the performance of a loophole free test of Bell's type—to close jointly the detection and locality loopholes.
... This problem has also a foundational dimension as playing a crucial role in performance of a loophole-free test for Bell's type [2] inequalities, see [3]- [8]. Such a test should finally close all possibilities to interpret quantum mechanics as emergent from a local realistic model (although, see, e.g., [9]- [18] for discussions, cf., e.g., [19]). 1 It is clear that without a test which is free from every loophole, the present foundational grounds of quantum mechanics can be questioned. And it is not only the foundations that can be questioned, but even the most successful quantum technologies such as quantum cryptography and quantum random generators. ...
... Now, (17) is introduced into (20). The integration in (18) related to the second term in (20) can be performed using the definition of the δ (n) distribution whereas for the first term an asymptotic analysis for large z, based on the standard Laplace transform ...
Article
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The paper explores the fundamental physical principles of quantum mechanics (in fact, quantum field theory) which limit the bit rate for long distances. Propagation of photons in optical fibers is modeled using methods of quantum electrodynamics. We define photon "duration" as the standard deviation of the photon arrival time; we find its asymptotics for long distances and then obtain the main result of the paper: the linear dependence of photon duration on the distance. This effect puts the limit to joint increasing of the photon flux and the distance from the source and it has important consequences both for quantum information technologies and quantum foundations. Once quantum communication develops into a real technology, it would be appealing to the engineers to increase both the photon flux and the distance. And here our "photon flux/distance effect" has to be taken into account (at least if successively emitted photons are considered as independent). This effect also has to be taken into account in a loophole free test of Bell's type -- to close jointly the detection and locality loopholes.
... On the contrary, as we have already pointed out in previous papers, it is a more detailed model inspired by the bouncer/walker experiments that can show the fertility of said analogy. It enables us to show that our model, being of the type of an " emergent quantum mechanics " [13] [14], can provide a deeper-level explanation of the dBB version of quantum mechanics (Chapter 2). ...
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Elements of a "deeper level" explanation of the deBroglie-Bohm (dBB) version of quantum mechanics are presented. Our explanation is based on an analogy of quantum wave-particle duality with bouncing droplets in an oscillating medium, the latter being identified as the vacuum's zero-point field. A hydrodynamic analogy of a similar type has recently come under criticism by Richardson et al., because despite striking similarities at a phenomenological level the governing equations related to the force on the particle are evidently different for the hydrodynamic and the quantum descriptions, respectively. However, said differences are not relevant if a radically different use of said analogy is being made, thereby essentially referring to emergent processes in our model. If the latter are taken into account, one can show that the forces on the particles are identical in both the dBB and our model. In particular, this identity results from an exact matching of our emergent velocity field with the Bohmian "guiding equation". One thus arrives at an explanation involving a deeper, i.e. subquantum, level of the dBB version of quantum mechanics. We show in particular how the classically-local approach of the usual hydrodynamical modeling can be overcome and how, as a consequence, the configuration-space version of dBB theory for $N$ particles can be completely substituted by a "superclassical" emergent dynamics of $N$ particles in real 3-dimensional space.
... Our research program thus pertains to the scope of theories on " Emergent Quantum Mechanics " . (For the proceedings of a first international conference exclusively devoted to this topic, see Grössing (2012) [13]. For their original models, see in particular the papers by Adler, Elze, Ord, Grössing et al., ...
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A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder's group on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schr\"odinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level. It is further demonstrated both analytically and with the aid of computer simulations that our model provides explanations for various quantum effects such as double-slit or n-slit interference. We show the averaged trajectories emerging from our model to be identical to Bohmian trajectories, albeit without the need to invoke complex wave functions or any other quantum mechanical tool. Finally, the model provides new insights into the origins of entanglement, and, in particular, into the phenomenon of a "systemic" nonlocality.
... Transmission of quantum information for long distances is one of the most important problems of theoretical and experimental research [1]. This problem has also a foundational dimension: in performance of a loophole-free test for Bell's type [2] inequalities, see34567, to close the century long debate on a possibility to combine peacefully local realism with quantum formalism, cf.8910111213141516. In this paper we study spatial and temporal dependencies of detection probabilities for photons propagating in optical fibres. ...
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The electromagnetic fields of a single optic fibre mode are quantized based on the observation that these fields can be derived from a scalar harmonic oscillator function depending on only time and the axial wavenumber. Asymptotic results for both the one-photon probability density and two-photon correlation density functions within the forward light cone are presented, showing an algebraic decay for large times or distances. This algebraic decay, increasing the uncertainty in the arrival time of the photons, also remains in the presence of dispersion shift, in qualitative agreement with experimental results. Also presented are explicit formulae to be used in parameter studies to optimize quantum optic fibre communications.
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