Searcharxiv⌕ Search

arXiv subjects

Gerhard Groessing

Publications and source records attributed to Gerhard Groessing.

33 records · Page 2Linked to original sources
arXiv2011

An explanation of interference effects in the double slit experiment: Classical trajectories plus ballistic diffusion caused by zero-point fluctuations

A classical explanation of interference effects in the double slit experiment is proposed. We claim that for every single "particle" a thermal context can be defined, which reflects its embedding within boundary conditions as given by the totality of arrangements in an experimental apparatus. To account for this context, we introduce a "path excitation field", which derives from the thermodynamics of the zero-point vacuum and which represents all possible paths a "particle" can take via thermal path fluctuations. The intensity distribution on a screen behind a double slit is calculated, as well as the corresponding trajectories and the probability density current. The trajectories are shown to obey a "no crossing" rule with respect to the central line, i.e., between the two slits and orthogonal to their connecting line. This agrees with the Bohmian interpretation, but appears here without the necessity of invoking the quantum potential.

quant-ph↗
arXiv2011

A classical explanation of quantization

In the context of our recently developed emergent quantum mechanics, and, in particular, based on an assumed sub-quantum thermodynamics, the necessity of energy quantization as originally postulated by Max Planck is explained by means of purely classical physics. Moreover, under the same premises, also the energy spectrum of the quantum mechanical harmonic oscillator is derived. Essentially, Planck's constant h is shown to be indicative of a particle's "zitterbewegung" and thus of a fundamental angular momentum. The latter is identified with quantum mechanical spin, a residue of which is thus present even in the non-relativistic Schroedinger theory.

quant-ph↗
arXiv2010

Elements of sub-quantum thermodynamics: quantum motion as ballistic diffusion

By modelling quantum systems as emerging from a (classical) sub-quantum thermodynamics, the quantum mechanical "decay of the wave packet" is shown to simply result from sub-quantum diffusion with a specific diffusion coefficient varying in time due to a particle's changing thermal environment. It is thereby proven that free quantum motion strictly equals ballistic diffusion. The exact quantum mechanical trajectory distributions and the velocity field of the Gaussian wave packet are thus derived solely from classical physics. Moreover, also quantum motion in a linear (e.g., gravitational) potential is shown to equal said ballistic diffusion. Quantitative statements on the trajectories' characteristic behaviours are obtained which provide a detailed "micro-causal" explanation in full accordance with momentum conservation.

physics.gen-ph↗
arXiv2010

Emergence and Collapse of Quantum Mechanical Superposition: Orthogonality of Reversible Dynamics and Irreversible Diffusion

Based on the modelling of quantum systems with the aid of (classical) non-equilibrium thermodynamics, both the emergence and the collapse of the superposition principle are understood within one and the same framework. Both are shown to depend in crucial ways on whether or not an average orthogonality is maintained between reversible Schroedinger dynamics and irreversible processes of diffusion. Moreover, said orthogonality is already in full operation when dealing with a single free Gaussian wave packet. In an application, the quantum mechanical "decay of the wave packet" is shown to simply result from sub-quantum diffusion with a specific diffusivity varying in time due to a particle's changing thermal environment. The exact quantum mechanical trajectory distributions and the velocity field of the Gaussian wave packet, as well as Born's rule, are thus all derived solely from classical physics.

quant-ph↗
arXiv2008

On the Thermodynamic Origin of the Quantum Potential

The quantum potential is shown to result from the presence of a subtle thermal vacuum energy distributed across the whole domain of an experimental setup. Explicitly, its form is demonstrated to be exactly identical to the heat distribution derived from the defining equation for classical diffusion-wave fields. For a single free particle path, this thermal energy does not significantly affect particle motion. However, in between different paths, or at interfaces, the accumulation-depletion law for diffusion waves provides an immediate new understanding of the quantum potential's main features.

quant-ph↗
arXiv2008

Diffusion Waves in Sub-Quantum Thermodynamics: Resolution of Einstein's 'Particle-in-a-box' Objection

Einstein's objection against both the completeness claim of the orthodox version and the Bohmian interpretation of quantum theory, using the example of a 'particle in a box', is reiterated and resolved. This is done by proving that the corresponding quantum mechanical states exactly match classical analogues. The latter are shown to result from the recently elaborated physics of diffusion waves.

quant-ph↗
arXiv2008

The Vacuum Fluctuation Theorem: Exact Schroedinger Equation via Nonequilibrium Thermodynamics

By assuming that a particle of energy hbar.omega is actually a dissipative system maintained in a nonequilibrium steady state by a constant throughput of energy (heat flow), the exact Schroedinger equation is derived, both for conservative and nonconservative systems. Thereby, only universal properties of oscillators and nonequilibrium thermostatting are used, such that a maximal model independence of the hypothesised sub-quantum physics is guaranteed. It is claimed that this represents the shortest derivation of the Schroedinger equation from (modern) classical physics in the literature, and the only exact one, too. Moreover, a "vacuum fluctuation theorem" is presented, with particular emphasis on possible applications for a better understanding of quantum mechanical nonlocal effects.

quant-ph↗
arXiv2005

Fluid Clocks: Emergence of quantum theory from sub-quantum dynamics

It is argued that any operational measure of time is inseparably bound to the presence of a periodic process in some medium. Since, as first formulated by Einstein's (1905) equation for the energy, all "particles" (neutrons, electrons, photons, etc.) are each characterized by a specific "frequency", the inverse of this frequency is the smallest operational unit of time available in principle. With a corresponding "coarse graining" of an otherwise practically idealized, continuous time (i.e., with the latter then holding on time scales much larger than the coarse grained one), one can show that the basic features of quantum theory can be derived from a minimal set of assumptions. In particular, it is shown here how the Schroedinger equation can be derived from classical physics modified only by said assumption of a coarse grained time and the presence of so-called "zero-point fluctuations". The latter relate to the dynamics of a "fluid" vacuum, which is today known to be a far cry from just being "empty space". Consequently, it is shown that time and matter, when discussed from a physical point of view, must by necessity be considered in one common framework.

quant-ph↗
arXiv2004

Observing Quantum Systems

An introduction to some basic ideas of the author's "quantum cybernetics" is given, which depicts waves and "particles" as mutually dependent system components, thus defining "organizationally closed systems" characterized by a fundamental circular causality. According to this, a new derivation of quantum theory's most fundamental equation, the Schroedinger equation, is presented. Finally, it is shown that quantum systems can be described by what Heinz von Foerster has called "nontrivial machines", whereas the corresponding classical counterparts turn out to behave as "trivial machines".

quant-ph↗
arXiv2004

From Classical Hamiltonian Flow to Quantum Theory: Derivation of the Schroedinger Equation

It is shown how the essentials of quantum theory, i.e., the Schroedinger equation and the Heisenberg uncertainty relations, can be derived from classical physics. Next to the empirically grounded quantisation of energy and momentum, the only input is given by the assumption of fluctuations in energy and momentum to be added to the classical motion. Extending into the relativistic regime for spinless particles, this procedure leads also to a derivation of the Klein-Gordon equation. Comparing classical Hamiltonian flow with quantum theory, then, the essential difference is given by a vanishing divergence of the velocity of the probability current in the former, whereas the latter results from a much less stringent requirement, i.e., that only the average over fluctuations and positions of the average divergence be identical to zero.

quant-ph↗
arXiv2002

Derivation of the Schroedinger Equation and the Klein-Gordon Equation from First Principles

The Schroedinger- and Klein-Gordon equations are directly derived from classical Lagrangians. The only inputs are given by the discreteness of energy (E=hbar.w) and momentum (p=hbar.k), respectively, as well as the assumed existence of a space-pervading field of "zero-point energy" (E_0=hbar.w/2 per spatial dimension) associated to each particle of energy E. The latter leads to an additional kinetic energy term in the classical Lagrangian, which alone suffices to pass from classical to quantum mechanics. Moreover, Heisenberg's uncertainty relations are also derived within this framework, i.e., without referring to quantum mechanical or other complex-numbered functions.

quant-ph↗
arXiv2002

Quantum Cybernetics: A New Perspective for Nelson's Stochastic Theory, Nonlocality, and the Klein-Gordon Equation

The Klein-Gordon equation is shown to be equivalent to coupled partial differential equations for a sub-quantum Brownian movement of a ''particle'', which is both passively affected by, and actively affecting, a diffusion process of its generally nonlocal environment. This indicates circularly causal, or ''cybernetic'', relationships between ''particles'' and their surroundings. Moreover, in the relativistic domain, the original stochastic theory of Nelson is shown to hold as a limiting case only, i.e., for a vanishing quantum potential.

quant-ph↗
arXiv2002

A Simple Model for the Evolution of Evolution

A simple model of macroevolution is proposed exhibiting both the property of punctuated equilibrium and the dynamics of potentialities for different species to evolve towards increasingly higher complexity. It is based on the phenomenon of "fractal evolution" which has been shown to constitute a fundamental property of nonlinear discretized systems with one memory- or random-based feedback loop. The latter involves a basic "cognitive" function of each species given by the power of distinction of states within some predefined resolution. The introduction of a realistic background noise limiting the range of the feedback operation yields a pattern signature in fitness space with a distribution of temporal boost/mutation distances according to a randomized devil's staircase function. Introducing a further level in the hierarchy of the system's rules, the possibility of an adaptive evolutionary change of the resolution itself is implemented, thereby providing a time-dependent measure of the species' cognitive abilities: an additional feedback loop makes use of the inevitable intrinsic fluctuations within the fitness landscape to direct the temporal change of the resolution. Feeding back the small adaptive changes of resolution into the essentially directionless variations of the patterns' lifetimes in fitness space effectively leads to a clear tendency towards increasing evolution potentials for each species ("hierarchically emergent fractal evolution").

physics.bio-ph↗
arXiv2002

Fractal Evolution of Normalized Feedback Systems on a Lattice

Highly nonlinear behavior of a system of discrete sites on a lattice is observed when a specific feedback loop is introduced into models employing coupled map lattices, quantum cellular automata, or the real-valued analogues of the latter. It is shown that the combination of two operations, i.e. i) enhancement of a site's value when fulfilling a feedback condition and ii) normalization of the system after each time step, produces relatively short-lived spatio-temporal patterns whose mean lifetime can be considered as emergent order parameter of the system. This mean lifetime obeys a scaling law involving a control parameter which tunes the "fault tolerance" of the feedback condition. Thus, within appropriate ranges of the systems variables, the dynamical properties can be characterized by a "fractal evolution dimension" (as opposed to a "fractal dimension").

nlin.AO↗