Abstract: 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.
You may also want to read the sequel of this paper, i.e.:
"Diffusion Waves in Sub-Quantum Thermodynamics:
Resolution of Einstein's 'Particle-in-a-box' Objection", to be published.
See quant-ph/arXiv:0806.4462.
Schematic distinction of classical Hamiltonian flow (left) and quantum flow (right), with the circles indicating the propagation of spherical Hamilton-Jacobi wave surfaces.
The dotted lines (right) indicate symbolically that the waves pictured
represent only the local surroundings of a generally extending undulatory probability field,
thus illustrating that the fluctuations are to be seen in the context of the whole (nonlocal) environment.
Abstract: It is shown how the essentials of quantum theory, i.e., the Schrödinger 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.
You may also want to read a more recent AINS-paper, simplifying and expanding on the former one:
"Classical Physics Revisited:
Derivation and Explanation of the Quantum Mechanical Superposition Principle
and Born's Rule",
to be published.
Abstract: Under the only assumptions that energy and momentum of a particle
i) come in multiples of Planck's quantum of action, and ii) are subject to fluctuations related to the Huygens waves originating from the particle's embedded-ness in the surrounding "vacuum", one can derive the essentials of quantum physics from classical physics. In fact, the suggested classical Lagrangian can via a simple transformation law be "translated" into the familiar Lagrangian leading to the Schrödinger equation. Moreover, said transformation law is necessary and sufficient also to derive and explain the quantum mechanical superposition principle as well as Born's rule. Explicit examples are given which show that, at least in the cases discussed, the calculations within the language of classical physics are based on intuitively plausible modelling and are also done easier and faster than the corresponding ones due to orthodox quantum mechanics. This calls for the establishment of a more encompassing "dictionary" to provide more useful "translations" between the two languages.
Toward a Unification of Relativity and Quantum Theory via Circularly Causal Modeling
Gerhard Grössing
,
Austrian Institute for Nonlinear Studies, Vienna
THE PUBLISHER'S ANNOUNCEMENT: This book, written for non-specialists, discusses the apparent conflict between relativity and quantum mechanics, concentrating particularly on what Einstein called "spooky actions at a distance." The author proposes a resolution based on a causal interpretation introduced by Louis deBroglie and elaborated by David Bohm. He shows that one can introduce a "medium" or "aether" in a manner consistent with both relativity and quantum theory, and which allows one to unify the two theories via the identification of circularly causal processes at their core. The mathematics is kept simple, making the discussion accessible to a wide audience. Several crucial experiments are discussed in detail.
Table of Contents
Preface.Contents.Introduction. Quantum Theory and the Special Theory of Relativity. Quantum Cybernetics. Experiments. Gravity as a Pure Quantum Phenomenon: Mach's Principle Revisited. Implications of Circular Causality at the Quantum Level.
Coda: On the Meaning of Nonlocality. References. Index.
Vol. 32, No. 3-4 (2001): Special Issue on "Time’s Arrow".
A Festschrift on the Occasion of the 10th Anniversary of the
Austrian Institute for Nonlinear Studies
Contents
G. Grössing (AINS), Preface
M. Jeitler (CERN), Time’s Arrow in Particle Physics
G. Grössing (AINS), Nonlocality and the Time-Ordering of Events
F. Benatti, R. Floreanini, and A. Lapel (Univ. Trieste, INFN), Open Quantum Systems and Complete Positivity
H. Rauch (Atominstitut, Vienna), Unavoidable Quantum Losses in Zeno-Like Neutron Experiments
M. Courbage (Univ. Paris), Time Operator in Quantum Mechanics and Some Stochastic Processes With Long Memory
C. C. Martin and R. Gordon (Univ. Saskatchewan, Univ. Manitoba), The Evolution of Perception
A. Riegler (Free Univ. Brussels), The Cognitive Ratchet
S. Fussy, G. Grössing, and H. Schwabl (AINS), Irreversibility in Models of Macroevolution
R. Gordon (Univ. Manitoba), Making Waves: the Paradigms of Developmental Biology and their Impact on Artificial Life and Embryonics
TIME'S ARROW:
IRREVERSIBILITY FROM QUANTUM SYSTEMS TO BIOLOGICAL EVOLUTION
A Symposium as part of EMCSR 2000 - University of Vienna / Main Building, April 25 - 28, 2000.
Most of the fundamental laws in the natural sciences are formulated as time-symmetric ones, thereby
reflecting the conception from classical dynamics of time as a mere parameter. A notable exception is
the Second Law of thermodynamics, which introduces an arrow of time into physics. Although this law
states that the entropy in a closed system can only remain constant or increase, but never decrease, its
relation to other areas of the natural sciences has not been very clear.
In particular, there exist two areas "adjacent" to thermodynamics, which at first sight seem to largely
oppose the Second Law, albeit for different reasons. On the one hand, quantum theory is characterized
by time-symmetric fundamental equations (like the Schrödinger equation or some relativistic analogue
thereof). On the other hand, biological evolution has recently been shown to exhibit features of time-
symmetric "punctuated equilibrium" behavior. Still, evolution might generally have to be characterized by
a progressive trend of increasing order. However, even this time-asymmetry apparently would be in
opposition to the entropy law.
In this symposium, we intend to collect evidence for an arrow of time in the fields just mentioned, i. e.,
quantum theory and evolutionary biology. For, contrary to widespread belief, the solutions to the
fundamental equations of quantum theory do show time irreversible behavior due to a breaking of their
inherent symmetries. Similarly, irreversibility also characterizes laboratory experiments and computer
models of biological evolution. So, we are confronted with the scenario that in both fields some
fundamental laws may be time-symmetric, while any concrete systemic behavior generally is not,
because it represents an emergent phenomenon.
Ideally, participants could compare the latter with more general (thermodynamic or other) considerations
to enquire whether the concepts of irreversibility in the quantum and biological domains, respectively,
are radically different, or whether they share common, perhaps basic, systemic characteristics.
Note also the
INVITED LECTURE ON THE OCCASION OF THE 10TH ANNIVERSARY OF AINS:
Friday, April 28, 16:00 - 17:00, University of Vienna / Main Building;
Prof. Richard Gordon (Univ. of Manitoba), MAKING WAVES: THE PARADIGMS
OF DEVELOPMENTAL BIOLOGY AND THEIR IMPACT ON ARTIFICIAL LIFE AND EMBRYONICS
Serious Matter: The John-Bell – Scandal
Serious
Matter: The John-Bell – Scandal
Abstract:In a festive lecture at the
University of Vienna in 1987, on the occasion of Erwin Schrödinger’s 100th
birthday, the famous physicist John Bell complained about the “scandal”
(literally) that the so-called “deBroglie-Bohm interpretation” (BBI) of quantum
theory was not taught at the universities and treated on an equal footing with
the predominant “Copenhagen interpretation”. On the contrary, over decades, and
up to the present day, the BBI has almost always been marginalized or grossly
misrepresented by leading quantum physicists.
Actually, John Bell devoted practically all of his papers on quantum
theory to the implications around the BBI, as can easily be seen from the
collection of said papers in his book on “Speakable and Unspeakable in Quantum
Mechanics”. Now, in November 2000, a symposium was held at the University of
Vienna on the occasion of the 10th anniversary of Bell’s death.Physicists were invited to talk at this
symposium who only recently had published utterly wrong “arguments” calling for
the dismissal of the BBI. However, not a single exponent of the BBI was to give
a talk, although the symposium was performed in the name of John Bell. Thus,
the scandal is being prolonged.
Moreover, the series of (often provably intentional) misrepresentations
of the BBI is continued in articles celebrating “100 years of quantum theory”….
If one can say that much of traditional science
operates by an implicit linear mapping of objects of knowledge onto observing
knowledge acquisitors (i. e., by linear information transfer from objects
to observers), then one may very well characterize the present situation
in the natural sciences as one of a movement towards a "nonlinear", e. g.,
circular, relation between objects of knowledge and their investigators
(observers). Concerning the formal meaning of the word, the extension of linear models in the sciences to nonlinear ones has opened vast new areas of research, including investigations of systems with unprecedented degrees of complexity. In this regard, our interests focus on nonlinear models in Quantum Theory, Theoretical Biology and Medicine, and in new methods and tools of Systems Theory and studies of Complexity. With our research about various topics in said fields, we aim at a deeper understanding than it would be possible via linear approaches only.
Our small institute was founded in 1990, with three
staff members ever since, as well as occasional short-term collaborators.
The funding is completely private. We are in contact, and sometimes in
collaboration, with a number of national and international research institutions,
or scientists, respectively.
