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Born's Rule as Signature of a Superclassical Current Algebra
Quantum Physics · Submitted 27 Aug 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim By proving the absence of third order interferences in three-path systems it is shown that Born's rule is a natural consequence of our theory.
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The abstract, sentence by sentence
We present a new tool for calculating the interference patterns and particle trajectories of a double-, three- and N-slit system on the basis of an emergent sub-quantum theory developed by our group throughout the last years. The quantum itself is considered as an emergent system representing an off-equilibrium steady state oscillation maintained by a constant throughput of energy provided by a classical zero-point energy field. We introduce the concept of a "relational causality" which allows for evaluating structural interdependences of different systems levels, i.e. in our case of the relations between partial and total probability density currents, respectively. Combined with the application of 21st century classical physics like, e.g., modern nonequilibrium thermodynamics, we thus arrive at a "superclassical" theory. Within this framework, the proposed current algebra directly leads to a new formulation of the guiding equation which is equivalent to the original one of the de Broglie-Bohm theory. By proving the absence of third order interferences in three-path systems it is shown that Born's rule is a natural consequence of our theory. Considering the series of one-, double-, or, generally, of N-slit systems, with the first appearance of an interference term in the double slit case, we can explain the violation of Sorkin's first order sum rule, just as the validity of all higher order sum rules. Moreover, the Talbot patterns and Talbot distance for an arbitrary N-slit device can be reproduced exactly by our model without any quantum physics tool.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a new tool for calculating the interference patterns and particle trajectories of a double-, three- and N-slit system on the basis of an emergent sub-quantum theory developed by our group throughout the last years. | contribution 0.99 | 0.87 | 0.08 | asserted 1.00 |
| s1 | The quantum itself is considered as an emergent system representing an off-equilibrium steady state oscillation maintained by a constant throughput of energy provided by a classical zero-point energy field. | method 0.46 | 0.23 | 0.05 | asserted 1.00 |
| s2 | We introduce the concept of a "relational causality" which allows for evaluating structural interdependences of different systems levels, i.e. in our case of the relations between partial and total probability density currents, respectively. | contribution 0.65 | 0.79 | 0.05 | asserted 0.93 |
| s3 | Combined with the application of 21st century classical physics like, e.g., modern nonequilibrium thermodynamics, we thus arrive at a "superclassical" theory. | contribution 0.44 | 0.72 | 0.11 | asserted 0.99 |
| s4 | Within this framework, the proposed current algebra directly leads to a new formulation of the guiding equation which is equivalent to the original one of the de Broglie-Bohm theory. | result 0.66 | 0.84 | 0.14 | asserted 1.00 |
| s5 | By proving the absence of third order interferences in three-path systems it is shown that Born's rule is a natural consequence of our theory. | result 0.88 | 0.89 | 0.62 | asserted 1.00 |
| s6 | Considering the series of one-, double-, or, generally, of N-slit systems, with the first appearance of an interference term in the double slit case, we can explain the violation of Sorkin's first order sum rule, just as the validity of all higher order sum rules. | result 0.83 | 0.80 | 0.15 | asserted 0.96 |
| s7 | Moreover, the Talbot patterns and Talbot distance for an arbitrary N-slit device can be reproduced exactly by our model without any quantum physics tool. | result 1.00 | 0.86 | 0.11 | asserted 1.00 |
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The paper
Original abstract
We present a new tool for calculating the interference patterns and particle trajectories of a double-, three- and N-slit system on the basis of an emergent sub-quantum theory developed by our group throughout the last years. The quantum itself is considered as an emergent system representing an off-equilibrium steady state oscillation maintained by a constant throughput of energy provided by a classical zero-point energy field. We introduce the concept of a "relational causality" which allows for evaluating structural interdependences of different systems levels, i.e. in our case of the relations between partial and total probability density currents, respectively. Combined with the application of 21st century classical physics like, e.g., modern nonequilibrium thermodynamics, we thus arrive at a "superclassical" theory. Within this framework, the proposed current algebra directly leads to a new formulation of the guiding equation which is equivalent to the original one of the de Broglie-Bohm theory. By proving the absence of third order interferences in three-path systems it is shown that Born's rule is a natural consequence of our theory. Considering the series of one-, double-, or, generally, of N-slit systems, with the first appearance of an interference term in the double slit case, we can explain the violation of Sorkin's first order sum rule, just as the validity of all higher order sum rules. Moreover, the Talbot patterns and Talbot distance for an arbitrary N-slit device can be reproduced exactly by our model without any quantum physics tool.
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How the literature uses it
6 arXiv papers cite this in 14 sentences
Papers citing it · 12 sentences without a confident label
Builds on it 2 papers
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Reducing the general case discussed in [ref] to the double-slit case, one notes for the first and second channels the emergent velocity vectors $v_1(2),u_1(2)R,$ and $u_1(2)L$, together with associated amplitudes $R_1(2)$, respectively.
The Quantum Sweeper Effect · Introduction · 0.95
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Reducing the general case discussed in [ref] to the double-slit case, we note for the first and second channels the emergent velocity vectors $v_1(2),u_1(2)R,$ and $u_1(2)L$ with associated amplitudes $R_1(2)$, respectively.
Extreme beam attenuation in double-slit experiments: Quantum and subquantum scenarios · 2.2 Short review of the superclassical approach to quantum mechanics · 1.00
What it cites · 25 sentences without a confident label
Uses the method or tool of 1 paper
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As opposed to this analytical procedure, we use the simulation tools disclosed in [ref] , which are displayed in the computer simulations of Fig. [ref] for a 7-slit and a 27-slit setup, respectively.
Modeling double slit interference via anomalous diffusion: independently variable slit widths · $N$-slit interference and the quantum Talbot effect · 1.00
Compares with 1 paper
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This well-known fact, representing the “heart” of quantum mechanics, is to be contrasted with Sorkin's results for the following, so-called “second order sum rule” [ref] : [equation] This result is remarkable insofar as it can be inferred that interference terms theoretically always originate from pairings of paths, but never from triples etc.
Quantum Mechanics as Quantum Measure Theory · Three-slit interference and Born's rule · 0.81
Cites as background 2 papers
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From the theoretical point of view interference-type phenomena have been analyzed thoroughly [ref] , for the cases of only one open slit up to $𝑁$ open slits.
Quantum Mechanics as Quantum Measure Theory · Three-slit interference and Born's rule · 0.96
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Said term is in close relation to the recently developed models of superstatistics, where a macroscopically observed emergent behavior is the result of a superposition of two or more statistical systems operating at vastly different space-time scales [ref] .
The emergence of Special and Doubly Special Relativity · A superclassical current algebra · 0.95
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