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Emergent Fractal Attractor Corresponds with Foundational Quantum Problems

Blair Macdonald

Published Jul 1, 2021• 0 citations
OpenAlex

Abstract

The field of foundational quantum mechanics originated nearly one hundred years ago yet remains one of the greatest mysteries to physicists today. The experiment in this study tests whether the geometry of fractals, according to a simple isolated iterating fractal (the Koch Snowflake), correspond to the accepted description of 1) electromagnetic wave-particles (light) and 2) quantum enigmas. In this investigation, an experiment was conducted on an isolated iterating Koch Snowflake fractal. The propagation of changes to triangle ‘bits’ was observed and measured quantitively and the implications of these changes described and discussed. It was found the fractal when in isolation, behaves as a quantum entity. The fractal has, 1) wave-particle duality, 2) an oscillating, exponential, sinusoidal wave of discrete ‘bits’ of information and 3) in superposition. Constant light speed ‘c' was reasoned to be a property of the growth behaviour of the fractal. It was discussed that a concept and a direction of time would be experienced by an observer within the fractal set, and it was reasoned, corresponding to special relativity, this perception of time would slow to a stop when travelling at the frontier of the set and speed of propagation bits. The quantum ‘measurement problem’, ‘uncertainty principle’, and ‘entanglement’ were all addressed as also being a problem of isolated fractals within fractal landscapes or fields where ‘position’ is only ‘known’ by the addition of information or markers. The quantum-classical interface is a problem of the fractal and is scale-invariant. From this experiment, the opportunity arises to model and analyse what is viewed behind the observer as the fractal iterates. This dual retrospective perspective may offer a unification between quantum mechanics and cosmological mathematics, observations, and conjectures; in so doing possibly explaining the vacuum catastrophe. All these problems may all be different, dual and complementary aspects of the one fractal geometry.

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The field of foundational quantum mechanics originated nearly one hundred years ago yet remains one of the greatest mysteries to physicists today. The experiment in this study tests whether the geometry of fractals, according to a simple isolated iterating fractal (the Koch Snowflake), correspond to the accepted description of 1) electromagnetic wave-particles (light) and 2) quantum enigmas. In this investigation, an experiment was conducted on an isolated iterating Koch Snowflake fractal. The propagation of changes to triangle ‘bits’ was observed and measured quantitively and the implications of these changes described and discussed. It was found the fractal when in isolation, behaves as a quantum entity. The fractal has, 1) wave-particle duality, 2) an oscillating, exponential, sinusoidal wave of discrete ‘bits’ of information and 3) in superposition. Constant light speed ‘c' was reasoned to be a property of the growth behaviour of the fractal. It was discussed that a concept and a direction of time would be experienced by an observer within the fractal set, and it was reasoned, corresponding to special relativity, this perception of time would slow to a stop when travelling at the frontier of the set and speed of propagation bits. The quantum ‘measurement problem’, ‘uncertainty principle’, and ‘entanglement’ were all addressed as also being a problem of isolated fractals within fractal landscapes or fields where ‘position’ is only ‘known’ by the addition of information or markers. The quantum-classical interface is a problem of the fractal and is scale-invariant. From this experiment, the opportunity arises to model and analyse what is viewed behind the observer as the fractal iterates. This dual retrospective perspective may offer a unification between quantum mechanics and cosmological mathematics, observations, and conjectures; in so doing possibly explaining the vacuum catastrophe. All these problems may all be different, dual and complementary aspects of the one fractal geometry.
Making sense of the nearly 100-hundred-year-old quantum nature of light and matter, with its — to name a few — wave-particle duality, measurement problem, and entanglement ‘spooky action at the distance’ — remains the greatest questions to physics. Since the 1980s, fractal geometry, a new and exciting field of mathematics — that the fathers of quantum mechanics did not have and has not been tested for quantum properties — has developed. Can the isolated fractal explain the quantum? An experiment was conducted on a simple — but isolated — fractal testing whether the geometry of fractals corresponds to quantum enigmas. It was found the isolated fractal emerges by a duality of propagation — of an oscillating sinusoidal wave — of ‘bits’ — of information — iterating in a superposition of time, scale, and symmetry, with a possible constant speed, demonstrating all the hypothesised. The quantum ‘measurement problem’ was addressed as being a problem of isolated scale-invariant fractals — or fractal landscapes — where position is only ‘known’ when additional (fractal) information is added — which ‘equally’ gives rise to a (quantum-like) ‘uncertainty’ problem. Also, quantum entanglement and other quantum features were explained by the fractal model. Consequences of the model were discussed, notably to its relevance to the nature of light (the speed of it etc.), the behaviour of the atom, time, knowledge and our reality, and the model’s direct inextricable connection with cosmological observations and conjectures. Finally, it was concluded that the model is preliminary but fundamental.
This work confronts the enduring interpretive challenge of wave-particle duality by proposing a unified conceptual framework that reinterprets physical waves as self-similar fractal information processes and particles as stable, localized excitation patterns of an underlying field. Our framework provides an operational synthesis between Wheeler's "it from bit" and Bohm's implicate order, effecting an ontological shift to an information-theoretic process ontology. In the optical regime, light propagation is reconceptualized as coherent information reconstruction mediated by the polarization field, dissolving the paradox of photon identity. Prism dispersion is reinterpreted as spatial unfolding of frequency-domain fractal structures. In the quantum domain, the double-slit interference pattern is connected to the fractal geometry of Wiener paths, providing an intuitive geometric basis for probability amplitude superposition. The framework resolves wave-particle duality by recognizing both aspects as complementary manifestations of a deeper information-reconstructive substrate.
This work confronts the enduring interpretive challenge of wave-particle duality by proposing a unified conceptual framework that reinterprets physical waves as self-similar fractal information processes and particles as stable, localized excitation patterns of an underlying field. Our framework provides an operational synthesis between Wheeler's "it from bit" and Bohm's implicate order, effecting an ontological shift to an information-theoretic process ontology. In the optical regime, light propagation is reconceptualized as coherent information reconstruction mediated by the polarization field, dissolving the paradox of photon identity. Prism dispersion is reinterpreted as spatial unfolding of frequency-domain fractal structures. In the quantum domain, the double-slit interference pattern is connected to the fractal geometry of Wiener paths, providing an intuitive geometric basis for probability amplitude superposition. The framework resolves wave-particle duality by recognizing both aspects as complementary manifestations of a deeper information-reconstructive substrate.
The substrate field theory, developed in the first three papers of this series, posits a universal physical medium whose rigidity K and effective density ρ₀ determine the speed of light and whose dissipation governs cosmological redshift and orbital decay. In this paper, we show that the same substrate field naturally gives rise to all quantum phenomena as emergent properties of its microscopic structure. The substrate is assumed to possess a discrete granularity at a fundamental scale l₀, leading to quantization of energy and momentum. Linear excitations of the substrate—wave packets—exhibit wave–particle duality. The linearity of the wave equation allows coherent superpositions, giving rise to superposition and entanglement. The substrate's inherent dissipation provides a physical mechanism for decoherence, resolving the measurement problem without invoking a conscious observer. The Heisenberg uncertainty relation emerges as a Fourier property of wave packets in the substrate. Thus quantum mechanics is not a fundamental theory but an effective description of substrate dynamics at microscopic scales. This framework unifies quantum phenomena with classical physics, cosmology, and thermodynamics, eliminating the need for quantum postulates and explaining the apparent "weirdness" of the quantum world as natural consequences of a physical medium.Part IV of the Substrate Field Theory series
The wave-particle duality mystery, present in the language of quantum physics since its historical origins 100 years ago, has no real correspondence with the actual behaviour of nature when it is observed. The dilemma of the so-called “single particle interference” experiments is not between particles versus waves: the interference in quantum physics is between probability amplitudes for different untagged alternatives in a definite transition between states. This article shows that the same conceptual basis is involved in a plethora of “two-state systems” as a consequence of the linear superposition principle, no matter whether the observables refer to either spatial or internal properties. Several examples, from the Young double-slit interference experiments to neutrino flavour oscillation experiments, are discussed in a common interpretation language.
Standard physics is built upon a foundational duality: the macroscopic world governed by deterministic classical mechanics and general relativity, and the microscopic world governed by probabilistic quantum mechanics, whose foundational expression is the Heisenberg uncertainty principle . This paper demonstrates, within the Conjugate Photonic Model (CPM), that this duality is an artefact of incomplete knowledge rather than a property of nature. Three universal constants — the speed of light , the vacuum impedance , and Planck's constant — operate identically at both the microscopic (electron hopfion, photonic disc) and macroscopic (FEL, optics, electromagnetism) scales, eliminating the conceptual basis for dual physics. The Heisenberg principle is reinterpreted as a statistical consequence of measuring the time-average of the deterministic trajectory of the electron hopfion at traversal frequency , inaccessible to current temporal resolution but not inaccessible in principle. The Schrödinger cat paradox is resolved: the cat has a definite state at all times, determined by the internal phase of the electron hopfion. A structural equation for photon emission as a function of is derived: . The Free-Electron Laser provides the experimental isolation mechanism that forces the deterministic machinery into full visibility. The universe is a single, causal, deterministic system of organised EM field — the apparent duality dissolves when the internal phase variable is recognised as the missing element of the description.