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.
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.
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.
More than a hundred years ago, a series of discoveries, especially in physics, began to subtly (or maybe not) reveal some mysterious properties of matter, properties that in some fashion or other were not acceptable to our established way of perceiving Reality. Strangely enough, these properties were not taken seriously by science because they pointed to a reality that seemed too fantastical to be true, a reality that seemed to have no substance or permanence. These so called mysterious properties matter, for lack of a better word, turn out to be fundamentally related to the following discoveries: The ambiguous wave-particle duality. As in de Broglie matter-waves and the Compton properties of particles. The ubiquitous appearance of the cycle constant (τ=2π=C⁄r) in physical mathematical relations. The general applicability of the Fourier Transform to represent/model physical motion and other natural processes. The Heisenberg Uncertainty Principle and its mysterious constraint between conjugate variables, momentum and position for example. Quantum Mechanics and its collapse of the wavefunction. The surprising mass-energy equivalence. As in Einstein’s E=mc^2. The perplexing isotropy of the speed of light. The mind boggling time dilation and length contraction of Einstein’s Special Relativity (SR). The contradictory fabric of SR/GR’s spacetime and its assignment of properties to the void. The surprisingly discrete nature of atomic properties. As in Quantum Mechanics (QM). Needless to say, no matter what science has tried in order to fit the above discoveries into our physical world, their implications continue to elude an intuitively acceptable explanation in material terms. This monograph, although not necessarily in chronological order, is a recapitulation of previous monographs written by the author in an attempt at a single-source theoretical explanation/clarification for the above mentioned list of “mysterious” properties of matter, in terms of one fundamental set of properties, the motional geometry of matter.
For over nine decades, quantum mechanics has profoundly shaped our understanding of nature, offering explanations for the stability of atoms, the formation of mole cules, the properties of materials, and phenomena such as light or radioactivity. It is essential to modern technologies—from microchips to lasers—and underpins the physics of elementary particles. Yet, despite its successes, it remains a deeply mysterious theory, confronting a central enigma: why does the quantum world behave so differently from everyday reality? Elements such as superposition and quantum entanglement—which allow particles to exist simultaneously in multiple states or remain interconnected regardless of distance—contradict classical world intuitions. This gap between microscopic and macroscopic behavior has given rise to what is known as the “measurement problem,” raising fundamental questions about the nature of reality. Diverging interpretations have led to two major schools of thought: anti-realism, promoted by Niels Bohr, which holds that reality depends on the observer and their interaction with measurement instruments; and realism, supported by Albert Einstein, which argues that quantum mechanics is incomplete and that eality exists independently of observation. Bohr’s complementary philosophy and Heisenberg’s uncertainty principle were central to the formulation of the “Copenhagen interpretation,” which became dominant in the 20th century. However, the persistent opposition of scientists like Einstein and Schrödinger inspired generations of physicists to seek a unification between quantum mechanics and relativity, culminating in new theories such as loop quantum gravity and string theory. Thus, the debate between realism and anti-realism remains alive, and philosophy continues to play a crucial role in exploring the new foundations of physics.
Quantum physics, which describes the strange behavior of light and matter at the smallest scales, is one of the most successful descriptions of reality, yet it is notoriously inaccessible. Here we provide an approachable explanation of quantum physics using simple thought experiments. We derive all relevant quantum predictions using minimal mathematics, without introducing the advanced calculations that are typically used to describe quantum physics. We focus on the two key surprises of quantum physics, namely wave-particle duality, a term that was introduced to capture the fact that single quantum particles in some respects behave like waves and in other respects like particles, and entanglement, which applies to two or more quantum particles and brings out the inherent contradiction between quantum physics and seemingly obvious assumptions regarding the nature of reality. Following arguments originally made by John Bell and Lucien Hardy, we show that the so-called local hidden variables are inadequate at explaining the behavior of entangled quantum particles. This means that one either has to give up on hidden variables, i.e., the idea that the outcomes of measurements on quantum particles are determined before an experiment is actually carried out, or one has to relinquish the principle of locality, which requires that no causal influences should be faster than the speed of light and is a cornerstone of Einstein's theory of relativity. Finally, we describe how these remarkable predictions of quantum physics have been confirmed in experiments. We have successfully used the present approach in a course that is open to all undergraduate students at the University of Calgary, without any prerequisites in mathematics or physics.
The Schrödinger's wave function can naturally be realized as an 'instantaneous resonant spatial mode' in which quantum particle moves and hence the Born's rule is derived after identifying its origin. This realization facilitates the visualization of `what's really going on?' in the Young's double-slit experiment which is known to be the central mystery of quantum mechanics. Also, an actual mechanism underlying the `spooky-action-at-a-distance', another mystery regarding the entangled quantum particles, is revealed. Wheeler's delayed choice experiments, delayed choice quantum eraser experiment and delayed choice entanglement swapping experiments are unambiguously and naturally explained at a single quantum level. The reality of Nature represented by the quantum mechanical formalism is conceptually intuitive and is independent of the measurement problem.
Abstract This chapter introduces the central mysteries of quantum mechanics. Quantum mechanics is an enormously successful theory that lies at the heart of modern physics, but there is no agreement on how to understand it. Simple experiments with light demonstrate why: in understanding those experiments, we have to shift inconsistently back and forth between thinking of the theory as assigning indefinite, delocalized, but known properties to a system, and assigning definite, localized, but unknown properties (this is called the ‘problem of measurement’). Furthermore, when we break a system into subsystems, the state of the system is not determined by the states of the subsystem (this is called ‘entanglement’), and simple arguments seem to tell us that the physical properties of entangled subsystems can influence one another non-locally—faster than light. These three mysteries—measurement, entanglement, non-locality—need to be addressed by any attempt to make sense of quantum theory.