This is final part of a 4-part presentation. In this part I focus on how the most important equations in quantum mechanics, those that are taken from statistics and encourage the Copenhagen interpretation, are really operations that reintegrate vector components of spacetime (energy in the form of motion) that had been separated and rescaled, to arrive at the desired observable in the new domain. This is presented for the purpose of supporting a better, more meaningful interpretation that leads to a demonstration of the wave structure and holomorphic nature of reality. Unlocking the mysteries of the universe means that there is a mystery, a lock and a key. Energy is the mystery, physical form (differentiated into separate units) is the lock, and recognizing the equivalence of space and time is the key. How to use that key is found in the harmony in nature through the Golden Ratio.
This is final part of a 4-part presentation. In this part I focus on how the most important equations in quantum mechanics, those that are taken from statistics and encourage the Copenhagen interpretation, are really operations that reintegrate vector components of spacetime (energy in the form of motion) that had been separated and rescaled, to arrive at the desired observable in the new domain. This is presented for the purpose of supporting a better, more meaningful interpretation that leads to a demonstration of the wave structure and holomorphic nature of reality. Unlocking the mysteries of the universe means that there is a mystery, a lock and a key. Energy is the mystery, physical form (differentiated into separate units) is the lock, and recognizing the equivalence of space and time is the key. How to use that key is found in the harmony in nature through the Golden Ratio.
This is the second part of a four-part presentation. In part 1 I introduced a relational model that allowed me to demonstrate the equivalence of space and time as S=Tc^2 and showed that S represents energy as the product of scalar space with spatial frequency and T represents energy as the product of time units with temporal frequency. Doing so revealed the equations for quantum energy of a particle to be the inverse domains scaled by Planck’s constant. In this context, they served as two components (base vectors) of a quantum wave function (a composite space-time vector). In this part, I will continue to develop the model and discuss how the projection of a unified concept onto a plane that represents their separation creates a scaling problem that can be dealt with a different ways.
This is the third part of a four-part presentation. Part 1 introduced a relational model that allowed us to demonstrate the equivalence of space and time as S=Tc^2 and showed that S represents energy as the product of scalar space with spatial frequency and T represents energy as the product of time units with temporal frequency. In this part, I continue to develop the model by replacing a the inverse scale with a polar coordinate system to solve what I call the frequency problem. By analogizing vector spaces (velocity and acceleration domain) and scalar space (space-time domain) with computer windows, I “click” to refocus the visual model on the domain of interest and show how mathematical operations, like quantum operators, transform scales and coordinates in one domain to project, translate, reflect and rotate geometric symbols in other domains and produce more complex relations (including the classical wave equation and the Klein-Gordon equation).
Quantum Mechanics is appropriately named because it is mostly about the mechanics used to work probability problems. There must be, and there is a better way to visualize the concepts of quantum physics so that teachers can present a consistent conceptual interpretation. In this paper, we use a graph (i.e. the image of a graphical map) to represent the relationships between space, time and motion but we interpose the linear space-time domain (the moving or relativistic reference frame in the region greater than one) with a logarithmic spatial-temporal frequency domain (the at-rest or quantum reference frame in the region between zero and one). This approach demonstrates space-time equivalence as S=Tc^2, and thereby reveals the de Broglie equations for energy of a quantum particle in exactly the same geometric relation as the total energy relations that include mass-energy equivalence. The model allows one to visualize the particle-wave duality as a change in perspective the same as you can visualize an object both at rest with respect to your classroom yet in motion with respect to the sun, provides a perspective on the meaning of time and the psychological time flux as an eternal process of transformation, reinterprets the speed of light as the speed at which darkness (the absence of information) recedes, and concludes that the solid objects that occupy 3-dimensional expanse of space can be viewed as holomorphic images, materialized by the interaction of fields that gain physical form by their transformation into divergence and curl.
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.
Quantum theory is the soul of contemporary physics. It was discovered in an adventurous way, under the urge to solve the puzzles posed by atomic spectra and blackbody radiation. But after its invention, it immediately became clear that it was not just a theory of specific physical systems: it was rather a new language of universal applicability. Already in 1928, the theory had received solid mathematical foundations by Hilbert, von Neumann, and Nordheim, and this work was brought to completion in the monumental work of von Neumann, in the form that we still study nowadays. The theory is extraordinarily successful, and its predictions have been confirmed to an astonishing level of precision in a large spectrum of experiments. However, almost 90 years after von Neumann's book, quantum theory remains mysterious. Its mathematical formulation – based on Hilbert spaces and self-adjoint operators – is far from having an intuitive interpretation. The association of physical systems to Hilbert spaces whose unit vectors represent pure states, the representation of transformations by unitary operators and of observables by self-adjoint operators – all such postulates look artificial and ad hoc . A slightly more operational approach is provided by the C * -algebraic formulation of quantum theory – still, this formulation relies on the assumption that observables form an algebra , where the physical meanings of the multiplication and the sum are far from clear. In short, the postulates of quantum theory impose mathematical structures without providing any simple reason for this choice: the mathematics of Hilbert spaces is adopted as a magic blackbox that “works well” at producing experimental predictions. However, in a satisfactory axiomatization of a physical theory the mathematical structures should emerge as a consequence of postulates that have a direct physical interpretation. By this we mean postulates referring, e.g., to primitive notions like physical system, measurement, or process, rather than notions like, e.g., Hilbert space, C * -algebra, unit vector, or selfadjoint operator. The crucial question thus remains unanswered: why quantum theory? Which are the principles at the basis of the theory? A case that is often invoked in contrast is that of Special Relativity theory, which directly follows from the simple understandable principle of relativity.
Quantum Mechanics is appropriately named because it is mostly about the mechanics of working out probability problems as they apply to the mysterious effect of measurement that makes energy present as quantum particle-waves. It is easy to visualize a quantum particle but there seems to be no way to visualize a “probability wave” so there has never been a clear interpretation of what quantum physics tells us – or should tell us – about the underlying essence of reality. Fortunately, a new approach was discovered and proven to work in biology that treats the mystery of life like a locking system and provides not only the key, but also the keyhole and the direction in which to turn it. In this paper the systems approach is introduced, including some background information on the history of how the systems approach has integrated elements of substance philosophy with process philosophy and has become a powerful tool for use in science. Here, it is applied to physics and used to represent the transformation of implicit energy into an explicit space-time quantum domain superimposed on a relativistic time-space background. These two “products” are then correlated with two of four blocks in a basic control-system diagram (input and output) commonly used in control-systems engineering. (The four blocks are input, transfer function, output and feedback function) Because they are explicit, they can be drawn explicitly on the space versus time plot as a map of motion. We emphasize that this is a map – an explicit projection of an implicit function (in this case, a plot of space versus time is a projection of the variance we call motion) represented as an implicit domain (a perpendicular dimension). We recognizing that a feedback function is equivalent to and therefore implies a back-projection or reflection back “up” into that “implicate order.” These two implicit functions (projection and reflection) are then correlated with the transfer function and feedback function in the control system. The motion function is related to the probability wave by the name used in statistics – the “variance” of a statistical distribution – and we point out that each axis of the space-time domain is scaled by standard “deviations,” which define the explicit scales. Because a standard deviation is the square root of a variance, the square space that maps as a relativistic scalar plot (a standard Cartesian coordinate system) of space versus time or “space-time” actually represents one of two square roots of the implicit variance we call motion. In essence, our measurements of this domain keep us rooted in physical reality. However, this coordinate system is shown to be just the root – one part of a “whole system” that includes a non-physical implicit feedback function. The feedback function is correlated with the “reflection” of the explicit domain, i.e. inverse-space and inverse-time, presented as a phase space called time-space and represented as a unit of spatial frequency versus temporal frequency. These frequency representations are shown to be the two well-known equations for quantum energy from quantum mechanics and they are used to identify energy-space as “the quantum domain” inside of, or superimposed on the background “relativistic domain,” which is a scalar space. These two domains are then shown to be coupled at the point where both scales are equal to “1”. As a whole, and in the language of quantum field theory, this model is a graphical representation of an energy-momentum tensor and as a visual model, it provides a clear conceptual interpretation of complexity theory, in which reality is expressed as the superposition of a self-organizing control system that convolves with a dissipative open system or “sea of disorder” and transforms it into physical units of order. This “holomorphic systems approach” is similar to, but much simpler and visually illustrative than the mathematically rigorous discussion On Symmetry and the Reality of Holomorphic Hartree–Fock Wavefunctions [1] or the Kohn-Sham Density Functional Theory [2]. Furthermore, it reveals that the question about the beginning of time is a question fallacy, by representing the equivalence of space and time as S=Tc2, and presents it geometrically to be the exact same relation as the mass-energy equivalence equation E=mc2. The model also reveals that quantized energy (which Huynh and Thom refer to as self-consistent fields or SCF) projects as a characteristic and allows one to visualize the solution to the particle-wave duality “problem” as being a change in perspective. It’s the change in perspective that makes the particle-like property and wave-like property appear as “emergent” – analogous to what would appear when one visualizes an object from two different perspectives – at rest with respect to one’s own body yet in motion relative to some other “moving” body. The approach also reveals how the transfer function and feedback function act to transform matter, adding the fourth component (the Controller) and making it a complete control system: a self-organizing, self-sensing system that can see itself explicitly and reflect upon itself implicitly. How that correlates with living systems becomes obvious.