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.
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.
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.
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.
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).
The purpose of this paper is to present a hypothesis: that frequency is the key to understanding the fundamental nature of time. Time and space are mirror images of each other and they are two different ways of expressing inverse frequency. The reason this is important is because, by starting with frequency the relationships of physics can be expressed by linear equations. It is known that frequency is directly proportional to and thus equivalent to quantum energy. By expressing the relationship of spatial frequency vs. temporal frequency as a simple geometric model, several well-known relationships fall into place without having to stretch the model into warped expressions of spacetime that require complicated hyperbolic functions or field equations. The result is a sensible interpretation of the meaning of time, spacetime, quantum particles and quantum wave functions. The model also lends itself directly to an understanding of how space and time become dissociated and transform into quantum bits of information, which automatically models reality as a quantum computer. The implications of these interpretations provide a bridge between physics, as a physical science, and life sciences that take in information from their surroundings, convolve it with itself as particles and thereby shape and reshape matter, allowing living organisms to change with time and adapt to their environment.
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.
In general relativity, the description of spacetime relies on idealised rods and clocks, which identify a reference frame. In any concrete scenario, reference frames are associated to physical systems, which are ultimately quantum in nature. A relativistic description of the laws of physics hence needs to take into account such quantum reference frames (QRFs), through which spacetime can be given an operational meaning. Here, we introduce the notion of a spacetime quantum reference frame, associated to a quantum particle in spacetime. Such formulation has the advantage of treating space and time on equal footing, and of allowing us to describe the dynamical evolution of a set of quantum systems from the perspective of another quantum system, where the parameter in which the rest of the physical systems evolves coincides with the proper time of the particle taken as the QRF. Crucially, the proper times in two different QRFs are not related by a standard transformation, but they might be in a quantum superposition one with respect to the other.Concretely, we consider a system of N relativistic quantum particles in a weak gravitational field, and introduce a timeless formulation in which the global state of the N particles appears "frozen", but the dynamical evolution is recovered in terms of relational quantities. The position and momentum Hilbert space of the particles is used to fix the QRF via a transformation to the local frame of the particle such that the metric is locally inertial at the origin of the QRF. The internal Hilbert space corresponds to the clock space, which keeps the proper time in the local frame of the particle. Thanks to this fully relational construction we show how the remaining particles evolve dynamically in the relational variables from the perspective of the QRF. The construction proposed here includes the Page-Wootters mechanism for non interacting clocks when the external degrees of freedom are neglected. Finally, we find that a quantum superposition of gravitational redshifts and a quantum superposition of special-relativistic time dilations can be observed in the QRF.