In This essay I shall derive the laws of nature from a simple mathematical system from a postulate that reality is indeed a mathematical structure. The system can be simulated by a computer program to generate many results that agree with Quantum mechanics. Also I will show that the system can be put in regular more familiar mathematical formalism. The postulate lead to assume particles are made of random lines were one end originates in a small region representing the particle and it extends to all other points in space and some ending on other particles. The points are really nothing but random numbers, hence reality is nothing but some relation between random numbers. Moreover, the lines are responsible for the interaction by a process of crossing or not crossing or meeting.The start point and the end point of these lines define space and the length of the line is interpreted as energy, time is just a change of state. The system unifies space, time, matter, energy and interaction, all in one coherent picture, so particles and the laws of nature governing them appear naturally. The simulations generate some basic Quantum Mechanics results and the 1/r law as in quantum field Theory. There are many other results such as the hydrogen 1s level where the universal constants like c, h, e and their relation that lead to Fine Structure constant automatically fall out of the simulation. Two such simulations are carried out; one is Bohr like model and the other Schrodinger like equations solution and show the equivalency. Also, the mass of the electron appear naturally using a simulation which is an extension of the Bohr model which in turn leads to the predicting the size of the proton. The system automatically displays the non-local behavior and explains the EPR in simple terms and shows the origin of spin. Some interesting formulas connecting proton to electron mass ratio, FSC and electron g-factor are produced. While it is shown that coulomb potential is produced by line crossing, Gravity appears when lines meet at a region of Planck's length(gravity needs more investigation).
In This essay I shall derive the laws of nature from a simple mathematical system from a postulate that reality is indeed a mathematical structure. The system can be simulated by a computer program to generate many results that agree with Quantum mechanics. Also I will show that the system can be put in regular more familiar mathematical formalism. The postulate lead to assume particles are made of random lines were one end originates in a small region representing the particle and it extends to all other points in space and some ending on other particles. The points are really nothing but random numbers, hence reality is nothing but some relation between random numbers. Moreover, the lines are responsible for the interaction by a process of crossing or not crossing or meeting.The start point and the end point of these lines define space and the length of the line is interpreted as energy, time is just a change of state. The system unifies space, time, matter, energy and interaction, all in one coherent picture, so particles and the laws of nature governing them appear naturally. The simulations generate some basic Quantum Mechanics results and the 1/r law as in quantum field Theory. There are many other results such as the hydrogen 1s level where the universal constants like c, h, e and their relation that lead to Fine Structure constant automatically fall out of the simulation. Two such simulations are carried out; one is Bohr like model and the other Schrodinger like equations solution and show the equivalency. Also, the mass of the electron appear naturally using a simulation which is an extension of the Bohr model which in turn leads to the predicting the size of the proton. The system automatically displays the non-local behavior and explains the EPR in simple terms and shows the origin of spin. Some interesting formulas connecting proton to electron mass ratio, FSC and electron g-factor are produced. While it is shown that coulomb potential is produced by line crossing, Gravity appears when lines meet at a region of Planck's length(gravity needs more investigation).
Despite its successes, quantum mechanics (QM) has remained mysterious to all who have encountered it. Starting with Bohr and progressing into the present, the departure from intuitive, physical reality has widened. The connection between QM and reality is more than just a “philosophical” issue. It reveals that QM is not a correct or complete theory of the physical world and that inescapable internal inconsistencies and incongruities arise when attempts are made to treat it as physical as opposed to a purely mathematical “tool.” Some of these issues are discussed in a review by F. Laloe [Am. J. Phys. 69, 655 (2001)]. In an attempt to provide some physical insight into atomic problems and starting with the same essential physics as Bohr of e moving in the Coulombic field of the proton and the wave equation as modified by Schrodinger, a classical approach is explored that yields a remarkably accurate model and provides insight into physics on the atomic level. The proverbial view, deeply seated in the wave-particle duality notion, that there is no large-scale physical counterpart to the nature of the electron may not be correct. Physical laws and intuition may be restored when dealing with the wave equation and quantummechanical problems. Specifically, a theory of classical quantum mechanics (CQM) is derived from first principles that successfully applies physical laws on all scales. Rather than using the postulated Schrodinger boundary condition “Ψ → 0 as r → ∞,” which leads to a purely mathematical model of the electron, the constraint is based on experimental observation. Using Maxwell’s equations, the classical wave equation is solved with the constraint that the bound (n = 1)state electron cannot radiate energy. By further application of Maxwell’s equations to electromagnetic and gravitational fields at particle production, the Schwarzschild metric is derived from the classical wave equation, which modifies general relativity to include conservation of spacetime in addition to momentum and matter/energy. The result gives a natural relationship among Maxwell’s equations, special relativity, and general relativity. CQM holds over a scale of spacetime of 85 orders of magnitude — it correctly predicts the nature of the universe from the scale of the quarks to that of the cosmos. A review is given by G. Landvogt [Internat. J. Hydrogen Energy 28, 1155 (2003)].
A deterministic quantum mechanics theory is presented in a series of papers starting with the present one. The proposed theory is shown to be consistent with the current mainstream statistical quantum theory as well as with classical physics. It produces solutions, which demonstrate that causality, physical reality, and determinism are restored and can explain in simple form concerns that are raised by results from the current mainstream statistical quantum theory. The meaning of particle- wave duality and complementarity, the possibility of a particle, like the electron, to cross through the nucleus as it does when the angular momentum of the electron is zero at the ground state of the hydrogen atom, the possibility of a point-size particle to have an “intrinsic spin”, the possibility of “quantum jumps” as the electron transitions instantaneously from one stable orbital to another without passing through the space in between the orbitals and does that at irregular time intervals, and the natural collapse of the wave function as part of the solution are some of the results that emerge from the proposed deterministic quantum mechanics theory. The phenomenon of entanglement is shown to be consistent with the proposed deterministic quantum mechanics theory. The Bohr-Schrödinger energy levels leading to the experimentally confirmed spectral lines, as well as the fine structure constant emerge directly from the solution of the equations governing theproposed deterministic quantum mechanics presented in Part II of these series of papers.
The framework rests on eight foundational postulates — eight statements about how reality is structured. Each postulate makes a specific claim. Together, they constrain everything that can happen. In plain English, the eight postulates say: 1. There is a real, physical time at the deepest level of reality. Time flows. 2. Time and space are not symmetric. (This sounds technical but just means time is special — it has a direction, space does not have a preferred direction.) 3. Time emerges from the substrate dynamics. It is not a separate thing — it comes from how the substrate vibrates. 4. There exist tiny excitations of the substrate, called time quanta. They are everywhere, all the time, propagating at the speed of light. 5. Reality has two layers. There is the underlying quantum stuff (call it Frame 1), and there are the definite outcomes we actually observe (Frame 2). A filter connects them. 6. Matter is, in a sense, the absence of substrate. Where the substrate field drops to zero, mass appears.7. The substrate has a particular shape — a Mexican-hat potential — that determines the physics of inflation, vacuum energy, and how the universe can be stable. 8. The substrate carries an extra electromagnetic-like force — a hidden gauge symmetry — with very specific properties. Time Quanta: The Tiny Observers Postulate 4 says that the substrate carries excitations called time quanta. These are like the photons of light, but they are excitations of the substrate field rather than the electromagnetic field. A few key facts about time quanta: • They are physically real, not a mathematical fiction • They exist everywhere, all the time • They propagate at the speed of light • They are unimaginably tiny — about one Planck length in size, which is something like a hundred-quintillionths of the diameter of a proton • They carry energy on the order of the Planck energy — extraordinarily large for one particle, but they are nearly massless when you average them. Where is the key insight: time quanta are constantly interacting with everything. Every atom, every electron, every macroscopic object is being constantly bombarded by time quanta from all directions. It is like rain. If you stand outside in a downpour, you are constantly being hit by water droplets. You feel them as pressure on your skin, as wetness in your hair. Each individual droplet is small, but the cumulative effect is large. Time quanta are like that, except they are everywhere, not just outside, and they are constant — there is no umbrella, no shelter from them. Every system in the universe is being continuously rained on by time quanta.
A case study of quantum mechanics is investigated in the framework of the philosophical opposition “mathematical model – reality”. All classical science obeys the postulate about the fundamental difference of model and reality, and thus distinguishing epistemology from ontology fundamentally. The theorems about the absence of hidden variables in quantum mechanics imply for it to be “complete” (versus Einstein’s opinion). That consistent completeness (unlike arithmetic to set theory in the foundations of mathematics in Gödel’s opinion) can be interpreted furthermore as the coincidence of model and reality. The paper discusses the option and fact of that coincidence it its base: the fundamental postulate formulated by Niels Bohr about what quantum mechanics studies (unlike all classical science). Quantum mechanics involves and develops further both identification and disjunctive distinction of the global space of the apparatus and the local space of the investigated quantum entity as complementary to each other. This results into the analogical complementarity of model and reality in quantum mechanics. The apparatus turns out to be both absolutely “transparent” and identically coinciding simultaneously with the reflected quantum reality. Thus, the coincidence of model and reality is postulated as necessary condition for cognition in quantum mechanics by Bohr’s postulate and further, embodied in its formalism of the separable complex Hilbert space, in turn, implying the theorems of the absence of hidden variables (or the equivalent to them “conservation of energy conservation” in quantum mechanics). What the apparatus and measured entity exchange cannot be energy (for the different exponents of energy), but quantum information (as a certain, unambiguously determined wave function) therefore a generalized law of conservation, from which the conservation of energy conservation is a corollary. Particularly, the local and global space (rigorously justified in the Standard model) share the complementarity isomorphic to that of model and reality in the foundation of quantum mechanics. On that background, one can think of the troubles of “quantum gravity” as fundamental, direct corollaries from the postulates of quantum mechanics. Gravity can be defined only as a relation or by a pair of non-orthogonal separable complex Hilbert space attachable whether to two “parts” or to a whole and its parts. On the contrary, all the three fundamental interactions in the Standard model are “flat” and only “properties”: they need only a single separable complex Hilbert space to be defined.
Chapter 4 deals with Quantum Mechanical (QM) phenomena. The first section describes the first attempts at quantization of energy, momentum, angular momentum, etc. We start with Plank's solution to the black-body problem, introducing the concept of photons: discrete packets of electromagnetic energy. We show how Plank's description of black-body radiation is perfectly fit by the cosmic microwave radiation, providing the strongest evidence for the Big-Bang at the origin of the Universe. We then describe Bohr's solution to the paradoxical stability of atoms, introducing quantization of angular momentum (or action) and correctly predicting the energy levels of the hydrogen atom. We show how Einstein used Plank's idea to explain the photo-electric effect (an effect exploited in CCD cameras and solar cells) and how he used Bohr's understanding of energy levels in atoms to provide an intuitive explanation of Plank's law. Einstein insight opened the way to the field of spectroscopy and the development of the laser. In the second section, following the lead of Dirac, we show that QM is equivalent to Linear Algebra in the space of complex functions (which describe the state of the system). We show that Schrödinger's equation is a natural consequence of that description, once the relation between energy and frequency established by Plank (for photons) and de Broglie (for particles) is taken into account. In the context of the chiral ammonia molecule we discuss the queerness of QM which describes physical systems as superposition of states (such as left and right chirality state of a molecule, dead and alive cat). We show that this queerness is nonetheless supported by experiments and is behind much of our technology: masers and lasers, atomic clocks, semiconductors (diodes, transistors, etc.). In the following section we introduce the representation of operators in QM (the equivalent of matrices in linear algebra): momentum, position, energy, etc. which correspond to measurements on the system. We show that the non-commutability of some operators (common with matrix operations) leads to Heisenberg uncertainty principle: the position and momentum of a particle cannot be determined with absolute precision. We discuss the solution of Schrödinger's equation for free particles demonstrating their equivalence with EM phenomena: particles undergo refraction and diffraction, exemplifying the particle/wave duality inherent to QM systems. We discuss QM tunneling and its use in the Scanning Tunneling Microscope. In the following section we study Dirac's equation: the successful attempt by Dirac to unify QM with Einstein's relativity, with the resulting prediction of anti-particles and spin. We then solve for the energy levels of electrons in the hydrogen atom (from Schrödinger's equation) and show that the existence of spin profoundly affects the behavior of electrons in an atom: they cannot share the same energy level, a rule known as Pauli's exclusion principle. Pauli's principle is central to the understanding of the chemical properties of atoms and fully explains Mendeleev's periodic table of the elements. In the next section we discuss along with two exactly soluble systems (diatomic rotational and vibrational levels), various approximations used to study systems (e.g. molecules) for which there are no analytical solutions. In particular, we introduce Pauling's variational approach, Hückel molecular orbital theory and time independent perturbation theory. We apply those approaches to determine the energy levels in alkenes, in multi-electron atoms and in systems under constant electric or magnetic field (such as in Magnetic Resonance Imaging). In the last section we discuss time dependent perturbation theory. We use it to establish the rules allowing for transitions between energy levels and revisit Einstein description of absorption/emission phenomena.
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.