Associative Space-Time Sedenions and Their Application in Relativistic Quantum Mechanics and Field Theory

We present an alternative sixteen-component hypercomplex scalar-vector values named “space-time sedenions”, generating associative noncommutative space-time Clifford algebra. The generalization of relativistic quantum mechanics and field theory equations based on sedenionic wave function and space-time operators is discussed.

New Approach to Synchronize General Relativity and Quantum Mechanics with Constant “K”-Resulting Dark Matter as a New Fundamental Force Particle

Planck scale plays a vital role in describing fundamental forces. Space time describes strength of fundamental force. In this paper, Einstein’s general relativity equation has been described in terms of contraction and expansion forces of space time. According to this, the space time with Planck diameter is a flat space time. This is the only diameter of space time that can be used as signal transformation in special relativity. This space time diameter defines the fundamental force which belongs to that space time. In quantum mechanics, this space time diameter is only the quantum of space which belongs to that particular fundamental force. Einstein’s general relativity equation and Planck parameters of quantum mechanics have been written in terms of equations containing a constant “K”, thus found a new equation for transformation of general relativity space time in to quantum space time. In this process of synchronization, there is a possibility of a new fundamental force between electromagnetic and gravitational forces with Planck length as its space time diameter. It is proposed that dark matter is that fundamental force carrying particle. By grand unification equation with space-time diameter, we found a coupling constant as per standard model “αs” for that fundamental force is 1.08 × 10-23. Its energy calculated as 113 MeV. A group of experimental scientists reported the energy of dark matter particle as 17 MeV. Thorough review may advance science further.

Zeno and the Wrong Understanding of Motion—A Philosophical-Mathematical Inquiry into the Concept of Finitude as a Peculiarity of Infinity

In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical at all. Zeno’s paradoxes indirectly prove that distances are not composed of extensionless points and, in general, that a higher dimension cannot be completely composed of lower ones. Conversely, lower dimensions can be understood as special cases of higher dimensions. To illustrate this approach, I consider Cantor’s only apparent proof that the real numbers are uncountable. However, his widely accepted indirect proof has the disadvantage that it depends on whether there is another way to make the real numbers countable. Cantor rightly assumes that there can be no smallest number between 0 and 1, and therefore no beginning of counting. For this reason he arbitrarily lists the real numbers in order to show with his diagonal method that this list can never be complete. The situation is different if we start with the largest number between 0 and 1 (0.999…) and use the method of an inverted triangle, which can be understood as a special fractal form. Here we can construct a vertical and a horizontal stratification with which it is actually possible to construct all real numbers between 0 and 1 without exception. Each column is infinite, and each number in that column is the starting point of a new triangle, while each row is finite. Even in a simple sine curve, we experience finiteness with respect to the y-axis and infinity with respect to the x-axis. The first parts of this article show that Zeno’s assumptions contradict the concept of motion as such, so it is not surprising that this misconstruction leads to contradictions. In the last part, I discuss Cantor’s diagonal method and explain the method of an inverted triangle that is internally structured like a fractal by repeating this inverted triangle at each column. The consequence is that we encounter two very different methods of counting. Vertically it is continuous, horizontally it is discrete. While Frege, Tarski, Cantor, Gödel and the Vienna Circle tried to derive the higher dimension from the lower, a procedure that always leads to new contradictions and antinomies (Tarski, Russell), I take the opposite approach here, in which I derive the lower dimension from the higher. This perspective seems to fail because Tarski, Russell, Wittgenstein, and especially the Vienna Circle have shown that the completeness of the absolute itself is logically contradictory. For this reason, we agree with Hegel in assuming that we can never fully comprehend the Absolute, but only its particular manifestations—otherwise we would be putting ourselves in the place of the Absolute, or even God. Nevertheless, we can understand the Absolute in its particular expressions, as I will show with the modest example of the triangle proof of the combined horizontal and vertical countability of the real numbers, which I developed in rejection of Cantor’s diagonal proof. .

The Singularity of the Big Bang Can Be Described in Greater Depth than the Limits of the Planck Time and Length

In this paper, we determine the frequency, energy and momentum of the primordial spherical wave at the birth of our universe, which are consistent with the fact that the total energy of our universe was created in the hot Big Bang. With this, we also indirectly demonstrate the consistency of previous works on the hypothesis of primary particles, by using their results. We obtain a hyper-high initial frequency of the spherical wave, which is not in contradiction with string theory.

On the Cosmic Evolution of the Quantum Vacuum Using Two Variable G Models and Winterberg’s Thesis

We work within a Winterberg framework where space, i.e., the vacuum, consists of a two component superfluid/super-solid made up of a vast assembly (sea) of positive and negative mass Planck particles, called planckions. These material particles interact indirectly, and have very strong restoring forces keeping them a finite distance apart from each other within their respective species. Because of their mass compensating effect, the vacuum appears massless, charge-less, without pressure, net energy density or entropy. In addition, we consider two varying G models, where G, is Newton’s constant, and G-1, increases with an increase in cosmological time. We argue that there are at least two competing models for the quantum vacuum within such a framework. The first follows a strict extension of Winterberg’s model. This leads to nonsensible results, if G increases, going back in cosmological time, as the length scale inherent in such a model will not scale properly. The second model introduces a different length scale, which does scale properly, but keeps the mass of the Planck particle as, ± the Planck mass. Moreover we establish a connection between ordinary matter, dark matter, and dark energy, where all three mass densities within the Friedman equation must be interpreted as residual vacuum energies, which only surface, once aggregate matter has formed, at relatively low CMB temperatures. The symmetry of the vacuum will be shown to be broken, because of the different scaling laws, beginning with the formation of elementary particles. Much like waves on an ocean where positive and negative planckion mass densities effectively cancel each other out and form a zero vacuum energy density/zero vacuum pressure surface, these positive mass densities are very small perturbations (anomalies) about the mean. This greatly alleviates, i.e., minimizes the cosmological constant problem, a long standing problem associated with the vacuum.

E-Infinity Dualities, Discontinuous Spacetimes, Xonic Quantum Physics and the Decisive Experiment

Using powerful concepts and tools borrowed from the seminal arsenal connecting physics fundamentals with esoteric set theoretical operations developed in recent years by Alexandria E-infinity theoretician M. S. El Naschie, this paper explores the deep implications of some of the dualities Dr El Naschie has identified and analyzed in his exposes, connecting them with our own Xonic Quantum Physics (XQP) which places dynamical action rather than spacetime and energy at the core of the System of the World.

The Meaning of Motions and Their Effects in Einstein’s Empty Space and in the Scenario of the Higgs Quantum Fluid Space

Motion is a ground-laying concept in physics. Its meaning however depends fundamentally on the assumptions about the nature of empty space. In Einstein’s theory of relativity (TR), no absolute references can be defined and only relative motions are relevant. This however makes it impossible to understand why the motion of matter obeys the principle of inertia and why there exist laws of motion. The Higgs theory introduces radical changes in the current view about the nature of empty space. It introduces the idea that space is filled up by a real and very powerful quantum fluid medium, giving mass to the elementary particles by the Higgs mechanism. This Higgs Quantum Space (HQS) is locally an absolute reference for rest and for motions. It not only recovers an intrinsic meaning for motions, however literally governs the inertial motion of matter-energy. In this new scenario, the velocity of light is fixed with respect to the local HQS and velocity of matter with respect to the local HQS and not relative velocities are responsible for all the effects of motion. The Higgs mechanism is too responsible for the gravitational dynamics;because it is mass that creates the gravitational fields. Actually several clear experimental observations demonstrate that the HQS is moving round the sun consistently with the planetary motions. The present work therefore replaces Einstein’s spacetime curvature by a Keplerian velocity field of the HQS. This velocity field creates the ingenious outside-inside centrifuge mechanism of gravity. It also causes all the observed effects of the gravitational fields on light and on clocks.

Space, Time, and the Creation of Universe

The understanding about the creation of our universe is explored in many philosophies, natural sciences, religions, ideologies, traditions, and disciplines. Current natural science cannot answer this question at the fundamental level. In this work, we combine the ancient Chinese Tao wisdom about the creation with quantum physics. We propose that everything comes from the emptiness. Our universe is manifested from the emptiness through two pairs of duality measurements： space and time duality pair and inclusion and exclusion duality pair. From this understanding, we are able to derive one mathematic formula describing our universe. It also yields a new metaphysical approach to derive and interpret string theory as well as produce more testable predictions from string theory. This work gives a new way to understand and mathematically describe how our universe is created and evolved. It provides another way to comprehend the meaning and function of space and time. It indicates that our universe is manifested from the emptiness through human actions. Space and time is a pair of duality action and codes that help manifest our universe. It provides answer to an important philosophical question about whether and why we can understand and mathematically describe our universe.

Developments of Space-Time, Complete Special Relativity, and Superluminal Entangled Communication

Time and space are two very important basic concepts in philosophy and nature.In special relativity we proved that there are necessarily two symmetrical topological structures separated by the light-cone,which includes the generalized Lorentz transformation(GLT)for the spacelike interval,in which phase velocity is superluminal.Based on quantum entanglement as new fifth interaction,we research a simple superluminal entangled communication,whose key is to establish two mutually entangled particles or devices Alice(A)and Bob(B).We observe and control the information of A position,and then can know the corresponding results of the other B.This is not to send directly information each other.It may be superluminal,and should agree and test GLT.Moreover,we research some new possible developments of time and space,such as the fractal dimension extended to the complex dimension,the higher dimensional time,and the arrow of time.A generalized Noether’s theorem is proposed.In quantum theory,we search the higher dimensional complex space in supersymmetry,and the space-time operators.

Infinite Freedom of Space-Time for Zero-Energy-Entity in Quantum Mechanics

Zero-energy state is investigated by taking infinitesimal energy and observing its uncertainty in space-time, adopting quantum mechanics. In this paper, the uncertainty in conventional quantum mechanics is found to be interpreted as freedom in space-time, which results in possibility of time travel and space transition of the zero-energy state, which could be information or mind. The wave function of a physical system composed of multiple particles or wave-packets is examined and found that it can be arbitrarily changed by grouping by observers. It leads to an idea that even infinitesimal energy or wave-packets in a heavy physical system may separately exist and it has the infinite freedom of space-time.

Emergence of Space-Time and Gravitation

In relativistic quantum mechanics, elementary particles are described by irreducible unitary representations of the Poincaré group. The same applies to the center-of-mass kinematics of a multi-particle system that is not subject to external forces. As shown in a previous article, for spin-1/2 particles, irreducibility leads to a correlation between the particles that has the structure of the electromagnetic interaction, as described by the perturbation algorithm of quantum electrodynamics. The present article examines the consequences of irreducibility for a multi-particle system of spinless particles. In this case, irreducibility causes a gravitational force, which in the classical limit is described by the field equations of conformal gravity. The strength of this force has the same order of magnitude as the strength of the empirical gravitational force.

The Space Structure, Force Fields, and Dark Matter

It is proposed that the digital space structure consists of attachment space (denoted as 1) for rest mass and detachment space (denoted as 0) for kinetic energy. Attachment space attaches to object permanently with zero speed, and detachment space detaches from the object at the speed of light. The combination of attachment space and detachment space brings about the three structures: binary lattice space, miscible space, and binary partition space. Binary lattice space, (1 0)n, consists of repetitive units of alternative attachment space and detachment space. In miscible space, attachment space is miscible to detachment space without separation. Binary partition space, (1)n(0)n, consists of separated continuous phases of attachment space and detachment space. Binary lattice space, miscible space, and binary partition space constitute quantum mechanics, special relativity, and the extreme force fields, respectively. Through the detachment space, a higher dimensional particle in attachment space is sliced into infinitely surrounding a lower dimensional core attachment space, resulting in a particle surrounding by gauge field in the form of binary lattice space. The 10d particle can be sliced into 9d, 8d, 7d, 6d, 5d, and 4d particles equally by mass, corresponding to baryonic particle as 4d and dark matter as other 5 particles, so the ratio between baryonic matter and dark matter is 1 to 5, in agreement with the observed ratio. At extreme conditions, such as extremely low temperature, the gauge force field in the form of binary lattice space is transformed into the extreme force field in the form of binary partition space to explain extreme phenomena, such as superconductivity.

Lower Bounds on Negative Energy Densities for the Scalar Field in Flat Spacetime

We obtain a lower bound on the spacetime-weighted average of the energy density for the scalar field in four-dimensional flat spacetime. The bound takes the form of a quantum inequality. The inequality does not rely on the quantum state and its form is only related to the weights, namely the spacetime sampling functions which are assumed to be smooth, positive and compactly supported. It is found that the inequality is just equal to the temporal quantum energy inequality. When the characteristic length of the temporal sampling function tends to zero, the lower bound becomes divergent. This is consistent with the fact that the spatial restriction on negative energy density does not exist in four-dimensional spacetime.

Quantum Dynamics via a Hidden Liouville Space

The traditional simulations may occasionally turn out to be challenging for the quantum dynamics, particularly those governed by the nonlinear Hamiltonians. In this work, we introduce a nonstandard iterative technique where the Liouville space is briefly expanded with an additional (virtual) space only within ultrashort subintervals. This tremendously reduces the cost of time-consuming calculations. We implement our technique for an example of a charged particle in both harmonic and anharmonic potentials. The temporal evolutions of the probability for the particle being in the ground state are obtained numerically and compared to the analytical solutions. We further discuss the physics insight of this technique based on a thought-experiment. Successive processes intrinsically “hitchhiking” via virtual space in discrete ultrashort time duration, are the hallmark of our technique. We believe that this technique has potential for solving numerous problems which often pose a challenge when using the traditional approach based on time-ordered exponentials.

New approach for obtaining the time-evolution law of a chaotic light field in a damping gaining-process

A new approach for studying the time-evolution law of a chaotic light field in a damping-gaining coexisting process is presented. The new differential equation for determining the parameter of the density operator p（t） is derived and the solution of f for the damping and gaining processes are studied separately. Our approach is direct and the result is concise since it is not necessary for us to know the Kraus operators in advance.

A More Accurate Determination of the Magnitude of Cosmic Inflation in the Big Bang Model

According to our hypothesis, at the very beginning of the Big Bang, a hyperenergetic spherical wave was created. We described its characteristics in our previous work, and the present work is based on them. Logically, we saw that in cosmic inflation the frequency of such a wave would decrease sharply. Based on the temperature that prevailed immediately after inflation according to the hot Big Bang model, we determined a measure of the size of the inflation in this model, in accordance with our hypothesis.

Interference Phase of Neutrino Oscillation in Schwarzschild-de Sitter Space-Time

We study the mass neutrino interference phase in Schwarzschild-de Sitter space time along the null trajectory and the geodesic line and obtain the effects of cosmological constant A on the neutrino oscillation. Firstly, in the high energy limit, we find that the phase along the geodesic keeps the double of that along the null. Secondly, we calculate the phase on the condition that the cosmological constant, A, is a small quantity. The correction of the phase due to A is given. Finally, we calculate the proper oscillation length in Schwarzschild-de Sitter space-time, which increases because of the existence of A, compared with the result in Schwarzschild space-time. All of our results can be reduced to those in Schwarzschild space-time as A approaches to zero.

Towards Understanding the Origins of Quantum Indeterminism and Non-Local Quantum Jumps

By Invoking symmetry principle, we present a self-consistent interpretation of the existing quantum theory which explains why our world is fundamentally indeterministic and that why non-local quantum jumps occur. Symmetry principle dictates that the concept of probability is more fundamental than the notion of the wave function in that the former can be derived directly from symmetries rather than have to be assumed as an additional axiom. It is argued that the notion of quantum probability and that of the wavefunction are intimately connected.

Space-Time Properties as Quantum Effects. Restrictions Imposed by Grothendieck’s Scheme Theory

In this paper we consider properties of the four-dimensional space-time manifold M caused by the proposition that, according to the scheme theory, the manifold M is locally isomorphic to the spectrum of the algebra A, M ≅Spec (A), where A is the commutative algebra of distributions of quantum-field densities. Points of the manifold M are defined as maximal ideals of density distributions. In order to determine the algebra A, it is necessary to define multiplication on densities and to eliminate those densities, which cannot be multiplied. This leads to essential restrictions imposed on densities and on space-time properties. It is found that the only possible case, when the commutative algebra A exists, is the case, when the quantum fields are in the space-time manifold M with the structure group SO (3, 1) (Lorentz group). The algebra A consists of distributions of densities with singularities in the closed future light cone subset. On account of the local isomorphism M ≅Spec (A) , the quantum fields exist only in the space-time manifold with the one-dimensional arrow of time. In the fermion sector the restrictions caused by the possibility to define the multiplication on the densities of spinor fields can explain the chirality violation. It is found that for bosons in the Higgs sector the charge conjugation symmetry violation on the densities of states can be observed. This symmetry violation can explain the matter-antimatter imbalance. It is found that in theoretical models with non-abelian gauge fields instanton distributions are impossible and tunneling effects between different topological vacua | n> do not occur. Diagram expansion with respect to the -algebra variables is considered.

The Unified Field

This is a Unified Field description based on the holographic Time Dilation Cosmology, TDC, model, which is an eternal continuum evolving forward in the forward direction of time, at the speed of light, c, at an invariant 1 s/s rate of time. This is the Fundamental Direction of Evolution, FDE. There is also an evolution down time dilation gradients, the Gravitational Direction of Evolution, GDE. These evolutions are gravity, which is the evolutionary force in time. Gravitational velocities are compensation for the difference in the rate of time, dRt, in a dilation field, and the dRtis equal to the compensatory velocity’s percentage of c, and is a measure of the force in time inducing the velocity. In applied force induced velocities, the dRt is a measure of the resistance in time to the induced velocity, which might be called “anti-gravity” or “negative gravity”. The two effects keep the continuum uniformly evolving forward at c. It is demonstrated that gravity is already a part of the electromagnetic field equations in way of the dRt element contained in the TDC velocity formula. Einstein’s energy formula is defined as a velocity formula and a modified version is used for charged elementary particle solutions. A time dilation-based derivation of the Lorentz force ties gravity directly to the electromagnetic field proving the unified field of gravity and the EMF. It is noted how we could possibly create gravity drives. This is followed by a discussion of black holes, proving supermassive objects, like massive black hole singularities, are impossible, and that black holes are massless Magnetospheric Eternally Collapsing Objects (MECOs) that are vortices in spacetime. .