The Symmetries of Quantum and Classical Information. The Ressurected “Ether" of Quantum Information

The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) “discrete reference frame” to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the “ether” from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or “quantum mechanics and information”). The identification of entanglement and gravity can be considered also as a ‘byproduct” implied by the transition from the smooth “ether of special and general relativity’ to the “flat” ether of quantum mechanics and information. The qubit ether is out of the “temporal screen” in general and is depicted on it as both matter and energy, both dark and visible.

PDE boundary conditions that eliminate quantum weirdness: a mathematical game inspired by Kurt Gödel and Alan Turing

Although boundary condition problems in quantum mathematics (QM) are well known, no one ever used boundary conditions technology to abolish quantum weirdness. We employ boundary conditions to build a mathematical game that is fun to learn, and by using it you will discover that quantum weirdness evaporates and vanishes. Our clever game is so designed that you can solve the boundary condition problems for a single point if-and-only-if you also solve the “weirdness” problem for all of quantum mathematics. Our approach differs radically from Dirichlet, Neumann, Robin, or Wolfram Alpha. We define domain Ω in one-dimension, on which a partial differential equation (PDE) is defined. Point α on ∂Ω is the location of a boundary condition game that involves an off-center bi-directional wave solution called Æ, an “elementary wave.” Study of this unusual, complex wave is called the Theory of Elementary Waves (TEW). We are inspired by Kurt Gödel and Alan Turing who built mathematical games that demonstrated that axiomatization of all mathematics was impossible. In our machine quantum weirdness vanishes if understood from the perspective of a single point α, because that pinpoint teaches us that nature is organized differently than we expect.

Four-Quadrant Riemann Problem for a 2×2 System II

In previous work, we considered a four-quadrant Riemann problem for a 2×2 hyperbolic system in which delta shock appears at the initial discontinuity without assuming that each jump of the initial data projects exactly one plane elementary wave. In this paper, we consider the case that does not involve a delta shock at the initial discontinuity. We classified 18 topologically distinct solutions and constructed analytic and numerical solutions for each case. The constructed analytic solutions show the rich structure of wave interactions in the Riemann problem, which coincide with the computed numerical solutions.

Solution of the Riemann problem for an ideal polytropic dusty gas in magnetogasdynamics

The main aim of this paper is, to obtain the analytical solution of the Riemann problem for a quasi-linear system of equations, which describe the one-dimensional unsteady flow of an ideal polytropic dusty gas in magnetogasdynamics without any restriction on the initial data. By using the Rankine-Hugoniot (R-H) and Lax conditions, the explicit expressions of elementary wave solutions (i. e., shock waves, simple waves and contact discontinuities) are derived. In the flow field, the velocity and density distributions for the compressive and rarefaction waves are discussed and shown graphically. It is also shown how the presence of small solid particles and magnetic field affect the velocity and density across the elementary waves. It is an interesting fact about this study that the results obtained for the Riemann problem are in closed form.

A Tiny, Counterintuitive Change to the Mathematics of the Schrodinger Wave Packet and Quantum ElectroDynamics Could Vastly Simplify How We View Nature

This article proposes that an unexpected approach to the mathematics of a Schro ̋dinger wave packet and Quantum Electro-Dynamics (QED), could vastly simplify how we perceive the world around us. It could get rid of most if not all quantum weirdness. Schro ̋dinger’s cat would be gone. Even things that we thought were unquestionably true about the quantum world would change. For example, the double slit experiment would no longer support wave particle duality. Experiments that appeared to say that entangled particles can communicate instantaneously over great distances, would no longer say that. Although the tiny mathematical change is counterintuitive, Occam’s razor dictates that we consider it because it simplifies how we view Nature in such a pervasive way. The change in question is to view a Schro ̋dinger wave packet as part of a larger Elementary Wave traveling in the opposite direction. It is known in quantum mechanics that the same wave can travel in two countervailing directions simultaneously. Equivalent changes would be made to QED and Quantum Field Theory. It is known in QM that there are zero energy waves: for example, the Schro ̋dinger wave carries amplitudes but not energy.

Spectral Particularities of Femtosecond Optical Pulses Propagating in Dispersive Medium

We have proposed a refined solution of the wave equation for a dispersive medium without restriction on the duration of an optical pulse. We apply a series of elementary wave packages (EWP) to the representation of superwideband signals (fs pulse). We investigate peculiarities of the propagation of waves with low and high frequencies through the one-resonance medium. We show the existence of a “precursor” for fs optical pulses. We propose a formula for the optical signal velocity (OSV). Its value does not exceed the light velocity in vacuum. We have designed a method of adaptation of EWP-pulses to time-domain spectroscopy.