Motion and Special Relativity in Complex Spaces

A natural extension of the Lorentz transformation to its complex version was constructed together with a parallel extension of the Minkowski M4 model for special relativity (SR) to complex C4 space-time. As the [signed] absolute values of complex coordinates of the underlying motion’s characterization in C4 one obtains a Newtonian-like type of motion whereas as the real parts of the complex motion’s description and of the complex Lorentz transformation, all the SR theory as modeled by M4 real space-time can be recovered. This means all the SR theory is preserved in the real subspace M4 of the space-time C4 while becoming simpler and clearer in the new complex model’s framework. Since velocities in the complex model can be determined geometrically, with no primary use of time, time turns out to be definable within the equivalent theory of the reduced complex C4 model to the C3 “para-space” model. That procedure allows us to separate time from the (para)space and consider all the SR theory as a theory of C3 alone. On the other hand, the complex time defined within the C3 theory is interpreted and modeled by the single separate C1 complex plane. The possibility for application of the C3 model to quantum mechanics is suggested. As such, the model C3 seems to have unifying abilities for application to different physical theories.

Special Relativity’s “Newtonization” in Complex “Para-Space”: The Two Theories Equivalence Question

Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The actual aim, however, is an additional analysis of the physical and para-physical phenomena’ behavior as we formally transport observable mechanical phenomena [motion] to non-real interior of the complex domain. As it turns out, such procedure, when properly set, corresponds to transition from relativistic to more classic (or, possibly, just classic) kind of the motion. This procedure, we call the “Newtonization of relativistic physical quantities and phenomena”, first of all, includes the mechanical motion’s characteristics in the C3. The algebraic structure of vector spaces was imposed and analyzed on both: the set of all relativistic velocities and on the set of the corresponding to them “Galilean” velocities. The key point of the analysis is realization that, as a matter of fact, the relativistic theory and the classical are equivalent at least as for the kinematics. This conclusion follows the fact that the two defined structures of topological vector spaces i.e., the structure imposed on sets of all relativistic velocities and the structure on set of all “Galilean” velocities, are both diffeomorphic in their topological parts and are isomorphic as the vector spaces. As for the relativistic theory, the two approaches: the hyperbolic (“classical” SR) with its four-vector formalism and Euclidean, where SR is modeled by the complex para-space C3, were analyzed and compared.

地质样品Sr-Pb柱分离的可行性研究

传统的Sr-Pb同位素分析一般需要Sr和Pb单独过柱,实验流程繁琐且费时。为优化实验流程、节约实验成本和提高实验效率,本文利用1 mL的Sr特效树脂分离柱探讨了Sr-Pb柱分离的可行性。实验结果表明,Sr-Pb柱分离法具有较低的化学全流程空白(Sr<0.3 ng和Pb<1 ng)和较高的Sr-Pb回收率(>90%),且能高效分离Rb和Sr,适合不同Rb/Sr值样品的高精度同位素组成分析。不同岩性的USGS岩石标样的Sr-Pb同位素组成在误差范围内均与推荐值一致,表明本实验方法稳定可靠。

On the Existence of a Minimum Universal Speed of Physical Transmissions Associated with Matter Wave in Special Relativity

In this work, we show that it is possible to establish coordinate transformations between inertial reference frames in the theory of special relativity with a minimum universal speed of physical transmissions. The established coordinate transformations, referred to as modified Lorentz transformations because they have almost identical form to the Lorentz transformations, also comply with the requirement of invariance of the Minkowski line element. Particularly, the minimum universal speed can be associated with the phase speed of de Broglie matter wave. As application, we also discuss the possibility to formulate relativistic classical and quantum mechanics for the special relativity associated with the modified Lorentz transformations, which describes physical processes that represent an expansion or a collapsing of massive quantum particles.

Does QM Embedded in 5th Dimensional Embedding Allow for Classical Black Hole Ideas Only in Early Universe, Whereas Corda Special Relativity Plus QM May Eliminate Event Horizons for Black Holes after Big Bang?

We first look at the possibility that the ideas of event horizons for black holes may have their application only in early universe conditions whereas Corda’s ground breaking work rejecting event horizons may be due to the formation of quantum mechanics free of an embedding in 5 dimensions allowing for a simpler more direct approach, which rejects the idea of a firewall. First, we present the idea of classical black hole physics applied only once as for the early universe, whereas in such a setting, there may be a way to present NLED and structure formation due to an initial entropy approach as outlined. Then the ideas of Corda’s breakthrough are presented for the reasons he illuminated in his recent work, due to QM being fully formed separate from higher dimensional embedding after the initial evolution of the universe.

Einstein’s Concept of Clock Synchronization Conflicts with the Second Relativity Postulate

Einstein defined clock synchronization whenever photon pulses with timetags traverse a fixed distance between two clocks with equal time spans ineither direction. Using the second relativity postulate, he found clocksmounted on a rod uniformly moving parallel with the rod’s length cannot besynchronized, but clocks attached to a stationary rod can. He dismissed thisdiscrepancy by claiming simultaneity and clock synchronization were not commonbetween inertial frames, but this paper proves with both Galilean and Lorentztransformations that simultaneity and clock synchronization are preservedbetween inertial frames. His derivation means moving clocks can never besynchronized in a “resting” inertial frame. Ultraprecise atomic clocks intimekeeping labs daily contradict his results. No algebraic error occurred inEinstein’s derivations. The two cases of clocksattached to a rod reveal three major conflicts with the currentsecond postulate. The net velocity between a photon source and detector plusthe “universal” velocity c is mathematically equivalent toEinstein’s clock synchronization method. As the ultraprecise timekeepingcommunity daily synchronizes atomic clocks on the moving Earth withultraprecise time uncertainty well below Einstein’s lowest limit ofsynchronization, the theoretical resolution of the apparent conflict isaccomplished by expanding the second relativity postulate to incorporate thenet velocity between the photon source and detector with the emitted velocity c as components of the total velocity c. This means the magnitudeof the total photon velocity can exceed the speed limit (299792458 m/s) set by the standard velocity c. .

Hamiltonian Formalism of de-Sitter Invariant Special Relativity

The Lagrangian of Einstein's special relativity with universal parameter c(SR_c)is invariant under Poincarétransformation,which preserves Lorentz metric η_μν.The SR_c has been extended to be one which is invariant underde Sitter transformation that preserves so-called Beltrami metric B_(μv).There are two universal parameters,c and R,inthis Special Relativity(denoted as SR_(cR)).The Lagrangian-Hamiltonian formulism of SR_(cR) is formulated in this paper.The canonic energy,canonic momenta,and 10 Noether charges corresponding to the space-time's,de Sitter symmetryare derived.The canonical quantization of the mechanics for SR_(CR)-free particle is performed.The physics related to itis discussed.

Three Kinds of Special Relativity via Inverse Wick Rotation

Since the special relativity can be viewed as the physics in an inverse Wick rotation of four-dimensional （4D） Euclid space, which is at almost equal footing with the 4D Riemann/Lobachevski space, there should be important physics in the inverse Wick rotation of 4D Riemann/Lobachevski space. Thus, there are three kinds of special relativity in de Sitter（dS）/Minkowski/anti-de Sitter（AdS） space at almost equal footing, respectively. There is an instanton tunnelling scenario in the Riemann-de Sitter case that may explain why A be positive and link with the multiverse.

Neutrino speed can exceed the speed of light within the frame work of the generlized special relativity and savckas model

The speed of Neutrino particles is shown to be greater than that of light as shown by the OPERA neutrino experiment at the underground Gran Sasso Laboratory. The result of this experiment can be explained within the framework of the Generalized Special Relativity and Savickas model.

Diagrammatic Approach for Investigating Two Dimensional Elastic Collisions in Momentum Space II: Special Relativity

The diagrammatic approach to the collision problems in Newtonian mechanics is useful. We show in this article that the same technique can be applied to the case of the special relativity. The two circles play an important role in Newtonian mechanics, while in the special relativity, we need one circle and one ellipse. The circle shows the collision in the center-of-mass system. And the ellipse shows the collision in the laboratory system. These two figures give all information on two dimensional elastic collisions in the special relativity.

Ohm’s Law Refutes Current Version of the Special Theory of Relativity

It is shown that Ohm’s law is not only the main electrical engineering law, but also a generally scientific worldview law of the extreme significance, as in the interpretation of Steinmetz it proves physical reality of imaginary numbers theoretically and experimentally in the most indisputable way. Thus, it refutes the principle of light speed non-exceedance, which is fundamental in the special theory of relativity. Moreover, unlike the MINOS and OPERA experiments recognized by physical com-munity as not enough reliable, which were conducted for the same purpose, alternative experiments were performed during the research of oscillation processes in linear electric circuits. Therefore, they are absolutely reliable and conclusive as can be repeated and verified in any electrical engineering laboratory. The principle of phy-sical reality of imaginary numbers proven by the electrical engineering experiments is generally scientific, since mathematics is the universal language of the exact sciences. Therefore, all scientific theories and hypotheses in quantum mechanics, relativity theory, geo-physics, cosmology, optics, radio electronics and other sciences should be adjusted accordingly, given the principle of physical reality of imaginary numbers. There is an example of how this can be done in the special theory of relativity and astrophysics. This approach allowed explanation of dark matter and dark energy, which correspond to the invisible parallel universes existing in extra dimensions.

From the Complete Yang Model to Snyder＇s Model, de Sitter Special Relativity and Their Duality

By means of the Dirac procedure, we re-examine Yang＇s quantized space-time model, its relation to Snyder＇s model, the dS special relativity and their UV IR duality. Starting from a dimensionless dS3-space in a （5＋1）- dimensional Mink-space a complete Yang model at both classical and quantum level can be presented and there really exists Snyder＇s model, the dS special relativity and the duality.

From De Sitter Special Relativity and Snyder's Model to Complete Yang Model

The de Sitter special relativity on the Beltrami-de Sitter-spacetime and Snyder＇s model in the momentum space can be combined together with an IR-UV duality to get the complete Yang model at both classical and quantum levels, which are related by the proposed Killing quantization. It is actually a special relativity based on the principle of relativity of three universal constants （c, ρp, R）.

Critical Comments on the Paper “On the Logical Inconsistency of the Special Theory of Relativity”

Special Relativity Theory is more than 110 years aged and during this period it was elaborated until minuscule details. However, there might be some logically deduced discrepancies, which demand a scrupulous study. Nonetheless, every search for inherent contradictions is an uphill task. The author of the considered paper proposed a situation with two series of synchronized clocks. Each series is at rest in its own frame of reference, but one of them is deemed to be stationary and other is moving with a constant relative velocity. The author believes this situation to be contradictable. But really, the suitable mathematical analysis proves that it is none other than a consequence of neglecting the basic tenets of the theory.

Reply to “Critical Comments on the Paper ‘On the Logical Inconsistency of the Special Theory of Relativity’”

It has been critically argued by V. A. Leus (Sobolev Institute of Mathematics, Novosibirsk, Russia) that in my proof that Einstein’s Special Theory of Relativity is logically inconsistent and therefore false, I violated the basic tenets of Special Relativity and foisted an alternative theory upon Einstein’s. A careful study of the critical analysis reveals however a failure to address the key arguments I adduced to prove Special Relativity logically inconsistent, and a concomitant invocation of Einstein’s theory to try to argue that my analysis is incorrect because it does not concur with Einstein. There is therefore no proof advanced of any alleged error in my analysis. In my paper I did not introduce an alternative theory. The aforementioned critical paper affords opportunity in rebuttal to amplify the invalidity of A. Einstein’s tacit assumption, in constructing the Special Theory of Relativity, that systems of clock-synchronised stationary observers consistent with Lorentz Transformation can be mathematically constructed. Since such systems of observers have in fact no mathematical existence the Special Theory of Relativity is logically inconsistent. It is therefore invalid. The consequences for physics, astronomy, and cosmology, are significant.

Analysis of a Stochastic Emission Theory Regarding Its Ability to Explain the Effects of Special Relativity

In this article, we investigate the physical consequences that would result if electromagnetic field quanta were emitted at random speeds by a source and if the receiver could only perceive the fraction of the quantum field that is slower than the speed of light in its individual rest frame. The analysis shows that this plausible hypothesis eliminates the weak points of conventional emission theories and that both postulates of special relativity are fulfilled. Furthermore, the results demonstrate that this theory can explain numerous experiments that are usually interpreted using different aspects of special relativity. However, the resulting quantum field theory is not equivalent to the special theory of relativity and requires neither spacetime nor Lorentz transformation. Furthermore, this approach offers a starting point for interpreting quantum effects and effects that contradict the special theory of relativity.

The Modification of Special Relativity

In this paper, the phenomenon of light velocity invariance is analyzed by using a new etheric view, and the physical mechanism of light velocity invariance is given, the principle of constancy of light velocity and the principle of special relativity are modified, and the Lorentz transformation is deduced by using these two modified principles. The relationship between mass and speed, the relationship between time and speed, and the relationship between length and speed are reanalyzed, and physical explanations different from the Special Relativity are given. Experiments for verification of the new theory are designed and presented. Experiment 1: Verify that the kinetic energy of a particle is only related to the speed of the particle relative to the ether, independent of the observer’s motion. Experiment 2: Verify that magnetic field is produced by electric charge’s motion relative to ether, and is independent of the observer. Experiment 3: Redoing the Michelson-Morley experiment on the space station to prove the existence of the ether. Experiment 4: Simulation of the generation and reversal of the Earth’s magnetic field, thus proving that the magnetic field is generated by the relative motion of the electric charge to the ether. Experiment 5: Simulate the formation of the natural iron meteorites and show that the atom becomes smaller with the increase of the etheric density of the space. Experiment 6: Aberrations contrast experiment to prove that for the observers on Earth, according to the theory of this paper, stars have aberration but the light sources on Earth have no aberration;according to the theory of special relativity, there are aberrations for both the stars and the light sources on Earth.

Determination of Photon and Elementary Particles Rest Masses Using Maxwell’s Equations and Generalized Potential Dependent Special Relativity

The nature and origin of the photon and elementary rest masses are some of the challeng-ing problems that physics face. The approaches used to solve these problems are complex and time-consuming. Specifically, the photon rest mass pays attention to theoretical physi-cists. Many experimental works show that the photon rest mass is non zero. This problem can be solved using generalized potential dependent special relativity, which has been de-rived using simple arguments, and Maxwell’s equations, besides the conventional Einstein energy-momentum relation. The results obtained show that the rest mass of photons and elementary particles are strongly dependent on the vacuum energy and a universal con-stant. This result conforms with the models that predict time decaying vacuum energy as-sociated with production of smaller rest mass particles followed by larger masses. The two potential dependent mass expressions conform with the cosmological models that suggest the photon is generated first by assuming the universe consisting of total constant vacuum with decaying cosmological part and mass generating part. Using Maxwell’s equations, beside plank and De Broglie hypothesis together with special relativity energy-momentum relation the photon rest mass is estimated. It was shown that the photon rest mass is ex-tremely small compared to the electron mass.

About the Conflicts between the Unitary Quantum Theory and the Special and General Relativity Theories

The authors discuss contradictions between the principal branches of the modern physical picture of the universe. Space and time have been shown in the Unitary Quantum Theory (UQT) not to be connected one with the other, unlike in the Special Theory of Relativity. In UQT, time becomes Newtonian again, and the growth of the particle’s mass with growing speed proceeds from other considerations of physics. Unlike the quantum theory, the modern gravitation theory (the general theory of relativity) is not confirmed by experiments and needs to be considerably revised.

The Use of The Special Theory of Relativity for the Meissner Effect in a Superconductor

The electromagnetic waves are considered in this article as the mediators of interaction in the Meissner Effect or the diamagnetic property of the superconductors. During the cooling of a superconductor electromagnetic waves may be released when the electrons occupy lower states of the energy. These electromagnetic waves may combine in circularly, elliptically and spherically rotating way, being called in this article the rounded electromagnetic fields. The application of the Lorentz transformation of the Special Theory of Relativity to the magnetic vectors of the mediating electromagnetic fields implies the magnetic orthogoniopedic effect inside the bulk of a superconductor in the Meissner Effect.