Reduced Compton Wavelength Research Articles

Exceedingly Small Quantum of Time Kshana Explains the Structure of an Electron

In this study, an effort is made to find the attributes of an electron based on Maharishi Vyasa’s definition of kshana or moment. Kshana or moment is a very small quanta of time defined by Maharishi Vyasa. It is the time taken by an elementary particle to change the direction from east to north. It is found that the value of a kshana in the case of pair production is approximately 2 × 10-21 sec, and the radius of the spinning electron or positron is equal to the reduced Compton wavelength. The mass of the electron is equal to the codata recommended value of electron mass and time required in pair production is about four kshanas equal to spinning period of an electron. During validation, in case of the photoelectric effect, spectral series of hydrogen atoms, Compton scattering, and the statistical concept of motion of electron, the value of the number of kshanas in a second is the same as that found in pair production.

Acceleration in quantum mechanics and electric charge quantization

In this study, we have discussed the implications of acceleration in quantum mechanics by means of a generalized derivative operator (GDO). A new Schrödinger equation is obtained which depends on the reduced Compton wavelength of the particle. We have discussed its implications in quantum mechanics for different types of potentials mainly the infinite wall potential, the gravitational linear field potential, the Cornell potential and the Coulomb repulsive potential. The corresponding wave functions and discrete energies are modified and differ from the results obtained in the conventional formalism. The major results obtained concerned the large improvement of the ground energy of the electron subject to the gravitational acceleration in addition to Cornell potential and the emergence of quantized electric charge in the theory without including Dirac monopoles or using gauge theories.

An Alternative Model of Proton and Neutron

Based on a model of fermions which implies a model of photons, a model of the neutron is constructed by merging two photons of equal energy propagating in opposite directions. The fermion model is outlined, and the merging of two photons is described in detail. The radius of the neutron obtained in this way is Rn = 0.84008… fm. This value is four times the reduced Compton wavelength of the neutron. Assuming the same model for the proton, one obtains a value of Rp = 0.84123… fm, which agrees with the most recent experimental value for the charge radius of the proton within the given limits of error. The neutral charge of the neutron is reproduced, and the positive charge of the proton follows within the model, if the proton is formed via the anti-neutron by losing one electron. S = ±ħ/2, and zero dipole moment, is also reproduced for proton and neutron. Further, a value of the magnetic moment of the neutron of μ= &minus2.00μN (μN: nuclear magnetic moment), and of the proton of μ = 2.666… μN is predicted. The deviation by ca. 5% from the recommended respective values of (&minus1.9130μn), and (2.793μn) is ascribed to the (g-2)-anomaly. Finally, the relation of the model with the established description of the nucleons in terms of three quarks bound by gluons is shortly discussed.

Magnetic monopole mass from fundamental lengths

With an assumption of n = 2 in the Dirac quantization condition,when the sequence comprised of the Bohr radius, reduced Compton wavelength and classical electron radius is extended and matched with its velocity sequence, these fundamental lengths are mirrored with a corresponding set of fundamental monopole lengths with the speed of light as the axis ofsymmetry. Monopole charge is g = 137 ecand mass is found to be 1 . 45 × 10- 3 eV / c2 . This result may fit with the extended relativity (tachyon) theory of Recami with a modification of the proposed charge quantization and electromagnetic coupling constant.

The ultimate limits of the relativistic rocket equation. The Planck photon rocket

In this paper we look at the ultimate limits of a photon propulsion rocket. The maximum velocity for a photon propulsion rocket is just below the speed of light and is a function of the reduced Compton wavelength of the heaviest subatomic particles in the rocket. We are basically combining the relativistic rocket equation with Haug's new insight on the maximum velocity for anything with rest mass.An interesting new finding is that in order to accelerate any subatomic “fundamental” particle to its maximum velocity, the particle rocket basically needs two Planck masses of initial load. This might sound illogical until one understands that subatomic particles with different masses have different maximum velocities. This can be generalized to large rockets and gives us the maximum theoretical velocity of a fully-efficient and ideal rocket. Further, no additional fuel is needed to accelerate a Planck mass particle to its maximum velocity; this also might sound absurd, but it has a very simple and logical solution that is explained in this paper.

Zitterbewegung and the Electron

Starting from a statistical model of the electron, which explains spin and spin measurements in terms of a probability density distribution resulting from a rapidly changing angular momentum during an extended Zitterbewegung, a light-like model of electron and Fermions is formulated. This model describes individual particles in terms of paths of a moving quantum. It is shown that this description allows one to reproduce observable properties as path-averages over a period of the fast extended Zitterbewegung in elementary calculations. The general topology of the paths may be described as a helical path, with a helix axis forming a circle around a fixed point in space. The radius of the helix and of the circle are equal and given by half the reduced Compton wave length of a photon of energy equal to the rest energy of the particle described. The paths depend on the relative velocity between the described entity and the observer, and represent the De Broglie wave. The merits of the proposed model are summarized and its role in relation to the established description by quantum mechanics discussed. It is concluded that it supports the existence of the proposed extended Zitterbewegung, and offers a description of quantum behaviour without quantum mechanics.

A novel quantum-mechanical interpretation of the Dirac equation

A novel interpretation is given of Dirac’s ‘wave equation for the relativistic electron’ as a quantum-mechanical one-particle equation. In this interpretation the electron and the positron are merely the two different ‘topological spin’ states of a single more fundamental particle, not distinct particles in their own right. The new interpretation is backed up by the existence of such ‘bi-particle’ structures in general relativity, in particular the ring singularity present in any spacelike section of the spacetime singularity of the maximal-analytically extended, topologically non-trivial, electromagnetic Kerr–Newman (KN)spacetime in the zero-gravity limit (here, ‘zero-gravity’ means the limit , where G is Newton’s constant of universal gravitation). This novel interpretation resolves the dilemma that Dirac’s wave equation seems to be capable of describing both the electron and the positron in ‘external’ fields in many relevant situations, while the bi-spinorial wave function has only a single position variable in its argument, not two—as it should if it were a quantum-mechanical two-particle wave equation. A Dirac equation is formulated for such a ring-like bi-particle which interacts with a static point charge located elsewhere in the topologically non-trivial physical space associated with the moving ring particle, the motion being governed by a de Broglie–Bohm type law extracted from the Dirac equation. As an application, the pertinent general-relativistic zero-gravity hydrogen problem is studied in the usual Born–Oppenheimer approximation. Its spectral results suggest that the zero-G KN magnetic moment be identified with the so-called ‘anomalous magnetic moment of the physical electron,’ not with the Bohr magneton, so that the ring radius is only a tiny fraction of the electron’s reduced Compton wavelength.

Zitterbewegung, internal momentum and spin of the circular travelling-wave electromagnetic model electron

The study of this paper demonstrates that electron has Dirac delta like internal momentum (u,p_{{\theta}}), going round in a circle of radius equal to half the reduced Compton wavelength of electron with tangential velocity c. The circular momentum p_{{\theta}} and energy u emanate from circular Dirac delta type rotating monochromatic electromagnetic (EM) wave that itself travels in another circle having radius equal to the reduced Compton wavelength of electron. The phenomenon of Zitterbewegung and the spin of electron are the natural consequences of the model. The spin is associated with the internal circulating momentum of electron in terms of four component spinor, which leads to the Dirac equation linking the EM electron model with quantum mechanical theory. Our model accurately explains the experimental results of electron channelling experiment, [P. Catillon et al., Found.Phys. 38, 659 (2008)], in which the momentum resonance is observed at 161.784MeV/c corresponding to Zitterbewegung frequency of 80.874MeV/c electron beam.

Quantum fluid model of coherent stimulated radiation by a dense relativistic cold electron beam

Using a quantum fluid model, the linear dispersion relation for FEL pumped by a short wavelength laser wiggler is deduced. Subsequently, a new quantum corrected resonance condition is obtained. It is shown that, in the limit of low energy electron beam and low frequency pump, the quantum recoil effect can be neglected, recovering the classical FEL resonance condition, ks=4kwγ2. On the other hand, for short wavelength and high energy electron beam, the quantum recoil effect becomes strong and the resonance condition turns into ks=2kw/ƛcγ3/2, with ƛc being the reduced Compton wavelength. As a result, a set of nonlinear coupled equations, which describes the quantum FEL dynamics as a three-wave interaction, is obtained. Neglecting wave propagation effects, this set of equations is solved numerically and results are presented.

FORMULATION OF THE SPINOR FIELD IN THE PRESENCE OF A MINIMAL LENGTH BASED ON THE QUESNE–TKACHUK ALGEBRA

In 2006 Quesne and Tkachuk (J. Phys. A: Math. Gen.39, 10909, (2006)) introduced a (D+1)-dimensional (β, β′)-two-parameter Lorentz-covariant deformed algebra which leads to a nonzero minimal length. In this work, the Lagrangian formulation of the spinor field in a (3+1)-dimensional space–time described by Quesne–Tkachuk Lorentz-covariant deformed algebra is studied in the case where β′ = 2β up to first order over deformation parameter β. It is shown that the modified Dirac equation which contains higher order derivative of the wave function describes two massive particles with different masses. We show that physically acceptable mass states can only exist for [Formula: see text]. Applying the condition [Formula: see text] to an electron, the upper bound for the isotropic minimal length becomes about 3 ×10-13m. This value is near to the reduced Compton wavelength of the electron [Formula: see text] and is not incompatible with the results obtained for the minimal length in previous investigations.

Modulational instability and nonlinear evolution of two-dimensional electrostatic wave packets in ultra-relativistic degenerate dense plasmas

We consider the nonlinear propagation of electrostatic wave packets in an ultra-relativistic (UR) degenerate dense electron–ion plasma, whose dynamics is governed by the nonlocal two-dimensional nonlinear Schrödinger-like equations. The coupled set of equations is then used to study the modulational instability (MI) of a uniform wave train to an infinitesimal perturbation of multidimensional form. The condition for the MI is obtained, and it is shown that the nondimensional parameter, β∝λCn01/3 (where λC is the reduced Compton wavelength and n0 is the particle number density) associated with the UR pressure of degenerate electrons, shifts the stable (unstable) regions at n0~1030cm-3 to unstable (stable) ones at higher densities, i.e., n0>̃7×1033. It is also found that the higher the values of n0, the lower is the growth rate of MI with cut-offs at lower wave numbers of modulation. Furthermore, the dynamical evolution of the wave packets is studied numerically. We show that either they disperse away or they blowup in a finite time, when the wave action is below or above the threshold. The results could be useful for understanding the properties of modulated wave packets and their multidimensional evolution in UR degenerate dense plasmas, such as those in the interior of white dwarfs and/or pre-Supernova stars.

The influence of the Lande g-factor in the classical general relativistic description of atomic and subatomic systems

We study the electromagnetic and gravitational fields of the proton and electron in terms of the Einsteinian gravity via the introduction of an arbitrary Lande g-factor in the Kerr–Newman solution. We show that at length scales of the order of the reduced Compton wavelength, corrections from different values of the g-factor are not negligible and discuss the presence of general relativistic effects in highly ionized heavy atoms. On the other hand, since at the Compton-wavelength scale the gravitational field becomes spin dominated rather than mass dominated, we also point out the necessity of including angular momentum as a source of corrections to Newtonian gravity in the quantum description of gravity at this scale.

Bilokale Feldtheorie der Elementarteilchen

Abstract The basic idea of this article is that in a bilocal field theory the Lorentz group can be replaced by the larger group SO (4;4) which contains SO (3;1) as a subgroup. On this basis a system of 24 coupled differential equations is introduced. In the special case of the pion the connection with the local field theory is discussed. It turns out that the application of the local field theory is limited by the reduced Compton wave length λ/2 π of the pion.

Quantum Effects in the Radiation from Accelerated Relativistic Electrons

The radiation associated with the operation of a betatron or synchrotron, due to the transverse acceleration of relativistic electrons by the magnetic field of the machine, is discussed qualitatively. Order of magnitude expressions for the angular opening of the cone within which the radiation is emitted, and for the wavelength of the maximum of the radiated spectrum, are obtained by means of qualitative arguments based on classical physics. It is then shown, from a consideration of the rate of spread of a wave packet that describes the electron, that quantum effects are negligible so long as the ratio γ of the total energy to the rest energy of the electron is small in comparison with the square root of the ratio of the orbit radius R to the reduced Compton wavelength λ̄c of the electron. This criterion for the validity of classical theory is substantially equivalent to, but not identical with, the commonly accepted criterion γ2≪R/λ̄c, which is derived from the assumption that the momentum of an emitted photon must be small in comparison with the momentum of the electron. Thus classical theory is expected to be valid for electron energies small in comparison with 1015 ev if the magnetic field strength does not exceed 104 oersted.