In previous papers we have shown how Schrödinger’s equation which includes an electromagnetic field interaction can be deduced from a fluid dynamical Lagrangian of a charged potential flow that interacts with an electromagnetic field. The quantum behaviour was derived from Fisher information terms which were added to the classical Lagrangian. It was thus shown that a quantum mechanical system is driven by information and not only electromagnetic fields. This program was applied also to Pauli’s equations by removing the restriction of potential flow and using the Clebsch formalism. Although the analysis was quite successful there were still terms that did not admit interpretation, some of them can be easily traced to the relativistic Dirac theory. Here we repeat the analysis for a relativistic flow, pointing to a new approach for deriving relativistic quantum mechanics.

Galaxies are rather big physical systems having a typical size of tens of kilo parsecs. Thus any change at the center of the galaxy will affect the outskirts only tens of thousand of years afterwards. Retardation seems to be neglected in current calculations of rotational velocities in the far edges of the galaxy and its surrounding gas. The differences between the velocities predicted by Newtonian theory and observational derivations are accommodated by either assuming "dark matter" or by introducing modifications to the laws of gravity in which MOdified Newtonian Dynamics (MOND) is one of the typical examples, celebrating now forty years since its inception. We show that there are overlapping conditions for retardation corrections in the weak approximation to general relativity and the low acceleration conditions for MOND corrections. We will also show that MOND interpolation formula is useful for calculating retardation effects provided an appropriate interpolation function is chosen.

Current spacecraft mass are mostly fuel, this is dictated by the lack of fueling stations in space and also by the Tsiolkovsky rocket equation which defines the mass ratio needed to escape earths gravity. The Tsiolkovsky rocket equation gives a relationship between the mass ratio and the final velocity in multiples of the exhaust speed, and dictates a high mass ration for current exhaust speeds. A relativistic motor exchanging momentum and energy with the electromagnetic field may mitigate such considerations, enabling efficient interplanetary travel. In this paper we will discuss the advantages and challenges of this novel mover for space transportation.

The general theory of relativity (GR) is symmetric under smooth coordinate transformations also known as diffeomorphisms. The general coordinate transformation group has a linear subgroup denoted the Lorentz group of symmetry which is maintained also in the weak field approximation to GR. The dominant operator in the weak field equation of GR is thus the d'Alembert (wave) operator which has a retarded potential solution. Galaxy Clusters are huge physical systems having dimensions of many hundreds of millions of light years. Thus any change at the cluster center will be noticed at the rim only hundreds of millions of years later. Those retardation effects are neglected in present day cluster modelling and in particular are neglected in virial calculations used to relate mass and velocities on the cluster. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper we will show that taking general relativity seriously without neglecting retardation effects one can explain the velocities in a galactic cluster without postulating dark matter. It should be stressed that the current approach does not require that velocities, $v$ are high, in fact the vast majority of cluster bodies are substantially subluminal. In other words, the ratio of $\frac{v}{c} \ll 1$. Typical velocities in galaxies are less than ~1000 km/s, which makes this ratio $0.01$ or smaller. However, one should consider the fact that every gravitational system even if it is made of subluminal bodies has a retardation distance, beyond which the retardation effect cannot be neglected. Every natural system such as stars and galaxies and even galactic clusters exchange mass with its environment. For example, the sun losses mass through the solar wind and galaxies accrete gas from the intergalactic medium. This means that all natural gravitational systems have a finite retardation distance. The question is thus quantitative, how large is the retardation distance? The change of mass of the sun is quite small and thus the retardation distance of the solar system is quite large allowing us to neglect retardation effects within the solar system. However, for galaxies and galaxy clusters the retardation distance is within the system itself and cannot be neglected.

In previous works we have developed the concept of a relativistic engine taking into account the phenomena of retardation of electromagnetic fields. We have shown that Newton’n third law cannot strictly hold in a distributed system, where the different parts are at a finite distance from each other and thus force imbalance is created at the system’s center of mass. As the system is affected by a total force for a finite period, mechanical momentum and energy are acquired by the system. In previous works we relied on the fact that the bodies were macroscopically natural. Lately we relaxed this assumption and studied charged bodies, thus analyzing the consequences on a possible electric relativistic engine. On the first paper on this subject we investigated this phenomena in general but gave an example of a system only at the stage of reaching a stationary state, a second paper was devoted to the same but on the atomic scale, here we shall analyze the charge relativistic engine in a general time dependent setting.

Electrons moving at slow speeds much lower that the speed of light are described by a wave function which is a solution of Pauli’s equation. This is a low velocity limit of the relativistic Dirac equation. Here we compare two approaches, one which is the more conservative Copenhagen’s interpretation denying a trajectory of the electron but allowing a trajectory to the electron expectation value through Ehrenfest theorem. The said expectation value is of course calculated using a solution of Pauli’s equation. A less orthodox approach is championed by Bohm, and attributes a velocity field to the electron also derived from the Pauli wave function. It is thus interesting to compare the trajectory followed by the electron according to Bohm and its expectation value according to Ehrenfest. Both similarities and differences will be considered.

In a previous paper we have shown that superluminal particles are allowed by the general relativistic theory of gravity provided that the metric is locally Euclidean. Here we calculate the probability density function of a canonical ensemble of superluminal particles as function of temperature. Although only the Lorentzian metric is stable for normal matter density, an Euclidian metric can be created under special gravitational circumstances and persist in a limited region of space-time consisting of the very early universe which is characterized by extremely high densities and temperatures. Superluminal particles also allow attaining thermodynamic equilibrium at a shorter duration and also suggest a rapid expansion of the matter density, thus making mechanism such as inflation (which demands invoking and ad-hoc scalar field) redundant. This is in accordance with Occam’s razor.

In a recent paper discussing Newton’s third law in the framework of special relativity for charged bodies, it was suggested that one can construct a practical relativistic motor provided high enough charge and current densities are available. As on the macroscopic scale charge density is limited by the phenomena of dielectric breakdown, it was suggested to take advantage of the high charge densities which are available on the microscopic scale. A preliminary analysis of this option denoted "nano relativistic scale" is studied in the current paper.

The current paper is devoted to the introduction of simpler Eulerian variational principles from which all the relevant equations of non-barotropic stationary magnetohydrodynamics can be derived for magnetic fields which lie on surfaces. A variational principle is given in terms of three independent variables for stationary non-barotropic magnetohydrodynamic flows. This is a smaller number of variables than the eight variables which appear in the standard equations of non-barotropic magnetohydrodynamics which are the magnetic field, the velocity field, the specific entropy and the density. We further investigate the case in which the flow along magnetic lines is not ideal.

Galaxies are huge physical systems having dimensions of many tens of thousands of light years. Thus any change at the galactic center will be noticed at the rim only tens of thousands of years later. Those retardation effects seems to be neglected in present day galactic modelling used to calculate rotational velocities of matter in the rims of the galaxy. The significant differences between the predictions of Newtonian theory and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this essay we will show that taking retardation effects into account one can explain the azimuthal velocities of galactic matter and the well known Tully-Fisher relations of galaxies.

In a recent paper we have a shown that the flattening of galactic rotation curves can be explained by retardation. However, this will rely on a temporal change of galactic mass. In our previous work we have kept only second order terms of the retardation time in our analysis, while higher terms in the Taylor expansion where not considered. Here we consider analysis to all orders and show that indeed a second order analysis will suffice, and higher order terms can be neglected.

Galaxies are huge physical systems having dimensions of many tens of thousands of light years. Thus any change at the galactic center will be noticed at the rim only tens of thousands of years later. Those retardation effects seems to be neglected in present day galactic modelling used to calculate rotational velocities of matter in the rims of the galaxy and surrounding gas. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper we will show that taking general relativity seriously without neglecting retardation effects one can explain the apparent excess matter leading to gravitational lensing in both galaxies and galaxy clusters.

Galaxies are huge physical systems having dimensions of many tens of thousands of light years. Thus any change at the galactic center will be noticed at the rim only tens of thousands of years later. Those retardation effects seems to be neglected in present day galactic modelling used to calculate rotational velocities of matter in the rims of the galaxy and surrounding gas. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper we will show that taking general relativity seriously without neglecting retardation effects one can explain the radial velocities of galactic matter without postulating dark matter. However, this will rely on a temporal change of galactic mass. We will compare two different mechanisms of density change, one is local, that is accretion of matter from the intergalactic medium. The other is global, that is the cosmological decrease of density due to the cosmic expansion. It will be shown that local effects are much more important in this respect.

The general theory of relativity (GR) is known to be invariant under smooth coordinate transformations (diffeomorphism). This group has a subgroup known as the Lorentz group of symmetry which is manifested in the weak field approximation to GR. The dominant operator in the weak field equation of GR is thus the d'Alembert (wave) operator which has a retarded potential solution. Galaxies are huge physical systems having dimensions of many tens of thousands of light years. Thus any change at the galactic center will be noticed at the rim only tens of thousands of years later. Those retardation effects are neglected in present day galactic modelling used to calculate rotational velocities of matter in the rims of the galaxy and surrounding gas. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper we will show that taking general relativity seriously without neglecting retardation effects one can explain the radial velocities of galactic matter in the M33 galaxy without postulating dark matter.

We study the generalized χ and η cross helicities for non-ideal non-barotropic magnetohydrodynamics (MHD). χ and η, the additional label translation symmetry group, have been used to generalize the cross helicity in ideal flows. Both new helicities are additional topological invariants of ideal MHD. To study there behaviour in non-ideal MHD, we derive the time derivative of both helicities using the non-ideal MHD equations taking viscosity, finite resistivity and heat conduction into account. Physical variables are divided into ideal and non-ideal quantities separately during the mathematical analysis for simplification. The analytical results indicate that χ and η cross helicities are not strict constant of motion in the non-ideal MHD and show the rate of dissipation which is compared to the dissipation of other topological constants of motion.

Newton's third law states that any action is countered by a reaction of equal magnitude but opposite direction. The total force in a system not affected by external forces is thus zero. However, according to the principles of relativity, a signal cannot propagate at speeds exceeding the speed of light. Hence the action and reaction cannot be generated at the same time due to the relativity of simultaneity. Thus, the total force cannot be null at a given time. In a previous paper \cite{MTAY1}, we have shown that Newt\-on'n third law cannot strictly hold in a distributed system, where the different parts are at a finite distance from each other. This is due to the finite speed of signal propagation, which cannot exceed the speed of light in the vacuum. A specific example of two current loops with time dependent currents demonstrated that the summing of the total force in the system does not add up to zero. This analysis led to the suggestion of a relativistic engine \cite{MTAY3,AY1}. As the system is affected by a total force for a finite period, the system acquires mechanical momentum and energy. Now the question then arises how can we accommodate the law of momentum and energy conservation. The subject of momentum conversation was discussed in \cite{MTAY4}, while preliminary results regarding energy conservation were discussed in \cite{AY2,RY,RY2}. Previous analysis relied on the fact that the bodies were macroscopically natural, which means that the number of electrons and ions is equal in every volume element. Here we relax this assumption and study charged bodies, thus analyzing the consequences on a possible electric relativistic engine.

The limitedness of the nonrenewable local energy resources in Israel, even in background of the later gas fields’ findings, continues to force the state to devote various efforts for the ‘green’ energy development. These efforts include installations both in the solar and in the wind energy, with a purpose to improve the diversity of energy sources. While the standard discounted cash flow (DCF) method using the net present value (NPV) criterion is extensively adopted to evaluate investments, the standard DCF method is inappropriate for the rapidly changing investment climate and for the managerial flexibility in investment decisions. In recent years, the real options analysis (ROA) technique is widely applied in many studies for valuation of renewable energy investment projects. Hence, we apply in this study the real options analysis approach for the valuation of wind energy turbines and apply it to the analysis of wind energy economic potential in Israel.

A new method for short circuit fault location is proposed based on instantaneous signal measurement and its derivatives, and is based on the retardation phenomena. The difference between the times in which a signal is registered in two detectors is used to locate the fault. Although a description of faults in terms of a lumped circuit is useful for elucidating the methods for detecting the fault. This description will not suffice to describe the fault signal propagation hence a distributed models is needed which is given in terms of the telegraph equations. Those equations are used to derive a transmission line transfer function, and an exact analytical description of the short circuit signal propagating in the transmission line is obtained. The analytical solution was verified both by numerical simulations and experimentally.

We study the connection between the phase and the amplitude of the wave function and the conditions under which this relationship exists. For this we use model of particle in a box. We have shown that the amplitude can be calculated from the phase and vice versa if the log Analytical uncertainty relations are satisfied.

SStatistical characteristics of the wind speed in Samaria region of Israel have been analyzed by processing 11 years of wind data provided by the Israeli Meteorological Service, recorded at 10 m height above the ground. The cumulative mean wind speed at measurement height was shown to be 4.53 m/s with standard deviation of 2.32 m/s. Prevailing wind direction is shown to be char-acterized by cumulative mean azimuth of 226° with standard deviation of 79.76°. The results were extrapolated to 70-meter height in order to estimate wind characteristics at hub height of a me-dium-scale wind turbine. Moreover, Weibull distribution parameters were calculated annually, monthly and seasonally, demonstrating a good match with histogram-based statistical repre-sentations. Shape parameter of the Weibull distribution was shown to reside within a narrow range of 1.93 to 2.15, allowing us to assume a Rayleigh distribution, thus simplifying wind tur-bines energy yield calculations. The novelty of the current paper is related to gathering wind statistics for a certain area (Samaria) we are not aware of any published statistics regarding wind velocity and direction in this area. The data may be interesting for potential regional wind energy development in which the obtained Weibull distribution can be used in calculations of expected power generation of particular turbines with known power dependence on velocity. We also point out that the fact that realistic wind velocity statistics is well described by an analytic formula (Weibull distribution) is not trivial, and in fact the fit may have been poor.

Nonionizing millimeter-waves (MMW) interact with cells in a variety of ways. Here the inhibited cell division effect was investigated using 85-105 GHz MMW irradiation within the ICNIRP (International Commission on Non-Ionizing Radiation Protection) non-thermal 20 mW/cm2 safety standards. Irradiation using a power density of about 1.0 mW/cm2 , SAR over 5-6 hours on 50 cells/μl samples of Saccharomyces cerevisiae model organism resulted in 62% growth rate reduction compared to the control (sham). The effect was specific for 85-105 GHz range, and was energy and cell density dependent. Irradiation of wild type and Δrad52 (DNA damage repair gene) deleted cells presented no differences of colony growth profiles indicating non-thermal MMW treatment does not cause permanent genetic alterations. Dose versus response relations studied using a standard horn antenna (~1.0 mW/cm2) and compared to that of a compact waveguide (17.17 mW/cm2) for increased power delivery resulted in complete termination of cell division via non-thermal processes supported by temperature rise measurements. We have shown that non-thermal MMW radiation has potential for future use in treatment of yeast related diseases and other targeted biomedical outcomes.

Nonionizing millimeter-waves (MMW) are reported to interact with cells in a variety of ways. Possible mechanisms of the inhibited cell division effect were investigated using 85-105 GHz MMW irradiation within the ICNIRP (International Commission on Non-Ionizing Radiation Protection) non-thermal 20 mW/cm² safety standards. ~1.0 mW/cm² exposure over 5-6 hours treatment on 50 cells/μl samples of Saccharomyces cerevisiae model organism, resulted in 62% growth rate reduction compared to control (sham). The effect was specific for 85-105 GHz range and energy dose and cell density dependent. Irradiation of wild type and Δrad52 (DNA damage repair gene) deletion cells presented no differences of colony growth profiles indicating non-thermal MMW treatment does not cause genetic alterations. Dose versus response relations studied using a standard horn antenna (~1.0 mW/cm²) and compared to that of a compact waveguide (17.17 mW/cm²) for increased power delivery resulted in complete termination of cell division via non-thermal processes supported by temperature rise measurements. Combinations of MMW mediated Structure Resonant Energy Transfer (SRET), membrane modulations eliciting signaling effects, and energetic resonance with biomolecules were indicated to be responsible for the observations reported. Our results provide novel mechanistic insights enabling innovative applications of nonionizing radiation procedures for eliciting targeted biomedical outcomes.

Therapeutically effective treatments of cancer are limited. To calibrate the efficiency of the novel technique we recently discovered to modulate cancer cell viability using tuned electromagnetic fields; H1299 human lung cancer cells were irradiated in a sweeping regime of W-band (75-105 GHz) millimeter waves (MMW) at 0.2 mW/cm² (2 W/m²). Effects on cell morphology, cell death and senescence were examined and compared to that of non-tumorigenic MCF-10A human epithelial cells. MMW irradiation led to alterations of cell and nucleus morphology of H1299 cells, significantly increasing mortality and senescence over 14 days of observation. Extended irradiation of 10 minutes duration resulted in complete death of exposed H1299 cell population within two days, while healthy MCF-10A cells remained unaffected even after 16 minutes of irradiation under the same conditions. Irradiation effects were observed to be specific to MMW treated H1299 cells and absent in the control group of non-irradiated cells. MMW irradiation affected nuclear morphology of H1299 cells only and not of the immortalized MCF-10A cells. Irradiation with low intensity MMW shows an antitumor effect on H1299 lung cancer cells. This method provides a novel treatment modality enabling targeted specificity for various types of cancers.

Efficiently targeted cancer therapy without causing detrimental side effects is necessary for alleviating patient care and improving survival rates. This paper presents observations of morphological changes in H1299 human lung cancer cells following W-band MMW irradiation (75 – 105 GHz) at a non-thermal power density of 0.2 mW/cm², investigated over 14 days of subsequent physiological incubation following exposure. Microscopic analyses of physical parameters measured indicate MMW irradiation induces significant morphological changes characteristic of apoptosis and senescence. The Immediate short-term responses translate into long-term effects, retained over the duration of the experiment(s); reminiscent of the phenomenon of Accelerated Cellular Senescence (ACS) achieving terminal tumorigenic cell growth. Further, results were observed to be treatment-specific in energy (dose) dependent manner and were achieved without the use of chemotherapeutic agents, ionizing radiation or thermal ablation employed in conventional methods; thereby overcoming associated side effects. Adaptation of the experimental parameters of this study for clinical oncology concomitant with current developmental trends of non-invasive medical endoscopy alleviates MMW therapy as an effective treatment procedure for human non-small cell lung cancer (NSCLC).

Disk galaxies have a typical dimension of few tens of thousands of light years. It follows from the theory of general relativity that any signal originating from the galactic center will be noticed at the outskirts of the galaxy only tens of thousands of years later. This retardation effect is absent in modelling used to calculate rotation curves throughout the entire galaxy and its external gas. The considerable differences between Newtonian action at a distance predictions and observed velocities are currently removed either by assuming dark matter or by suggesting various modifications to the laws of gravity, MOND being a long standing alternative to Newtonian gravity. In previous papers we have shown that applying general relativity in a rigorous fashion without mindlessly neglecting retardation, one can explain the radial velocities of galactic matter without modifying gravity or adding unseen matter. Moreover, it was shown that dark matter effects as they appear in gravitational lensing, the Tully-Fisher relation, and mass estimations based on the virial theorem could also be explained as retarded-gravity effects. In the original main paper on the subject only one galaxy (M33) was analysed in detail. This was later amended somewhat with a published study of eleven galaxies. Here we give a more comprehensive retardation analysis of 143 galaxies of different types from the SPARC Galaxy collection. We show that in most cases we obtain an excellent fit without postulating dark matter or modifying general relativity.