arXiv subjects

Stefan Popescu

Publications and source records attributed to Stefan Popescu.

At least 19 recordsLinked to original sources

arXiv2025

Universal partial tori

A De Bruijn cycle is a cyclic sequence in which every word of length $n$ over an alphabet $\mathcal{A}$ appears exactly once. De Bruijn tori are a two-dimensional analogue. Motivated by recent progress on universal partial cycles and words, which shorten De Bruijn cycles using a wildcard character, we introduce universal partial tori and matrices. We find them computationally and construct infinitely many of them using one-dimensional variants of universal cycles, including a new variant called a universal partial family.

math.CO↗

arXiv2008

Relativistic dynamics without collisions and conservation laws

We show that the relativistic expressions for momentum and energy as well as the way in which they transform could be derived without involving collisions and conservation laws. Our approach involves relativistic kinematics via the addition law of relativistic velocities.

physics.gen-ph↗

arXiv2008

Nonstandard Lorentz-Einstein transformations

The standard Lorentz transformations establish a relationship between the space-time coordinates of the same event when detected from two inertial reference frames I and I' in the standard arrangement. This event is characterized by the space-time coordinates E(x,tE) and E'(x',t'E), tE and t'E representing the readings of the standard synchronized clocks C(x) and C'(x') located in the two frames where the event takes place. We obtain the nonstandard Lorentz transformations establishing a "physically" correct relationship between the readings of the standard synchronized clocks and the readings of other clocks (ta,t'a) of the same inertial reference frames. This relationship of the type tE=f(x,ta), expresses the standard Lorentz transformations as a function of ta and t'a respectively. We present several cases of nonstandard Lorentz transformation (the case of radar detection, the case when one reference frame is filled with an ideal transparent dielectric and the case of relativity of the apparent, actual and synchronized positions of the same moving particle).

physics.gen-ph↗

arXiv2007

Lorentz transformation, time dilation, length contraction and Doppler Effect - all at once

We present a simple derivation of the Lorentz transformations for the space-time coordinates of the same event. It is based on the relative character of length and time interval as measured by observes in relative motion. We begin by accepting that the relative motion modifies in some particular way the result of these measurements. However we do not postulate the character of this distortion i.e. whatever it is dilation or contraction. The formulas accounting for length contraction, time dilation and Doppler shift are a byproduct of this derivation.

physics.gen-ph↗

arXiv2007

Relativistic electrodynamics as an extrapolation of relativistic kinematics

After having identified all the possible relationships between the electric field and the magnetic field in a given inertial reference frame we derive the transformation equations for the components of these fields. Special relativity is involved via the addition law of parallel speeds or via the Lorentz transformations for the space-time coordinates of the same event. Electricity and magnetism are involved via Gauss's and Ampere's laws. In this way we avoid the transformation equations for the Lorenz force components which are used in most derivations of the transformation equations for E and B fields.

physics.gen-ph↗

arXiv2007

Lorentz transformation by mimicking the Lorentz transformation

We show that starting with the fact that special relativity theory is concerned with a distortion of the observed length of a moving rod, without mentioning if it is a "contraction" or "dilation", we can derive the Lorentz transformations for the spacetime coordinates of the same event. This derivation is based on expressing the length of the moving rod as a sum of components with all the lengths involved in this summation being measured by the observers of the same inertial reference frame.

physics.gen-ph↗

arXiv2007

A generic rule that simplifies the derivation of the transformation equations accounting for the properties of the photon

We show that the transformation equation for the tardyon velocity involves two generic functions which in turn depend on the relative velocity of the involved reference frames, on the tardyon velocity u and on the polar angle which define the direction along which the tardyon moves. The same functions are further involved in the transformation equations for the space-time coordinates of the same event generated by a moving tardyon and for its relativistic mass, momentum and energy. Taking the limits of these functions for u approaching c we obtain exactly the transformation equations for the space-time coordinates of the same event generated by a photon and for its momentum and energy. The same procedure works also for the transition from a plane acoustic wave to an electromagnetic wave.

physics.gen-ph↗

arXiv2007

Counting energy packets in the electromagnetic wave

We discuss the concept of energy packets in respect to the energy transported by electromagnetic waves and we demonstrate that this physical quantity can be used in physical problems involving relativistic effects. This refined concept provides results compatible to those obtained by simpler definition of energy density when relativistic effects apply to the free electromagnetic waves. We found this concept further compatible to quantum theory perceptions and we show how it could be used to conciliate between different physical approaches including the classical electromagnetic wave theory, the special relativity and the quantum theories.

physics.gen-ph↗

arXiv2007

Learning more from the Lorentz transformations

Admitting the validity of Lorentz transformations for the space as time coordinates of the same event we derive their differential form in order to underline the correct prerequisites for the application of time and length contraction or dilation effects. Furthermore we quantify the simultaneity error occurring in the relativity theory. Having done this, we analyse the root cause of these effects and identify it with a finite phase velocity associated with the moving frame. We define this phase velocity by analogy to the de Broglie wave associated with a moving particle. Based on this construct we demonstrate that the phase of the de Broglie waves further extended for stationary particles is a relativistic invariant being the same for all corresponding observers. Also the phase of the electromagnetic waves transporting energy at light speed is a relativistic invariant. Therefore the universe and its matter / energy may be seen as a superposition of waves propagating such that their phase is the same for all corresponding observers. The wave phase may replace the time as an invariant and universal reference.

physics.gen-ph↗

arXiv2007

Relativistic velocity addition law derived from a machine gun analogy and time dilation only

We consider a scenario that involves a machine gun, the bullets it fires and a moving target, considered from the rest frame of the machine gun and from the rest frame of the target respectively. Involving the special relativity via its two postulates and the time dilation formula we derive the relativistic velocity addition law showing that it leads to the Lorentz transformations for the space-time coordinates of the same event.

physics.gen-ph↗

arXiv2007

Lorentz transformations: Einstein's derivation simplified

We show that the Lorentz transformations for the space-time coordinates of the same event are a direct consequence of the principle of relativity and of Einstein's distant clocks synchronization procedure. In our approach, imposing the linear character of the Lorentz transformations we guess that the transformation equation for the space coordinate has the form x=ax'+cbt'. Imposing the condition that it accounts for the time dilation relativistic effect and taking into account the fact that due to the clock synchronization a la Einstein the space-time coordinates of the same event in the two frames are related by x=ct and x'=ct', we find out expressions for a and b. Dividing the transformation equation for the space coordinate by c we obtain the transformation equation for the time coordinate t=at'+b/cx'. Combining the two transformation equations we obtain directly the inverse Lorentz transformations.

physics.gen-ph↗

arXiv2007

Quantization, Doppler shift and the invariance of the speed of light via the invariance of the counted numbers of photons: An interesting pedagogical problem

We show that when the observers are located in a plane electromagnetic wave it is not compulsory for them to take into account the time dilation and length contraction effects when the wave is detected from two inertial reference frames in relative motion. We also illustrate the difference between the approach that uses Einstein type of observers confronted with time dilation and length contraction effects and an unconventional approach that uses observers detecting information from the energy that arrives at their location.

physics.gen-ph↗

arXiv2006

Landing the uniformly accelerating observers

Observers of the uniformly accelerating observers or the observers who make up the system of uniformly accelerating observers reach the same velocity V at different times ti which depends on V and on theirs acceleration gi. Considering a platform that moves with constant velocity V, the observers can land smoothly on it. Their ages and locations in the inertial reference frame attached to the platform are reckoned and compared.

physics.gen-ph↗

arXiv2006

The system of uniformly accelerating observers

We begin with a scenario that involves point-like observers starting at t=0 from the origin O of an inertial reference frame. They move with all possible proper accelerations in the positive direction of the OX axis. Equipped with light sources the accelerating observers get involved in experiments like Doppler Effect, radar detection and radar echo. We derive formulas accounting for the experiments mentioned above. In the case of the Doppler Effect we take into account the non-locality aspect in the time interval measurement by accelerating observers.

physics.gen-ph↗

arXiv2006

Radar echo, Doppler Effect and Radar detection in the uniformly accelerated reference frame

The uniformly accelerated reference frame described by Hamilton, Desloge and Philpott involves the observers who perform the hyperbolic motion with constant proper acceleration gi. They start to move from different distances measured from the origin O of the inertial reference frame K(XOY), along its OX axis with zero initial velocity. Equipped with clocks and light sources they are engaged with each other in Radar echo, Doppler Effect and Radar detection experiments. They are also engaged in the same experiments with an inertial observer at rest in K(XOY) and located at its origin O. We derive formulas that account for the experiments mentioned above. We study also the landing conditions of the accelerating observers on a uniformly moving platform.

physics.gen-ph↗

arXiv2006

Relativistic addition of parallel velocities from time dilation

The relativistic addition of parallel velocities is derived involving relativity only via the time dilation formula, avoiding the length contraction used by many authors in conjunction with time dilation. The followed scenario involves a machine gun that fires successive bullets, considered from its rest frame and from the rest frame of the target, the bullets hit.

physics.gen-ph↗

arXiv2006

Accelerating observers measure the period of the oscillations taking place in an acoustic wave (non-longitudinal case)

We consider a scenario that involves a stationary source of acoustic waves located at the origin of the K(XOY) inertial reference frame and a receiver that performs the hyperbolic motion at a constant altitude. The observer measures the proper reception time of successive wave crests. We investigate its dependence on the propagation speed of the wave and on the altitude at which the motion takes place.

physics.gen-ph↗

arXiv2006

Time interval measurements by uniformly accelerating observers (non-longitudinal case)

We consider two non-longitudinal Doppler Effect experiments. The first one involves a stationary source of monochromatic light located at the origin O of the K(XOY) inertial reference frame and an observer R who performs the hyperbolic motion at a constant altitude. The second involves a stationary observer located at the origin O and a monochromatic source of light that performs the hyperbolic motion. In both cases we compare the relationship between emission and reception times of the same light signal and the relationship between the emission and the reception time intervals of two successive light signals.

physics.gen-ph↗