Related papers: A Geometrical Interpretation of Frequency
In signal processing, a signal is a function. Conceptually, replacing a function by its graph, and extending this approach to a more abstract setting, we define a signal as a submanifold M of a Riemannian manifold (with corners) that…
We show that using Fermi coordinates it is possible to describe the gravitational field of a wave using a gravitoelectromagnetic analogy. In particular, we show that using this approach, a new phenomenon, called gravitomagnetic resonance,…
A wave packet of a charged particle always make cyclic circular motion in a uniform magnetic field, just like a classical particle. The nonadiabatic geometric phase for an arbitrary wave packet can be expressed in terms of the mean value of…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
The structural analysis, i.e., the investigation of the differential-algebraic nature, of circuits containing simple elements, i.e., resistances, inductances and capacitances is well established. However, nowadays circuits contain all sorts…
The probabilistic prediction of quantum theory is mystery. I solved the mystery by a geometrical interpretation of a wave function. This suggests the unification between quantum theory and the theory of relativity. This suggests Many-Worlds…
Non-time-orthogonal frame analysis is applied to determine the frequency and wavelength of light as observed i) in a relativistically rotating frame when emission is from a source fixed in the non-rotating frame, ii) in a non-rotating frame…
The possibility of consistency between the basic quantum principles of quantum mechanics and wave function collapse is reexamined. A specific interpretation of environment is proposed for this aim and applied to decoherence. When the…
Although one can formulate an intuitive notion of instantaneous frequency, generalizing "frequency" as we understand it in e.g. the Fourier transform, a rigorous mathematical definition is lacking. In this paper, we consider a class of…
The fundamental role of line geometry in the study of wave motion is first introduced in the general context by way of the tangent planes to the instantaneous wave surfaces, in which it is first observed that the possible frequency-wave…
A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the…
Using geometric algebra and calculus to express the laws of electromagnetism we are able to present magnitudes and relations in a gradual way, escalating the number of dimensions. In the one-dimensional case, charge and current densities,…
In a frame of quasi-crystal approximation the dispersion equations are obtained for the wave vector of a coherent electromagnetic wave propagating in a media which contains a random set of parallel dielectric cylinders with possible…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
We show that there are physically relevant situations where gravitational waves do not inherit the frequency spectrum of their source but its wavenumber spectrum.
The 3-dimensional coherence matrix is interpreted by emphasising its invariance with respect to spatial rotations. Under these transformations, it naturally decomposes into a real symmetric positive definite matrix, interpreted as the…
Electromagnetic quantities such as energy density, momentum, spin, and helicity bring meaning and intuition to electromagnetism and possess intricate interrelations, particularly prominent in complex non-paraxial near-fields. These…
The existence of waves with negative frequency is a surprising and perhaps controversial claim which has recently been revisted in optics and for water waves. Here I explain a context within which to understand the meaning of the "negative…
In this paper, a geometrical interpretation of light diffraction is given using an infinity of fluctuating geodesics that represent paths of least time in an homogeneous space. Without using the wave theory, we provide a geometrical…
We analyze a technique of obtaining turbulence power spectrum using spectral line data along the velocity coordinate, which we refer to as Velocity Coordinate Spectrum (VCS). We formalize geometrical aspects of observation through a single…