Related papers: Kepler's laws without calculus
We consider the Lambek calculus, or non-commutative multiplicative intuitionistic linear logic, extended with iteration, or Kleene star, axiomatised by means of an $\omega$-rule, and prove that the derivability problem in this calculus is…
Numerically obtaining the inverse of a function is a common task for many scientific problems, often solved using a Newton iteration method. Here we describe an alternative scheme, based on switching variables followed by spline…
Basic properties of alternative flow equation in Quantum Gravity are studied. It is shown that the alternative flow equation for effective two-particle irreducible effective action is gauge independent and does not depend on IR parameter…
Amplitudes are the major logical object in Quantum Theory. Despite this fact they presents no physical reality and in consequence only observables can be experimetally checked. We discuss the possibility of a theory of Quantum Probabilities…
Starting from the well-known light-clock thought experiment to derive time dilation and length contraction, it is shown that finding the Lorentz Transformation requires nothing more than the most trivial vector addition formula. The form…
We propose a new derivation of Time-Independent Perturbation Theory (PT) that has a fundamental advantage over the usual derivations presented in textbooks on Quantum Mechanics (QM): it is simpler and much shorter. As such, it can provide…
We first review asymptotic twistor theory with its real subspace of null asymptotic twistors. This is followed by a description of an asymptotic version of the Kerr theorem that produces regular asymptotically shear free null geodesic…
It is shown that the correct expressions for momentum and kinetic energy of a particle moving at high speed were already implicit in physics going back to Maxwell. The demonstration begins with a thought experiment of Einstein by which he…
The logical inference approach to quantum theory, proposed earlier [Ann. Phys. 347 (2014) 45-73], is considered in a relativistic setting. It is shown that the Klein-Gordon equation for a massive, charged, and spinless particle derives from…
In the Kerr geometry, we calculate various surfaces of constant curvature invariants. These extend well beyond the Kerr horizon, and we argue that they might be of observational significance in connection with non-minimally coupled matter…
Observers at rest in two inertial reference frames are located within the propagation space of the same electromagnetic wave. Raising receiving antennas in a suitable way, these observers use the electromagnetic oscillations in the wave as…
Cluster-tilted algebras are trivial extensions of tilted algebras. This correspondence induces a surjective map from tilted algebras to cluster-tilted algebras. If B is a cluster-tilted algebra, we use the fibre of B under this map to study…
The Lorentz force can be obtained from Maxwell's equations in the Coulomb gauge provided that we assume that the electric portion of the force acted on a charge is known, and the magnetic component is perpendicular to the velocity of motion…
In this note, we give a simple, counting based proof of Fisher's Inequality that does not use any tools from linear algebra.
If one assumes there is probability of perception in quantum mechanics, then unitarity dictates that it must have the coefficient squared form, in agreement with experiment.
The principle which allows to construct new physical theories on the basis of classical mechanics by reduction of the number of its axiom without engaging new postulates is formulated. The arising incompleteness of theory manifests itself…
The relations between Bell's inequality and quantum probability trees are explained against the background offered by the concept of a quantum probability tree built in others works. It is shown that f we use a concept of probability tree…
Vectorial analysis relating to derivation of deflection of light is presented. Curvilinear acceleration is distinguished from the Newtonian polar conic acceleration. The difference between the two is due to the curvature term. Lorentz…
The formula for the relativistic Doppler effect is investigated in the context of two compelling invariance axioms. The axioms are expressed in terms of an abstract operation generalizing the relativistic addition of velocities. We prove…
The equations of the relativistic causal Newton gravity law for the planets of the solar system are studied in the approximation when the Sun rests at the coordinates origin and the planets do not iteract between each other.