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Introduction and Background
Published in John G. Papastavridis, Tensor Calculus and Analytical Dynamics, 2018
A CT is not to be confused with the more involved and physical concept of frame of reference transformation. For our purposes, a frame of reference is a conceptual framework of measuring rods (yardsticks) and clocks, extending into space and rigidly attachable to some reference-invariable body; i.e., a spatiotemporal coordinate system rigidly connected to that body.* Therefore, from the analytical viewpoint, such frame of reference transformations can be studied as explicitly time dependent (i.e., kinematical) CT; one CS rigidly attached, or embedded, to each frame, plus the time transformation: {q′=q′(q,t) , t′=t′(q,t)}↔{q=q(q′,t′),t=(q′, t′)}
Designing for Telepresence: The Delft Virtual Window System
Published in Peter Hancock, John Flach, Jeff Caird, Kim Vicente, Local Applications of the Ecological Approach to Human-Machine Systems, 2018
For the models of optic flow to be suited for spatial tasks the motion-movement ambiguity has to be solved10. To resolve motion-movement ambiguity (and scale ambiguity as well), it might be necessary to extend optic flow models to include actively controlled movements, and thus, accelerations into the models of optic flow. This points to a kinetic concept of optic flow rather than a merely kinematic one. In kinematics spatial variables, such as distances, velocities, and accelerations, are always relative, that is, they are always taken to some reference point. In studying the kinematics of two objects, we can picture either of them at rest and attribute the motion to the other. In a kinetic analysis, however, it is not arbitrary which particle is accelerating, even though distance and velocity are still relative. Coupled with accelerations, mass and inertia enter into the description. The accelerations objects undergo are independent of the frame of reference. An illustration of the difference between kinematics and kinetics is given by the Copernican revolution (although it was not the concern at the time). Earth-centered (Ptolemean) and sun-centered (Copernican) frames of reference are kinematically equivalent, but only the sun-centered system facilitates the explanation of movements through gravity.
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Published in Dmitry N. Lyubimov, Kirill N. Dolgopolov, L.S. Pinchuk, Quantum Effects in Tribology, 2017
Dmitry N. Lyubimov, Kirill N. Dolgopolov, L.S. Pinchuk
Galileo’s principle of relativity states that in all inertial frames of reference (the law of inertia is just in them) any mechanical process occurs identically (with the same initial conditions), i.e. they are absolutely equal. This corresponds to Newton’s corpuscular theory of light, according to which the emission of corpuscles is a mechanical process. The source of light that moves with velocity v emits corpuscles that fly with velocity c ± v, where c is the velocity of the corpuscles in the stationary system and the ± sign depends on whether the directions of the velocity vectors of light and its source are same or opposite. This conclusion, being natural for classical mechanics, was contrary to the results of fine experiments of a new fundamental physical doctrine – the theory of relativity that originated at the turn of 19th - 20th centuries. One of the fundamental conclusions of the relativity theory is the independence of the speed of light from the motion of its source.
Travelling light
Published in Journal of Modern Optics, 2021
The following argument in the book Relativity in Our Time: From Physics to Human Relations by Mendel Sachs resembles Einstein’s argument: The basic idea of the theory of relativity that convinced Einstein of its extreme simplicity is his principle of covariance, also referred to as the principle of relativity.This principle asserts that the laws of nature must have expressions independent of the frame of reference in which they are represented—from any particular observer’s view. This is equivalent to saying that the laws of nature are totally objective.We see, then, that the theory of relativity is based on a premise that is a law about laws, rather than a law that deals directly with physical phenomena. The idea about the objectivity of the laws of nature is, however, not really that new! For how could a law be a law, by definition of the word ‘law’, if it were not totally objective? [23]If the principle of relativity were equivalent to saying that the laws of nature are totally objective, that would be a powerful argument for it. It is hard to be against objectivity. However, this is a false equivalence, for two reasons. First, a law of nature, or any statement about nature, can be totally objective even if it has nothing to do with inertial coordinate systems. Objectivity is no more dependent on using inertial coordinate systems than on using Morse code. Second, Sachs confuses objectivity with uniformity. A coordinate-system-involving statement that is true in all inertial coordinate systems would have a certain kind of uniformity. It might also be objective, but in that case, it would not be objective because it was uniform. A statement that something is true in some inertial coordinate systems but not in all of them can also be objective. The principle of relativity imposes a uniformity condition that is compatible with objectivity but incidental to it.