Velocity reciprocity in relativity theory is the relation between two observers, each associated with a frame of reference and moving at different, but constant, velocities. That is, an observer-frame S observes another observer-frame S´ traveling with velocity +v relative to observer-frame S. A velocity reciprocity relation concerns the velocity of S that is observed by …
Galileo Galilei’s inclined plane experiment is described in his work Dialogues Concerning Two New Sciences, which I quote from the Dover edition. He speaks (through his character Salviati) of “those sciences where mathematical demonstrations are applied to natural phenomena, as is seen in the case of perspective, astronomy, mechanics, music, and others where the principles, …
What follows are excerpts from the book Science and Hypothesis by Henri Poincaré, translated (1905) from La Science et l’hypothèse (1902). p.xxiii The latter [definitions or conventions] are to be met with especially in mathematics and in the sciences to which it is applied. From them, indeed, the sciences derive their rigour; such conventions are …
There are three different contexts for 3D time with 1D space (stance), depending on whether stance is continuously increasing and, if so, whether there is a conversion factor between 3D space and 3D time: (A) Stance is not continuously increasing. This is the situation of a race or sport in which game time has a …
Vladimir Ignatowski (1875-1942) was a Russian physicist. “In 1910 he was to first who tried to derive the Lorentz transformation by group theory only using the relativity principle (postulate), and without the postulate of the constancy of the speed of light.” K M Browne gave a simplified derivation in the European Journal of Physics, 39 …
The following derivations are based on the exposition by G. G. Lombardi here. Time Dilation A clock is made by sending a pulse of light toward a mirror at a distance L and back to a receiver. Each “tick” is a round-trip to the mirror and back. The clock is shown at rest in the …
There are several ways of understanding the time of remote events. What follows is a summary of the basic ways of determining simultaneity. As a way of comparing the different ways consider transmitting a light signal to a remote location where it is reflected back. What is the time when the signal is reflected back? …
Albert Einstein’s book Relativity: The Special and General Theory was originally published in German and translated into English in 1920. In the second chapter he introduces “The System of Co-ordinates”. The following post gives Einstein’s text followed by a revision that exchanges length with duration and space with time. First, Einstein’s text, with alternative wordings …
There are three axes (dimensions) of motion with six degrees of freedom. There are two metrics of motion: a length metric and a duration metric. The length metric is the magnitude of the vector between two points, and is called distance. The duration metric is the magnitude of the vector between two instants, and is …
Here we expand 4D Galilean spacetime into 6D Galilean spacetime, based on section 1.3 Galilean spacetime of The Geometry of Relativistic Spacetime: from Euclid’s Geometry to Minkowski’s Spacetime by Jacques Bros (Séminaire Poincaré 1 (2005) 1 – 45). [p.3] We start with a representation space whose points are interpreted as the “physical events”. Any motion …
