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 …
As described in the previous post here, the three dimensions of motion are axes for traveling along (length) or revolving around (time). A measure of motion may be either (1) dependent on the the target motion, or (2) independent of the target motion. A measure that is independent is either available prior to or separately …
Although there are many experimental methods available to measure the speed of light, the underlying principle behind all methods [is] the simple kinematic relationship between constant velocity, distance and time given below: c = D / t (1) In all forms of the experiment, the objective is to measure the time required for the light …
Speed of a motion is the time rate of length change, that is, the length interval with respect to a timeline interval without regard to direction. Pace of a motion is the space rate of time change, that is, the time interval with respect to a baseline interval without regard to direction. The symbol for …
Two transformations of inertial reference frames are well-known: the Galilean and the Lorentz transformations. There is a third transformation as well, which will be called the dual Galilean transformation. Below is a derivation of all three transformations, closely following the paper Getting the Lorentz transformations without requiring an invariant speed by Andrea Pelissetto and Massimo …
Watches didn’t always exist. Neither did clocks that were transportable or manufactured in large quantities. I mention this because one way to determine the simultaneity of events is to have synchronized clocks transported to multiple locations – even an endless number of locations in theory. How can an observer determine the simultaneous events from their …
In a paper titled Nothing but Relativity (Eur. J. Phys. 24 (2003) 315-319) Palash B. Pal derived a formula for transformations between observers that is based on the relativity postulate but not a speed of light postulate. In a paper titled Nothing but Relativity, Redux (Eur. J. Phys. 28 (2007) 1145-1150) Joel W. Gannett presented …
Since one may associate either the arclength (travel length) or the arctime (travel time) with direction, one might think that the full coordinates for every event are of the form (s, t, ê), with arclength s, arctime t, and unit vector ê. Since the direction is a function of either the arclength or the arctime, …
Carlo Rovelli’s “Analysis of the Distinct Meanings of the Notion of “Time” in Different Physical Theories” (Il Nuovo Cimento B, Jan 1995, Vol 110, No 1, pp 81–93) describes ten distinct versions of the concept of time, which he arranges hierarchically. Here are excerpts from his article: We find ten distinct versions of the concept …
