Matters relating to length and duration in physics and transportation
V. I. Arnold’s Mathematical Methods of Classical Mechanics (Springer, 1989) provides a contemporary approach to classical mechanics. We follow the presentation here but modify it to six dimensions of space-time. 1 The principles of relativity and determinacy A series of experimental facts is at the basis of classical mechanics. We list some of them. A […]
Four-Dimensional Formulations of Newtonian Mechanics First we reproduce section 2 from Michael Friedman’s “Simultaneity in Newtonian Mechanics and Special Relativity” in Foundations of Space-Time Theories (ed. Earman et al., UMinn, 1977), p.405-407. Then we provide the dual. According to the spatio-temporal point of view, the basic object of both our theories is a four-dimensional manifold.
This blogger is focused on developing a new six-dimensional theory of time (an early version is posted here). The glossary is also being updated (see here). Good progress is being made, with the double frame and three-dimensional time aspect especially new. RG
We follow the treatment by David Tong of Cambridge University in his Classical Dynamics. A tempicle is defined as a moving object of insignificant time. The motion of a tempicle of vass n at the chronation t is governed by Newton’s Distance Domain Second Law, R = nb or, more precisely, R(t; t′) = h′
Written compositions organized by temporal order are narratives. Items such as descriptions of people, places, or objects are organized as they occur to the narrator, for example, as the narrator takes apart an object or walks through a building or meets various people. This is a common method of composition but there are others. Spatial
This is an update and expansion of the post here. Here is a derivation of the chorocosmic equations of motion, in which acceleration is constant. Let time = t, location = x, initial location = x(t0) = x0, velocity = v, initial velocity = v(t0) = v0, speed = v = |v|, and acceleration =
Note: as the research develops this post will be updated. Introduction Experience shows motion takes place in three dimensions. There are two measures of the extent of motion: length and duration. The length of motion in three dimensions comprises three-dimensional length space. The duration of motion in three dimensions comprises three-dimensional duration space. Length and
What is a clock? it is a device that measures time, but what are the essentials of a clock? I submit these are the essentials of a clock: (1) A clock requires a uniform motion. Because only the kinematics (not the dynamics) are significant, a uniform rotation is acceptable. But because the result will be
The post continues the ones here, here, and here. There are three dimensions of motion. The extent of motion in each dimension may be measured by either length or time (duration). There are three dimensions of length and three dimensions of time (duration) for a total of six dimensions. But there is no six-dimensional metric.
An observer is a body capable of use as a measurement apparatus. An inertial observer is an observer in inertial motion, i.e., one that is not accelerated with respect to an inertial system. An observer here shall mean an inertial observer. An observer makes measurements relative to a frame of reference. A frame of reference
