Explorations of multidimensional space and time with linear and angular motion.
This post relates to the previous post here, as well as posts on light conventions here and here. There comes a point in science in which a convention needs to be adopted in order to avoid confusion and ensure consistency. The tendency, however, is to think that the convention adopted is real, that is, that […]
A theory of levity might be hilarious but the basic sense of the word levity is lightness, the opposite of gravity’s heaviness. In Aristotle levity is like buoyancy, as some things in water float and others sink. Aristotle commits himself to gravity and levity as two distinct qualities, both of them positive. Fire has levity
This post is related to the one on circular orbits. I’ll continue to follow the exposition in Elements of Newtonian Mechanics by J.M. Knudsen and P.G. Hjorth (Spriner, 1995), this time starting with page 33. As before, the point is to derive a temporo-spatial theory that is symmetric with the spatio-temporal one. Although the parallel
This post is related to previous ones about base + 3D duration (3D time), such as here and here. Time is measured in terms of the annual calendar and the daily clock. Clocks are based on the apparent motion of the Sun and other celestial bodies across the sky, divided into 24 hours. The calendar
This follows posts on synchrony conventions such as here. Astronomers say things like this: “it takes sunlight an average of 8 minutes and 20 seconds to travel from the Sun to the Earth.” The statement above assumes the Einstein convention that the one-way speed of light is isotropic and so equal to one-half of the
Two key expressions for time domain dynamics are the momentum and the kinetic energy. Here we derive the corresponding distance domain expressions, which are called the levamentum and the kinetic lethargy. The momentum and kinetic energy are the force through time or space: momentum = mv = F Δt, an kinetic energy = mv²/2 =
The speed of a motion is its length of travel per unit of duration. Symbolically, speed is Δr/Δt. Pace is its duration per unit of length. Symbolically, pace is Δt/Δr. In both of these ratios, the denominator is chosen independently of the numerator. That is, the denominator is selected first, and then the numerator is
What does “no motion” mean for the measurement of speed or pace? There are two cases of no motion: either (1) the trajectory length is zero or (2) the trajectory duration is zero. Consider first the speed ratio (Δr/Δt). (1) the trajectory length is zero: then the speed is zero because it equals zero length
This post continues the discussion here and here. Simple motion is “a motion in a straight line, circle or circular arc, or helix”. Since a helix and all other motions are a combination of linear and circular motions, simple motion may be considered as linear or circular motion. There are two basic measures of simple
Although several new terms have been introduced on this blog (see glossary here), more are needed. For every concept and term about space there is a corresponding concept, and should be a corresponding term, about time. A place is “a particular portion of space, whether of definite or indefinite extent”. The corresponding term is a
