Explorations of multidimensional space and time with linear and angular motion.
The first edition of New Foundations for Classical Mechanics (1986) by David Hestenes included “Foundations of Mechanics” as Chapter 9. This was removed for lack of room in the second edition, but is available online as a pdf here. This length-time foundation may serve as a guide for the foundation of mechanics for duration-base. To […]
Let’s follow the orbit of a particle or the route of a vehicle as a curvilinear function with associated directions at every point. Measurement produces travel distance r, travel time t, with directions θ and φ. The directions may be considered as functions of either travel distance or travel time: θr, φr, θt, or φt.
The vass is to time (duration) as the mass is to space (length). As noted before here, the vass can be measured by a similar procedure as the mass. The mass and vass are inverses with opposite uses. The center of mass is the point that two or more particles (point masses) are balanced (or
First, here is a derivation of the spatio-temporal equations of motion, in which acceleration is constant. Let time = t, location = s, initial location = s(t0) = s0, velocity = v, initial velocity = v(t0) = v0, v = |v| = speed, and acceleration = a. First equation of motion v = ∫ a
It is often said that Newton’s laws are laws of nature, which can only be determined by observation. That’s true in the sense that the definitions required are based on inductive reasoning. However, once these definitions are in hand, it should be a deductive science. Here is a derivation of Newton’s spatio-temporal second law, with
I’ve discussed before how there may be two different one-way speeds of light since they are matters of convention. See here and here. This post is concerned with the transformation between two observers in such a case. I continue to work with the standard configuration, see here. The standard transformation of reference frames begins with
This post continues previous ones contrasting ancient and modern space and time, such as here. The above bronze-age depiction of the Sun on a chariot shows a common image from antiquity: the Sun crossing the heavens daily. The path of the Sun was also described as traversing a celestial circle (or sphere) and going around
With circular motion there is a radius and circumference that may be measured as distance or duration. Call the spatial circumference S, and the temporal circumference T, which is known as the period. Distinguish the spatial and temporal versions of the radius, R, and the angle of motion, θ, by using Rs and Rt, and
This post follows on the previous post here, as well as other posts such as here. The one-way speed of light is a convention (see John A. Winnie, Philosophy of Science, v. 37, 1970). The two-way (round-trip) speed of light is known to be c, but the one-way speed may vary between c/2 and infinity,
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
