Since Newton, time has been the usual and ultimate independent variable for physics. This contrasts with problems in transportation, where time is often optimized. Whether transporting goods across the world, commuters across town, or athletes to the finish line, length is the independent variable against which time is measured and optimized. If length is taken […]
The temporo-spatial kinematic units are straightforward opposites of spacio-temporal units: Dischronment has units of seconds, minutes, hours, days, or years. Pace and lenticity have units of distance over duration: s/m or min/km or min/mile. Compare speed and velocity with their units of m/s, km/hr, or mi/hr. Relentation has units of s/m² or min/km² or min/mile². Compare
This is an outline of an article on “The Symmetry of Space and Time”. I’ll update it as needed and add links to the parts as they are written. 0.0 Abstract 1.0 Introduction 1.1 Examples of multi-dimensional time, ancient and modern 1.2 Reference to related work 1.3 Overview of the paper 2.0 Simple motion in
First we show the work and energy in the linear motion of a particle with space-time (see J.M. Knudsen and P.G. Hjorth’s Elements of Newtonian Mechanics, 1995, p.51). Consider a particle of mass m moving along the r axis of r so all quantities are scalars. Newton’s second law is then m d²r/dt² = F,
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
