Among the instruments on a vehicle there may be a speedometer, an odometer, a clock, and a compass, which provide scalar (1D) readings of the vehicle’s location. But what is the location of the vehicle in a larger framework? The compass shows two dimensions must exist on a map of this framework, but of what […]
We need to distinguish between scalar (1D) and vector (3D) versions of both time and space. Motion in scalar (1D) time and scalar (1D) space is measured by clocks and linear references, respectively, and apply throughout the associated vector space or vector time (in Newtonian mechanics). Scalar time is what a clock measures, which is
The measurement of the length of a motion follows the course of motion at its own pace. It is a measurement of something passive, and the motion may be past when the measurement takes place. Cartesian space lacks direction. The independent axes are just coordinates that describe a passive space. The origin is arbitrary and
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
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.
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
This follows a post on synchrony conventions here. The question is, What is the meaning of here and now for what is observed? Is everything than an observer observes part of their here and now? Some things observed may be a long distance away. Some things observed may be from signals sent in the past,
The value of an independent variable may be selected first, and so is arbitrary, even subjective. One may select anything or everything within its range. A graph normally covers a whole range of the independent variable. Given an independent time interval, different travel rates result in different travel distances or, the other way around, different
Consider two circular motions, one a wheel and the other a clock (click for animations): The wheel is the target motion to be measured. The clock is the reference motion, which maintains a constant angular velocity.
I’ve written about the inverse perspectives of travelers and shippers versus observers and scientists here. This post focuses on the language used, primarily the expectation of what motions larger or smaller values of measures correspond to. For an observer we’re accustomed to larger values corresponding to faster, more powerful motions. But travelers are usually trying
