space & time

Matters relating to length and duration in physics and transportation

Distance domain dynamics

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 = […]

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Four rates of motion

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

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No motion as zero speed or pace

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

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Simple motion for space and time

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

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Places with time

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

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Conventions of here and now

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,

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Places and events

A place is a location within space. An event is a location within time. Past, present, and future are adjectives that modify place or event. We may speak of places in the past or of events in the past. Here indicates the present place. Now indicates the present event. The locus of events in the

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Four space and time dimensions

Since the development of relativity theory, space and time have been combined in a four-dimensional continuum. Because the speed of light is an absolute value in relativity theory, it acts as a conversion factor between space and time. Accordingly, the four dimensions may be understood as any combination of space and time: 4 + 0:

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2D space + 2D time

I’ve written that the perspective of 1D space + 3D time is just as legitimate as the usual 3D space + 1D time. Is there an intermediate perspective of 2D space + 2D time? In a sense, Yes. This is the perspective of 2D images. Maps are usually 2D images of space but they may

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Space and time standards

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

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