Explorations of multidimensional space and time with linear and angular motion.
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 […]
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:
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
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
Space is measured from a specified point, which is called an origin or zero point in space. The spatial location of all other points in space are relative to this zero point. The zero point may represent “here” from which other locations near and far are measured. Or the zero point may be a beginning
Clocks can easily be placed on moving bodies or observers to measure travel time continuously. A moving body can have on-board devices to measure cumulative travel distance. Observers have more difficulty measuring the cumulative travel distance of an external body but it can be done by motion tracking devices. If the distance is long, multiple
This post follows the previous one on circular motion. A timeline shows a linear representation of time (click to enlarge): A calendar can be linear, too: Linear calendars and clocks could be thought of as representing a kind of distance. It’s as if a clock were fastened to a wheel moving along a line. The
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.
As I’ve noted several times, the physics of the observer takes duration as the dependent variable and measures the corresponding length or other variable. This fits well with the finding that gravity is an approximately constant acceleration, g, which equals 9.81 m/s². What is gravity in the context of an independently chosen distance and dependent
The Sun is like a clock. Sun and sundial (click for animation) Hours correspond to the Sun’s motion. 24-hour clock (for animation click here) This 24-hour clock is a representation of looking south. The sun rises on the left and sets on the right. At noon the sun and the clock appear straight up.
