Explorations of multidimensional space and time with linear and angular motion.
Expanding on the previous post here, this is a summary of the equations of motion for space-time and time-space. See also the Time-space Glossary option above. r = displacement magnitude, t = time magnitude, v = velocity, v0 = initial velocity, a = acceleration, w = lenticity, w0 = initial lenticity, b = relentation. Space-time […]
The classic equations of motion are for 3D space + 1D time (3+1). Equations of motion for 1D space + 3D time (1+3) were presented here. How do these equations relate to each other? Can one convert directly from one form to the other form? Consider 1D space + 1D time (1+1), which can be
I’ve compiled a glossary of new terms on the top menu of this blog, or see here. These terms were coined for the study of 1D space + 3D time. It will be updated as needed. A parallel comparison of spatio-temporal and temporo-spatial terms was added here.
An isodistance map shows the contours of equal distances from a central point. These would be circles on a map if distance is measured “as the crow flies.” The shapes vary if distance depends on a road network: But how do you tell if two distances are the same? Different observers have different distance measuring
I have written about the characteristic (modal) rate for a mode of travel. This rate provides a factor for converting spatial into temporal measures and vice versa. The characteristic rate is the maximum (free flow) rate, though it could be the minimum rate. A characteristic rate is independent of any and all particular rates in
What I’ve called the characteristic rate (modal rate) of travel or motion may be any rate independent of the travel mode, such as the minimum or maximum rate. The best-known example is the speed of light in a vacuum, c, which is generally considered the maximum speed for physics. A characteristic rate that is a
What is the “distance” between two point events? That would include the length in both space and time. The measurement of the length of time between events depends on the mode of travel between them. For example, the time between leaving one’s residence and arriving at work depends on how one commutes. If the trip
This is a continuation of a series of posts, see here. V Temporal direction is direction in a 1D space + 3D time geometry. So to understand direction in 3D time, one must understand a certain context. This is like understanding a map because direction is something that appears on a map but not a
How practical is the mechanics of time-space? It’s at least as practical as the mechanics of space-time and in some case is easier to understand or more appropriate. This post continues a series to illustrate this based on the website Physics: Problems and Solutions, Kinematics. Problem 2.1 Is it possible that a vehicle could relentate†
Traditional expressions and units are often associated with motions. For example, English farmers used the distance and area of land that their animals could plow for units of measure: A furlong was the length of a plowed furrow, i.e. furrow-long. An acre was the area that could normally be plowed by an ox in a
