space & time

Explorations of multidimensional space and time with linear and angular motion.

Travel time and temporal displacement

There’s a basic distinction between the travel distance (or flight length) and the displacement. There should be a corresponding distinction between the travel time (or flight time) and the temporal displacement – which I’ll call the dischronment (dis-time-ment vs. dis-place-ment). The travel time is the total duration of the trip, and the travel distance is […]

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Galileo doesn’t lead to Lorentz

I haven’t mentioned this before because I have a solution to it but there is a problem with deriving the Lorentz transformation from the Galilean transformation. If one uses the spatial Galilean transformation, the gamma factor leads to the Lorentz transformation. But if one uses the temporal Galilean transformation, the gamma factor does not lead

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Transformations for time and space

The standard transformation of reference frames begins with two frames in uniform relative motion along one axis (usually called x). Here we take the spatial axis to be the r-axis, which parallels the spatial axis of motion. Similarly, the temporal axis is taken to be the t-axis, which parallels the temporal axis of motion. One

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Six dimensions of space-time

If one travels a distance X east, then goes a distance Y north, that is the same as going a distance √(X² + Y²) northeast. But if one travels for a time X east, then goes for a time Y north, is that the same as going for a time √(X² + Y²) northeast? No,

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Time scale maps

Maps of travel times have various names, e.g., time scale maps, isochrone maps, etc. Often a geographic map forms the background so that travel time is superimposed on distance traveled. Occasionally, the time scale replaces the distance scale and the map looks distorted from a geographic perspective, but is correct from a travel time perspective.

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A new geometry for space and time

This blog has described how as the distances between places cover three dimensions of space, so the durations between events cover three dimensions of time. One way of looking at this is as a map with the distance and duration given between places, such as this from the Interstate Drive Times and Distances: There are

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Why time is three dimensional

The case for 3D time is very simple: space is based on the measurement of distance and time is based on the measurement of duration. As the distances between places cover three dimensions of space, so the durations between events cover three dimensions of time. As distance may be measured going from or toward a

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Time conventions

The natural concept of time is solar time, which is based on the Sun’s position in the sky. But local solar time or local mean time varies by longitude. With the spread of railroads in the 19th century, there was a need for time zones to standardize time and simplify east and west travel. The

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