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 […]
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†
Although the six dimensional space-time invariant interval represents space and time, we do not observe it as 6D. Instead, we observe space and time as 4D in one of two ways. The full 6D space-time interval expressed in spatial units is: s² = Δr² – c²Δw² = Δr1² + Δr2² + Δr3² – c²Δw1² –
A bidirectional transformation applies to all observers, and so must work for any direction, including observer and observed with the roles switched. A physics for all observers should be bidirectional if possible. This works for mechanics but for thermodynamics entropy is inherently directional. The Galilean transformation is for one direction with no characteristic (modal) rate.
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
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
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
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,
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
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
