space & time

Movement in its simplest form is a trip from A to B. There are two ways one can look at such a movement: (1) as the line segment from A to B, or (2) as the angle between the lines from A to a reference point and A to B. Each of these may be […]

The dimensions of an object are measured by movements, whether by moving a measuring device or moving one’s eyes while a measuring device stays in the same position. Movements themselves are measured by comparing them with standard movements, such as a movement with constant velocity. A movement compared with a standard linear movement generates a

Since time is three-dimensional, what is the total time given the time in each dimension? The answer is exactly like the total distance. Consider the times t1, t2, and t3. If these are the coordinates of three successive movements, then the total time is their sum: t = t1 + t2 + t3. But if

The instantaneous movement of a particle may be represented by a velocity vector, which describes an instantaneous motion by its magnitude and direction: the magnitude is the ratio of the differentials of the distance and time in each dimension of the movement (dri/dti); the direction is the direction of the instantaneous tangent in each dimension

Our culture is oriented toward space, geography, geometry, and spatial relationships. We can easily understand items on a map. Even time can be put on a map, as with an isochrone map such as the contour lines (isochrones) representing equal distances or drive times from an urban center. 3D visualizations extend this to more dimensions.

I keep going over this because it has been so overlooked for 100 years. The Galilean transformation (GT) is based on three space dimensions and one time dimension (3S+1T). Once it is realized that time is just as dimensional as space, there is a dual Galilean transformation based on one space dimension and three time

To measure means to compare with a standard. A physical movement may be measured in terms of the most direct movement between its beginning and ending. There are two kinds of measures of movement, magnitude and angle, which each have two aspects, spatial and temporal. First, the magnitude of movement: (1) Spatial measurement of the

It’s a good exercise to check the invariant interval for both subluminal and superluminal objects. Let’s do this with the delta form of the Lorentz transformations: Subluminal case: This is a check that c²(Δt´)² – (Δx´)² – (Δy´)² – (Δz´)² = c²(Δt)² – (Δx)² – (Δy)² – (Δz)². The Lorentz transformation is cΔt´ = γ (cΔt – vΔx/c), Δx´

Because of the directionality, symmetry, and convertibility of space and time, there could be three dimensions of both (3S+3T). However, the formation of rates, notably velocity and lenticity, effectively reduces the dimensionality to either three dimensions of space and one of time (3S+1T) or one dimension of space and three of time (1S+3T). Also, the

The conventionality thesis in physics concerns the conventionality of simultaneity, which states that the choice of a characteristic synchrony is a convention, not an observable. This arises because the speed of light in a vacuum can only be measured as a two-way speed, so the one-way speeds are either taken to be the same (the