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

The movement of an object is a change in its spatial and temporal location. The measurement of a movement by a ratio apart from direction is either a speed or a pace. Speed is a change in distance per a given duration. Pace is a change in duration per a given distance. If direction is

This is a re-do of the post Lorentz for space & time both relative? By making a few rearrangements, the contradictions disappear. Case 1 This case begins with: r´ = r – vt or t´ = t – rv/c². Consider then a linear function of these: r´ = γ (r – vt) or t´ =

The solution to the quandary posed in the previous post, Limitations of the Lorentz transformation, is to begin with an alternate form of relative motion. In the case of the stantial component this is r´ = r – tc²/v. The relative stantial transformation is then: r´ = γ (r – tc²/v) and its inverse r

Looking back at the previous posts, we can see that if we begin with the relativity of the spatial component of movement, the Lorentz transformation turns out one way: r´ = γ (r – vt) and its inverse r = γ (r´ + vt´) along with a characteristic speed, c, in all reference frames: r