iSoul In the beginning is reality

Movement and dimensions

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 combined with the ratio, it is either a velocity or a celerity. Velocity is a speed with direction. Celerity is a pace with direction.

There is a relation between measures of movement and dimensions. If movement is measured by velocity, the denominator is a vector of space, which means space is considered multidimensional. But if movement is measured by celerity, the denominator is a vector of time, which means time is considered multidimensional.

Max Tegmark in his 1997 letter On the dimensionality of spacetime gives his judgment concerning the number of space and time dimensions in a chart:

TegmarkThe chart indicates that one space dimension with three time dimensions (1+3D) includes only tachyons (objects traveling at more than the speed of light) and not bradyons (or tardyons, objects traveling at less than the speed of light). Bradyons exist in 1+3D, see Subluminal and superluminal Lorentz transformations.

The statement “We are here.” for 3+1D reflects its status as a cultural commonplace and the use of velocity. There is however equal justification for using 1+3D and celerity. Minkowski showed the way to use either 3+1D or 1+3D by using hyperbolic geometry.

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