Symmetric laws of physics

Because of the symmetry of space and time, the laws of physics should be symmetric in space and time, or at least show their symmetry. Granted, one must either use the speed (change in position per unit of time) or the pace (change in time per unit of length). But other than such choices, the form of a law of physics should show the symmetry of space and time.

I have written on Galileo revised, in which the symmetry of space and time leads to a modification of the Galilean transformation. The addendum includes the need to make the transformations for space and time similar. If the spatial displacement is r, the temporal displacement is t, the relative velocity v, relative lenticity u, conversion constant from time to space is c, from space to time is c´, β = v/c, and β´ = u/ = 1/β, then the following transformations fulfill these requirements:

= (1 – β) r and= (1 – β) t, or

= (1 – β´) r and= (1 – β´) t.

The same requirements may be applied to the Lorentz transformation as well, with its inclusion of the Lorentz factor, γ, and a similar factor, γ´:

= (1 – β) γr and= (1 – β) γt, or

= (1 – β´) γ´r and= (1 – β´) γ´t.

where γ2 = c2 / (c2v2) = 1 / (1 – β2) and γ´2 = 2 / (2u2) = 1 / (1 – β´2) = 1 / (1 – 1/β2).

The similarity between these transformations is remarkable. Since (v/c)2 approaches zero faster than (v/c), the Lorentz factor approaches one and the Lorentz transformation approaches the revised Galilean transformation for relatively small velocities. Both transformations include a standard conversion between time and space, that is, an absolute speed, contrary to the original Galilean (and Newtonian) assumption of an absolute time.