The use of space (stance) as an independent variable and time as a dependent variable leads to inverse ratios. There is pace instead of speed, that is, change in time per unit of length instead of change in length per unit of time. But a faster pace is a smaller number, which is counterintuitive and …
What follows are four derivations of the Lorentz transformation from the complete Galilei (Galilean) transformations for space with time (3+1) and time with space (1+3). Their intersection is linear space and time (1+1), which is the focus of the derivations. The other dimensions may be reached by rotations for space or time. I. Space with …
A previous post on this subject is here. One reference for this post is V. A. Ugarov’s Special Theory of Relativity (Mir, 1979). A light clock is a device with an emission-reflection-reception cycle of light that registers the current timeline point and placeline point in units of cycle length and duration. Consider two identical light …
A clock-rod is a linear or planar clock with a parallel rod attached to it. A mechanical or electronic clock-rod might look like this: Three clock-rods mutually perpendicular would measure length and duration in all directions. A light clock-rod is conceptually like this: The clock and rod are parallel to each other so that parallel …
This relates to the post here. There are three dimensions of motion with two measures of the extent of motion, which makes a total of six metric dimensions of motion. But these six metric dimensions collapse into two structures of one and three dimensions as the conversion factor approaches infinity. With the pace of light, …
Is color an absorption phenomena or an emission phenomena? The answer is that it’s both. But absorption works subtractively whereas emission works additively. The question then is whether color is subtractive or additive. Again the answer is that it’s both. Color is a duality. Does an artist work with subtractive colors or additive colors? Here …
From Galileo’s Dialogue Concerning the Two Chief World Systems, translated by Stillman Drake (UC Press, 1967): Salv. Now imagine yourself in a boat with your eyes fixed on point of the sail yard. Do you think that because the boat is moving along briskly, you will have to move your eyes in order to keep …
The Principle of Relativity states that the laws of physics are the same in all inertial frames of reference (IRF). Since a frame of reference includes an orientation, that is, a convention as to which rectilinear semi-axes are positive (and so which are negative), and since there is no preferred frame of reference, each frame …
This is a follow-on to posts here and here. It is common to derive the Lorentz transformation assuming velocity reciprocity, which seems to say that if a body at rest in frame of reference S´ is observed from a frame of reference S that travels with relative velocity +v, then a body at rest in …
Galilean relativity is a relational theory of motion as a function of time, which leads to the Galilean transformation. Here is a defense of Galilean relativity from two postulates: (1) The Galilean principle of relativity, which states that the laws of mechanics are invariant under a Galilean transformation. (2) A convention that rectilinear coordinates for …
