This is a topic I have addressed before, such as here. In this post I want to show some similarities and differences between the Galilean (Galileo) transformation and what I’m now calling the dual-Galilean transformation. There are many expositions of the Galilean transformation, such as here. It is standard to describe them in terms of […]
It is not well known that the Theory of Relativity is almost misnamed. Relativity was well known in physics since Galileo Galilei. That is, the relativity of space was well known. With Albert Einstein’s derivation of the Lorentz transform, the relativity of time was introduced. But the relativity of time was not of the same
Motion science is variously called mechanics, dynamics, kinetics, or kinematics. This post will be concerned with the study of motion apart from its causes or consequences. Kinematics is the branch of classical mechanics which describes the motion of points (alternatively “particles”), bodies (objects), and systems of bodies without consideration of the masses of those objects
Note: previous posts on this topic are here and here. Motion flows. That is, there is always motion independent of us. We can also make standard motions that are effectively independent of us. They are called clocks. They can be used as standards of comparison to measure other motions. Clocks are needed for synchronous measurement
Although there are three dimensions of length and three dimensions of duration, I have pointed out before that we measure movement as either 3D length + 1D time (3+1) or 1D stance + 3D duration (1+3) or 1D stance + 1D time (1+1). The (1+3) perspective is the focus of this post. The measurement of
I have a “metric cube” which is a decimeter-sized cube that was used in the 1990s to promote the metric system: It was useful to hold 90mm discs but could also be used as a 3D ruler to measure length in three dimensions at the same time. One could instead use a 1D ruler three
What would it mean for space to be one-dimensional? It would be similar to 1D time. Imagine a clock, except that instead of marking durations, it marks distances. It’s like an odometer for a vehicle that moves at a constant speed and never stops. Like this with units of distance (metres, kilometres, miles, etc.):
In a sense every speed is a local conversion of space and time. But a characteristic speed (or modal speed) has the following properties: (1) The speed is relative to a mode of travel or movement. (2) The speed reflects extreme travel conditions in the mode. (3) The speed serves as a general conversion between
Observation changes conceptions. A full conceptual space-time is pre-observation, not a priori in Kant’s terms because it comes after many observations and experiments. It is a categorical induction: a conceptional scheme that makes observational sense and forms the basis for deduction. That is how science operates. With a conception of space-time in hand, one may
I’ve written about terminology and used new terms before, for example, Movement and dimensions. I want to take another look at coining new terms needed for studying movement and the symmetry of space and time. In what follows, the terms pace, lenticity and relentation have new senses. Consider these parallel terms, defined with respect to
