# Knowing

epistemology, science, kinds of knowledge, methodology

## General Galilean invariance

The following is generalized from the explanation of Galilean invariance here. Chorocosm (inertial frames) Among the axioms from Newton’s theory are: (1) There exists an original inertial frame in which Newton’s laws are true. An inertial frame is a reference frame in uniform motion relative to the original inertial frame. (2) All inertial frames share …

## Worlds of motion

Kinecosm is the world of motion, which is the subject of kinematics. Since the extent of motion has two measures: length and duration, the kinecosm has two subworlds: Length space is the three-dimensional world of length, which is commonly called space. Duration space is the three-dimensional world of duration. Chorocosm is length space with time. …

## Time transformation

The length part of the Galilean transformation is: with the relative velocity v. The time part of the Galilean transformation is: so that time is the same for all observers. Einstein made time relative and symmetric with length (at least in one dimension) by assuming an absolute speed of light, c. With β = v/c …

## Rod-clocks and clock-rods

Consider an analogue clock with a dial and a hand, i.e., a pointer, reimagined as two circular bands: The Dial band is at rest relative to the observer and the Hand band turns clockwise at a fixed rate. The pointer on the Hand band points to the marking on the Dial band that indicates the …

## Harmonic motion with inertial reference frames

This post is similar to the post on light clocks here. Simple harmonic motion (SHM) is like the spring below: The equation for describing the period is where T is the period, m is the mass, and k is the spring constant. The displacement for each cycle is zero since it returns to its starting point. …

## Rod-clocks in a frame of reference

Space is the three-dimensional domain in which motion occurs. Time is a one-dimensional domain in which a reference uniform motion occurs. The extent of a motion is measured either as a length or a duration by a rod-clock. A rod-clock is a linear rod combined with a linear clock, like this: The pointer moves in uniform …

## Lorentz with round-trip light

This builds on the post Lorentz transformation derivations but given the round-trip light postulate (RTLP) here which states: The mean round-trip speed of light in vacant space is a constant, c, which is independent of the motion of the emitting body. From this empirical principle the round-trip Lorentz transformations may be derived, which are of the …

## Defining multi-dimensional time

The revised SI metric system is based on seven defined constants and seven base units. One defined constant is c, the (round-trip mean) speed of light in a vacuum, is defined as exactly 299 792 458 metres per second (before metres and seconds are defined). The unit of time, the second, is defined as (2019): …

## Newtonian light wave front

Consider the standard relativity configuration. Let a spherical light wave be emitted from the coincident coordinate origins at t=0 and t′=0. For the rest frame, the spherical wave front is given by x² + y² + z² = c²t². For the frame moving at velocity v parallel to the x-axis, two-way light must be considered. …

## Time-space transformations

This post is based on David Tong’s Newtonian Mechanics, 1.2.1 Galilean Relativity. Given one facilial frame system, S, in which a tempicle has coordinates t(x), we can always construct another facilial frame system, S′, in which a tempical has coordinates t′(x) by any combination of the following transformations: Translations: t′ = t + a, for …