# physics

## Symmetry of space and time

The duality between space and time leads to many dual principles. For example, Fermat’s principle says that light travels between two given points along the path of shortest time. The dual to this is that light travels between given points in time along the path of shortest length in space. But as long as there …

## An introduction to dual physics, part 2

According to the McGraw-Hill Dictionary of Physics, mass is “A quantitative measure of a body’s resistance to being accelerated; equal to the inverse of the ratio of the body’s acceleration to the acceleration of a standard mass under otherwise identical conditions.” This is because the ratio of two masses equals the inverse ratio of the …

## An introduction to dual physics, part 1

In order to keep things as simple as possible, I’m starting to name the dual to standard physics with the qualifier “dual”, so that dual physics, dual mechanics, dual speed (not two speeds), dual velocity, etc. refer to their dual terms. Like tangent and cotangent, there is an inverse relationship between physics and dual physics. …

## Terminology for space and time, part 1

There are several senses of the words space and time that need to be carefully distinguished in order to avoid confusion. Let’s start with natural philosophy in the tradition of Aristotle: Space is “the feature of physical being according to which each such being can be identified as occupying a place — and, as such, …

## Direction and units of magnitude

I want to clarify the statement in the previous post that “the three dimensions of direction are the same for space and time”. I have made the point that vectors in physics have various units of magnitude but direction is the same for all of them. That is accurate in the sense that directionality is …

## Six-dimensional spacetime

First consider the dual to Minkowski spacetime. Recall that the invariant interval of Minkowski spacetime has one dimension of time with three dimensions of space: (ds)² = (c dt)² – (dx1)² – (dx2)² – (dx3)² = (c dt)² – (dr)² where t is the time coordinate and x1, x2, and x3 are space coordinates of …

## Duals for Galilean and Lorentz transformations

In Newtonian mechanics inertial frames of reference are related by a Galilean transformation and time is absolute. In the special theory of relativity (STR) inertial frames of reference are related by a Lorentz transformation and the speed of light is absolute. By taking account of the three dimensions of time with a single dimension of …

## Geometric vectors in physics

The concept of a vector in physics is similar to that of mathematics: a geometric object with both magnitude and direction. The magnitude is in units that may be any physical units. The direction is in angular units such as radians or degrees. These are called geometric vectors (also known as Euclidian vectors). Note that …

## Speeds and velocities

A common word-problem in arithmetic goes something like this: If someone takes a road trip and for half of the time they go one speed and for the other half they go another speed, how should their average speed be determined? The answer is that the average speed is the arithmetic mean of the two …

## Direction and dimension

What does it mean to say that space has three dimensions? It means that space has directions that have three dimensions, that is, three degrees of freedom. The dimensions are the directions in the space. It’s not that there are some dimensions that are spatial and others are something else but that space is characterized …