physics

Symmetries and relativities

Total energy is conserved because time is homogeneous (time translation invariance). Total linear momentum is conserved because space is homogeneous (space translation invariance). Total angular momentum is conserved because space is isotropic (rotational invariance). These are examples of how symmetries determine the laws of physics. Another way of looking at it is that linear and …

Distance, duration and dimension

There are many kinds of space. The most common space is that of positions, that is, distances and directions. There is also velocity-space. There is force-space. There is duration-space, too. Particles travel on trajectories, points move on curves, vehicles travel on streets or routes, etc. Trajectories have distances traveled, travel times (durations), velocities, accelerations, etc. …

Coordinate lattices

Rindler’s Essential Relativity is a well-written monograph that we can use to explore time and relativity. He describes the coordinate lattice of a single inertial frame of reference (section 2.5). Let us consider it with an eye toward the corresponding temporal coordinate lattice. Start with the observer at the origin of an inertial frame, with …

Independent and dependent time

We are so accustomed to having time as the independent variable that it takes effort to think of it as the dependent variable. This reflects the Newtonian absolute time. But either time or space can be an independent variable. The Einsteinian the use of simultaneity is another reflection of the independence of time. If time …

It’s time to list the claims about time made in this series of blog posts. Time is 3-dimensional. This is the over-arching claim which is explained and expanded by the other claims. Time is duration with direction. That is, time is a vector variable similar to a position vector in space. Time as ordinarily conceived …

Reality and relativity

As a realist I respect what is often called “common sense.” This means that our faculties of discerning reality in everyday life are basically correct. Yes, we make some mistakes, we can get fooled by a illusionist, but we almost always agree what it is that happens when things happen to us or in front …

What is single-value time?

Time is commonly expressed by a single value, a numerical expression of a point in time. A sequence of these points is also called time. Because of this, time is commonly considered one-dimensional. Since time actually has three dimensions, what does this single value for time represent? It must be some function of the three-dimensional …

Parametric time and space

Parametric equations are equations in terms of a single parameter. An example is the parametric equation for a circle: x = r cos(t), y = r sin(t), for a circle with radius r with rectilinear coordinates x and y. It’s best if the parameter represents a causal variable but time is often used whether or …

Speed and its inverse

Physics and transportation have many things in common, in particular they both deal with objects that move or travel. The case of an object that happens to stay in place should be considered as well. An object that may move is called a body or particle or vehicle. The path, route, or course of an …

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 …