The Science of Time: This is taken from appendix 5 of my new book, How to Time Travel, which will be available on Amazon in early September 2013.

What happens as the frames of reference move at velocities close to the speed of light? To address this question, we need to discuss the Lorenz transformation.

Time is relative (Lorenz transformation)

To transfer the time coordinates between frames moving close to the speed of light, an entirely new transformation methodology needed to be developed. Einstein became painfully aware of this during the development of his famous special theory of relativity. As a result, he utilized the Lorenz transformation. Some authors give Einstein credit as having developed the Lorenz transformation. This is not historically correct. The Lorenz transformation was in existence prior to Einstein’s publication of the special theory of relativity in 1905. In fact, numerous physicists, including Voigt (1887), Lorentz (1895), Larmor (1897), and Poincaré (1905), contributed to its formulation. It was Poincaré, in 1905, who brought it into its final modern form and named it the Lorenz transformation. It is fair, though, to say that Einstein rederived the Lorenz transformation in the context of special relativity.

Just what is the Lorenz transformation, and how does it treat the time coordinate between frames moving at a constant rate close to the speed of light? It takes into account that light travels at a finite speed (approximately 186,000 miles/second), and that speed is a constant in any frame of reference moving at a constant velocity, typically referred to as an inertial frame of reference. As a result, according to the Lorenz transformation, different observers moving at different velocities or at rest will not measure time in the same way. Indeed, they may measure different elapsed times, and even a different orderings of events.

Time as a coordinate

At this point, it may appear obvious that time is a coordinate. Both the Galilean and Lorenz transformations view time as a coordinate, and they only differ in how they translate the time coordinate between initial frames of reference. Intuitively, when you think of time as a coordinate, it makes sense. For example, when you set a meeting, you not only set the place (i.e., the spatial coordinates), but the time (i.e., the temporal coordinate). In this context, time is a coordinate (i.e., also known as “coordinate time”). This terminology distinguishes it from “proper time,” which is not a coordinate, but rather a process. In Einstein’s special theory of relativity, “proper time” (also known as “clock time”) is a measure of change, such as the number of rotations of a simple mechanical clock’s hands. It is arbitrary. For example, proper time may refer to the time it takes a candle to burn down to a specific point. Before we go further, let us be perfectly clear on the distinction of time as a coordinate (“coordinate time”) and proper time (“clock time”). If you specify that you will meet someone at a specific time, you are using “coordinate time.” If you say it takes the second hand of your watch one minute to make a compete revolution, you are talking about proper time (“clock time”). You may wonder if coordinate time and proper time are related. It turns out they are. Einstein’s special theory of relativity relates coordinate time, proper time, and space to each other via spacetime, which we will discuss next. Stay tuned for The Science of Time – Part 3/3