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Relativistic Definitions

Frames of Reference

We now need to be more precise about some of the terms that we will be using. Observers are simply people or instruments capable of making and recording measurements. Einstein's special theory of relativity is based on the idea of reference frames. A reference frame is simply "where a person (or other observer) happens to be standing". You, at this moment, are probably sitting at your computer. That is your current reference frame. You feel like you are stationary, even though you know the earth is revolving on its axis and orbiting around the sun. Here is an important fact about reference frames: There is no such thing as an absolute frame of reference in our universe. By saying absolute, what is actually meant is that there is no place in the universe that is completely stationary. This statement says that since everything is moving, all motion is relative. Think about it - the earth itself is moving, so even though you are standing still, you are in motion. You are moving through both space and time at all times. Because there is no place or object in the universe that is stationary, there is no single place or object on which to base all other motion.

A frame of reference can also be thought of as a set of three orthogonal meter sticks, with a clock attached. The meter sticks provide coordinates with respect to which we can measure the position of objects or events, and hence their displacements as they move. The clock is needed to measure time, so that we can measure velocities and accelerations. Of course, such a frame of reference is useless unless it also holds an observer. Since both the observer and the frame of reference are crucial and hence inseparable for the following, we will often use the terms interchangeably. Both terms will refer to a system of measuring sticks and a clock, with the mechanism to record observations. For simplicity, we will restrict consideration to motion in one direction, so that each frame of reference only contains one-meter stick and all the meter sticks in every frame of reference point along the same direction. v.

Gamma ( )

The measurable effects of relativity are based on gamma. Gamma depends only on the speed of a particle and is always larger than 1. By definition:

For example, when an electron has traveled ten feet along the accelerator is has a speed of 0.99c, and the value of gamma at that speed is 7.09. When the electron reaches the end of the linac, its speed is 0.99999999995c where gamma equals 100,000.

What do these gamma values tell us about the relativistic effects detected at SLAC? Notice that when the speed of the object is very much less than the speed of light (v << c), gamma is approximately equal to 1. This is a non-relativistic situation (Newtonian).