by David Colarusso - April 21st, 2007
Last time we covered the two postulates of special relativity, and next time we’ll use geometry to derive some of its consequences, but first we need to learn some nomenclature. It’s not exciting, but it will prove helpful in the long run.
The Tabletop Explainer
Episode Eight (9)
Special Relativity (2 of 5): Nomenclature
Last week we covered the two postulates of special relativity, and next week we’ll use geometry to derive some of its consequences, but first we need to learn some nomenclature. It’s not exciting, but it will prove helpful in the long run. Keep an eye out for the following terms: space-time diagram, line of constant position, line of constant time, space-time event, and world line.
We’re used to documenting things with film, but let’s make things even simpler. Say we replace film with a large roll of paper and attach a marker to those objects we find interesting. For now, this block on wheels, and a road sign. All the while our paper moves with a constant speed downwards. This produces what physicists call a space-time diagram.
By virtue of our setup, the vertical contains information about time and the horizontal about position. The lines traced by the markers are know as world lines because they document the history, the world, of their owners.
To read our diagram, we employ the use of constant lines of position and time.
A line of constant position represents one place. Any collection of events occurring on a line of constant position occur at the same place, just at different times.
Similarly, a line of constant time represents one instant. Any collection of events occupying a line of constant time take place at the same time but in different places.
This diagram is simply a graph of time verses position.
With our two types of constant lines, we can define any point in our diagram. Such a point represents a particular place at a particular time, something we’ll call a space-time event.
A world line is nothing more than a record of these events for its owner. By working backwards, from our intersection of constant lines we can tell where and when something happened.
Next time, we’ll make use of space-time diagrams and the two postulates to derive consequences of special relativity using only simple geometry.