The Special Theory of Relativity by Bohm David

Author:Bohm, David [David Bohm]
Language: eng
Format: epub, mobi
Publisher: Taylor and Francis

26

The Minkowski Diagram and the K Calculus

Thus far we have discussed Einstein’s relativistic notions of space and time from a physical and mathematical point of view—the mathematical treatment being based largely on the formulas (14–3) and (14–4) for a Lorentz transformation. We shall now give a geometrical way developed by Minkowski for considering the meaning of the theory of relativity, which helps to bring out the significance of the theory in a different light.

We begin with the so-called “Minkowski diagram” for space and time (see Figure 26–1). In discussing this diagram we first consider an observer Ω1, at rest in the laboratory. We represent the time coordinate as measured by this observer by the line OA and one of the space coordinates (z) by the line OB. In principle we should include the other two space coordinates, x and y, so that the diagram ought to be four-dimensional. However, for many purposes it will be sufficient to deal with z and t, so that a two-dimensional diagram will suffice.

Each point on this diagram refers to an event (such as the flashing of a light signal). Every real event must, of course, take place during some interval of time and occupy some region of space. However, if the time interval is very short and the region of space is correspondingly small, we may replace the actual extended event by the simplifying abstraction of a point event.

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