Minkowski space-time diagram

Non-locality in terms of special relativity is best explained by the Minkowski space-time diagram, shown in figure 2. A stationary object follows a world-... 

The field equations of general relativity are rarely used without simplifying assumptions. The most common application treats of a mass, sufficiently distant from other masses, so as to move uniformly in a straight line. All applications of special relativity are of this type, in order to stay in Minkowski space-time. A body that moves inertially (or at rest) is thus assumed to have four-dimensionally straight world lines from which they deviate only under acceleration or rotation. The well-known Minkowski diagram of special relativity is a graphical representation of this assumption and therefore refers to a highly idealized situation. 

The common two-dimensional representation is done in terms of a time axis and one space axis, which is interpreted as three space directions at the same time. The so-called time cone, and by implication the complementary space cone, extends into a further undefined dimension, perpendicular to the x,t plane of the diagram. To get the complete picture it is necessary to superimpose three mutually perpendicular Minkowski bodies of this type, which is only posssible in four dimensions. In this superposition the time axis does not remain fixed and becomes entangled with the space directions as seen in three-dimensional space. The three-dimensional surface of the generalized hght cone of Figure 4.2 becomes a surface in four-dimensional space-time that separates all space into two equivalent regions. 

Minkowski therefore considered that the s-diagram represents the universe as it really is. He suggested that the separation of events which exist in the s-diagram into a series of happenings in space and time is due to the one-sided view which any particular observer necessarily gets. This is discussed more fully in Appendix 16. 

Figure 3.2 Minkowski diagram showing three space dimensions x drawn perpendicular to the direction of time flow t.

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