1.3.3 Latticework of clocks

Events are specified by a place and a time of happening, and in spacetime physics these are determined by imagining a cubical latticework, with identical clocks placed at each intersection (Figure 1.7). These clocks are synchronised in light travel time, which means that each clock indicates the time employed by light to reach its point from another reference point. To synchronise these clocks, an imaginary flash of light is made started from the reference clock, which spreads out in all directions as a sphere. Whenever this flash of light reaches a nearby clock, it sets the time for that clock to read, so if a clock is 10 meters away, then it will read 10 meters of light travel time.
The previous paragraph describes how to derive, from the two dimensional spacetime curvature, to the three dimensional stretched model for gravity. What the model in fact represents, is that a mass placed within the lattice, would cause it to stretch inwards as shown in Figure 1.5e. When a ray of light enters the gravitational field of the mass, it will find that the clocks at each of the encountered intersections, get more and more distant as it approaches the mass. On the other hand, it is universally recognised that the speed of light is constant, therefore, the travelling beam of light cannot accelerate to reach the next clock in time such that its speed is measured to be constant.
Considering the drawing of Figure 1.7, if the lattice is stretched from either sides, the space between two nodes or clocks increases, while the two clocks will still read the same time. A beam of light reaching the first clock in the direction of the stretching, must arrive at the next clock at the time indicated on the clock, without accelerating. It does this, because space is not the only thing that gets stretched, in fact, as the two clocks get further apart, they will always read the same time, which means that also the time between the two clocks gets stretched of the same amount. Therefore, to an observer placed between the two clocks, the speed of light will measure the same as an observer placed somewhere else simply because his clock will run slow. As a consequence of this statement, time near a large mass, must run slower on the surface than on a ship in orbit around the mass. Ref. [1][2].


 

Figure 1.7 - Latticework used to determine events in spacetime. Each intersection between two or more sticks is represented by a clock.

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