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Time Dilation by Gravitation Help

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By — McGraw-Hill Professional
Updated on Sep 12, 2011

Time Dilation by Gravitation

The spatial curvature caused by intense acceleration or gravitation produces an effective slowing down of time. Remember the fundamental axiom of special relativity: The speed of light is constant, no matter what the point of view. The laser beam traveling across the space ship, as shown in some of the illustrations in this chapter, always moves at the same speed. This is one thing about which all observers in all reference frames must agree.

The path of the light ray as it travels from the laser to the screen is longer in the situation shown by Fig. 20-7 than in the situation shown by Fig. 20-6. This is partly because the ray takes a diagonal path rather than traveling straight across. In addition, however, the path is curved. This increases the time interval even more. From the vantage point of a passenger in the space ship, the curved path shown in Fig. 20-7 represents the shortest possible path the light ray can take across the vessel between the point at which it leaves the laser and the point at which it strikes the screen.

Fig. 20-6 . As seen from within the ship, the laser beam travels in straight line across the vessel when it is not accelerating.

Fig. 20-7 . As seen from within the ship, the laser beam travels in curved path across the vessel when it is accelerating at a high rate.

The laser device itself can be turned slightly, pointing a little bit toward the front of the ship; this will cause the beam to arrive at the center of the screen (Fig. 20-9) instead of off-center. However, the path of the beam is still curved and is still longer than its path when the ship is not accelerating (see Fig. 20-6). The laser represents the most accurate possible timepiece because it is based on the speed of light, which is an absolute constant. Thus time dilation is produced by acceleration not only as seen by observers looking at the ship from the outside but also for passengers within the vessel itself. In this respect, acceleration and gravitation are even more powerful “time dilators” than relative motion.

Suspending our disbelief again, and assuming that we could experience such intense acceleration force (or gravitation) without being physically crushed, we will actually perceive time as slowing down inside the vessel under conditions such as those that produce spatial curvature such as shown in Figs. 20-7, 20-9 or 20-10. Clocks will really seem to run more slowly, even from reference frames inside the ship. In addition, everything inside the ship will appear bent out of shape.

Fig. 20-9 . Even if the laser is turned so that the light ray hits the center of the screen, the path of the ray is curved when the ship accelerates at a high rate.

Fig. 20-10 . If the acceleration is great enough, the spatial curvature becomes extreme.

Practice problems of these concepts can be found at: Relativity Theory Practice Test

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