11.5 Space-Time in Relativity

11.5 Space-Time in Relativity

Space is said to be a three-dimensional extent in which all objects and events occur. It provides a framework to define the position and motion of various objects under the influence of some force.

Time measures the sequence and duration of events. In the theory of relativity, time is not absolute; it is considered the fourth dimension. For example, oscillatory motion, such as that of a swinging pendulum, relies on time to determine the frequency of oscillations. Another example is time dilation, a phenomenon discussed earlier in this chapter, where time passes more slowly for an observer moving at extremely high speeds compared to one at rest. The special theory of relativity explains that space and time are related to each other. It describes how space and time are influenced by gravity and speed, such as the bending of light around massive objects like stars.

Space-time is, in fact, a mathematical model that unifies space-time into a single continuum. It is a concept used to describe all points of space and time and their relation to each other. According to Einstein's theory, space-time is curved especially near massive bodies and for speeds approaching the speed of light. We can hypothetically visualize this as a fabric sheet. If a heavy ball is placed over this sheet, it curves as shown in Fig. 11.2.

Objects such as stars and planets cause space-time to curve around themselves, much like an elastic fabric deforms when holding a ball. The more massive the object, the deeper the curve.

Consequently, we do not speak of a force of gravity acting on bodies; instead, we say that bodies and light rays move along geodesics (analogous to straight lines in plane geometry) in curved space-time. Thus, a body at rest or moving slowly near a massive object would follow a geodesic toward that object.

Einstein's theory provides a physical picture of how gravity works. Newton discovered the inverse square law of gravity but explicitly stated that he offered no explanation for why gravity should follow this law. Einstein's theory also describes gravity as following an inverse square law (except in strong gravitational fields), but it explains why this is so. This is why Einstein's theory is considered an advancement over Newton's, even though it encompasses Newton's theory and yields the same results as Newton's theory in all but very strong gravitational fields.

The bending of starlight caused by the Sun's gravity was measured during a solar eclipse in 1919. The results matched Einstein's theory rather than Newton's, leading to Einstein's theory being hailed as a scientific triumph. Another success of Einstein's theory was the detection of gravitational waves, produced by some celestial events causing disturbances (squeezes and stretches) in the curvature of space-time. These waves were detected in 2015 and announced in 2016.

Bending of starlight by the Sun

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Light from the star $A$ is deflected as it passes close to the Sun on its way to Earth. We see the star in the apparent direction $B$, shifted by the angle $\phi$. Einstein predicted that $\phi = 1.745$ seconds of angle which was found to be the same during the solar eclipse of 1919.

Hypothetical Example of Space Time

Let a spaceship be travelling to a star with half of the speed of light. Let it takes eight years to reach to the star, from the point of view of the observer on the Earth. From the Earth's point of view, the clocks on the spaceship are moving slowly, so that less time passes on the spaceship compared to the Earth.

For the spaceship occupants, the length of the journey has contracted which they cover in less time. The occupants of the spaceship record $7$ years to reach their destination, rather than $8$ years.

Interesting Information

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If you are on some spaceship moving extremely fast through space near a black hole like in movie, "Interstellar" then you could miss $7$ years on the Earth in every hour.