14.22:
Space-Time Curvature and the General Theory of Relativity
In Newton's gravitational theory, the gravitational force acts instantly across empty space between any two widely separated masses. However, the speed of light is an upper limit for any physical interaction.
Newton could not explain why the mass used in the Law of Gravitation is the same as inertial mass used in his second law of motion.
Einstein stated that since gravity and acceleration are equivalent, the two masses are the same. He addressed the contradiction for speed of light, by re-envisioning space as an invisible fabric called space-time, having three spatial dimensions and one temporal dimension.
He proposed that in the presence of a large mass, this fabric curves and wraps around it. Therefore, any smaller mass follows the shortest path around the larger mass on the curved space-time fabric.
During a total solar eclipse in 1919, a star behind the Sun was visible slightly away from it, as predicted by the general theory of relativity. This observation proved that the light from the star followed the shortest path on the curved space-time around the Sun.
14.22:
Space-Time Curvature and the General Theory of Relativity
In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than the speed of light in a vacuum, which thus serves as the speed limit of the universe.
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of motion, although remarkably accurate even for speeds of many thousands of miles per second, begin to fail when the relative motion between objects approaches the speed of light in a vacuum. Moreover, the special theory of relativity reveals a fundamental limitation of Newton's laws.
According to Newton's laws of motion and Newton's law of gravitation, all actions happen instantaneously. Since Einstein's special theory of relativity states there is a speed limit in the universe, such instantaneous action happening over a finite distance is not fundamentally possible.
In 1915, Einstein proposed a solution to this problem in the general theory of relativity, in which he formalized the principle of equivalence in mathematical terms. According to the theory, gravitation is not a force between two objects; instead, it is an effect of the two objects on the space-time around them, which in turn determines their dynamics.
In the special and general theories of relativity, space and time are treated on an equal footing. The curvature is not of space alone but of the combined entity ‘space-time.'
For weak gravitational fields, the results of general relativity do not differ significantly from Newton's law of gravitation. However, for intense gravitational fields, the results diverge, and general relativity has been shown to predict the correct results. These effects have been observed in our Sun's relatively weak gravitational field at the distance of Mercury's orbit. Since the mid-1800s, Mercury's elliptical orbit has been carefully measured. However, although it is elliptical, its motion is complicated by the fact that the perihelion position of the ellipse slowly advances. Most of the advance is due to the gravitational pull of other planets, but a small portion of that advancement could not be accounted for by Newton's laws. There was even a search for a “companion” planet that would explain the discrepancy at one time. However, general relativity correctly predicts the measurements.
This text is adapted from Openstax, University Physics Volume 1, Section 13.7: Einstein's Theory of Gravity.