# General Relativity

## History, Basic Concepts Of The Theory, Consequences Of General RelativityGeneral relativity, Experimental verification

The theory of relativity was developed by the German physicist Albert Einstein (1879–1955) in the early twentieth century and quickly became one of the basic organizing ideas of **physics**. Relativity actually consists of two theories, the special theory (announced in 1905) and the general (1915). Special relativity describes the effects of straight-line, constant-velocity **motion** on the **mass** and size of objects and on the passage of **time**; it also states that mass and **energy** can be transformed into each other and that movement faster than the speed of **light** is impossible. General relativity describes the effects of curved or accelerated motion and of gravitational fields on mass, size, and time; it also states that **matter** and "empty" **space** influence each other in a complex fashion and that the Universe is finite in size. According to relativity, our commonsense notions of space and time are only approximately true at best and are completely unreliable in many situations (e.g., in intense gravitational fields or for relative speeds approaching that of light). Relativity's predictions have been extensively tested by experiment and found to be highly accurate; relativity is thus a "theory" in the scientific sense that it is a structure of ideas that explains a specific aspect of nature, not in the sense of being doubtful or speculative.

*Principle of equivalence*

Einstein's general theory of relativity, announced in 1915, uses the principle of equivalence to explain the **force** of gravity. There are two logically equivalent statements of this principle. First, consider an enclosed room on the Earth. In it, one feels a downward gravitational force. This force is what we call weight; it causes unsupported objects to accelerate downward at a rate of 32 ft/s^{2} (9.8 m/s^{2}). Now imagine an identical room located in space, far from any masses. There will be no gravitational forces in the room, but if the room is accelerated "upward" (in the direction of its ceiling) at 9.8 m/s^{2}—say, by a rocket attacked to its base—then unsupported objects in the room will accelerate toward its floor at rate of 9.8 m/s^{2}, and a person standing in the room will feel normal Earth weight. We experience a similar effect when we are pushed back into the seat of a rapidly accelerating car. This type of force is termed an inertial force and is a result of being located in an accelerating (noninertial) reference frame. The inertial force acts in the opposite direction of the acceleration producing it (i.e., the room accelerates toward its ceiling, objects in the room "fall" toward its floor). Is it possible to tell, solely by means of observations made inside the room, whether the room is on Earth or not? No; the conclusion is that gravitational forces are indistinguishable from inertial forces in an accelerating reference frame.

What if the room in space is not accelerating? Then there will be no inertial forces, so objects in the room will not fall and the occupants will be weightless. Now imagine that the room is magically transported back to Earth, but by a slight error it appears in the air 100 feet above the ground rather than on the surface. The Earth's gravity will at once begin to accelerate the room downward at 9.8 m/s^{2}. Just as when the room is accelerating in space, this acceleration will produce an inertial force that is indistinguishable from a gravitational force. In this case, however, the inertial force is *upward* and the gravitational force (the Earth's pull) is *downward*. These forces **cancel** out exactly, rendering the occupants of the room weightless—for as long as it takes the room to fall 100 ft (30.5 m), at least. In general, then, objects that are in free fall—that is, falling freely in a gravitational field—will be weightless. Astronauts in orbit around the Earth are weightless not because there is no gravity there, but because they are in free fall. You can test the claim that freely falling objects will be weightless by putting a small hole in the bottom of an empty plastic milk jug and filling the jug with water. Drop the jug, uncovering the hole at the moment of release. While the jug is falling no water will come out the hole, proving that freely falling water is weightless.

The second statement of the principle of equivalence involves the concept of mass. Mass appears in two distinct ways in Newton's laws. In Newton's second law of motion, the amount of force required to accelerate an object increases as its mass increases. That is, it takes twice as much force to accelerate two kilograms of mass at a given rate as it takes to accelerate one kilogram of mass. The sort of mass that appears in Newton's second law is termed the *intertial* mass. Meanwhile, in Newton's law of gravity the gravitational force between two objects increases as the mass of the objects increases. The mass in the law of gravity is termed the *gravitational* mass. The inertial mass and gravitational mass of an object are expressed using the same units and are always equal, but there is no obvious reason, in Newtonian physics, why they should be. Newtonian physicists were obliged to accept the identity of inertial and gravitational mass as a sort of perfect coincidence. Einstein, however, declared that they are exactly the same thing. This is the second statement of the principle of equivalence.

These two statements of the principle of equivalence are logically equivalent, meaning that it is possible to use either statement to prove the other. The principle of equivalence is the basic assumption behind the general theory of relativity.

*Geometrical nature of gravity*

From the principle of equivalence, Einstein was able to derive the general theory of relativity. General relativity explains the force of gravity as a result of the geometry of space-time. To see how it does so, consider the example given above of the enclosed room being accelerated in space far from any masses. A person in the room throws a ball **perpendicular** to the direction of acceleration—that is, across the room. Because the ball is not being pushed directly by whatever is accelerating the room, it follows a path that is curved as seen by the person in the room. (You would see the same effect if you rolled a marble on a tray in an accelerating car. The marble's path would **curve** toward the back of the car.) Now imagine that the ball is replaced by a beam of light shining sideways in the enclosed, accelerating room. The person in the room sees the light beam follow a curved path, just as the ball does and for the same reason. The only difference is that the deflection of the light beam—how much it drops as it crosses the room—is smaller than the deflection of the ball, because the light is moving so fast it gets to the wall of the room before the room can move very far.

Now consider the same enclosed room at rest on the surface of Earth. A ball thrown sideways will follow a downward curved path because of Earth's gravitational field. What will a light beam do? The principle of equivalence states that it is not possible to distinguish between gravitational forces and inertial forces; therefore, any experiment must have the same result in the room at rest on Earth as in the room accelerated in space. The equivalence principle thus predicts that a light beam will therefore be deflected downward in the room on Earth just as it would in the accelerated room in space. In other words, light *falls*.

The question is, why? Light has no mass. According to Newton's law of gravity, only mass is affected by gravity. Light, therefore, which is weightless, should move in a straight line. Einstein proposed that in a sense it *does* move in a straight line; that, in fact, the nature of straight lines is changed by the presence of mass, and this geometrical change is what gravity *is*. Another way of saying this is that space-time is "curved." (The physical meaning of this statement is far from obvious, and this description is not meant to offer a complete explanation of the concept of curved space-time.)

Prior to Einstein, people thought of space and time as being independent of each other, and of space as being absolute (unaffected by matter and energy in it) and flat (Euclidean in geometry). Euclidean geometry is the set of rules that describes the geometry of flat surfaces and is studied in high-school geometry classes. In general relativity, however, space-time is not necessarily Euclidean; the presence of a mass curves or warps space-time. This warping is similar to the curvature in a horizontal sheet of rubber that is stretched downward by a weight placed in the center. The curvature of spacetime is impossible to visualize, because it is the curvature of a four-dimensional space rather than of than a two-dimensional surface, but can be described mathematically and is quite real. The curvature of space-time produces the effects we call gravity. When we travel long distances on the surface of the Earth, we must follow a curved path because the surface of the Earth is curved; similarly, an object traveling in curved spacetime follows a curved path. For example, the Earth orbits the Sun because space-time near the Sun is curved. The Earth's nearly circular path around the Sun is analogous to the path of marble circling the upper part of a curved funnel, refusing to fall in; an object falling straight toward the Sun is like a marble rolling straight down into the funnel.

One consequence of the curvature of space-time by matter is that the Universe is finite in size. This does not mean that space comes to an end, as the space inside a **balloon** is comes to an end at the inner surface of the balloon; space is finite but unbounded. Physicists often compare our situation to that of imaginary two-dimensional (perfectly flat) beings living on the surface of a **sphere**, who can make measurements only on the surface of the sphere and cannot see or even visualize the three-dimensional space in which their sphere is embedded. If they explore the whole surface of their universe they will find that it has only so many square inches of surface (is finite) but has no edges (is unbounded). Our universe is analogous. Furthermore, according to general relativity, the size of the Universe depends directly on the amount of matter and energy in it.

*Bending of light*

The first experimental confirmation of general relativity occurred in 1919, shortly after the theory was published. Newton's law of gravity predicts that gravity will not deflect light, which is massless; however, the principle of equivalence, on which general relativity is founded, predicts that gravity will bend light rays. The nearest mass large enough to have a noticeable effect on light is the Sun. The apparent position of a **star** almost blocked by the Sun should be measurably shifted as the light from the star is bent by the Sun's gravity. As described above, observations made during the total eclipse of 1919 found the predicted shift.

More recently, this effect has been observed in the form of gravitational lenses. If a **galaxy** is located directly between us and a more distant object, say a **quasar**, the mass of the galaxy bends the light coming almost straight towards us (but passing around the galaxy) from the more distant object. If the amount of bending is just right, light from the quasar that would otherwise have missed us is focused on us by the galaxy's gravity. When this occurs we may see two or more images of the quasar, dotted around the image of the intervening galaxy. A number of gravitational lenses have been observed.

*Binary pulsar*

The 1993 Nobel prize in physics was awarded to U.S. physicists Joseph Taylor (1941–) and Russell Hulse (1950–) for their 1974 discovery of a binary **pulsar**. A pulsar, or rapidly rotating **neutron star**, is the final state of some stars; a star become a **neutron** star if, once its nuclear fuel has burnt out, its gravity is strong enough to collapse it to about the size of a small city. A binary pulsar is two pulsars orbiting each other. Because pulsars are extremely dense they have extremely strong enough gravitational fields. Binary pulsars therefore provide an excellent experimental test of general relativity's predictions, which vary most from the predictions of Newtonian theory for strong fields. General relativity predicts that some systems of objects—including binary pulsars—should emit gravity waves that travel at the speed of light, and that these waves should remove energy from such systems. This energy loss should slowly brake the speed of **rotation** of a binary pulsar. Taylor and Hulse were able to measure a binary pulsar's rate of slowing, and showed that it agreed with the predictions of general relativity.

## Additional topics

- Special Relativity - History, Special Relativity, Space-time, Unusual Effects Of Motion, Speed Of Light Limit
- General Relativity - History
- General Relativity - Basic Concepts Of The Theory
- General Relativity - Consequences Of General Relativity
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