PH206 Topics

# General relativity

The theory of general relativity was invented by Albert Einstein. It is important to net here that the word "theory" can be used in two different ways. Theory can mean an idea that might be true, but is not proven. Theory can also mean a large group of concepts that are connected, forming a body of understanding, that have been proven to be true. In the case of general relativity, the word "theory" is used in the latter sense. It has been experimentally verified in a number of ways.

General relativity describes spacetime as having curvature which depends on the density of matter/energy. This density affects the motion of particles. The particles, in turn, affect the density configuration. In short, matter/energy tells spacetime how to curve, and curvature of spacetime tells matter/light how to move.

• Gravity is the central focus of the theory
• Idea of forces replaced with curvature of spacetime
• Equivalence principle – light affected by gravity
• Density of matter tells spacetime how to curve
• Curvature of spacetime tells matter how to move
• Experimental verification
• Deflection of starlight about the sun
• Precession of Mercury’s orbit
• Harvard Tower
• Gravity wave detection

The equivalence principle equates gravitational acceleration with acceleration caused by changing velocity due to any other source. For example, if you are standing on the surface of Earth and drop a rock, the rock speeds up at a rate of 9.8 m/s2. For simplicity, let's round that off to 10 m/s2. This means that the rock would speed up at a rate of 10 meters per second each second it was falling. If you dropped it over a cliff, so it had time to fall, after one second it would be moving at 10 m/s. After two seconds, it would be moving at 20 m/s, and so on. This disregards the force of air resistance. If you were standing on the surface of Earth, you would not be falling, since your feet would be in contact with the ground, but you would still feel the pull of gravity as well as a force pushing upward against your feet.

If you were sitting in a rocket on the surface of Earth, you would feel the gravitational force with a strength of about 10 m/s2. If you were in a rocket far from Earth that was speeding up by 10 meters per second, every second, because of fuel being burned and exhausted out of the engines, you would feel an acceleration of 10 m/s2. The accelerations produced in these two cases would be equivalent in every way.

This is quite different from the Newtonian way of thinking about gravity. The gravitational force can be written as a product of two masses and the inverse squared distance.

This formulation of the gravitational force implies that if a particle has no mass, like a photon, that it would not feel any force due to gravity.

The equivalence principle predicts that since a photon's path as observed in an accelerating frame would be curved, the same should hold true for a photon's path in a gravitational field.

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Bending of starlight due to a gravitational field was first observed in 1919 by Arthur Eddington during a total eclipse of the sun with simultaneous observations made in several locations in other parts of the world.

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General relativity implies that the elliptical orbit of a planet will precess over time, since time passes more slowly closer to a dense object like a star. The precession of the planet Mercury was measured to agree with the prediction made by general relativity.

Another experimental verification of general relativity was made at Harvard in 1959 when Robert Pound and John Rebka measured a gravitational redshift of photons climbing upward in Earth's gravitational field.