The Theory of Relativity

1589

• While the myth that Galileo dropped two balls of different weights from the leaning tower of Pisa to falsify Aristotle's belief is wrong, he did do something of equal relevance.

• Galileo rolled two balls of different weights down a slope and recorded equal acceleration in both cases.

1676

• Danish astronomer Ole Christensen Roemer discovered that the speed of light was finite but high based on the observation that eclipses of Jupiter’s moons appeared later the farther one was from Jupiter.

• He did not, however, succeed in giving an accurate speed of light. The speed he gave was 140000 miles per second as opposed to 186000 miles per second.

1687

• Galileo's observations laid the foundation of Newton’s laws of motion which were first stated in his book Principia Mathematica.

• According to the first law, if a body is not acted on by any force, it will continue to move in a straight line with constant speed.

• According to the second law, the force (corresponding to the weight of the balls) shares a direct relation with acceleration and mass whereas acceleration shares an inverse relation with mass, i.e., F = ma.

• According to an additional law which is used to describe gravity, every body attracts every other body with a force directly proportional to their masses. This justifies the falling of bodies with the same rate.

• According to Newton's law of gravity, F ∝ 1/d^2 (where F is force, and d is distance between two bodies). This law predicts orbits with great precision. If there were any altercations in this law, it could either result in the orbits spiraling into the Sun instead of being elliptical or gravity from distant stars dominating over gravity from Earth.

• The introduction of relative speeds meant an absence of absolute rest. Thus, an event could not be given an absolute position in space. However, absolute time still held true.

1865

• British physicist James Clerk Maxwell gave a thorough theory of propagation of light by unifying the partial theories concerning forces of electricity and magnetism. This predicted the existence of disturbances in the electromagnetic field like ripples in a pond.

• The naming of waves was on the basis of their wavelength (distance between two consecutive wave crests). For eg,

Wavelength	Name
1 meter (+)	Radio waves
Few centimeters	Microwaves
1/10000 centimeter (+)	Infra-red
1/40000000 - 1/80000000 centimeter	Visible light
Shorter than above	Ultraviolet, X rays, Gamma rays

• Maxwell’s and Newton’s theories were inconsistent with one another. Maxwell’s theory proposed a fixed speed for light waves but Newton’s theory got rid of absolute rest. This led to the suggestion of the presence of a substance known as ‘ether’ everywhere in the surroundings. The speed of light relative to ether would, therefore, remain constant but it could vary for different observers moving through ether.

1887 – 1905

• Albert Michelson and Edward Morley conducted an experiment in which they measured the speed of light in the direction of Earth’s motion (moving towards the light source) and at right angles to this motion. They found that the speed of light was equal, which disproved the existence of ether.

• Dutch physicist Hendrik Lorentz tried to justify the results of the Michelson-Morley experiment by the contraction of length and slowing of time.

• In a renowned paper, Albert Einstein, then unknown, raised a point that the idea of ether was not required if only absolute time was given up. French mathematician Henri Poincaré made a similar argument.

Theory of Relativity

• The fundamental postulate of relativity is that the laws of physics are the same for all inertial frames (or freely moving observers, despite their velocities).

• The theory of relativity states that no object can travel at the speed of light or faster than light, except waves without any intrinsic mass and light itself. This is due to the equation, E = mc^2 (where E is energy, m is mass, and c is the speed of light). As an object nears the speed of light, its mass increases and, correspondingly, more energy is required to the extent where both mass and energy become infinite.

• The speed of light is the distance it has travelled upon the time taken by it to travel that distance. Since all observers must agree on the speed but not the distance, they must also disagree on the time. Thus, the theory of relativity abandoned absolute time.

• To describe an event, one needs three spatial coordinates and one time coordinate.

• If one visualizes the circular ripples in a two-dimensional pond in a three-dimensional model, one gets a cone whose tip is at the place and time where the stone struck the water in the pond. Similarly, if one visualizes the light from an event, one gets a three-dimensional cone in the four-dimensional model of the universe.

• The future light cone of an event consists of future events influenced by the event. The past light cone of an event consists of past events leading up to the event. The region outside the future and past light cone in called elsewhere and is not influenced by the event in any manner.

1908-1914

• The special theory of relativity ensues when gravity is disregarded.

• While the special theory of relativity accurately explained the speed of light, it was in conflict with Newton’s law of gravity which stated that if one changed the distribution of matter in one region of space, the change in the gravitational field would be felt instantaneously everywhere else in the universe. This implied that gravitational signals could travel faster than light. Further, to define instantaneous, one had to refer to absolute time which was abolished in favor of personal time.

• Einstein tried unsuccessfully to make these theories compatible with one another.

1915

• Finally, Einstein proposed the general theory of relativity.

• The general theory of relativity viewed gravity as a result of the fact that space-time was curved or warped, instead of viewing it as an ordinary force. Celestial bodies do not move in a certain orbit because they are made to do so by gravity, instead they follow the shortest path in curved space-time which is a geodesic.

• Even though bodies follow straight lines in a four-dimensional model of the universe, they appear to be following curved paths in our three-dimensional view (like an airplane appears to travel in a straight line over hilly ground but its shadow is curved).

• As predicted by the general theory of relativity and verified by observation, the orbit of Mercury, it being the closest planet to the Sun, rotates about the Sun at a rate of approximately one degree in ten thousand years.

• The general theory of relativity predicts that light and light cones should also be bent by gravity. This would lead to the deflection in the apparent position of a star when viewed from Earth.

1962

• The general theory of relativity predicted that time should run slower near a massive body such as Earth. There is a direct relation between the energy of light and its frequency. As light travels upward in Earth’s gravity, it would lose energy and therefore its frequency would decrease. So, time would appear slower closer to the surface of Earth (where gravity is more) and faster away from the surface of Earth (where gravity is lesser).

• This was proven by experiment when a difference was observed between the time shown in a clock placed at the bottom of a water tower and a clock placed at the top of a water tower.

Important Examples

• Michelson-Morley Experiment: The Michelson-Morley experiment disproved the existence of ether. In this experiment, light emitted from a light source was made to be either reflected or passed through a half silvered mirror. These rays met with mirrors equidistant to the half silvered mirror and got reflected. Some part of light from both these reflected rays was passed through the half silvered mirror in the direction of the detector. After changing the direction of this apparatus numerous times, it was noticed that the light rays always had the same interference pattern (the pattern formed by the crests and troughs of one ray with the crests and troughs of another ray). This meant that ether had no influence on light and therefore did not exist.

• Flying two airplanes in opposite directions: The Earth rotates from west to east. Two airplanes were made to fly in opposite directions with an accurate clock placed in each of them. One of the airplanes flew from west to east while the other flew from east to west. Earth's motion is added to the velocity of the airplane flying from west to east (in the direction of Earth's motion). More velocity meant lesser time since velocity and time share an inverse relation. Thus, the time shown on the clock inside the plane moving eastward was lesser than the time shown on the clock inside the plane moving westward.

• The Twins Paradox: In the twins paradox, one twin in sent in space and travels near the speed of light whereas the other twin remains back on Earth. The time for the twin in space would move slower as compared to the twin on Earth. Thus, when they meet after some time, the twin in space would have aged less. It is worth noting that this is only a paradox when we consider absolute time as opposed to personal time.

• A person in a closed box: Einstein noticed that there was a close connection between acceleration and gravity. A person in a closed box would not be able to tell the difference between standing in a stationary elevator on Earth or being accelerated in a rocket in space. Similarly, the person would not be able to tell the difference between being in a free fall in the elevator to the bottom of the shaft or being in a rocket whose motor is turned off.

Sources: A Brief History of Time by Stephen Hawking The Universe in a Nutshell by Stephen Hawking