Theory of Relativity

Albert Einstein proposed and published the two interrelated theories, which combined together is known as the theory of relativity. He published special relativity theory in 1905 and general relativity theory in 1915. Here, the special relativity theory can be applied to all physical phenomena in the absence of gravity. But the general relativity theory mainly explains the law of gravitation and its relation with other forces of nature. The general relativity theory can be applied to the cosmological and astrophysical realms. This article explains Albert Einstein’s theory of relativity, with its postulates, facts, and examples in detail. 

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The above image shows the Einstein law, which is also known as the mass-energy equivalence equation.

Albert Einstein Theory of Relativity

General Theory of Relativity 

Albert Einstein developed the general theory of relativity from 1907 to 1915. The general theory of relativity is also known as the theory of gravitation. According to this theory, the gravitational force between two bodies completely depends on their masses and on the distance between two bodies. He also found that time and space are interlinked to each other and are referred to as space-time. Through the equation of the general theory of relativity, he found that massive objects caused a distortion in space-time. In 1915, Einstein derived the field equation related to the curvature of spacetime with the energy, mass, and any momentum within it. 

Consequences of General Theory of Relativity

1. Gravitational time Dilation. Usually, the clock will run slow in deeper gravitational wells. 

2. The change in the orientation of the rotational axis of a rotating body is known as precession. According to  Newton's theory of gravity, the orbits precess is unexpected. 

3. The light rays get deflected due to the presence of a gravitational field. 

4. While heavy objects like earth are spinning, they should twist and change the space-time around them.

5. He also predicted the expansion of space due to the collision of two objects in the universe. These ripples in space-time are known as gravitational waves.

Special Theory of Relativity

In 1905, Einstein published the paper "On the Electrodynamics of Moving Bodies", in which he explained how speed affects mass, time, and space. The special theory of relativity is based on two postulates, which are opposite to classical mechanics. As the outcome of the special theory of relativity, Einstein’s law E = mc2 was framed. This means energy is equal to the product of mass and square of the speed of light. The speed of light remains constant. Due to mass-energy equivalence, energy and mass are equivalent and transmutable. 

Consequences of Special Theory of Relativity

1. If the two events occur simultaneously, the observer at rest may not notice the simultaneous events, but the observer in relative motion can experience it due to the relativity of simultaneity. 

2. The time of the clock in a moving state will run slower than the clock in a stationary state, due to time dilation. 

3. The length of the moving object will get shorter in the direction they travel with respect to the observer, due to the length contraction. 

4. No object in the universe can travel faster than the speed of light in vacuum. So, the maximum speed of all the objects is finite. 

5. Even the object with the effect of gravity can travel only at the speed of light.  They cannot travel faster than the speed of light.

Time Dilation Equation 

The time dilation is the one of the interesting relativistic phenomena that explains the concept of time passing slower for an observer who is in relative motion to another observer. The equation relating exact time and time determined by an Earth-bound observer suggests that the relative velocity of an object under motion will not exceed the speed of light. The equation for calculating time dilation is given below:

\[\Delta T = \frac{\Delta t}{\sqrt{1-\frac{v^{2}}{c^{2}}}}\]

Here, 

ΔT represents the time interval measured from the stationary frame.

ΔT represents the time interval measured from the moving frame.

v represents the relative velocity of the moving reference frame.

c represents the speed of light in vacuum. 

Postulates of Special Theory of Relativity

1. First Postulate (Principle of Relativity): The laws of Physics are the same for all inertial frames of reference related to one another.

2. Second Postulate (Invariance of C): The speed of light in a vacuum or empty space is equal for all the observers in any inertial frame of reference. Here, the velocity of light c is independent of the motion of the emitting body.

Facts About Theory of Relativity

1. The satellite in the atmosphere remains stationary and sends signals to the GPS system in the car. The GPS unit in the car receives information at higher accelerations due to the earth’s gravity.  

2. Metals like gold, copper look shiny and appear red, yellow, or orange in colour due to the absorption and re-emission of light based on the theory of relativity. 

3. Gold does not get corroded easily, because it has only one electron in its outermost orbit, and the electrons are strongly attracted to its nucleus. So, it could not react with any other material. 

4. Based on the theory of relativity, even though mercury is a strong metal, it remains liquid at room temperature. It is because mercury has a unique electronic configuration and it is impossible to take out electrons from its orbits.

5. The cathode ray tube in the television also works on the relativistic effects.

6. The general theory of relativity is also used to measure the distant objects in the universe.

Theory of Relativity Examples

1. The behaviour of mercury in its orbit. Mercury includes a positively elliptical orbit so that it is only about \[\frac{2}{3}\]times as far from the Sun at perihelion as it is at aphelion. The gravitational influences (or we can say gravitational perturbations) of the other planets on Mercury construct a calculable refinement of Mercury’s perihelion. 

2. The light entering the earth’s atmosphere gets bent due to the gravity of the earth.

3. The observer on earth can notice the time running slow in the spaceship while comparing to his own clock. 

The theory of relativity equation with its postulates and facts about the theory of relativity with examples are described above in detail.