Theory of Relativity

Relativity is a theorem formulated by Albert Einstein, which states that space and time are relative, and all motion must be relative to a frame of reference.

It states:

• There is no absolute reference frame. One can measure velocity if the object or momentum is only in relation to other objects.
• The speed of light is constant irrespective of who measures it or how fast the person measuring it is moving.

Albert Einstein's Theory of Relativity encompasses two theories: Special Relativity Theory and General Relativity Theory.

Special Theory of Relativity

Einstein first introduced this term in the year 1905. It is a theorem that deals with the structure of space-time. Einstein explained this theory based on two postulates -

• The laws of physics are the same for all, irrespective of the observer's velocity.
• The speed of light is always constant regardless of the motion of the light source or the motion of the observer.

This is the theory which laid the foundation of time travel. According to Einstein, the rate at which time tics decreases with the increase of the person's velocity. But this is hard to notice as the decrease in time is relatively very low compared to the increase in time. So, it can be assumed that if you can equal the velocity of light, you will be in a situation where time is still. This phenomenon is called Time Dilation. There are other surprising consequences of this theory, such as -

• Relativity of simultaneity - two actions, simultaneous for one person, may not be simultaneous for another person in relative motion.
• Length Shrinking: Objects are measured and appear shorter in the direction they are moving with respect to the observer.
• Mass - Energy Equivalence: Study of relativity led to one of the greatest inventions, i.e., $E = mc^2$ where E is Energy, m stands for mass and c for the velocity of light. Many scientists observed that the object's mass increases with the velocity but never knew how to calculate it. This equation is the answer to their problem, which explains that the increased relativistic weight of the object is equal to the kinetic energy divided by the square of the speed of light.

General Theory of Relativity

General Relativity theory, developed by Einstein in 1907-1915, states that being at rest in the gravitational field and accelerating are identical physically. For example, an observer can see the ball fall the same way on the rocket and on Earth. This is due to the rocket's acceleration, which equals 9.8 m/s^2. This theory relates to Newton’s gravitational theory and special relativity.

Some Consequences of General Relativity are :

• Gravitational Time Dilation: Gravity influences the passage of time. Clocks in the deeper gravitational wells run slower than in general gravitational levels.
• Light rays will bend in the gravitational field.
• The universe is expanding, and parts of it are moving away from Earth faster than the speed of light.

Difference Between Special and General Theory of Relativity

Frame Of Reference

A frame of reference is a set of coordinates that can be used to determine the positions and velocities of objects in that frame. It is a standard relative to which motion and rest may be measured.

A relativistic reference frame includes the coordinate time, which does not equate across different reference frames moving relatively to each other. This differs from Galilean relativity, in which all possible coordinate times are essentially equivalent.

If we ask A what velocity of B is, he will say it is at rest. But if we ask the same question to C, he will say B is moving with a velocity V in the positive X direction. So we can see before specifying the velocity we have to specify in which frame we are or in simple terms, we need to define a frame of reference.

Types of Frame of Reference

• Inertial Frame of Reference

  An inertial frame of reference is a frame where Newton's law holds true. That means if no external force is acting on a body it will stay at rest or remain in uniform motion. Suppose a body is kept on the surface of the earth, for a person on earth it is at rest while for a person on the moon it is in motion.

Actually, the term inertial frame is relative i.e. first we assume a reference frame to be the inertial frame of reference. So a more general definition of an inertial frame would be: Inertial frame is at rest or moves with constant velocity with respect to my assumed inertial reference frame.

• Non-Inertial Frame of Reference

  Now we can define a non-inertial frame as a frame that is accelerated with respect to the assumed inertial frame of reference. Newton's law will not hold true in these frames. So in the above example if I assume earth to be an inertial reference frame the moon becomes a non-inertial reference frame as it is in accelerated motion with respect to earth. But if we want to make Newto's law hold here we need to take some mysterious forces also known as pseudo forces.

Is earth an inertial frame of reference?

Earth can not be a inertial frame of reference because it is revolving around the sun and also on its own axis. A accelerated object can't be taken as inertial frame of reference and a reference frame attached to an non-inertial frame also can't be taken as inertial frame of reference.