In 1905, famous scientist *Albert Einstein* introduced the special theory of relativity. This special relativity is based on the following two fundamental postulates. These two postulates are called fundamental *postulates of the special theory of relativity*. The two postulates are stated and discussed below.

## First Postulate

The first law of special relativity states that the laws of physics may be expressed in equations having the same form in all frames of reference moving at constant velocity with respect to one another.

The frame of reference in which the first law of Newton’s laws of motion is applied is called inertial frame of reference. If any object is in inertia (stationary or moving), then its state will not change unless an external force is applied to it. According to this postulate if two observers are in linear motion at constant velocity, then any physical law will remain unchanged. Any inertial reference frame is as good as any other for expressing the laws of physics because the laws are same in all such frames.

## Second Postulate

In the vacuum, the speed of light, measured in any inertial reference frame, always has the same value of ‘c’ to all observers. This speed does not depend on the direction of transmission of light and the relative velocity of the source and the observer.

Due to this postulate the existence of ether medium cannot be accepted at all. Before Einstein scientists believed that light traveled at the speed c only when measured with respect to the ether. According to this view, an observer moving relative to the ether would measure a speed for light that was slower or faster than ‘c’, depending on whether the observer moved with or against the light. But *Michelson-Morley’s experiment *and later on other experiments proved that speed of light did not depend on the motion of the observer relative to the source of the light. It is a constant.

## Galilean Transformation

A particle in space can be located from a knowledge of its coordinates with reference to a *particular frame of reference*. These coordinates will be different in different frames of reference.

Sometimes it is necessary to transform the coordinates from one reference frame to another. This transformation of coordinates of a particle from one *inertial frame *of reference to another *inertial frame* of reference is called *Galilean transformation*.

Such set of equations that relate space-time coordinates of an event are called *transformation equations*.

Let us consider two inertial frames of references S and S^′ having cartesian coordinate axes as XYZ and X^′ Y^′ Z^′ and origins O and O^′ respectively.

At time t=0 , both the frames are at rest so that their origin O and O^′ coincide with each other.

Now let, S^′ frame start moving away from S with constant velocity v along the positive direction of x-axis.

Let an event occurs at point P at any instant of time. The coordinates of point P w.r.t. observer O in * *S frame are (x,y,z,t).

The coordinates of the point P w.r.t. the observer O^′ in S^′ frame are (x^′,y^′,z^′,t^′).

From the figure we have,

OA=OO^′+O^′A =>x=vt+x^′ =>x^′=x-vtAs there is no relative motion along y and z axis therefore

y=y^′, z=z^′

As the time is considered to be absolute in nature i.e. time remains the same in all inertial frames of references so t=t^′.

∴ The required Galilean transformation equations are

x^′=x-vt, y=y^′, z=z^′, t=t^′.

### Velocity Transformation

Let the velocity of *P* be V according to S at time t and V′ according to S′ at the corresponding time t′.

Let *P* be moving in the x-direction under the action of a force.

According to S | According to S′ |

Mass = m | Mass = m^′ |

Force = F | Force = F^′ |

Position coordinates of P(x,y,z,t) at t | Position coordinates of P(x^′,y^′,z^′,t^′) at t^′ |

### Acceleration Transformation

Let the acceleration of *P* be a according to S at time t and a^′ according to S′ at the corresponding time t^′.

In classical physics, m=m^′ and F=F^′.

Let us suppose that Newton’s law of motion is found to be valid in S, i.e. F=ma.

∴ F^′=m^′a^′

So, if Newton’s law is valid in *S*, then it is also valid in S′.

Since Newton’s laws of motion are the basis of all laws of classical mechanics, we arrive at the following principle of relativity-

*All laws of classical mechanics are valid in any two coordinate systems moving uniformly relative to each other.*

This is called the principle of classical or Newtonian relativity.

## Frequently Asked Questions (FAQs)

**1. What is the Special Theory of Relativity introduced by Albert Einstein in 1905?**

The Special Theory of Relativity is a scientific theory proposed by Albert Einstein in 1905 that revolutionized our understanding of space, time, and motion, particularly when dealing with objects moving at significant fractions of the speed of light.

**2. What are the fundamental postulates of the Special Theory of Relativity?**

The two fundamental postulates are:

- The laws of physics are expressed in equations with the same form in all frames of reference moving at constant velocity with respect to one another.
- The speed of light in a vacuum is always constant, regardless of the motion of the source or observer.

**3. What is an inertial frame of reference?**

An inertial frame of reference is a reference frame that is moving at a constant velocity or is at rest. In this frame, Newton’s laws of motion hold true without the need for additional forces or accelerations.

**4. What does the first postulate of special relativity state?**

The first postulate states that the laws of physics can be expressed in equations with the same form in all frames of reference moving at constant velocity. This means that physical laws remain consistent across different inertial frames.

**5. How does the second postulate challenge previous beliefs about light?**

The second postulate asserts that the speed of light is constant in all inertial frames of reference, regardless of the motion of the source or observer. This contradicted the earlier notion of the existence of aether, a hypothetical medium through which light was thought to travel.

**6. What is Galilean transformation?**

Galilean transformation refers to the transformation of coordinates from one inertial frame of reference to another. It is used to relate the space-time coordinates of an event in one frame to those in another inertial frame.

**7. How does the Special Theory of Relativity impact our understanding of space and time?**

Einstein’s theory introduced the concept that space and time are not absolute but are interconnected in a spacetime continuum. Additionally, it showed that time dilation and length contraction occur as an object’s velocity approaches the speed of light.

**8. How does the theory explain the principle of equivalence between inertial and accelerated motion?** Einstein’s theory revealed that the effects of gravity are indistinguishable from the effects of acceleration. This principle, known as the equivalence principle, is a cornerstone of his theory of general relativity.

**9. Can the Special Theory of Relativity be applied to all situations?**

The Special Theory of Relativity is particularly applicable at velocities much lower than the speed of light. It becomes less accurate as velocities approach the speed of light, at which point Einstein’s General Theory of Relativity becomes more relevant.

**10. How has the Special Theory of Relativity impacted modern physics and technology?**

Einstein’s theory laid the foundation for many modern advancements, including nuclear energy, GPS technology, and our understanding of the cosmos. It fundamentally altered our perception of space, time, and the nature of reality.

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