## Galilean Transformation

Galilean transformation in Newtonian mechanics is used to alter the coordinates of two references; within the restrictions of classical physics, it fluctuates only by constant relative motion. A Galilean group is applicable to time dimensions and four spaces, establishing Galilean geometry. It is basically an assembly of motions that applies to Galilean or classical relativity.

Homogeneous and heterogeneous Galilean transformations are replaced by Lorentz transformations and Poincare transformations, respectively, in the case of special relativity. In a Newtonian framework, only the Galilean transformation equations are valid. Still, for the coordinate system, these equations are not valid since the coordinate systems move around the speed of light with respect to each other.

### Galilean Invariance

The laws leading all fundamental motions are the equivalent in all inertial frames; this has been suggested by Galilean invariance or relativity. A ship is moving on a calm sea at a constant velocity; using this example, Galileo derived these hypotheses. Since the state of motion of the ship is that it is moving with a constant velocity, still, it can’t be deduced by any viewer under the deck.

Precisely, Newtonian mechanics is the term that Galilean invariance generally refers to. Related to one another, under this transformation, Newton’s laws stand correct in all frames.

Significances of Galilean Relativity are:

- In all the reference points, which move in a constant velocity with respect to one another, the basic physics laws are the same.
- A common time is shared by all inertial frames.

### Equations of Galilean Transformation

The connection of a single random event between the (x, y, z, t) and (x′, y′, z′, t′) coordinates under the Galilean transformation is explained by these equations. In a constant relative motion with velocity v in their shared x and x′ directions, in two coordinate systems S and S′, the transformations are considered with their coordinate origins meeting at time.

x′=x−vt

t=t′=0.

y′=y

z′=z

t′=t

This transformation is observed as a shear mapping in the grammar of linear algebra and is specified with a matrix on a vector. The transformation works on only two elements with motion parallel to the x-axis.

Even though matrix representations are not strictly essential for Galilean transformation, it gives them ways in special relativity for direct assessment to transformation methodologies.

### Here are Some Limitations of Galilean Transformations

The cases that could not be translated by Galilean transformations are listed below:

- The real findings of the Michelson-Morley experiment were not decoded by Galilean Transformation.
- Galilean Transformation breaks the rules of the Special theory of relativity.
- The speed of light is always relative to the motion and reference points in Galilean transformations, whereas, in Maxwell’s electromagnetic theory, the speed of light is constant in all circumstances.

## Introduction to Relativity

Albert Einstein articulated a theorem called Relativity, which states that all the motion must be relative to a frame of reference, and also the time and space relative to each other. It is a concept that explains how the laws of Physics are equivalent everywhere. This theory is hard to understand, but it is simple.

The theory states that:

- If the object or momentum is only in relation to other objects, then one can measure velocity; that is, there is no reference frame.
- The speed of light is constant regardless of who is measuring it or how fast or quick a person is measuring its movement.

Two theories, covered by Albert Einstein’s theory of Relativity are:

### Special Theory of Relativity

It is a theorem that deals with the space-time structure; Einstein first presented this term in the year 1905. Based on the following two hypotheses, Einstein explained this theory –

- Irrespective of the velocity of the observer, the laws of physics are equal for all.
- Irrespective of the motion of the source of light or the motion of the observer, the speed of light will always remain constant.

The foundation of time travel was laid by the Special Theory of Relativity**. **According to Einstein, with the increase in velocity of the person, the rate of time ticking decreases. But this is tough to notice because as compared to the increase in time, the decrease in the time is relatively very low. So, it can be presumed that you will be in a situation where time is still if you can run equal to the velocity of light. This phenomenon is termed as Time Dilation.

## There are other amazing significances of this theory –

- Relativity of simultaneity: In a relative motion, two actions which are simultaneous for one person may not be simultaneous for another person.
- Shrinking of length: With respect to the observer, the objects appear shorter in the direction that they are moving.
- Mass-Energy Equivalence: E = mc
^{2}, where E stands for energy, m for mass, and c for the velocity of light. This equation clarifies that the kinetic energy divided by the square of the speed of light is equal to the bigger relativistic weight of the object.

### General Theory of Relativity

The General Relativity theory developed by Einstein states that being in acceleration or being at rest in the gravitational field, these two activities are physically identical. For example, a viewer can observe or see a ball falling on the rocket the same way as on the Earth. The reason behind this is the acceleration of the rocket, which is equal to 9.8 m/s^{2}. Special Relativity and Newton’s gravitational theory are related to this theory.

#### The consequences of General Relativity theory are listed below:

- The passage of time is affected by gravity. Clocks, in general, gravitational levels run faster than the deeper gravitational wells. This is also known as Gravitational Time Dilation.
- Gravitational fields can be bent by light rays.
- The parts of the universe are moving away from Earth faster than the speed of light because the universe is expanding.

### Some applications of Einstein’s Theory of Relativity in real life:

- Global Positioning System
- The yellow colour of gold
- The liquid form of mercury
- Concept of light
- Old television