# Special Theory of Relativity

## What is Special Theory Of Relativity?

The theory of special relativity is the explanation of space and time and its movement of objects at a constant speed in a straight path. Here the speed of the object movement is likened to the speed of light, the mass of the same object becomes infinite, and therefore, it is restricted to go at any faster speed than that of light. Concepted in 1905 by Albert Einstein, the theory of special relativity further explores the acceleration of such objects and serves as the base for Einstein's Theory of General Relativity in 1915.

### The Two Primary Postulates of Albert Einstein's Special Theory of Relativity

• The Laws of Physics are uniform throughout

• The speed of light in a vacuum is equal to the speed of light in any other space, irrespective of its source.

It counters the popular belief where universal time is dependent and represented as a reference frame and spatial position.

The principle of Galilean relativity is retained in Einstein's special theory of relativity. This theory refers to the body (either at rest or in uniform motion in a straight line), to follow the principle of inertia. For example, if you're standing on a highway and a bus passes you by at 80km/hr, then, relative to somebody sitting inside the bus, you are traveling at 80km/hr in the opposite direction to that of the bus.

Special relativity is only constrained to objects that can move in uniform motion to each other, and cannot be discerned. The speed of light and traveling at its speed can be approached but never attained by any object. The famous Einstein equation, E=mc2, also came into being. It was expressed that mass and energy can often be interchanged, and the increased relativistic mass from its Kinetic Energy E can be divided by c2.

### Space-Time Diagrams

The entire region of space-time that is located outside of the light cone is taken as elsewhere.  The term cT invariantly puts time into a mathematical equation with space. The German physicist Hermann Minkowski further stated that the universe could be considered similar to a four-dimensional coordinate plane with x, y, z, and ct representing the length, width, height, and time of it, respectively. Therefore, a four-dimensional space-time continuum can be:

However, one of the limitations of the space-time diagram is its explicit spatial coordinate x. As the light cone is drawn, the second spatial coordinate y, it points out of the plane, but the third spatial coordinate needs to be at right angles to ct and x-axis, which cannot be represented via a line.

### Space and Time Relativity

For the speed of light to be taken constant, Einstein replaced the entire space and time with relative definitions to that of an observer. Imagine two passengers in a train, where one passenger stands across a straight platform and the other sitting inside a train, moving at a constant speed along with the platform. The fixed (standing) passenger can easily mark a fixed point on the track and keep a close watch on the time, while the passenger inside the train can choose a spot on the platform and measure the time with his watch. This made Einstein come to the face of simultaneity, and the particular theory of relativity can be illustrated with the following example:

An observer, standing on a field, observed lightning in two (fixed) trees, located at 60km ahead of each other. The lightning struck at the same time when a moving passenger sitting inside a bus passed the observer. For the observer, each image travels at the same distance, and he sees it simultaneously. However, for the moving observer, one of the events is closer to the other. This made Einstein conclude that even simultaneity is relative. Therefore, he took inspirations for new equations of time and space from the Lorentz transformation,

x’ = $\frac{x-\nu t}{\sqrt{1-\frac{\nu^{2}}{c^{2}}}}$ and t’ = $\frac{t- \frac{\nu x}{c^{2}}}{\sqrt{1 - \frac{\nu^{2}}{c^{2}}}}$

where t’ is time measured by the moving observer, and c refers to the speed of light. From the above two equations, Einstein developed a new equation that described the relationships between velocities

u’ = $\frac{u + \nu}{1 + \frac{u {\nu}'}{c^{2}}}$

Where u and u’ are the speed of the respective moving objects as observed by the observer in relation to each other. Therefore, the first postulate rings true in this case where the speed of light remains constant for all of the observers.

It led Einstein to combine time and space equations into two physical principles: conservation of energy and conservation of mass that remains constant in a closed system. Thus the second postulate of the special theory of relativity also rings true in this equation.

For an observer moving inside a spacecraft, the rest mass is termed as mass m0, and the fixed observer's mass is considered to be having mass m can be expressed as:

m = $\frac{m_{0}}{\sqrt{1 - \frac{\nu^{2}}{c^{2}}}}$ , where v and c are the speed of one observer in relation to each other, and c is the speed of light.