What is Special Theory of Relativity | Physics for EmSAT Achieve PDF Download

Introduction

• The laws of physics are consistent and unchanging regardless of the observer's reference frame.
• The speed of light in a vacuum remains constant regardless of the relative motion of the observer or the source of light.

Originally proposed by Albert Einstein in 1905 in his paper "On the Electrodynamics of Moving Bodies," special relativity has far-reaching implications, including the concept of mass-energy equivalence, the relativity of simultaneity, length contraction, and a universal speed limit. In this theory, the traditional notion of an absolute and universally shared time is replaced by a concept of time that depends on the observer's reference frame and spatial position.

In the theory of relativity, reference frames hold significant importance as they serve as a basis for measuring the timing of events using clocks. An event refers to a specific occurrence that can be associated with a particular location in space relative to a given reference frame. For example, an event could be the detonation of a firework.

Postulates of Special Relativity

• The Principle of Relativity states that the altered states of physical systems remain unaffected, regardless of whether these state changes are observed from one system or another that is in uniform translatory motion relative to each other.
• The Principle of Invariant Light Speed states that light always travels through empty space at a specific velocity, denoted as "c," which remains constant and unaffected by the motion of the emitting body.

The development of Special Relativity is influenced not only by the two postulates mentioned earlier, but also by factors such as the previous history of clocks and the concept of isotropy.

Relativity and the Integration of Electromagnetism

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

Space and Time Relativity

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, 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 velocitiesWhere 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:

 , where v and c are the speed of one observer in relation to each other, and c is the speed of light.