Introduction to Mass Energy Equivalence Albert Einstein’s equation E=mc2E=mc^2E=mc2 is one of the most famous equations in physics, symbolizing the deep connection between mass and energy. This elegant formula encapsulates a groundbreaking idea: ...
The Variation of Mass with Velocity: Special Theory of Relativity
Introduction to the Concept of Variation of Mass Albert Einstein's Special Theory of Relativity introduced several groundbreaking ideas that reshaped our understanding of physics. Among these, the concept of the variation of mass with velocity st ...
Lorentz Transformation: Lorentz Transformation forms a Group
Introduction: The Elegance of Symmetry in Physics In the vast and intricate world of physics, symmetry plays a crucial role. One of the most profound examples of symmetry is found in the Lorentz transformation. When we say the Lorentz transformat ...
Lagrangian and Lagrange’s Equation from Hamilton’s Principle in Classical Mechanics
Introduction to Classical Mechanics Classical mechanics is a cornerstone of physics, describing how objects move and interact with forces. It encompasses various formulations, each providing unique insights and tools for solving mechanical proble ...
Geodesics: Shortest Path Between Two Points in a Curved Space
When we think about the shortest path between two points, we often envision a straight line on a flat surface. However, in the realm of curved spaces, the concept of the shortest path takes on a new form known as a "geodesic." Understanding geodesic ...
Special Cases of Euler’s Equation: Calculus of Variation
Welcome, fellow math enthusiasts, to an intriguing journey through the world of the calculus of variations! Today, we will explore the special cases of Euler's Equation, a cornerstone in this field. Whether you are a seasoned mathematician or a curi ...
Euler-Lagrange Equation in Calculus of Variations
Euler's equation, also known as the Euler-Lagrange equation, is a fundamental concept in the calculus of variations, a branch of mathematics that deals with finding the extremum (minimum or maximum) of a functional. In this context, a functional is ...
The Relativistic Addition Law of Velocities or Velocity Addition Theorem
Introduction to the Addition Law of Velocities In our everyday experiences, velocities simply add up. If you're walking at 5 km/h on a train moving at 60 km/h, your speed relative to the ground is just 65 km/h. This intuitive rule, however, break ...
Consequences of Lorentz Transformation – Length Contraction, Time Dilation and Simultaneity of Two Events
Introduction to Lorentz Transformation Welcome, fellow enthusiasts of the cosmos, to an exciting exploration of the consequences of the Lorentz Transformation. In the world of physics, few concepts are as mind-bending and transformative as those ...
Lorentz Transformation – Special Theory of Relativity
Welcome, curious minds, to an exhilarating journey through one of the most fascinating concepts in modern physics—the Lorentz Transformation within the realm of the Special Theory of Relativity. Whether you're a seasoned physicist or just someone wi ...