Einstein's famous equation, E=mc², relates energy (E) and mass (m) to the speed of light (c) squared. It is a fundamental result of his theory of special relativity, which he developed in 1905.
Einstein arrived at this equation through a combination of theoretical insights and mathematical reasoning. Here's a simplified explanation of his thought process:
Principle of Relativity: Einstein started with the principle of relativity, which states that the laws of physics should appear the same to all observers in uniform motion relative to each other. In other words, the fundamental physical laws should be the same regardless of an observer's motion.
Constancy of the Speed of Light: Building on the principle of relativity, Einstein incorporated the experimental evidence that the speed of light in a vacuum is always the same for all observers, regardless of their relative motion. This constancy of the speed of light contradicted classical physics, which assumed a fixed reference frame.
Time Dilation: Einstein introduced the concept of time dilation, which means that time can appear to run slower for objects in motion relative to stationary objects. He mathematically derived the time dilation equation based on the constancy of the speed of light. This equation showed that as an object's velocity approaches the speed of light, time slows down for that object.
Equivalence of Energy and Mass: Einstein combined the principle of equivalence between energy and mass, as suggested by previous work, such as the mass-energy equivalence principle proposed by J.J. Thomson and Max Planck. This principle states that mass can be converted into energy and vice versa. Einstein realized that if energy and mass were equivalent, the equation for energy should include a mass term.
Derivation of E=mc²: By incorporating the concepts of time dilation and the equivalence of energy and mass, Einstein used mathematical reasoning and transformations to derive the equation E=mc². The equation implies that energy (E) is proportional to mass (m) multiplied by the speed of light (c) squared, where the speed of light serves as a conversion factor between mass and energy.
Einstein's equation E=mc² revolutionized our understanding of the relationship between mass and energy and laid the foundation for further advancements in physics, particularly in the field of nuclear energy and the development of atomic weapons.