Energy and Matter: E=mc² in Practice

The relationship E=mc² derived by Albert Einstein connects mass and energy and lies at the core of nuclear energy, particle physics, and cosmology. Understanding this connection is necessary to make sense of the processes occurring in stars, the operation of atomic reactors, and modern accelerators. In the course, you will learn the physical interpretation of this equation and how to apply it to specific problems. The course program covers the following topics: relativistic mass and rest energy; Lorentz transformations and their connection to energy and momentum; deriving E=mc² from the principles of special relativity; calculating nuclear binding energy and the mass defect; applying the formula to nuclear reactions and particle annihilation. You will work through examples from nuclear physics, such as helium synthesis in the Sun and uranium fission, as well as problems on determining energy release in reactions. Special attention is given to translating theoretical formulas into numerical estimates and analyzing dimensions. The course methodology is based on a step-by-step breakdown of problems with an emphasis on the physical meaning of each stage. You will learn to avoid common mistakes such as confusing total and kinetic energy, incorrect use of units, or ignoring relativistic effects at high speeds. Practical exercises will help you consolidate skills for estimating orders of magnitude and checking results for plausibility. The course is intended for students of physics and mathematics specialties, physics teachers at secondary and higher education levels, engineers working in nuclear energy, and anyone who wants to deepen their understanding of fundamental laws of nature at a level sufficient to solve standard problems. Upon completion of the course, you will master the conceptual toolkit of relativistic dynamics, be able to derive the E=mc² relation independently from basic principles, perform energy-release calculations in nuclear processes, and interpret the resulting numerical values in the context of physics. You will also gain the skill of critically checking results against conservation laws and orders of magnitude.