![]() ![]() Unlearning the Newtonian concept of time and replacing it with the far richer version in relativity theory can be quite a challenge. In particular, Newtonian mechanics rests on an oversimplified conception of time. You see, the problem with Newton’s laws isn’t merely that the equations aren’t quite right it’s that the underlying concepts turn out to be inadequate. What makes relativity difficult to learn is not the mathematics, but the concepts. The main difference you’ll notice is that a lot of the formulas now involve square roots. The mathematics of special relativity is no more difficult than that of Newtonian mechanics: basic algebra and calculus, using derivatives to define velocity and acceleration. That theory is beyond the scope of these brief lessons.) (Ten years later Einstein published what he called his general theory of relativity, which is actually a revised theory of gravity. Relativity replaces Newton’s laws, and the related principles of momentum and energy conservation, with new versions that are accurate at all speeds. It tells us that Newton’s laws of motion are only approximate, and become especially inaccurate when we apply them to objects that move extremely fast. This “theory” is a revised framework for the laws of mechanics. “Relativity” is short for what Albert Einstein called his “special theory of relativity”, published in 1905. ![]() In preparing these lessons I’ve drawn heavily on the treatments in the three special relativity texts listed at the end under Further Reading. This is nearly double the class time for relativity that a traditional introductory course would allocate, but in my mind it’s the absolute minimum. In my own introductory physics course I deliver these five lessons during five 50-minute class sessions, and we spend two more class sessions discussing the assigned homework problems. I’ve tried to emphasize depth more than breadth, addressing the most important conceptual issues and introducing the conceptual tools (including spacetime diagrams) that show how the theory fits together. It is intended as a compromise between the extremely rushed treatments of relativity that appear in standard introductory physics textbooks, and the more leisurely treatments that appear in books dedicated to teaching just relativity. This introduction to special relativity is for anyone who is already comfortable with the Newtonian concepts of velocity, acceleration, momentum, and energy. As a result of our analyses, we believe that the Compton effect provides the clearest pedagogical test for the need of relativity in the case of gamma ray scattering while allowing both the classical and relativistic results to explain the original x-ray results of Compton.Relativity in Five Lessons Relativity in Five Lessons Daniel V. This left the initial conclusion in doubt and we began a serious look at what would the answer be. Further thought led to the realization that the electron receives only the difference in the energies of the incoming and outgoing photons. The first response given to the question was that the relevant energies were relativistic and hence this approach would not work. However, in the senior author's class one of the student coauthors of this paper, Sandeep Giri, asked what would happen if classical expressions for the electrons' momentum ( m v) and kinetic energy were used. Indeed, this works well for explaining the effect. The shift in photon wavelengths is usually introduced and derived using special relativity. In a usual modern physics class the Compton effect is used as the pedagogical model for introducing relativity into quantum effects. ![]()
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