Special Relativity

Student Learning Objectives
Lessons / Lecture Notes
Important Equations
Example Problems
Applets and Animations

Student Learning Objectives

• To understand the two postulates of special relativity.
• To understand how the principle of relativity leads to time dilation and length contraction.
• To solve novel problems using the equations for time dilation and length contraction.
• To explore relativistic energy and momentum.
• To recognize the significance of Einstein’s famous equation E = mc2.

Lessons / Lecture Notes

PY106 Notes from Boston University (algebra-based):

HyperPhysics (calculus-based)

Important Equations

Example Problems

Problem 1
Klingon spacecraft has a speed of 0.75 c with respect to the earth.  The Klingons measure 37.0 hours for the time interval between two events on the earth.  What value for the time interval would they measure if their ship had a speed of 0.94 c with respect to the Earth? (Solutions)

Problem 2
(a) A spaceship travels toward the Earth at a speed of 0.97c. The occupants of the ship are standing with their torsos parallel to the direction of travel. According to Earth observers, they are about 0.50 m tall and 0.50 m wide. What are the occupants’ height and width according to others on the spaceship? (Solutions)

(b) A rocket of mass 1.40 × 105 kg has a relativistic momentum the magnitude of which is 3.15 × 1013 kg m/s.  How fast as the rocket traveling? (Solutions)

Applets and Animations
 Simultaneity A tutorial that shows how the relative nature of the simultaneity of two events must follow from the existence of length contraction. Simultaneous Events The Simultaneous Events program displays the effect of relative motion on the relative ordering of events in special relativity.   In the default scenario two simultaneous events are observed in a stationary reference frame (the Other Frame) and the spacetime diagram of the observation of these events is depicted in another reference frame (the Home Frame). Simultaneity The Simultaneity model displays the effect of relative motion on the relative ordering of the detection of events.  The wave source and two equidistant detectors are at rest in reference frame S', which moves with constant velocity, v, in frame S. Einstein's Train and Tunnel The Einstein's Train and Tunnel model displays the famous thought experiment from special relativity where a train enters a tunnel as seen from two points of view.  In one case the train is seen in the reference frame of the tunnel, while in the other case the train is seen in its reference frame. Michelson Morley Experiment A simple analogy involving two swimmers that sets up the Michelson-Morley Experiment. Time Dilation A demonstration that the phenomenon of time dilation from the special theory of relativity necessarily follows from the idea that the speed of light is the same value for all observers. Twin Paradox There are many ways of approaching this classic "paradox". Here we discuss it as an example of the relativistic Doppler effect. Twin Paradox The Twin Paradox program displays the effect of time dilation on a moving twin as seen from a stationary twin.   In the default scenario the light signals sent from the moving twin are depicted using a spacetime diagram and are shown as seen in the stationary twin's reference frame (the Home Frame). Length Contraction A tutorial that shows how relativistic length contraction must follow from the existence of time dilation. Proper Length The GR Proper Length program simulates the distance between points using the Schwarzschild metric.  It displays the proper length between two points and the light-travel path.  It is distributed as a ready-to-run (compiled) Java archive.