Relativistic Dynamics in 1D with a constant force

Developed by Larry Engelhardt

In these exercises, you will determine the motion of a proton in a uniform electric field. We will begin by simulating a proton in an electric field using the NON-relativistic version of Newton’s 2nd Law. Then we will modify this simulation to take special relativity into account. In the process, we will observe the transition from non-relativistic to relativistic dynamics. In order to generate results, we will see that we need to be careful when working with non-SI units. In particular, we will need to pay close attention to factors of eV and c.

Subject Area Modern Physics
Level Beyond the First Year
Available Implementations IPython/Jupyter Notebook and Python
Learning Objectives

Students will be able to:

  • Execute a working simulation, and explain non-relativistic, constant force motion (Exercise 1)
  • Manipulate and explain the units that appear in the context of relativistic motion (Exercise 2)
  • Interpret plots of energy vs. time for non-relativistic motion (Exercises 2)
  • Observe and explain when the non-relativistic form of Newton’s 2nd Law breaks down (Exercise 3)
  • Derive the relativistic form of Newton’s 2nd Law (Exercise 4)
  • Modify a non-relativistic simulation to incorporate relativity (Exercise 5)
  • Produce and interpret plots for relativistic motion (Exercises 6, 7, 8)
  • Validate numerical results by comparing with an analytical solution (Exercise 7)
  • Apply simulated results to a particle accelerator (Exercises 9 and 10)
  • Rewrite code to store data in arrays using array indices rather than by appending data to arrays (Exercise 11)
Time to Complete 120 min