Modern Physics: Animations

1. Relativity I: Time, Space, and Motion

• The Reference Frame Exploration uses mountains and airplanes—and also birds—to demonstrate time dilation, length contraction, the relativity of simultaneity, and spacetime diagrams. Play around with it! Make sure you click between the mountains, the airplanes, and the birds, to see the same scene from all three perspectives.

• The Doppler Effect animation shows a stationary target, and a moving source that emits a steady wave. As you watch it, note how the target sees the pulses appearing to be crowded together as the source approaches the target, and spread apart as the source recedes.

3. The Quantum Revolution I: From Light Waves to Photons

• The Single Photon Interference Simulator allows you to run your own one-photon-at-a-time double-slit experiment. You can choose the wavelength of the light, the distance between the slits, the distance to the screen, and the speed at which the photons emerge. Watch the pattern on the back wall appear one dot at a time, appearing utterly random at first, but eventually revealing a consistent pattern of nodes and antinodes.

• The Double Slit Simulator is less cool, but it also requires less patience: you see the final pattern immediately instead of watching it emerge.

• External Link: The article "Feynman’s double-slit experiment gets a makeover" contains a video of the double-slit experiment, once again emerging one dot at a time. This one is not configurable because it is based on actual data rather than numerical simulation. Also, by the way, this experiment used electrons, demonstrating that they have the same wave-like properties as photons. (When you get to the article, you have to scroll down for a while to find the video to click on. But the article is interesting too!)

5. The Schrödinger Equation

• The Infinite Square Well allows you to create a wavefunction as a linear superposition of the first five energy eigenstates, and see how the probabilities evolve in time. (If it looks boring at first, that's because for any individual energy eigenstates, the probabilities don't change over time. Make a superposition!)

6. Unbound States

• Building a Wave Packet shows how, as you add more and more sine waves with slightly different frequencies, they create a localized "wave packet."

• Group Velocity vs. Phase Velocity shows such a wave packet moving, and how the "group velocity" (the velocity of the packet itself) can be much faster than the "phase velocity" (the velocities of the individual waves that make up the packet).

• The Scattering animation shows a wave packet approaching a potential barrier, where the packet splits into a reflected wave and a transmitted wave. You can see how increasing the barrier—either its height, or its width—increases the reflected wave and reduces the transmitted wave. Keep in mind, as you watch, that the behavior is all generated by Schrödinger's equation.