Superluminal Motion Simulation and Activity
Apparent superluminal or ÒFaster-than-LightÓ motion is a common feature of relativistic jets of plasma that stream outward from the center of some distant, active galaxies. A Quicktime movie of the jet in the quasar 1222+216 from the MOJAVE program shows this effect, click to the right of the image below:
Understanding this effect involves realizing that while the jet is not actually flowing faster than the speed of light, it is flowing very close to the speed of light (at least 99.8% of light speed for the jet in the movie above). The jet is also flowing toward us, very close to our line-of-sight. So as the plasma in the jet gives off light, it also ÒchasesÓ after the light it emits... so the emitted light is all bunched up in time. When that light gets to Earth, we think only 14 years have gone by in the movie above, but actually at least 2800 years have passed in the galaxy!
To see a 3-D movie simulation of this effect, click here for mpeg (or quicktime).
The blue spheres in the movie represent the light emitted from the plasma moving down the jet. Graphs on the right of the movie show how far apart the light is really emitted within the jet as compared to how close together the light arrives at Earth. The opposite effect would happen if the jet was flowing away from usÉ it would appear slower than it really is.
To see a 3-D movie simulation of a jet flowing away, click here for mpeg (or quicktime).
Vpython Simulation
Vpython is a 3-D visualization library for the python environment available from http://www.vpython.org/ . The simulation movies linked above were created using a simulation written in vpython. If you would like the simulation code itself to play with and make changes, you can download it by clicking this link.
An In-Class Activity
Studying superluminal motion can be a very interesting experience for students who have just learned about Relativity in a Modern Physics course. No time dilation or Lorentz transformations are required to understand the effect, just pure geometry and careful thinking. However, this point-of-view effect (from a fixed location in space) is often novel to students because relativistic effects are usually introduced with the mental picture that there is a ruler and clock at every point in space and only the movement of frames is what matters. The explanation of the superluminal motion effect can be naturally extended to encompass the Doppler effect as well.
IÕve been working on a laboratory exercise for an introductory level course that includes relativity. A first version of the exercise (not tested in class yet!), along with the associated files is available in the following directory: click here. I will update the activity after I've had a chance to field test it this Fall.
Elements of this activity could be used as an in-class exercise instead. Note that the movie of 1222+216 in the activity directory is somewhat different from the movie at the top of this webpageÉ it eliminates some of the extraneous information that might be distracting or confusing when using this as a learning exercise. Comments on this activity are welcome.
Acknowledgements and Disclaimer
Any errors, omissions, or opinions in the work presented here are mine alone. This work has been supported by NSF grant AST-0707693. Thanks to my colleagues in the MOJAVE collaboration. Last modified, May 26, 2011 by D. C. Homan, homan + d + ÒatÓ + denison.edu