Einstein–Podolsky–Rosen paradox (EPR paradox) is a thought experiment proposed by physicists Albert Einstein, Boris Podolsky and Nathan Rosen (EPR), with which they argued that the description of physical reality provided by quantum mechanics was incomplete (https://en.wikipedia.org/wiki/EPR_paradox)
Readings: Be sure to read John Norton’s e-book chapter (Lecture 5.2).
You may also wish to have a look at the SEP article by Arthur Fine on The Einstein-Podolsky-Rosen Argument in Quantum Theory or Laszlo Szabo’s The Einstein-Podolsky-Rosen Argument and the Bell Inequalities. (Links all down below!) Background.
It would be hard to evaluate the incompleteness thesis without some discussion of the phenomenon of entanglement, so you should expect to discuss this briefly; however, you will not have enough words available to develop all of quantum mechanics in this essay, so you should try to extract only the bits of quantum mechanics that you need to make your point.
Make sure you are giving a clear reconstruction either of the EPR argument or Einstein’s argument given in his Autobiographical Notes. Finally, articulate which assumption of Einstein’s argument is suspect and why.