That's what Randy and Jim explore as we discuss two paradoxes that try to explain this. Both paradoxes are similar in nature in that they involve a double slit experiment and a measurement that should allow the experimenter to determine which slit the electron goes through and without disturbing the electron. The first of these uses a charged capacitor with movable plates situated directly behind the screen in which the slits are cut and in the gap behind the slits, and whose capacitance will differ depending upon the path the electron takes. The second has a charged, cylindrical capacitor situated within the screen that will rotate in different directions depending upon the slit the electron passes through. In both situations, the electron feels no net force from the the charged capacitor and so should not react to it.
In this episode, we talk about Aharonov and Rohrlich's Quantum Paradoxes, chapter 4: "Phases and Gauges". Additional topics we discuss are the Aharonov-Bohm effect, the vector potential.
We're reading Quantum Paradoxes by Yakir Aharonov and Daniel Rohrlich. This is a technical book that is making an argument for a specific interpretation of quantum theory. The first half of the book uses paradoxes to explore the meaning of quantum theory and describe its mathematics, then after interpretations of quantum mechanics are discussed in the middle chapter, an interpretation of quantum mechanics is explored with paradoxes based on weak quantum measurements.