Can we accurately determine the trajectory of an electron using a SG detector?

[entropy1]

Would this be an accurate portrayal of measuring the spin of an electron with a SG detector?:

• The electron is in a superposition of spin-up and spin-down;
• Upon entering the magnetic field of the SG detector, the electron enters a superposition of an upward trajectory and a downward trajectory;
• When detected, the electron gets entangled with the detector, yielding a branch in which the detector detected the electron on the upward side, and another branch in which the detector detected the electron on the downward side;
• In case of detecting the electron on the upward side, it retroactively took the upward trajectory, and in case of detecting the electron on the downward side, it retroactively took the downward trajectory.

 

[Lord Jestocost]

One cannot meaningfully talk about what an electron is doing between observations, even not retroactively. The measurement of an electron's spin “creates” an electron-with-spin-up or an electron-with-spin-down; but neither entity can be considered already to be in existence prior to the measurement being made.

 

[entropy1]

If the electron gets detected somewhere, it doesn't carry the information of the trajectory it followed. Is that the cause that we can't speak of the trajectory of that specific electron?

 

[PeroK]

If the electron gets detected somewhere, it doesn't carry the information of the trajectory it followed. Is that the cause that we can't speak of the trajectory of that specific electron?

It's fundamental to QM that the electron simply did not follow a well-defined trajectory. Until measurement, its position was described by a wave-function. You know the probability with which you would have detected the electron somewhere, if you have looked for it, but no more.