The movement of the electron is usually not detected in a quantum field because people do not have enough tools that can measure the movement of electrons. It is not only in the quantum field that the movement of electrons cannot be detected, but they also cannot be detected anywhere else too. There are also some reports that electrons may not specifically have a location, unlike protons and neutrons, that are usually found near the nucleus.
The direction of the movement of electrons also cannot be determined because they might move from one place to another. This principle is called the Uncertainty Principle. There are still some people who refer to this when they are studying not only electrons but also the other parts of the atom.
One of the things said about the electron is that it is something that has never been truly observed probably because it cannot be observed fully in a quantum field and it also cannot be directly observed anywhere else. We do not have the right tools in order to monitor electrons to show that they exist.
There are still a lot of things that are not known about the electron. There is not enough proof that will actually show that electrons exist. All of the things that we know about electrons are based on some theories and studies that were done before. The only reason why these theories and studies are being followed is that they make a lot of sense.
According to the Heisenberg Uncertainty Principle, the main reason why it will be hard to detect the movement of the electron in a quantum field is that the electrons do not have their own specific locations. They also do not have a direction of motion so trying to understand their movement will not be necessary and will not provide any definite results.
It also does not help that the electrons are all moving around in all different directions and doing different motions at the same time. The Uncertainty Principle was proposed back in 1927 and a lot of scientists and professionals still refer to this when they are studying electrons and anything related to electrons.