The inability to observe both the wave and particle nature of an electron simultaneously is a fundamental characteristic of quantum mechanics known as the wave-particle duality. It arises from the way measurements and observations are made in the quantum realm.
When we perform a measurement on an electron, such as determining its position or momentum, we interact with the electron in a way that disturbs its quantum state. This disturbance causes the electron's wave function to collapse to a specific value, revealing it as a localized particle with a definite position or momentum. In this state, the wave-like nature of the electron is no longer evident.
On the other hand, when we want to observe the wave-like behavior of an electron, we typically need to use experimental setups that involve interference or diffraction phenomena, such as the famous double-slit experiment. These setups allow us to observe the wave-like characteristics of electrons, such as the interference pattern formed when electrons pass through a double-slit arrangement.
However, when we set up an experiment to observe the wave-like behavior, we usually cannot simultaneously determine the exact position or momentum of the electron. The wave function is spread out over a region, and attempting to pinpoint the electron's position would cause the wave function to collapse, making the interference or diffraction pattern disappear.
This limitation is not due to any technological constraint but is inherent in the nature of quantum mechanics itself. It's a fundamental aspect of the theory that arises from the mathematical formalism and has been confirmed by numerous experiments.
In summary, the wave-particle duality of electrons and other quantum particles means that we can observe either their wave-like behavior or their particle-like behavior, but not both simultaneously. The act of measurement or observation disrupts the quantum state and forces the particle to behave as either a wave or a particle, depending on the context.