In quantum mechanics, the phenomenon that allows two electrons to be "forever bonded" is known as quantum entanglement. When electrons become entangled, the state of one electron instantaneously correlates with the state of the other, irrespective of the distance separating them. This correlation persists until an external interaction alters their states. The entangled electrons exhibit a unique dependency such that measurement applied to one electron determines the state of the second.
Entanglement results from interactions where the quantum states of two or more particles become intertwined such that their composite system can no longer be described independently of each other. This contradicts classical intuition, as the quantum mechanical description suggests a non-local connection that Einstein famously termed "spooky action at a distance."
In quantum field theory, electrons, like all fermions, follow the Pauli exclusion principle prohibiting two identical fermions from occupying the same quantum state simultaneously. However, entanglement does not violate this, as the entangled electrons, while correlated, remain in distinct, non-overlapping quantum states.
Entanglement has profound implications for quantum information science, including potential applications in quantum computing and secure quantum communication. The ability of entangled states to maintain coherence over vast distances offers intriguing possibilities for developing new technologies based on these quantum properties. While theoretically bonded as per their state dependencies, entangled electrons can still interact with their environment, a process that typically results in decoherence, affecting the persistence of their entangled state.