The spin of an entangled electron can vary depending on the specific entangled state in which it is prepared. The spin of an electron is an intrinsic property that characterizes its angular momentum. It is often described in terms of its projection along a particular axis, typically denoted as "up" or "down" relative to that axis.
In an entangled state involving two or more electrons, their spins become correlated, meaning that the states of their spins are intertwined in a way that cannot be described independently for each electron. The entangled state of the electrons determines the possible outcomes when their spins are measured.
For example, in the case of a maximally entangled state known as a Bell state, such as the singlet state:
|ψ⟩ = (1/√2)(|↑↓⟩ - |↓↑⟩),
where |↑⟩ represents an electron with spin "up" along a particular axis, and |↓⟩ represents an electron with spin "down," the spin of one electron is always opposite to the spin of the other electron when measured along that axis.
However, it's important to note that the spin measurement along any given axis is not predetermined before measurement. The act of measuring the spin of one electron will instantaneously affect the spin of the other entangled electron, even if they are separated by large distances. This property is known as non-locality and is one of the intriguing features of entanglement in quantum mechanics.
In summary, the specific spin of an entangled electron is not determined until it is measured, but the measurement outcomes of entangled electrons will exhibit correlations that depend on the entangled state in which they were prepared.