 where \(\mathbf{n}\) is an arbitrarily chosen direction, and \(|\mathbf{n}+\rangle , |\mathbf{n}-\rangle\) are spin-up and spin-down eigenstates of spin in the \(\mathbf{n}\) direction. The state is rotationally invariant, and hence the expression (13) represents the state for any direction \(\mathbf{n}\). If Stern-Gerlach experiments are performed on the two particles, then, regardless of the direction of the axes of the devices, there is equal probability of both results on each side. If experiments are done with the axes of the two devices aligned, the results are guaranteed to be opposite; spin-up on one will be obtained in one experiment if and only if spin-down is obtained on the other. If the axes are at right angles, the results are probabilistically independent. In the general case, with device axes in directions given by unit vectors \(\mathbf{a}, \mathbf{b}\), respectively, with results labelled \(\pm 1\), then the expectation value of the product of the outcomes is given by