Probability amplitudes have special significance because they act in quantum mechanics as the equivalent of conventional probabilities, with many analogous laws, as described above. For example, in the classic double-slit experiment, electrons are fired randomly at two slits, and the probability distribution of detecting electrons at all parts on a large screen placed behind the slits, is questioned. An intuitive answer is that P (through either slit) = P (through first slit) + P (through second slit), where P (event) is the probability of that event. This is obvious if one assumes that an electron passes through either slit. When no measurement apparatus that determines through which slit the electrons travel is installed, the observed probability distribution on the screen reflects the interference pattern that is common with light waves. If one assumes the above law to be true, then this pattern cannot be explained. The particles cannot be said to go through either slit and the simple explanation does not work. The correct explanation is, however, by the association of probability amplitudes to each event. The complex amplitudes which represent the electron passing each slit (ψ first and ψ second) follow the law of precisely the form expected: ψ total = ψ first + ψ second. This is the principle of quantum superposition. The probability, which is the modulus squared of the probability amplitude, then, follows the interference pattern under the requirement that amplitudes are complex: P = | ψ ψ first + ψ ψ second | 2 = | ψ ψ first | 2 + | ψ ψ second | 2 + 2 | ψ ψ first | | ψ ψ second | cos ⁡ ⁡ ( φ φ 1 − − φ φ 2 ) . Here, φ φ 1 and φ φ 2 are the arguments of ψ first and ψ second respectively. A purely real formulation has too few dimensions to describe the system's state when superposition is taken into account. That is, without the arguments of the amplitudes, we cannot describe the phase-dependent interference. The crucial term 2 | ψ ψ first | | ψ ψ second | cos ⁡ ⁡ ( φ φ 1 − − φ φ 2 ) is called the "interference term", and this would be missing if we had added the probabilities.