The Glashow-Weinberg-Salam model unifies electromagnetism and the weak interaction as different aspects of a single SU(2)_L x U(1)_Y gauge theory. Spontaneous symmetry breaking via the Higgs mechanism gives mass to the W+, W-, and Z bosons while leaving the photon massless. The weak and electromagnetic interactions appear different only because the symmetry is broken at the electroweak scale (approximately 246 GeV).
The electroweak theory, formulated by Glashow, Weinberg, and Salam (Nobel Prize 1979), unifies the electromagnetic and weak interactions into a single gauge theory based on the group SU(2)_L x U(1)_Y. The SU(2)_L factor acts only on left-handed fermions (explaining the parity violation of the weak force), and U(1)_Y is the hypercharge symmetry. Before symmetry breaking, the theory has four massless gauge bosons: three from SU(2)_L (W1, W2, W3) and one from U(1)_Y (B).
The Higgs mechanism breaks SU(2)_L x U(1)_Y to U(1)_EM, the gauge symmetry of electromagnetism. A complex scalar doublet phi with a Mexican hat potential acquires a vacuum expectation value v = 246 GeV. Three of the four scalar degrees of freedom become the longitudinal components of the W+, W-, and Z bosons, which acquire masses m_W = gv/2 approximately 80 GeV and m_Z = m_W/cos(theta_W) approximately 91 GeV. The fourth scalar is the physical Higgs boson (125 GeV). The photon, corresponding to the unbroken U(1)_EM generator Q = T_3 + Y/2, remains massless.
The weak mixing angle theta_W parametrizes the mixing between the SU(2)_L and U(1)_Y gauge bosons. The photon and Z are linear combinations of W3 and B, rotated by theta_W. The value sin^2(theta_W) approximately 0.23 is determined experimentally and relates the SU(2) coupling g, the U(1) coupling g', and the electromagnetic coupling e by e = g sin(theta_W) = g' cos(theta_W). This single parameter connects the strengths of the electromagnetic and weak interactions.
The apparent difference between electromagnetism and the weak force at everyday energies is entirely due to the large masses of the W and Z bosons. The weak interaction appears short-range (approximately 10^{-18} m) because the massive W and Z propagators fall off exponentially: the effective potential goes as e^{-M_W r}/r rather than 1/r. At energies above the electroweak scale, the boson masses become irrelevant and the full SU(2)_L x U(1)_Y symmetry is effectively restored. The electromagnetic and weak interactions become comparable in strength, as directly confirmed by high-energy experiments at the LHC.