Two blocks of masses \(m_1\) and \(m_2\), with \(m_1 > m_2\), are connected by a light, inextensible string that passes over a uniform solid disk pulley of mass \(M\) and radius \(R\). The pulley is mounted on a frictionless horizontal axle, and the string does not slip along the pulley rim as the system accelerates from rest. The tensions in the string segments attached to \(m_1\) and \(m_2\) are \(T_1\) and \(T_2\), respectively. In terms of \(m_1\), \(m_2\), \(M\), and fundamental constants, what is the magnitude of the difference in string tensions, \(T_1 - T_2\)?