How do virtual particles break the energy conservation?

Yes(in small picture) and No(in big picture) let me explain: 1.Quantum mechanically the elementary particles tend to interact with each other in all the possible ways. read more

Virtual particles do not necessarily carry the same mass of corresponding real particle, (real particle and virtual particle form particle & anti-particle pair. For every real particle there's some kind of antiparticle) although they always conserve energy and momentum. read more

At least since Feynman came along, most of use a form of perturbation theory in which virtual particles obey conservation of energy-momentum. Instead, what virtual particles get to do that real particles don't is "lie off-shell". read more

We are really using the quantum-mechanical approximation method known as perturbation theory. In perturbation theory, systems can go through intermediate "virtual states" that normally have energies different from that of the initial and final states. read more