We use the Liénard–Wiechert potential to show that very violent fluctuations are experienced by an electromagnetic charged extended particle when it is perturbed from its rest state. The feedback interaction of Coulombian and radiative fields among different charged parts of the particle makes uniform motion unstable. Then, we show that radiative fields and radiation reaction produce dissipative and antidamping effects, triggering a self-oscillation. Finally, we compute the self-potential, which in addition to rest and kinetic energy, gives rise to a new contribution that shares features with the quantum potential. We suggest that this contribution to self-energy produces a symmetry breaking of the Lorentz group, bridging classical electromagnetism and quantum mechanics.

Using a hybrid cellular automaton, we investigate the transient and asymptotic dynamics of the cell-mediated immune response to tumour growth. We analyse the correspondence between this dynamics and the three phases of the theory of immunoedition: elimination, equilibrium and escape. Our results demonstrate that the immune system can keep a tumour dormant for long periods of time, but that this dormancy is based on a frail equilibrium between the mechanisms that spur the immune response and the growth of the tumour. Thus, we question the capacity of the cell-mediated immune response to sustain long periods of dormancy, as those appearing in recurrent disease. We suggest that its role might be rather to synergize with other types of tumour dormancy. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’.