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Mass is commonly considered an intrinsic property of matter, but modern physics reveals particle masses to have complex origins, such as the Higgs mechanism in high-energy physics^,. In crystal lattices such as graphene, relativistic Dirac particles can exist as low-energy quasiparticles with masses imparted by lattice symmetry-breaking perturbations^{, , –}. These mass-generating mechanisms all assume Hermiticity, or the conservation of energy in detail. Using a photonic synthetic lattice, we show experimentally that Dirac masses can be generated by means of non-Hermitian perturbations based on optical gain and loss. We then explore how the spacetime engineering of the gain and loss-induced Dirac mass affects the quasiparticles. As we show, the quasiparticles undergo Klein tunnelling at spatial boundaries, but a local breaking of a non-Hermitian symmetry can produce a new flux non-conservation effect at …