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Unifying quantum mechanics and special relativity, the Dirac equation describes the behaviour of relativistic quantum particles, including imaginary-mass particles with faster-than-light speeds (e.g., tachyon). However, experimental searches for such particles remain negative so far. Fortunately, there are possibilities to investigate the relativistic quantum effects by quantum simulations using a controllable system. However, these simulations are mostly explored in closed physical systems that hinders the demonstration of imaginary-mass particles, whereas the general open framework would promise more possibilities in quantum simulations. Here, we reveal that the dynamic behaviors of imaginary-mass particles can be mapped to the transfer of wave packet in a non-Hermitian silicon optical lattice. We experimentally demonstrate a super-divergent dynamics of tachyon that travels faster than massless particles (e.g., photon). Besides, our simulation suggests another kind of imaginary-mass particles that have rarely been explored, which show non-divergent behaviors with imaginary energy. It is the first experimental quantum simulation being able to observe the imaginary-mass particles that have never been experimentally verified. Our work provides a fully controllable and extensible platform to investigate relativistic quantum phenomena at a chip-scale level, which would inspire more insightful explorations in quantum effects with non-Hermiticity.