  In this paper we formalize, using the Nyquist-Shannon theorem, a fundamental
temporal resolution limit for numerical experiments in complex systems. A
consequence of this limit is aliasing, the introduction of spurious frequencies
due to sampling. By imposing these limits on the uncertainty principle in
harmonic analysis, we show that by increasing the sampling interval $\Delta t$,
we can also artificially stretch the temporal behavior of our numerical
experiment. Importantly, in limiting cases, we could even observe a new
artificially created absorbing state. Our findings are validated in
deterministic and stochastic simulations. In deterministic systems, we analyzed
the Kuramoto model in which aliasing could be observed. In stochastic
simulations, we formalized and compared different simulation approaches and
showed their temporal limits. Gillespie-like simulations fully capture the
continuous-time Markov chain processes, being lossless. Asynchronous cellular
automata methods capture the same transitions as the continuous-time process
but lose the temporal information about the process. Finally, synchronous
cellular automata simulations solve a sampled chain. By comparing these
methods, we show that if $\Delta t$ is not small enough, the cellular automata
approach fails to capture the original continuous-time Markov chain since the
sampling is already built into the simulation method. Our results point to a
fundamental limitation that cannot be overcome by traditional methods of
numerical simulations.
