A Thought Experiment to Challenge the Special Relativity Theory

The experimental evidences cited to support the Special Relativity Theory ( SRT) , including Einstein's thought experiments, involve experimental setups in which the components (light sources, beam-splitters, mirrors, detectors, etc.) are all at rest relative to each other. An example is the Michelson-Morley experiment. In such experiments it is possible to define the 'rest frame' of the experiment in which proper lengths, proper times and hence the experimental outcome can be determined. Then Lorentz Transformation is applied to determine times and lengths in other inertial frames and to determine the same experimental result in other frames. What if no 'rest frame' can be defined for an experiment? Imagine a light speed experiment in space where all the components are in arbitrary relative motion. In such an experiment, it would be impossible to define the 'rest frame' of the experiment, and hence impossible to determine proper lengths, proper times and to determine the experimental outcome.