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The impact of local space anisotropy on the transverse Doppler effect isexamined. Two types of laboratory experiments aimed at seeking and measuringthe local space anisotropy are proposed. In terms of the conventional specialrelativity theory, which treats 3D space to be locally isotropic, theexperiments are of the type of ``null-experiments''. In the first-typeexperiments, a feasible Doppler shift of frequency is measured by theM\"ossbauer effect, with the M\"ossbauer source and absorber being located attwo identical and diametrically opposed distances from the center of a rapidlyrotating rotor, while the $\gamma$-quanta are recorded by two stationary andoppositely positioned proportional counters. Either of the counters recordsonly those $\gamma$-quanta that passed through the absorber at the moment ofthe passage of the latter near a counter. The second-type experiments are madeusing the latest radio physics techniques for generating monochromaticoscillations and for recording weak signals. The effect expected due to spaceanisotropy consists in frequency modulation of the harmonic oscillations comingto a receiver that rotates at a constant velocity around the monochromatic waveemitter. In this case the modulation depth proves to be proportional to thespace anisotropy magnitude.

Some physical displays of the space anisotropy relevant to the feasibility of its being detected at a laboratory