  According to Eugene Wigner, quantum mechanics is a physics of Fourier
transformations, and special relativity is a physics of Lorentz
transformations. Since two-by-two matrices with unit determinant form the group
SL(2,c) which acts as the universal covering group of the Lorentz group, the
two-by-two matrices constitute the natural language for special relativity. The
central language for optical instruments is the two-by-two matrix called the
beam transfer matrix, or the so-called ABCD matrix. It is shown that the ABCD
matrices also form the SL(2,C) group. Thus, it is possible to perform
experiments in special relativity using optical instruments. Likewise, the
optical instruments can be explained in terms of the symmetry of relativistic
particles.
