Rudolf Ludwig Mössbauer, the German physicist who is now over 80 years old discovered the effect named after him in 1957, and in 1961 was awarded the Nobel Prize for Physics for this important discovery. The effect was used by Pound and Rebka in 1960 and by Pound and Snider in 1965 to measure the gravitational redshift, and thus their experimental successes proved the correctness of predictions derived from Einstein’s general theory of relativity as well as his special theory of relativity. Pound, et al measured the difference in redshift of gamma ray photons moving up and down a tower 22.5 meters high at Harvard University. It describes the emission or absorption by a nucleus embedded in a crystal lattice without the usual consequence of recoiling and subsequently spread out its radiative energies. This can only occur if the nucleus is strongly bound in the crystal structure such that all recoil energy is shared by the whole crystal and not just around the immediate neighborhood of the nucleus. It means the emission or absorption of very precisely defined wavelengths and the observation of very sharp spectral energy resonance.

Although the resultant measurement Δ�� gives the value of the energy shift of an emitted or absorbed gamma photon, it is derived by dividing the square of the transition energy ��² by the energy due to mass of the atoms of the crystal lattice: Δ��~��²/2����² where �� is the transition energy, �� is the mass of the atoms containing the transient nuclei. For sharp emission or absorption �� becomes the mass of the whole crystal and Δ�� is practically zero, indicating very sharp spectral resonance. With respect to the quadratic forms of square of energy: ��²=Q(2)=(��₂-��₁)²=��₁₁|��₁|²��������₁₁+��₂₂|��₂|²��������₂₂-��₁₂|��₁||��₂|��������₁₂-��₂₁|��₁||��₂| ��������₂₁ where for one probable set of solutions ��₁₂=��₂₁=90° and ��₁₁=��₂₂=0°. If |��₁|=|��₂| then ��₁₁=��₂₂=½ and ½|��₁|²+½|��₂|²=��². Moreover, the orthogonality of space-time lattices implies that the quadratic forms (��₂-��₁)² and (��₂+��₁)² are equal, which is easily proved by showing that their corresponding direction cosine matrices are the identity matrix.