Our radiology residents are asking why there are only two relaxation times T1 T2.
To simplify things from the pedagogic point of view to relate this to the principle of duality: photon (T1) and electromagnetic wave (B1 creating a phasing of spins in X Y).
Should this be considered as heretic and burnt at the stake
The relaxation times T1 and T2 were described phenomenologically by Felix Bloch at al representing changes in the net magnetization (M) after RF-stimulation. T1 reflects changes along the direction (z-) of the main magnetic field; T2 reflects transverse (xy-) behavior. There are only two relaxation times because the directions "longitudinal" and "transverse" seem to encompass the cardinal directions in three-dimensional space. The transverse (x- and y-) directions are generally arbitrary and indistinguishable so only a single T2 value is usually applied.
However, some tissues and materials have T2 anisotropy, meaning their observed T2 values differ depending on orientation, so I suppose you could say there are more than one transverse relaxation time for these substances, but they are still called T2's.
Additionally, in the rotating frame another type of relaxation time is frequency distinguished, T1ρ ("T1-rho"). This relaxation time is somewhat of a hybrid between T1 and T2 that can be measured in when a spin-locking pulse is applied to a system. See our paper from 1996 for further explanation:
Ulmer JL, Mathews VP, Hamilton CA, Elster AD, Moran PR. Magnetization transfer or spin-lock? An investigation of off-resonance saturation pulse imaging with varying frequency offsets. AJNR Am J Neuroradiol 1996; 17:805-819.
I have never heard of the "duality" explanation above; it is not correct at all and should be abandoned/discouraged.
This relaxation time is somewhat of a hybrid between T1 and T2 that can be measured in when a spin-locking pulse is applied to a system.