Further Contents of E = mc^{2}
Let us look at the energymomentum relations for massive and massless particles. They are E = p^{2}/2m and E = cp respectively. As you know, it was Einstein who unified these relations with his special relativity.


As for the internal spacetime symmetries, massive particles have
the O(3)like symmetry which produces the concept of spin.
Massless particles have the symmetry which is like the twodimensional
Euclidean group. Wigner made these observations in his 1939 paper
on "inhomogeneous Lorentz group" where introduces the little group as
the subgroup of the Lorentz group whose transformations leave the
fourmomentum of a given particle invariant.
If the massive particle is at rest, its O(3)like symmetry leads to the concept of spin. For the massless particle, the rotational degree of freedom of the E(2)like little group corresponds to the helicity. The translational degrees of freedom have been shown to correspond to gauge transformations. Indeed, massive and massless particles appear to have two distinct internal spacetime symmetries. Can they be unified as Einstein did for the energymomentum relation?
In order to answer this question, let us boost a particle with spin. Its longitudinal component remains invariant and is called the helicity. How about its transverse components? They become contracted to the translationallike degrees of freedom in the E(2)like little group, which physically are gauge degrees of freedom. Together with D. Han and D. Son, I published a series of papers in the 1980s establishing that Wigner's little group together with group contraction techniques unifies the internal spacetime symmetries of massive and massless particles.
 
Einstein's Genealogy
 
 
 

You are then invited to build your own house. How are you going to build your own house? With what? In order to build a house consistent with it neighborhood is to find a Lorentzcovariant entity which takes different forms for slow and fast particles.
See next page.
portrait by Bulent Atalay (1978)