Physics: How does the Correspondence principle relate to the special theory of relativity?

Could someone eplain the Correspondence principle and how it relates to the special theory of relativity?





Will be quick to award BA, thanks in advance for any help|||in Quantum Mechanics, the correspondence principle is that for large quantum numbers (large energies) the classical limit is reached.


Likewise, in relativity, the correspondence principle is that for slow speeds relative to the velocity of light, classical mechanics is recovered (as it should!).





One example:





The relativistic energy obeys the equation:





E = mc^2/sqrt(1-v^2/c^2)





if v%26lt;%26lt;c, the the square root can be approximated by





1/sqrt(1-v^2/c^2) ~ 1 + 1/2 v^2/c^2 + O(v^4/c^4).





Hence, for small v/c, the relativistic energy reduces to:





E ~ mc^2 ( 1 + 1/2 v^2/c^2) = mc^2 + 1/2 m v^2.


The constant term mc^2 is the rest energy. The kinetic energy is read of as 1/2 m v^2 , the classical result.