Well here's a small but interesting effect. The Lorentz transformation equations dont go over *completely* into the Galilean transformation equations as (v/c) tends to zero!

What happens is that gamma tends to 1, and this means that the transformations for all the spatial coordinates tend towards the respective galilean transformations. Look at the equation for time however:

t' = gamma(t-ux/c^2)

Notice that if x is very large then even if u/c is very small you would still get a substantial effect!

One way out is to say that we should take the limit c tending to inf. Thats not very satisfying however, because what we're actually concerned with is the ratio v/c . Conclusion: This peculiarity is just a fact of life!