Lorentz contraction of electric field lines for a point charge in uniform motion

We examine a logical foundation of depicting a Lorentz contraction of a Coulomb field (an electric field of a point charge in uniform motion) by means of the 'Lorentz contracted' field lines. Two existing arguments for a contraction of field lines sound appealing and lead to very simple calculations yielding the correct results. However, one of them is a victim to subtle logical weaknesses, as it relies on ascribing a degree of physical reality to the electric field lines. The other one correctly proves what it sets out to prove. But it does not provide a proof, or even a suggestion, of an additional result that can be obtained by a new poof that we present here. Though our idea is very simple, the calculations used to prove it - based on a little known, half a century old result by Tsien - are somewhat more involved than those from past arguments.