Can I invent a new opening?

The title of this post is borrowed from a question I recently saw on Quora. Answers seemed to range from 'No' to "sure, but it won't be any good". The general consensus is that all 'openings' have been invented, although the OP may find a new variation.
Of course this depends upon deciding what is an opening, and what is a variation. For example 1.e4 e5 2.Nf3 Nc6 is not yet an opening, with 3.Bc4 , 3.Bb5 or 3.Nc3 all becoming named openings, but after 3.Bc4 Nf6, 4.d4 and 4.Ng5 are only variations of the Two Knights Opening. As with most things in chess, history and convention take precedence over logic.
However, variations can be discovered (and possibly named), even if they might not be good. Just today I came across a line against the Caro-Kann which I had previously been unaware of, the Apocalypse Variation! It starts with 1.e4 c6 2.Nf3 d5 3.exd cxd 4.Ne5 I have seen White's 4th move given a ! and a ? and while I would lean towards ?! it has claimed some high profile victims. The idea is to keep the knight on e5 for as long as possible, or to exchange it at an advantageous time. Oddly, for such an aggressive idea, this line seems devoid of cheap traps, although I did see a few games end with Qxf7#.
To give you a feel for this line, here is a game between a couple of very strong GM's. I don't know if Black was caught by surprise, but his play looks a little unconvincing, giving White a fairly easy path to victory.

Petrosian,Tigran L (2580) - Macieja,Bartlomiej (2616) [B10]
Lake Sevan Martuni (4), 09.07.2007