You have two cars.
They're travelling right at each other on a collision course; each one is going at precisely 50mph.
They hit each other...as you could assume.
Does that equate to one car hitting a wall at 100mph? Or is it something different?
I became interested in this paradox after watching Mythbusters' rendition of it (which is, of course, the best show in our current universe).
Their take on it was conducted through a full scale test. Their findings showed that the collision was identical to ONE car hitting a concrete wall.
The momentum equations behind this make sense, too. The car on the left (let's say they both have a mass of 10kg and are travelling at 20m/s) has a momentum of (10kg)(20m/s)=200kg*m/s. Equally, the car on the right has the same momentum.
So, the car on the left's momentum is negated by the car on the right.
That's the "real world" test result.
Any other arguments may hold validity...but I strongly reject your reality and substitute my own.