The American vs. of Life on Mars takes place in the parallel universe that Rose Tyler is trapped in.When the half-human Doctor was left behind, they grew a new TARDIS from the piece of TARDIS coral that the original Doctor gave them as a gift (in a deleted scene). So they went travelling across space and time in their universe until the TARDIS broke down permanently. They married, the Doctor took Rose's last name, and they gave birth to a son named Sam. Some years later, after Rose had gotten used to staying in one time, the Doctor got cold feet and left to fix the TARDIS, going off on his own. Sam Tyler, being part Time Lord, has a natural feel for the flow of time; when he was hit by a car, he reflexively sent his consciousness back near the point in time where his father left him and manifested a new physical body in a bizarre sort of regeneration affected by his human DNA. A few sheets of psychic paper also got sent back, insuring that adult!Sam had a history in 1973.
Most of the American vs. of Life on Mars takes place in a MMORPG.Okay, not sure if it's wild enough, but here it is. But it leaves the scary implication that Ray Carling is not the product of a more barbaric time. (Admittedly, if there's any place where an enlightened society can contain people like Ray Carling and Gene Hunt, America will be it.)
In the American Life on Mars, 2035 isn't real, either.And Sam would've eventually started seeing mysterious hints of 1973 when there was no clear reason for him to.
Life on Mars takes place in the same universe as Inception, and Sam is dreaming the whole time.1973 is one level of dreaming and the spaceship is another.
The "spaceman" reality at the end of the American series is the second level of Purgatory.The "period cop drama" is the first level, once you accept your death your soul moves on to a more challenging scenario.