I saw the movie, nice one :)
No secret numbers, ranks, and files, but this chess variant brings some Quantum Physics into chess:
Quantum Chess
http://research.cs.queensu.ca/Parallel/QuantumChess/QuantumChess.html
"In Quantum Chess, a player does not know the identity of a piece (that is, whether it is a pawn, a rook, a bishop, and so on) until the piece is selected for a move."
Short Story: http://www.strangehorizons.com/2000/20001120/secret_number.shtml
Movie: http://secretnumber.colinlevy.com/
Consider the implications for chess of the existence of a secret number, an integer, that is greater than three and less than four.
That would obviously imply the existence of a secret rank between the 3rd and 4th ranks and a secret file between the c-and d-files. And I guess there would have to be a secret rank between the 6th and 5th ranks (3 and 4 counting from the other side), and also between the f- and e-files.