Does 4E D&D specify what the real-world size of a battlemap "square" is? Reference/citation desired.
A single battlemap square represents a 5 foot by 5 foot space.
From the PHB, p266:
A 1-inch square on the battle grid represents a 5-foot square in the game world. So a dungeon room that is 40 feet by 50 feet would be 8 squares by 10 squares, which is a huge room but a good size for a busy combat encounter.
This is answered in multiple rule books.
Battle Grid or Dungeon Tiles: Combat in D&D plays out on a grid of 1-inch squares.
A 1-inch square on the battle grid represents a 5-foot square in the game world.
Rule Compendium, pg.200
battle grid: The network of 1-inch squares that represents an encounter area.
Battle Grid: A battle grid is very important for running combat encounters, for reasons outlined in the Player’s Handbook. [...] The grid should be marked in 1-inch squares.