Can I place my rooks upside down at the beginning of the game? Numerous times I’ve read that it’s illegal to use an upside down rook to represent a promoted queen because “it’s still a rook”. Does that imply that I can begin the game with my rooks upside down? They are still rooks; they are still centred on their squares. Sorry for semi-frivolous question but I would enjoy to read the authoritative answer. Thanks so much!
EDIT: Or maybe one could use an upside down rook to indicate the castling right is gone on that side, if the rook has wandered away from its starting square and then returned :D Practical! Almost sensible! :)
The FIDE laws of chess say nothing about upside-down rooks. However, starting with upside-down rooks is silly and if your opponent complains that it is annoying, I would expect the claim to be upheld.


  11.5 It is forbidden to distract or annoy the opponent in any manner whatsoever.


https://handbook.fide.com/chapter/E012018

The proper way of dealing with a missing queen (or any other piece) needed for promotion is to stop the clock and call the arbiter for assistance. However, the upside-down rook tradition comes from less formal settings, or maybe lower-budget situations where no arbiters with spare pieces in their pockets are close at hand.

It is interesting to note that the USCF rules explicitly allow the use of upside-down rooks for promotion:


  8F7. Promoted piece not available. If the desired piece is not available to replace a promoted pawn, the player may stop both clocks in order to locate that piece and place it on the board. A player who cannot quickly find such a piece may request the assistance of the director. It is common practice, however, to play using an upside-down rook for a second queen. In the absence of the player’s announcement to the contrary, an upside-down rook shall be considered a queen.


Just, Tim. US Chess Federation’s: Official Rules of Chess, 7th Edition.