In most ways, it is the same as standerd chess.
The Exceptions
Pieces or pawns can travel through time according to the following rules:
1: The piece has to be next to the King
2: The King can't be in check
3: The peice can't travel more than 10 moves
4: The peice can only travel foward in time
5: If the King is in check on the move the peice was supposed to come in, and the only legal move is to move the King to get out of check, then the peice is lost in time, and it gets captured.
6. You cannot say "I have to move the Queen, so i'm going to let my pawn get lost in time." That is illegal.
7. The piece can appear at any empty square, and pawns cannot appear on the first or last rank
For the king, the same rules apply except #s 1 and 4.
Traveling back in time:
1. only the King can do it.
2. The King can't be in check
3. It is limited to 5 moves back
4. It is limited to 2 backwards moves per person
5. There has to be at least 1 other piece or pawn of the same color, and another King does not count.
Winning the game:
There are 3 ways to win the game.
1. Checkmate one or more Kings
2. Make your opponent's King lost in time
3. Fork 2 or more Kings in a way that your opponent can't capture the forking peice
An example of notation:
1. d2//to5 Nc6
2. e4 Nf6
3. Qg4 Nd4
4. e5 Nf3+xP
5. Qxf3 Ng4
6. K//to2
2. K a4// FTF
In this game, White sent a pawn to move 5, Then on move 4, Black Checked the White King, Which captured the pawn.
White sent his king back in time to undo
the pawn capture, and FTF means from the future.
I very much like this variant, and it would be easy to program.