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### The DeLorean

Fairy chess has this and that, but I don't recall a piece
that can move through time. But how shall the DeLorean move?

I have no idea, since you run into the usual time paradoxes.
I see two main possibilities:
a) Parallel universes. The time travel creates a new timeline.
Well, slap me with a trout, but haven't we exactly that
with retro variation problems?
b) A stable time loop. Now that reminds me of a posteriori logic...

Feel free to expand, I'm a 2# expert :-)

"Parallel universes. [..Don't we have] exactly that with retro variation problems?"

Hm, perhaps, but if this counts as parallel universes, then so does try-play and actual play (in one universe White played 1. T?; in another, White played 1. K!) and so does branching in the solution-tree.

One chess phenomenon which for me looks more like bending Time's straight arrow is when the side to move captures a pawn en passant with no proof that that is legal, and later castles to prove the en passant capture legal.

Alex Levit has had exactly the same idea with the stable time loops (although he called the piece "The Terminator", not "DeLorean", still close) and has composed a clever h#2 with a terminator pawn that arrives from future as a promoted piece so original has to promote and then travel back in time to close the loop:
https://alex-levit.livejournal.com/1023.html

(4) Posted by Hauke Reddmann [Wednesday, Aug 21, 2019 10:28]

@Rosie: Yes, exactly this I was thinking.
QDimitri: There is nothing new under the sun :-)
Here is how I thought how a new timeline would work:

(= 2+4 )

DeLorean h1 (moves only in time), series# in 5

Solution: 1.e4...5.exf8Q 6.Qxd8 takes one move too long.
Thus: 1.e4...5.e8DL! (now moves back in time so that
the new timeline is this diagram - already at move 1!
(= 3+4 )

And now 1.e4...5.exd8Q#.

Please be careful when crossing zebra walks :-)

Hauke

So the stipulation should be series checkmate in at least one timeline :)
And 5.exf8=DL doesn't work because you cannot time-travel to a square occupied in the past?

Tangentially related, the computational complexity in closed timelike curves is a thing! There are papers, this one doesn't even require the mathematical background from the reader (sort of):
www.scottaaronson.com/papers/philos.pdf