# Hardy's Paradox | Quantum Double Double Slit Experiment

If you take a laser and shine it at a wall with two holes in it, you have the famous
double slit experiment - where waves coming through two slits interfere with each other
to be bright in some places on the wall, and dark in others.
And this works with quantum particles, too, since they behave in wave-like ways: send
a cat towards the slits, and it’ll show up at a point on the wall.
Send a bunch of cats, and their accumulation reveals the same interference pattern as a
light wave .
Now imagine you add another, competing double slit experiment, with another cat, that shares
one of the slits with the first setup.
Of course, if you send the second cat over and over towards these two slits , the points
where it hits the wall will give a similar interference pattern.
And at this point here for one cat, and this point here for the other, those cats never
show up, no matter how many times you send them through the slits.
Their wavelike behavior causes what’s called “destructive interference”; if cats were
light, these points would be in cat-darkness.
But weird things happen if you send both cats at their double slits at the same time.
The top cat goes through the top and middle slits and then towards the wall, and the bottom
cat goes through the bottom and middle slits and then towards the wall; and things would
again go as expected, of course, except that the cats get in each others’ way going through
the middle slit.
Maybe the slit’s too small for two cats to fit through simultaneously, or maybe, yeah!
maybe one cat is actually made of antimatter so if both go through the middle slit, they
annihilate each other and never make it to the wall.
Either way, the situation is now this: the cats traverse the slits in a quantum superposition
of top cat top/bottom cat middle, top cat top/bottom cat bottom, and top cat middle/bottom
cat bottom.
There’s no “both cats in the middle” in the superposition, since the cats can’t
traverse the middle slit together.
And since the superposition is missing the “both cats in the middle” option, the
interference patterns change and it’s possible for the cats to end up in the places on the
wall where before there was cat darkness.
This isn’t at all surprising for waves - I mean, different amounts of wave coming through
the slits means a different interference pattern.
To see why, remember that individually, the cat darkness arose because the cat’s wave-particle
superposition went through both slits and interfered with itself to result in zero probability
of the cat ending up there.
So if the bottom cat DOES end up there, it must not have been able to interfere with
itself, so it must not have gone through both slits, so there must have been something blocking
one - the other cat, in the middle.
And if the top cat ends up in its previously cat-free spot, then it must not have gone
through both slits either - the bottom cat must have been blocking the middle slit.
This wouldn’t be a problem, except that when you actually do this experiment , some
of the time BOTH cats end up in the previously cat-free spots.
And we know they can’t both have gone through the middle slit, because they would have annihilated
each other - so each cat must have been blocked from going through the middle slit by the
other cat having gone through the middle slit, simultaneously.
Which of course seems impossible, and is why this situation has been called a paradox . And
it’s certainly thought-provoking if you like to think about local realism or contextuality
or weak measurement values or the interaction between classical logic and quantum mechanics.
But it’s not really that surprising, as long as you believe that quantum particles
can be in superpositions (which happens all the time and has been incredibly well experimentally
confirmed).
As we said earlier, the two cats pass through the slits in the superposition “top middle”
plus “middle bottom” plus “top bottom”, which include both apparently necessary “blockages”
of the middle slit by one cat or the other, and it’s this superposition that results
in the changed interference pattern that allows for the possibility that both cats simultaneously
end up in the previously cat-dark locations.
If all of this seems a bit weird - yeah, it is!
But it’s worth remembering that weirdness and paradox are not one and the same . And
the quantum cat/antimatter-cat double double-slit experiment is fully consistent with the predictions
and experimental results of quantum mechanics.
Sometimes the universe is just weird!
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