Hardy’s Paradox | Quantum Double Double Slit Experiment

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. But there’s something weird about this when
particles are involved. 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! If you (or somebody you know, who maybe you’re
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