“Entanglement” is a bit tricky to explain, versus “correlation” —
which has a perfectly classical interpretation.
Say I tear a page of paper in two, crumple up the two pieces into
balls and (at random) hand one to Adam and the other to Betty. They
then go their separate ways and — sometime later — Adam unfolds his
piece of paper. There’s a 50% chance that he got the top half, and 50%
that he got the bottom half. But if he got the top half, we know for
certain that Betty got the bottom half (and vice versa).
In this regard, the entangled state behaves exactly the same way. What
distinguishes the entangled state from the merely correlated is
something that doesn’t have a classical analogue. So let me shift from
pieces of paper to photons.
You’re probably familiar with the polaroid filters in good sunglasses.
They absorb light polarized along the horizontal axis, but transmit
light polarized along the vertical axis.
Say, instead of crumpled pieces of paper, I send Adam and Betty a pair
In the correlated state, one photon is polarized horizontally, and one
photon is polarized vertically, and there’s a 50% chance that Adam got
the first while Betty got the second and a 50% chance that it’s the
other way around.
Adam and Betty send their photons through polaroid filters, both
aligned vertically. If Adam’s photon makes it through the filter, we
can be certain that Betty’s gets absorbed and vice versa. Same is true
if they both align their filters horizontally.
Say Adam aligns his filter horizontally, while Betty aligns hers
vertically. Then either both photons make it though (with 50%
probability) or both get absorbed (also with 50% probability).
All of the above statements are also true in the entangled state.
The tricky thing, the thing that makes the entangled state different
from the correlated state, is what happens if both Adam and Betty
align their filters at a 45° angle. Now there’s a 50% chance that
Adam’s photon makes it through his filter, and a 50% chance that
Betty’s photon makes it through her filter.
(You can check this yourself, if you’re willing to sacrifice an old
pair of sunglasses. Polarize a beam of light with one sunglass lens,
and view it through the other sunglass lens. As you rotate the second
lens, the intensity varies from 100% (when the lenses are aligned) to
0 (when they are at 90°). The intensity is 50% when the second lens is
So what is the probability that both Adam and Betty’s photons make it
through? Well, if there’s a 50% chance that his made it through and a
50% chance that hers made it through, then you might surmise that
there’s a 25% chance that both made it through.
That’s indeed the correct answer in the correlated state.
In fact, in the correlated state, each of the 4 possible outcomes
(both photons made it through, Adam’s made it through but Betty’s got
absorbed, Adam’s got absorbed but Betty’s made it through or both got
absorbed) has a 25% chance of taking place.
But, in the entangled state, things are different.
In the entangled state, the probability that both photons made it
through is 50% – the same as the probability that one made it through.
In other words, if Adam’s photon made it through the 45° filter, then
we can be certain that Betty’s made it through. And if Adam’s was
absorbed, so was Betty’s. There’s zero chance that one of their
photons made it through while the other got absorbed.
Unfortunately, while it’s fairly easy to create the correlated state
with classical tools (polaroid filters, half-silvered mirrors, …),
creating the entangled state requires some quantum mechanical
ingredients. So you’ll just have to believe me that quantum mechanics
allows for a state of two photons with all of the aforementioned
Sorry if this explanation was a bit convoluted; I told you that
entanglement is subtle…
Getting back to the answer, it needs to be noted that in the Copenhagen interpretation of quantum mechanics, the paradox persists and instantaneous influences are indeed required to explain the phenomena.
But there is indeed a class of interpretations (Consistent Histories, Many Worlds, etc.) in which the paradox is claimed to be non-existent.