When quantum entanglement is explained in "layman's terms", it seems (to me) that the first premise, that we have to accept on faith, is that a particle doesn't have a certain property (the particle is not IN one state or another) until that property is measured.
For example, I have read that a particle may have "spin up" or "spin down" but — here's where I get lost — it's not that we don't KNOW which spin the particle has until we measure it, but actually the particle has NEITHER spin until we measure it.
Now, if we accept that premise, then we can see how spooky it is, when two particles are created with correlated spins — if one has spin up, the other has spin down, but neither particle "has" either spin until one of them is measured. At that instant, the other particle "assumes" the other spin.
At least that's how I interpret things I have read.
Certainly, if we accept that a particle doesn't actually HAVE the property until it is measured, but rather the particle exists in a superposition of states until the measurement is made, then we "regular citizens" can understand what is meant by "spooky action at a distance". (As soon as one particle is measured, the other particle assumes the "other" spin, no matter how far away it is. How did the second particle know the first particle was measured? That, I think, is the spooky action at a distance (and the information transfer can be faster than light).)
However, from a layman's perspective, I want to cry out "but the particle does have a definite spin, we just don't KNOW what it is, until it is measured! Duh!"
Now, I can't believe that all of the physics community hasn't thought of that objection — but — here's my point — although the spooky action at a distance can be explained to us, once we accept the premise of superposition — Why isn't the fact of superposition explainable also, in terms mortals can understand? I have looked, but I haven't found a layman's explanation of why we should accept the fact that a particle doesn't have a particular spin, or other property, until it's measured. It sure seems that the particles "have" the properties, even though we haven't measured them yet.
I know that much of quantum mechanics is not "intuitive". If anyone can explain why particles don't have a definite property, even before we measure them, I would be grateful.
Best Answer
The assumption (if you cry it or not) "but the particle does have a definite spin, we just don't KNOW what it is, until it is measured! Duh!" is called realism, or in mathier speak, a theory of hidden variables.
Bell's inequalities now say that no theory that fulfills local realism (equivalently that has local hidden variables) can ever predict the correct results of a quantum mechanical experiment.
So we are faced with a problem: Do we give up locality or realism?
Most people choose realism, since giving up locality would totally destroy our conceptions of causality. It is possible that there is a non-local theory that assigns a definite value to every property at all times, but due to its non-locality, it would be even more unintuitive than "particles do not have definite properties".
There is no intuitive explanation for the non-realism of reality (there has to be a way to phrase that better...) because our intuitions have been forged in the macroscopic world which is, to good approximation, classical. But the non-realism is an effect that has no classical analogon, so we cannot understand it in pretty simple pictures or beautiful just-so stories.
Sometimes, we just have to take the world the way it is. (I have assumed that you do not want the whole QM story of non-commuting observables and eigenbases and so on to explain why we, formally from QM principles, expect realism to be false. If I have erred in that respect, just tell me)