[asayers]

No, it's actually quite different.

The scenario you outlined is quite important and actually has a name: it's the "Bertlmann's Socks" thought experiment, and if you want to read about it I'd seriously recommend the paper by the great J S Bell[1].

To use the language of your example, both pens begin in a superposition of clockwise and anti-clockwise. It's not the case that each pen has a particular spin value, and that we're simply unaware of which has which. The pens really are in a superposition.

Until, that is, a measurement is made on one of them. At this point the joint pen-pen system collapses and both pens have determinate spin values. The nature of the entanglement ensures that those spin values are different.

The notion that quantum-entangled particles could have well-defined properties that we're just ignorant of was actually pretty popular in the early days of quantum mechanics. In fact, the theory was put forward by Einstein, among others. As it turns out, however, that we can test for this. The tests have been done, and it seems Einstein was wrong on this one.

[1]: J. S. Bell (1980), "Bertlmann's Socks and the Nature of Reality"

[confluence]

Cool. But what if the two pens are spun randomly in a box by say a random number generator spinner (each is pen is still anti-correlated - you just don't get the spin) - such that you do not know that what state they are in (superposition?). Then, probabilistically, they are both clockwise and anti-clockwise - until of course you look at it, a point at which they "snap" to a specific spin (which they already were in? You just didn't know it yet). Wouldn't that give you your unpredictable states.

I'm sorry if this sounds stupid - I just want to understand.

[asayers]

It's not stupid - the difference between uncertainty and superposition is subtle. Let's simplify to the case of one pen.

Say the pen is spun in the box by a classical random number generator. You don't know which way the pen is spinning, but you do know that it's either been spun one way or the other. You might say that the probability of finding it spinning clockwise when you open the box is 1/2.

Now say the pen is prepared in a superposition of the two spin states, again in the box. As before, we might say that the probability of discovering the pen spinning clockwise is 1/2. However, this time we the probability isn't generated by our lack of knowledge: we know exactly what state then pen is in. When we open the box, however, the pen will change instantly to the state of spinning clockwise, or the state of spinning anti-clockwise.

In the quantum case, the probability is an expression of what we think will happen to the pen, not what we think has happened to it.

It is hard to grasp, and harder still to believe. There is, however, good reason for thinking that, sometimes, the pen changed just as we opened the box.

[confluence]

I see - superposition and uncertainty are distinct concepts that should be thought of differently.