I finally think I’ve got it…

OK, I’m not entirely sure Rob Spekkens understood me, but I think I got it anyway.  So, here’s how I guess I could explain it, then, to a student.  You prepare a bag with two marbles – one black and the other red.  You have someone reach in and randomly grab one.  Before they look at it, you chuck the other one far, far away.  If the person then looks at their marble and sees that it is red, then the other one must be black and is known instantaneously, even though there’s no violation of relativity in that sense.  Conversely, any measurement made on the black marble is independent of whether or not we’ve looked at the red marble.  The only difference is that, in quantum systems, the state isn’t necessarily pre-determined.

Taking Bob Griffiths’ consistent histories interpretation, the above (as well as true entanglement) could be rephrased in terms of events.  Suppose the measurements of the marbles are events A and B respectively.  While they are not causally linked (neither is in the past or future lightcone of the other), there is another event C such that A and B are both in its future lightcone (and it is in their past lightcones).  Event C is what, in a sense, pre-determines A and B.  So event C is the preparation.  In our marble example, it is our act of first preparing the red and black marbles and then having someone choose one. 

In any case, that is how a measurement can affect our knowledge – my making our measurement, we immediately know the state of the other particle without the need to measure it (assuming the two are entangled).

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