The spookiness continues with the quantum mechanical notion of locality. Einstein proposed an experiment called an "Einstein box" to demonstrate that particles must have some way to directly affect one another, that they must observe locality.
He proposed that we consider a box in which we place one electron. Let us say we choose to start this experiment in Tucson, Arizona. At any given time, that electron can be anywhere in the box. The probability that it is in a particular place is given by a mathematical "wave" function.
Note the notion of the wave function is not that it describes our lack of understanding of where the particle is. Instead, it is as if the particle actually does exist in a mixture of different positions within the box. If we were to open the box suddenly and peer inside, then the moment we spot that electron the wave function is said to collapse to a single point.
Let us suppose that we resist the temptation to peek inside. Instead, we close our eyes and insert a partition to physically divide the box into two equal halves. If we do this in the right way, then we can preserve the same wave function as before, with the result that we still will not know in which half of the box the electron resides.
This story gets interesting if we package up the one half of the box and ship it somewhere far away, like Rome, Italy. Now where is that one electron?
If our friend in Rome opens the box and sees an electron, then suddenly there should be zero electrons in the half-box that stayed in Tucson. Likewise, if we open the box in Tucson, then the friend in Italy will be disappointed. So what is going on here?
How can two boxes separated by half a world instantly communicate with each other and know what to do? Isn't this an example of spooky action at a distance? Einstein thought so! In the next installment we will consider another thought experiment that will take us a step closer towards understanding the state of this active field of quantum mechanics.