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Being a layman in the sense that I enjoy reading about physics concepts, but lack the deeper mathematical understanding, I've been trying to wrap my mind around the concept of quantum entanglement and why it is so "spooky".

So, in my thought experiment, imagine:

  1. We have an electron with known quantifiable properties represented macroscopically by a container of 100 black beads.
  2. We have another electron represented by another container of 100 white beads.
  3. For the sake of the example, let us assume that the size of each bead isn't exact, but the density of each is exactly that of some fluid whose volume and density remains fairly constant despite external influences (I don't want to get caught up in some pedantic argument over this aspect of the experiment, but I want to keep it simple, so we'll call it water).
  4. We "entangle" the electrons. (Macroscopically, we dump the two sets of beads into a Galton Board with an even number of bins whose results we cannot see. We know that the statistical distribution of the beads follows a given "wave function" - in this case the binomial probability curve. But that is all we know.)
  5. We "separate" the electrons and move them to distant locations. (Macroscopically, we place the beads from even numbered bins into a container of water that is allowed to spill water out to maintain a constant volume. We do the same for the odd numbered bins. We seal and ship each container of water and beads to opposite coasts.)

The result is that I have two containers weighing exactly the same and externally look identical. But I do not know anything about their content collectively until I analyze the content of one of the containers.

I have a measuring device that can count the beads in a given container and tell me the number of black versus white beads, and another that can tell me the total weight of the beads in a given container. When I take these measurements (my "wave function collapses"), I know what results my counterpart will have measured in the other container whether he or she does so at the same instant or a year from now.

Macroscopically, the results of my example appear no different to me than the results of even the most convoluted of experiments to test quantum entanglement. There's no "spooky action at a distance" going on here. Entangling was the action and that didn't happen at a distance. Measuring is not an action - it's just observation. I can't change the results found in a container as I measure some property of its contents. I'm not violating the speed of light or causing some information paradox.

The point is, I'm just not seeing the mystery here. It just seems like intuitive common sense to me. So, I feel as though I am missing something significant about quantum entanglement. Is it possible to take my macroscopic example and modify it in some way to demonstrate the big mystery that I must be missing?

Mitselplik
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1 Answers1

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Consider the four observables "weight of container A", "weight of container B", "number of beads in A" and "number of beads in B". You can treat these as classical random variables governed by a joint probability distribution (as you've told us explicitly in point 4.) So there is no entanglement here.

The fact that you can write down an example with no entanglement does not tell us anything about what happens in an example with entanglement.

As for the question in your final paragraph, suppose that you repeat this experiment many times and discover that a) whenever you and your faraway friend both measure number, you always get exactly complementary results (if one measures 98, the other measures 102). b) Whenever one of you measures number and the other measures weight, you always get exactly complementary results (if one gets, say, 89 beads then the other gets 111 grams). c) Whenever you both measure weight, you always get the same result (if one gets 101 grams, the other gets 101 grams). Now the observables are entangled --- you can confirm with a little computation that there is no joint probability distribution that fits these observations. Therefore they can't have been generated by anything like your Galton board.

[What happens if you both measure both weight AND number? Then the above is impossible. Therefore this will only work in a situation where you are each constrained to measure only one or the other --- as is the case in real-world entanglement.]

WillO
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