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Quantum mechanics (QM) is a scientific theory; thus it is the description of a mathematical pattern or order present in physical phenomena. Its usefulness relies on the fact that it provides us with a mathematical method to make exact probabilistic predictions about the observable result of many experiments (actually in its current form of all experiments in which gravity has no significant relevance). That's why QM has been used so extensively to build useful machines. No mystery so far, and no need to understand anything beyond the complicated but dumb matter of how to apply QM's equations, a task in which computers turn out to be very handy.

Immediately after the successful modeling of phenomena by QM, things became mysterious when people tried to understand what kind of physical reality would produce said results (or in philosophical terms, how QM discoveries affect our metaphysical beliefs). Most physical scientists then (as today) are “physical realists” which means that there is a mechanistic reality out there which produces our observations of physical phenomena, including the mathematical order in them. Virtually all physical realists also believe that science is the way to go in order to find out how reality is and most certainly how physical reality is. Now the order QM revealed is present in quantum phenomena is a statistical order. The question at hand then is what mechanical reality would produce that statistical order for us to observe. Surprisingly enough that question turned out to be very difficult to answer. It's not that it can't be answered, but each suggested description of reality appeared to do more harm than good as a defense of physical realism. Each was in one or the other way deeply disturbing to our reason, hence the talk about “mystery” and “paradox” and so on. Moreover, the very fact that there are many realist theories (descriptions of possible physical realities) each of which would perfectly well produce all phenomena predicted by QM, not to mention the fact that physicists deeply disagree among themselves which is the correct one while most just shrug their shoulders, greatly weakens he idea that the physical sciences describe reality or at least suffice for describing reality. But the following point should be clear: The mystery does not reside in QM but in trying to describe a mechanistic reality that would produce the observations that QM correctly predicts.

Interestingly enough one can understand the problem without learning anything whatsoever about QM. QM drew our attention to a particular order present in our observations of the world. A very small set of experimental results is sufficient to explain why this order is so problematic for physical realists. So we can dispense with QM – even if that scientific theory should be supplanted by a different one the factual observations that produce the mystery would remain:

We shall set up four simple table-top experiments and describe the observations they produce. To set up the experiments we shall need some channels (basically empty tubes) to interconnect boxes. One box (the “generator” or “G”) has a button on top and connects to one channel, some other boxes (the “detector” or “D”) have a light on top and also connect to one channel. Here then is the simplest experiment (where “---“ symbolizes a channel):

G---D 1

We observe that every time we push the button of G, almost instantly the light at D flashes. For the physical realist the only possible interpretation is that that G produces some kind of physical thing or effect (let’s call it a “phyt”) which travels through the channel to D and causes its light to flash. To the right of D we write down statistical probability that D will flash if the generator’s button is pushed, in this case a “1” since the light always flashes when we push the button. These probabilities are the observational results of the experiments.

To set up the other experiments we shall need one generator G, two identical detectors D, and three more boxes (B1, B2, B3), each with one channel connection at one side and two channel connections at the other side. B1 and B3 have one input channel and two output channels, whereas B2 has two inputs and one output. What is inside these boxes is irrelevant; it suffices to know that such observational results exist (below I will describe how these boxes can be constructed). Finally, in some experiments a channel is blocked which is symbolized by “ | “, so nothing can pass through. Here then are the experiments and their results:

In the experiments #2 - #4 the phyt produced by G is fed into B1. In the second experiment the two channels to the right of B1 lead to two detectors. At each push of the button one of these detectors flashes, in an apparently random fashion, hence the probabilities 1/2. In the third experiment on the contrary only the upper detector flashes each time we press the button. In the fourth experiment we block the upper channel between B1 and B2. In half the tries no detector flashes, and in the other half of the tries one of the detectors flashes n a random fashion, hence the probabilities 1/4.

That’s all. The question now is to describe a mechanistic reality that would give rise to such observational results, and particularly what happens when the phyt produced by the generator leaves B1. It turns out this is quite difficult to describe such a reality. The unexpected insight here is that while it is easy enough to mechanistically model the observations themselves (indeed I just did that - as does QM if one specifies what’s inside the boxes), it turns out to be quite difficult to mechanistically model the reality which gives rise to the same observations. Below I will discuss why it is so difficult to find a solution about what is really happening. Before continuing to read perhaps the reader would like to try to think for herself which mechanistic reality would produce these observations.

We've already described the realist implications of the first experiment.

The second experiment is not difficult to interpret realistically either: The phyt arrives at B1, which randomly sends it either to the upper or to the lower channel. When the phyt arrives at the corresponding detector we see its lamp flash.

The third experiment is not difficult to interpret either: As before B2 sends the phyt either through the upper or the lower channel, and so the phyt arrives to B2, which in both cases forwards it to B3. Now when B3 receives a phyt it always sends it to the upper channel, and that's why always the upper D and never the lower D flashes.

The fourth experiment is where the problem becomes apparent. Suppose we push the button, G produces a phyt which arrives at B1, and B1 in this try happens to send the phyt through the upper channel. That channel is blocked, so the phyt never arrives to B2 and thus from now on nothing happens. Neither detector flashes, just as expected. But suppose we push the button again and now B1 happens to send the phyt through the lower channel, which is thus received by B2 which forwards it to B3. We would expect B3 to send it to the upper channel, but in fact half the times B3 sends it to the lower channel and thus causes the lower detector to flash. But why should B3 change its behavior? B3 is not in any way connected to the channels that leave B1 so the fact that we interrupted the upper channel cannot have any effect on B3. But then B3 should continue behaving as it did before, but doesn't.

Above we tried to model reality imagining that the phyt is one concrete thing, a particle-like entity. We are free to imagine whatever we like, so we shall imagine that the phyt is the kind of thing that can split apart and be in several places at once, can recombine, can be amplified or destroyed, in short a malleable kind of thing which reminds us the way a wave on water behaves.

So let's revisit the third and fourth experiments assuming that the phyt is a wave which passing through B1 separates into two halves one of which passes through upper channel and the other half through the lower channel. At the third experiment B2 receives the two halves, recombines them into a complete phyt which is sent to B3. B3, having received a complete phyt sends it to the upper channel thus causing only the upper D to flash. In the fourth experiment, sine the upper channel is blocked, B2 receives only half the phyt from the lower channel which it forwards to B3. B3 having received only half a phyt changes its behavior: Half the times B3 destroys the half phyt and nothing is sent towards the detectors which therefore don't flash, and the other half of the times B3 makes the phyt whole again and sends it either to the upper or to the lower channels, thus producing the observed results. So now we have a description of reality that explains the observations of the third and fourth experiment.

Let's revisit the first two experiments to see if this interpretation works. The wave nature of the phyt does not in any way affect the first experiment. The whole phyt will arrive at D which always flashes. But what about the second experiment? B1 receives a full phyt and as before splits it into two halves sending each half through the upper and lower channels to reach the respective detectors. We may specify that when a detector receives half a phyt it will flash only half the times. The problem is that in this case one would expect in some tries both detectors to flash together, and in some tries none of them to flash. But this does not comport with observed reality, since at the second experiment always one or the other detector flashes. So assuming that the phyt behaves as a wave hasn't solved the problem either.

The founders of QM solved this apparently intractable problem by describing a reality which would produce all our observations. As we shall see their solution (later called “Copenhagen interpretation”) was very strange, and even though it worked it troubled many a physical realist.

[to be continued]