Electrons (and everything else) are waves and particles—but not at the same time in the same relationship—no Law of Contradiction violation. Let me try to explain, using, as you would find in any physics book, the two slit interference experiment.
Suppose we have a source of electrons, called an electron gun. We fire electrons (keeping the gun fixed) horizontally at barrier with two small holes (slits). Behind the slits is a screen that can measure electrons. On the screen, we show a plot that records the number of electrons hitting the screen at that location. In effect, it gives the probability that an electron will hit the screen at a given spot. Where the plot is big, as near the peak, there is a big probability that an electron will the screen. Where the plot is small, there is little chance.
In the first round of experiments, we close one slit, fire electrons for a while, and see what happens. In the next round, we close the other slit and see what happens. We get the results shown in Figure 1. These should be reasonable. In the first case, the electron can only go through the upper slit, so we get a plot that is sharply peaked just behind the upper slit. In the second case, we get similar results when we open just the lower slit.
So far, electrons look like particles (bullets). Nothing wavelike is happening here. The electrons all go through the open slit and only found where we would expect, and are not found where we don’t expect.
Next we ask, what happens if both slits are open? In Figure 2, we show that experiment. The thin dashed red plot is what you might expect: just the combination of the two cases above. The thick blue plot is what you actually get. The result is very wave-like, as if the electron were a wave, and part of the electron (wave) went through the upper slit, and part through the lower slit, and then the two waves interfered (Figure 3), like if you drop two stones in a pond and circular waves from each stone collide and interfere. Note especially that you find a wave-like probability (called an interference pattern) that has peaks in places that no “bullet” could actually hit, i.e., no “line of sight”.
This cannot be, you say, each electron had to have gone through either the upper slit or the lower slit, but not both. But that is only true if the electron is a particle and not a wave. But maybe it is an artifact of the experiment—maybe there are so many electrons, some going through the upper slit and some going through the lower slit, and the so-called interference pattern is a result of complicated collisions among these many electrons. Alas, this is not the case, because we can reduce the rate of the gun to ensure that it fires only one electron an hour, giving each electron plenty of time to reach the screen. The experiment takes much longer, but if we wait long enough the same result, the wave-like interference pattern, emerges! In particular, as we watch the screen detecting one electron per hour, we notice that sometimes the screen records a hit where no "bullet" should have been able to reach. And other locations, which have line of sight back through a slit to the gun, never receive a hit!
Still we are not convinced that a electron can go through both slits at the same time, so we enhance our experiment by placing a detector behind the upper slit. We again fire the electrons slowly. If it goes through the upper slit, we detect it, if it goes through the lower slit, we don't. In either case, we know which slit the electron went through. Now what happens? Amazingly we have forced the electrons to resume behaving like particles (bullets), and the interference pattern is not formed, instead we get the particle like result of Figure 4!
This is all real. All these experiments have been done (in more sophisticated forms) and the results verified. It is said to be understood: If an experiment probes the particle-like nature of an electron, the electron behaves like a particle; if it probes its wave-like nature, it behaves like a wave. No experiment can probe both. An electron is a wave and a particle, but not both at the same time.
We say we understand it, but for me it is more accurate to say I accept it. In fact, at some level it is both incomprehensible and indispensable (J. I. Packer's description of a feature of a true antinomy). But that’s the way it is.
Does this have anything to do with anything?Such is the case with God’s sovereignty and man’s responsibility. That too is an antinomy. As Packer writes in his wonderful book Evangelism & The Sovereignty of God (InterVarsity, 1961) God is both King and Judge, God is Sovereign and yet man is a responsible moral agent, man cannot choose God on his own, and yet is punished for his disbelief. Antinomy—incomprehensible yet indispensable. And, as Packer tells us, we must never set them at loggerheads.
As Spurgeon, when asked to reconcile human freedom with divine predestination, said, (as quoted by Packer) "I never reconcile friends."
So it is. This has been a prelude, more on this to come—I am working on a Sunday school lesson on Calvinism and Evangelism.