When they say an electron has both a particle and a wave nature, what do they actually mean? How do you explain this phenomenon to a lay person?

If you are saying “explain,” do you mean “rectify using normal sense”? If not, I’m not able to.

A common sense statement is that an electron is an atomized bullet. We always know the location and direction it’s going. If you aim it at an iron plate that has two holes and it bounces off, or it passes through hole A, or through hole B. That single electron can’t possibly traverse both holes, isn’t it? The common sense!

The the light beam can be considered as a wave similar to waves in the ocean when they pass through the seawall, which has some gaps light that passes through two holes is released onto on the other side as two circular patterns simultaneouslyIn some locations, those oscillations are phased and you’ll get constructive interference. In other locations you can encounter destructive interference (the surface of the water is flat in the case of the seawall). It’s impossible to take the entire wave all in one spot, isn’t it? The common sense!

Unfortunately, conventional wisdom is not the case. It is not just that (and do) detect light in discrete “quanta” of fixed energy, even after it’s completed the whole thing of interference to prove that it’s a real wave — but we are also able to observe similar patterns of interference that detect electrons that are downstream of the plate that has two holes inside even though we are 100% certain we’re firing only one electron at the single time for example, one at a time.

The light, that is definitely an electromagnetic wave, behaves as particles (the photon).
Electrons, which are definitely particles, behave similarly to waves.

These are real-world facts proved by millions of experiments. The quantum mechanics math was developed to allow us to make predictions regarding these kinds of experiments. The generations that have followed “natural philosophers” have tried in trying to “explain” the phenomena using terms that are more appealing to “common common sense”. They’ve been unsuccessful. It’s common sense . to be changed. Take it on.

To say it more calmly it is enough to be accustomed the concept of quantum mechanics. A lot of people have done that. You too can do it.

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