So somewhere along the line, as you go smaller and smaller from planets to potatoes to protons, things that normally behave like classical massive particles start to display wavy characteristics. It is not a sharp transition, and there is no exact size where we can say larger things are just particles and smaller things are waves. It’s a gradual thing. All massive particles have wave properties, it’s just that the effects are too small to observe until you get down to particles that are clusters of only a few atoms; smaller even than particles of smoke.
When you do get to the realm of atoms and molecules, or go smaller yet to the particles that make up atoms, then the situation is much like that of photons of light. A proton or a neutron or an electron can still behave like a particle, a localized chunk of mass. Or it can display interference effects like a wave. It all depends, literally, on how you look at it. The specific measurement determines which aspect is observed. And, in the absence of any specific measurement, both wave and particle aspects are required to completely describe the object.
It is the same complementary picture that had finally emerged for electromagnetic radiation and photons, where confusion caused by apparently conflicting observations had reigned since Newton’s time. Now at least we take some comfort in the symmetry of nature. Both light and matter display the same sort of wave-particle duality. Photons and matter particles both carry energy and momentum in discrete chunks, and both have wavelengths and frequencies leading to interference effects.
De Broglie, Einstein, and Planck had shown us the relationships between energy, frequency, momentum, and wavelength that were consistent with special relativity and common to both light and matter. The only difference between photons and other particles was that the photons had zero mass, and therefore could only have one speed, the speed of light.
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