Are We Made of Fields or Particles?
All objects in our world seem to be made of tiny particles. Atoms, molecules, protons, electrons, and such. Small particles stick together to make bigger objects like chairs, planets and people. So far so good.
This particle picture of reality is very reasonable and it explains how everyday things work. Car engines, water pumps, volcanoes. Chemistry is all about combinations of atoms and molecules.
Some things in our world are certainly not particles -- like gravity, magnetic fields, and radio waves. Those things are fields. So we can say our world is made up of both particles and fields. Fields move the particles around and make them stick together. It makes sense.
This world-view of particles and fields became blurred when quantum effects were discovered. In 1905 Einstein got a Nobel Prize for his explanation of the photoelectric effect. He concluded that light waves must be made of discrete, quantized particles (photons).
Now, 100 years later, we know that it was actually the atoms in the cathode that were quantized, not the light. Light is just a continuous waving electromagnetic field, not made of tiny "corpuscles." The quantization comes from the discrete electron energy levels in atoms. (Here is a reference).
Interference
When two waves overlap there are some places where they add up and others where they subtract. The result is an interference pattern with dark lines and bright spots. Interference and diffraction are wave behaviors. So it was a shock when scientists discovered that ordinary matter also makes interference patterns. Electron microscopes show very clear electron diffraction patterns. If electrons are point particles this makes no sense. Particles can't subtract. Molecular beams also make interference patterns, so are molecules waves? Particles can't make interference patterns.
Duality
The popular explanation for this is "wave-particle duality." This is a baffling concept where particles sometimes behave like waves and waves sometimes collapse into particles. This crazy idea leads to all kinds of paradoxes, violations of locality, causality, and common sense. The problems are serious. Schrodinger's cat, Einstein's bubble, Bell's inequality, spooky actions, the "measurement problem" and wave-function collapse, to name a few.
Field Theory
In the 1980's a new and different world-view slowly became clear that says everything is just fields. Nothing but fields. Any particles that we experience, like atoms and electrons, are fundamentally waves (vibrations) in a medium of fields. The easiest way to visualize this is to think of how light works. Light is a wave in the electromagnetic field. X-rays and gamma rays may look like particles, but if we zoom in we see they are really just waves. Electrons look like particles, but if we zoom in, we see electrons are really just waves in the Dirac field. Quarks are waves in the quark field. By now we know there are 24 of these fields. Eight gluon fields, the Higgs field, W and Z boson fields, the Dirac (electron) field, 6 quark fields, and a few more. This is now the "Standard Model" of quantum field theory.
It's a crazy zoo, but this picture of reality is much more reasonable than the magical paradoxes of "wave-particle duality." Magic is not physics.
The fields I am talking about are real physical fields like magnets and gravity, not "probability amplitudes." The Schrödinger wave equation is usually understood to represent probability. I could never imagine how waves of probability propagate in space. Does probability have mass? Does probability always travel at the speed of light? Can two probability waves collide? Real physical fields carry momentum, spin, charge, mass, and energy from one place to another. Real physical waves can be absorbed, reflected, transmitted, and emitted.
When waves are confined inside a cavity the frequencies and energies are quantized. Only the resonant frequencies are stable. This resonance explains how atoms only emit and absorb certain spectral lines. In atoms, the electron wave is trapped in the resonant cavity formed by the positively charged nucleus. Only certain wavelengths (or energies) are stable.
Conclusion
Solid objects are made of atoms, and atoms are ultimately made of dozens of oscillating fields. The old familiar particle concept is great for describing atoms and electrons, as long as we remember that the underlying reality is pure fields.
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