OK...so how, precisely does a vibration make the transition from vibration to radiation? What mechanism causes and governs that process...and precisely why does some electromagnetic radiation behave as both wave and particle...what is the mechanism that causes that phenomenon to appear in different circumstances?
That is a fair enough question. This is the short answer.
Four different experimental laws involving electricity and magnetism were discovered by four different scientists. Maxwell consolidated the four experimental laws into what's now called Maxwell's equations. The equations show that vibrating charges emit waves.
This new prediction lead to many experiments. Hertz was the first to test radio frequency transmission to verify Maxwell's equations. Through many experiments and observations it was later concluded that these waves were also the basis of light, Xrays, infrared, etc.
The
wave nature of light was well-known for centuries: At high light levels, experiments observed diffraction. The
particle nature became more apparent about 100 years ago. At very low light levels the light came in “chunks”. Einstein first explained the chunkiness as separate particles and got the Nobel Prize for the “Photoelectric Effect”.
The nature of EM radiation came from experiments that defied intuition and were a puzzle. Some experiments showed the wave nature and other experiments showed the particle nature. Quantum mechanics came about and showed a way mathematics could verify and predict experiments on the dual nature of light and particles. Light traveling through space acts like waves. Light interacting with matter acts like particles.
As you can see, many repeatable, observations, tests, and measurements lead to understanding the nature and behavior of light and matter. All of these behaviors are successfully codified in the Schroedinger equation, and later Quantum Electrodynamics. This cohesive codified understanding is what allows scientists to make deeper statements about observations that are either seen or predicted.
The major example here is that, between objects at any temperatures, radiation exchange is the only thing that makes sense in the total picture of all past experiments. You are arguing from the perspective of observations, tests, and measurements. I am too, along with the whole scientific community.