Tukuk-OSA magnetron generates radio waves at 2.45 GHz — the same family of frequency as Wi-Fi and Bluetooth, far below anything that can damage DNA (ionising radiation starts hundreds of thousands of times higher in energy). Inside the shiny box the waves form standing patterns, and water molecules — little electric dipoles — are flipped back and forth billions of times a second by the alternating field; molecular friction turns that agitation into heat, mostly in the water-rich parts of the food. Metal is banned because it acts as an antenna: induced currents build until they arc across points, pitting the walls.
The honest physics of “cooked from the inside out” is a myth with a twist: the waves penetrate only about a centimetre or two into typical food, so heating actually starts at the surface layers and spreads inward by conduction, exactly like a conventional oven but from both sides of a thin portion. That is also why a dense frozen edge stays cold while the thin centre runs hot, and why the turntable (or a stirring paddle in the mode) exists — the standing-wave pattern has hot and cold stripes roughly hand-width apart, which is why you should leave food to stand after beeping: conduction evens out the stripes.
The dead-simple tests that settle every argument: microwaves do not make food radioactive (the wave energy is too low to alter nuclei — if it were, the oven would be a bomb); they do not “kill nutrients more than other cooking” in any consistent way — any heat degrades some vitamins, and microwaving wins on time and water volume because nutrient loss mostly tracks those two; and the box leaks negligibly when intact, since the mesh in the window has holes far smaller than the 12 cm wavelength it blocks.