Bohr's big idea, stated simply
By the late 1920s the experiments had piled up an apparent contradiction: the same electron is a wave in one test and a particle in another. The Danish physicist Niels Bohr offered a way to hold the contradiction without going mad. His proposal, called complementarity, is at heart a single graceful sentence: the wave description and the particle description are both needed for a full account of a quantum object, yet they can never be displayed in the same experiment. They are complementary — partners that complete each other precisely because they take turns.
The key word is and never both at once. It is not that we are too clumsy to see both faces together, or that we lack a clever enough instrument. Bohr's claim is that the question "is it really a wave or really a particle, when no one is looking?" has no answer, because the answer depends on which question you put to nature. Ask a wave question (let it interfere), get a wave. Ask a particle question (which slit?), get a particle. There is no view from nowhere that catches it being both.
The double slit was the proof all along
You have already watched complementarity in action; the last guide was a demonstration of it. When you let the electron interfere and refuse to ask which slit, you see the wave — bands, no path. When you insist on the path with a detector, you see the particle — clumps, no bands. The apparatus you choose decides which face appears, and the two apparatuses are physically incompatible: a setup that reveals the path is, by its very construction, a setup that destroys the bands. The which-path trade-off is not a coincidence — it is complementarity made visible.
A wider pattern in the quantum world
Wave-versus-particle is the most famous complementary pair, but Bohr saw it as one instance of a broader truth. The most famous cousin is Heisenberg's uncertainty principle: you cannot simultaneously know a particle's exact position and its exact motion. Pin down one sharply and the other goes fuzzy. Position and momentum are complementary in just the same spirit as wave and particle — each is real, both are needed, neither can be had at full sharpness alongside the other. Once you spot the shape, you see it everywhere in quantum theory.
Complementarity became a pillar of the Copenhagen interpretation — the practical, widely taught way of thinking about quantum mechanics that grew up around Bohr in the city he worked in. Its attitude is famously down-to-earth: stop asking what the electron 'really is' between measurements, since no experiment can answer it, and focus on what your chosen apparatus will actually show. To some that is liberating honesty; to others it is a frustrating refusal to say what is really going on. Either way, it has guided working physicists for a century.
Where this leaves us
Let us be honest about what complementarity does and does not do. It does not explain why nature is built this way; it does not lift the strangeness or tell you the electron's secret inner life. What it does is keep you sane and accurate. It hands you a rule you can actually use: pick your experiment, expect the matching face, and never demand the other face from the same setup. Whether that rule is the deepest truth or just a wise stance is a question later interpretations of quantum mechanics fight over to this day.
And so the track closes where it began, but with new eyes. "Is it a wave or a particle?" was the wrong question all along. The right one is: "Which face am I asking to see?" A quantum object is a single thing rich enough to answer either question truthfully, and humble enough never to pretend it can answer both at once. Carry that with you, and the deepest oddity in physics turns from a paradox into a strange but trustworthy rule of the world.