Why can sugar turn into alcohol without a single living cell?

Because the work is done by a molecule, not by life itself: an enzyme. An enzyme is a biological macromolecule, usually a protein, that acts as a catalyst, speeding up a chemical reaction without being used up. In 1897 the chemist Eduard Buchner showed that yeast's fermenting power survives even when no yeast cell is left alive.

Louis Pasteur had thought otherwise. Studying how yeast turns sugar into alcohol, he concluded fermentation was caused by a vital force inside living yeast cells, "ferments" thought to work only within living organisms. He wrote that fermentation was tied to the life of the yeast cells, not their death.

Buchner put that to the test. He combined dry yeast with quartz and kieselguhr and pulverized it with a pestle and mortar, producing a cell-free extract. In a series of experiments at the University of Berlin, he found that sugar was fermented by such yeast extracts even when there were no living yeast cells in the mixture. He named the responsible enzyme "zymase", and in 1907 he won the Nobel Prize in Chemistry for his discovery of cell-free fermentation.

That discovery helped reframe what an enzyme is: not a spark of life, but a molecule with a job. Enzymes are known to catalyze over 5,000 types of biochemical reactions, and they work by lowering the energy a reaction needs to get started, often by factors of millions. One enzyme, orotidine 5′-phosphate decarboxylase, speeds up a reaction that would otherwise take millions of years so that it happens in milliseconds. Their high specificity comes from their three-dimensional shape, which fits the molecule they act on, an idea first pictured as a lock and its key.