How exactly did the food dispensers work on the Constitution class Enterprise, and other ships of that period?
Originally I thought they were just fancy ordering and preparation systems, maybe even with a human on the other end, that dispensed what you ordered like machines in an automat. However in "Tomorrow is Yesterday", someone said he wanted some chicken soup and a man put a card into a slot next to the dispenser, pushed a button, and a bowl of chicken soup instantly appeared from the food hole. It took the same amount of time as a TNG replicator. So there must be some techno-magic at work. Is this explained anywhere? How did the food get created and delivered that fast?
I'm only interested in answers from the "prime timeline" and the Original Continuity. (not the New/Discovery Continuity) Otherwise, evidence from any non-canon material is acceptable. Logical theories also welcome