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A lodestone resonator is one of a number of fictional devices which appear in Philip Pullman’s His Dark Materials series of fantasy novels. The item allows two people to communicate over vast differences, even between the various universes which make up the world of the books.
The lodestone resonator is introduced as an item used by the Gallivespians who are fighting against the Authority in the war against Heaven. It is not made entirely clear whether lodestone resonators exist solely in the universe the tiny race of Gallivespians hail from, or whether they can be found in many different universes. It does appear that the Gallivespians did at least invent their own lodestone resonators, though whether they invented them with the intention of communicating across universes, or simply for long-distance communication within their universe, is unknown.
A lodestone resonator is a simple device, consisting of a small rod of lodestone mounted on a piece of wood or some other base. It is then played like a violin, by moving a bow back and forth across it to generate sound which travels across any distance instantly. These sounds are used in a manner similar to Morse code, allowing messages to be transmitted with no time delay.
Lodestone is another name for Fe3O4, magnetite. It is particularly used for highly-magnetized forms of magnetite, which were used in early compasses as needles, pointing to the magnetic north and south poles. More generally, the term lodestone is often used for anything that is seen to have a great attraction. So the term lodestone resonator refers both to the literal presence of lodestone, and its ability to find its "mate" across any distance.
The seeming science behind the function of the lodestone resonator in His Dark Materials has to do with what is known as quantum entanglement. According to the mythos of the books, the two pieces of lodestone to be used have each of their particles entangled on a quantum level, so that when something happens to one, it immediately happens to the second.
While quantum entanglement is in fact accepted as a sound theory in the real world, sometimes called "spooky communication at a distance," it is important to note that the entanglement happens solely on the quantum level. The entanglement refers to the fact that if, for example, one entangled particle has a spin of up, the other will be observed to have a spin of down. This sort of quantum information, however, does not translate to classical information. Because of the limits of relativity, classical information cannot travel faster than the speed of light. The no-communication theorem deals with this, asserting that no actual information is transmitted.
Although science in our world seems relatively confident that an item such as the lodestone resonator would not work, it nonetheless makes an excellent addition to Pullman’s world. Since the characters travel between a multitude of different universes, traditional radio communication would be impossible. The lodestone resonator allows characters to stay in contact with one another, even between universes.