Once Before Time - Martin Bojowald [24]
In the classical world, we are not used to superpositions. To be sure, there are sometimes doubts before a suspicion becomes brutal certainty, but we are convinced that some possibility is realized; we simply do not know which one. In quantum mechanics all this is different. Here, too, there is uncertainty, but one can prove mathematically that superpositions bring in a new quality. There is no doubt that microscopic objects really do exist in superpositions of different states; this has been confirmed by many measurements. Superpositions have not been observed for macroscopic objects such as a cat, even though it would in principle be possible. Bringing and keeping larger objects in a superposition is simply more complicated. This explains why we are not used to this feature from our common classical experience, and thus our intuition struggles with the concept of superpositions. The following passage presents a further visualization of a superposition together with its eventual collapse:
She was a little spider. From her own thread she had made a web, and she was hungry. Besides, what else could she be doing? Now she was lying motionlessly in her corner, her legs stretched out and all her eyes staring up through the web, waiting for something to happen. She did not think much, for, to be honest, she did not even know what a spider should be thinking about. She was just passing her time, in expectation of this unmistakable event announcing that her hunger would be stilled.
Before long, something crossed her mind. Not a thought, for she still did not know what a spider could be thinking about. From somewhere, she did not know how, she remembered that spiders were sometimes supposed to eat their own, females the males. She shuddered. At least she would be at the winning end. She had grown hungrier, as she realized.
She did not know how long she had been lying there, still in her comfortable position. In fact, her feeling for time was not so well developed. Although she instinctively knew that things changed—her stomach was often empty as the web, but every once in a while there was a feast—she had no concept of time. Was it more boring to lie waiting like this, or when time would not exist at all? What a crazy idea. She almost fell asleep.
At last, her full attention was called upon. She had heard a shrill sound which, as she fancied, had made her web vibrate. This noise, so familiar and yet alien to her little world, had only briefly made her anger boil over about the disruption of her peaceful rest. Then, knowing what this meant, she jumped up in excitement: soon, she would no longer be hungry. Although she did not know how, she knew the meaning of the sound, and clearly made out a few distinctly separated words: “Dinner’s ready!” The little spider died, unremembered, and she ran downstairs.
Just as the apparent contradiction of the last sentence here resolves the superposition of “she” (a girl pretending to be a spider) and “the spider,” a measurement at a quantum mechanical system renders its state definite by the collapse of the wave function.
Superpositions play an important role in quantum theory and its applications. They would be an integral part in the construction of quantum