We used to believe light was a wave, then we discovered it had the properties of a particle that we call a photon. Now we know it, like all elementary quantum objects, is both a wave and a particle!
In amidst the forget-me-nots, undeciduous trees and fuchsias unknown, Alice found herself lost among the nevergreens, each casting its shadow of doubt on her path.
"Erwin! Erwin, where are you?"
"Who?" came the reply, startling Alice.
"Who's there?" she called.
"If you were to open your eyes you would see," came the reply. She could hear a gentle pitter-patter of something falling on wood.
"I'm afraid if I open them I shall observe Erwin and he might vanish to somewhere else, so I'm keeping my eyes closed to be sure."
"If it helps, I can assure you that it's only you, me and an overgrown garden. I cannot see anything that might be called Erwin... unless, of course, you have taken to calling flowers by that name, but Erwin does not sound like a good name for a flower, and they are so very particular about that kind of thing."
"What?" Alice said, now more confused than she had been before, just looking without looking.
"What?" came the emphatic echo, followed by a pitter-patter against wood.
"What?" she replied, sensing that one of them must break the symmetry soon or the word would lose its meaning, perhaps taking with it any chance of conversation. If one word were to lose its meaning, what would happen to the rest?
"I imagine you meant to say 'Pardon, I do not think I quite understood your meaning, could you please repeat what you were saying, thank you' rather than 'What?', which is not the kind of thing a well brought up young lady would say. But perhaps I assume too much."
"Oh!" But thinking better of it, and recovering quickly, Alice said, "I am so very sorry, but I did not understand what you were telling me. I was looking for Erwin. He is a cat. A Cheshire Cat. If you please."
"A Cheshire Cat? And what, pray tell, is one of those? Without knowing what one is, I cannot rightly tell whether it pleases me or not."
Alice decided that seeing might be better than not. Carrying out a conversation with a stranger was difficult enough, but with a stranger one could not see was both difficult and strange. And if observing Erwin might cause him to be somewhere else, perhaps observing where he was not might cause him to be there. She opened her eyes.
Alice had certainly seen caterpillars before, but the kind of caterpillar she knew would fit on a leaf and be more likely to eat them than smoke them, dried, through a large hookah. Caterpillars were not normally taller than girls her age or, indeed, girls of any age. She had never seen caterpillars play dice, let alone with any kind of skill, casting them idly and without a second glance upon a plank. A cloud of smoke and probability surrounded the caterpillar. And she was quite sure caterpillars did not talk.
But alas, much of what she had been certain about had, on closer inspection, become less so. Before she had opened her eyes she had had a very good idea of where she was going, but little clue as to where she was. Now she could see where she was — the nevergreens were quite consistent and forget-me-nots quite memorable — she was less sure of her heading and concerned she might become entangled in the imaginary roots.
"And now you can see," said the caterpillar, "are you able to answer the question? What manner of cat is Erwin that you seek him here and there?"
"He is a light cat with dark stripes. Or a dark cat with light stripes. I'm not sure which. He's neither here nor there, though sometimes both, and he often vanishes. Except for his smile. Except when that also goes. And he says he is not fond of boxes. I do not know him well, but I am worried for him. He said something about 'wave functions', which made little sense to me as I have seen him appear and disappear but never wave, and 'collapsing', which caused me the greatest of concern."
"Why, that is quite the most decoherent description of any kind of cat I have ever heard! Although I do agree about the boxes."
"He said many other things, but I'm afraid cannot remember them."
"Information should never be lost, although cats often are," said the caterpillar, somewhat gruntled. "All of which leads me to the disappointing conclusion that your quandary and quarry is both unusual and not. A lost cat in a garden..." Another puff on the hookah. "Have you tried a saucer of milk to draw him out?"
"He is no ordinary cat, so I am not sure a classical solution would work. But thank you."
"There are indeed many hidden variables at play. Perhaps one filled with secrets rather than milk?"
"I am not sure I know enough secrets to fill a saucer."
"In that case, young lady, I'm afraid you have exhausted both me and my suggestions. But I have one remaining suggestion: the rabbit. He's into this sort of thing. He's always rushing around, so you will find him eventually. Can't miss him. He's blue or red, depending on whether he's coming or going — white if you can keep up with him. Sometimes he can be found — and lost — tunnelling, jumping from one excited state to another. Keeps complaining that his pocket watch keeps stopping. It's all that rushing around, I suspect."
"Thank you," said Alice, curtsying. "How do I leave here to find him?"
"Why, the same way you came in."
Alice closed her eyes. "Oh yes, I know." And with that she was on her way.