A QUANTUM FABLE (with apologies to Lewis Carroll)

Alice was beginning to wish that she hadn't been QUITE so curious about why a White Rabbit would be carrying a pocket watch, and that she had refrained from following it down that rabbit hole to find out. For now she was hopelessly lost in the dark woods where she had last seen the White Rabbit.

Just about then she came upon a small path that appeared to meander aimless through the forest. Under the axiom that any path must invariably lead somewhere, she decided to follow it. After walking down it a bit, she was startled to sees a rather large gray cat sitting on a bough of a tree a few yards off. But then she thought, "At least now I shall have someone to ask directions of." (For, since falling down the rabbit hole, she had met all sorts of talking animals and now thought nothing at all of starting up a conversation with them.)

Approaching the tree, she began, "Sir, would you tell me, please, which way I ought to go from here?"

"That depends a good deal on what you mean by the words 'way', 'go', and 'here'," said the Cat.

Recognizing a logical positivist, Alice tried another question: "What sort of people live around here?", and promptly followed it with philosophically precise definitions of the words "here", "people", "live" and, just to be sure, "what", "sort" and "around".

Satisfied, the Cat replied, "In THAT direction," waving a paw, "lives a Hatter, and in THAT direction," waving the other paw, "lives a March Hare. Visit either you like; they're both post-modern philosophers."

"But I don't want to go among post-modernists!" Alice remarked, looking in the directions the Cat had pointed to. When she looked back towards the tree however, she was surprised to see that there was now a small, rather scruffy orange cat where the gray cat had been the moment before.

"Could you tell me where the gray cat went that was just sitting there?" Alice asked the Cat.

"I've no idea to whom you could be referring," the Cat responded. "I've been sitting here, by myself, all day and, as you can plainly see, I am an ORANGE cat! I have always BEEN an orange cat, and I always WILL be an orange cat!!"

But then, just as he was about to start into his familiar recitation of how his ancestors had all come over with William of Orange, (which he regularly bores all his friends to death with), he changed in the blink of an eye into a white Persian cat, and then into a Norwegian Forest cat, and then into a black-and-tan Tabby.

Alice, feeling rather proud of herself (for they had just covered the new theories coming from the Continent in her lessons the previous week), realized then that he was actually a SCHROEDINGER cat. "Your wave function," she explained, as much to herself as to the Cat, "consists of a super-position of different eigenstates of, I suppose, a 'Catness' operator." (Although she DID wonder why his wave function, after collapsing to an eigenstate, didn't stay collapsed like a proper wave function. "Perhaps it's artistic license," she thought.)

And then, to show off her new knowledge, she launched into a long discourse, using a lot of words that she didn't QUITE understand, on wave-particle duality, entanglement, and both the Copenhagen AND the many-worlds interpretations.

"Stuff and nonsense!!" replied the Cat (now a beautiful Russian Blue). Being a cat, AND a 19th-century one at that, he was of course a firm believer in Newtonian determinism and would have none of this new-fangled Germanic uncertainty. Just thinking about it, he said, made him quite giddy!

Alice then noticed a large steel box lying on the ground just behind the tree. "I see you're admiring my box," said the Cat. "It IS a lovely box, isn't it? A gift from a human pet of mine. Although I'm not entirely certain what all that stuff inside is for."

The box had an open trap door at the top and, moving closer, Alice could indeed see some sort of complicated apparatus inside, with what looked to be a Geiger counter and a broken glass vial. She thought it best though not to look any further, for fear of what else might be in there.

"But when I first saw you," asked the Siamese cat who now sat in the tree, "and you inquired about a 'Mr. Dodgson', didn't you have rather short dark hair?"

Alice thought this question very curious. Perturbed, she started to wonder if she might, likewise, be a Schroedinger Alice! " ..and consist of a super-position of Tenniel-Alice and Liddell-Alice states!!" Alice was certain she would not care for that at all, "for it would cause all sorts of confusion!"

These deep metaphysical waters were beginning to make poor Alice's head quite dizzy and she decided it was time to say goodbye to the Schroedinger Cat. She had seen hatters before, so she thought she would pay a visit to the March Hare, even if he WAS a post-modernist. ("Maybe he is of the neo-pragmatist school," Alice hoped.)

She thanked the Cat for the directions and started on down the path. But after walking a bit she thought "Did he say this goes to the March Hare's or to the Hatter's house?" and turned around to ask. In the distance, she could still just make out the shape of the Cat in his tree, only now he seemed to be rapidly disappearing and then reappearing in a quite curious, flickering sort of fashion.

"Of course!" thought Alice, as she remembered what her tutor had taught her about double-slit experiments and quantum interference. She decided not to disturb him further and instead continued to propagate along the path towards what she hoped was the March Hare's house. As she walked, she tried to recall what Derrida had written on the deconstruction of mid-19th-century Victorian literature. "For it is almost certain to come up," she said to herself.

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