Schroeder’s Magic Kittycat

“Bedtime, Teena.”

“Aw, Mommie, I had another question for Uncle Sy.  And I’m not sleepy yet anyhow.”

“Well, if we’re just sitting here relaxing, I suppose.  Sy, make your answer as boring as possible.”

“You know me better than that, Sis, but I’ll try.  What’s your question, Teena?”

“You said something once about quantum and Schroeder’s famous kittycat.  Why is it famous?  If it’s quantum it must be a very, very small cat.  Is it magic?”

“???… Oh, Schrödinger’s Cat.  It’s a pretend cat, not a real one, but it’s famous because it’s both asleep and awake.”

“I see what you did there, Sy.”

“Yeah, Sis, but it’s for a good cause, right?”

“But Uncle Sy, how can you tell?  Sometimes Tommie our kittycat looks sound asleep but he’s not really because he can hear when Mommie opens the cat-food can.”

“Schrödinger’s Cat is special.  Whenever he’s awake his eyes are wide open and whenever he’s asleep his eyes are shut.  And he’s in a box.”

“Tommie loves to sit in boxes.”

“Schrödinger’s Cat’s box is sealed tight.  You can’t see into it.”

“So how do you know whether he’s asleep?”

“That was Mr Schrödinger’s point.  We can’t know, so we have to suppose it’s both.  Many people have made jokes about that.  Mr. Schrödinger said the usual interpretation of quantum mechanics is ridiculous and his cat story was his way of proving that.  The cat doesn’t even have to be quantum-small and the story still works.”

“How could it be halfway?  Either his eyes are open or they’re … wait, sometimes Tommie squints, is that it?”

“Nice try, but no.  Do you remember when we were looking at the bird murmuration and I asked you to point to its middle?”

“Oh, yes, and it was making a beautiful spiral.  Mommie, you should have seen it!”

“Were there any birds right at its middle?”

“Um, no-o.  All around the middle but not right there.”

“Birds to the left, birds to the right, but no birds in the middle.  But if I’d I asked you to point to the place where the birds were, you’d’ve pointed to the middle.”

“Uh-huh.”

“You see how that’s like Mr Schrödinger’s cat’s situation?  It’s really asleep or maybe it’s really awake, but if we’re asked for just one answer we’d have to say ‘halfway between.’  Which is silly just like Mr Schrödinger said — by the usual quantum calculation we’d have to consider his cat to be half awake.  That was part of the long argument between Mr Einstein and the other scientist.”

“Wait, Sy, I didn’t hear that part of you two’s conversation on the porch.  What argument was that?”

“This was Einstein’s big debate with Niels Bohr.  Bohr maintained that all we could ever know about the quantum world are the probabilities the calculations yielded.  Einstein held that the probabilities had to result from processes taking place in some underlying reality.  Cat reality here, which we can resolve by opening the box, but the same issue applies across the board at the quantum level.  The problem’s more general than it appears, because much the same issue appears any time you can have a mixture of two or more states.  Are you asleep yet, Sweetie?”

“Nnn, kp tkng.”

“OK.  Entanglement, for instance.  Pretty much the same logic that Schrödinger disparaged can also apply to quantum particles on different paths through space.  Fire off any process that emits a pair of particles, photons for instance.  The wave function that describes both of them together persists through time so if you measure a property for one of them, say polarization direction, you know what that property is for the other one without traveling to measure it.  So far, so good.  What drove Einstein to deplore the whole theory is that the first particle instantaneously notifies the other one that it’s been measured.  That goes directly counter to Einstein’s Theory of Relativity which says that communication can’t go any faster than the speed of light.  Aaand I think she’s asleep.”

“Nice job, Sy, I’ll put her to bed.  We may discuss entanglement sometime.  G’night, Sy.”

“G’night, Sis.  Let me know the next time you do that meatloaf recipe.”

Cat emerging from murmuration~~ Rich Olcott

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Buttered Cats — The QM perspective

You may have heard recently about the “buttered cat paradox,” a proposition that starts from two time-honored claims:

  • Cats always land on their feet.
  • Buttered toast always lands buttered side down.

“The paradox arises when one considers what would happen if one attached a piece of buttered toast (butter side up) to the back of a cat, then dropped the cat from a large height. …
“[There are those who suggest] that the experiment will produce an anti-gravity effect. They propose that as the cat falls towards the ground, it will slow down and start to rotate, eventually reaching a steady state of hovering a short distance from the ground while rotating at high speed as both the buttered side of the toast and the cat’s feet attempt to land on the ground.”

~~ en.wikipedia.org/wiki/Buttered_cat_paradox

After extensive research (I poked around with Google a little), I’ve concluded that no-one has addressed the situation properly from the quantum mechanical perspective. The cat+toast system in flight clearly meets the Schrödinger conditions — we cannot make an a priori prediction one way or the other so we must consider the system to be in a 50:50 mix of both positions (cat-up and cat-down).

In a physical experiment with a live cat it’s probable that cat+toast actually would be rotating. As is the case with unpolarized light, we must consider the system’s state to be a 50:50 mixture of clockwise and counter-clockwise rotation about its roll axis (defined as one running from the cat’s nose to the base of its tail). Poor kitty would be spinning in two opposing directions at the same time.

Online discussions of the problem have alluded to some of the above considerations. Some writers have even suggested that the combined action of the two opposing adages could generate infinite rotational acceleration and even anti-gravity effects. Those are clearly incorrect conclusions – the concurrent counter-rotations would automatically cancel out any externally observable effects. As to the anti-gravity proposal, not even Bustopher Jones is heavy enough to bend space like a black hole. Anyway, he has white spats.

However, the community appears to have completely missed the Heisenbergian implications of the configuration.

The Heisenberg Uncertainty Principle declares that it’s impossible to obtain simultaneous accurate values for two paired variables such as a particle’s position and momentum. The better the measurement of one variable, the less certain you can be of the other, and vice-versa. There’s an old joke about a cop who pulled a physicist to the side of the road and angrily asked her, “Do you have any idea how fast you were going?”  “I’m afraid not, officer, but I know exactly where I am.”

It’s less commonly known that energy and time are another such pair of variables – the stronger the explosion, the harder it is to determine precisely when it started.

Suppose now that our cat+toast system is falling slowly, perhaps in a low-gravity environment. The landing, when it finally occurs, will be gentle and extend over an arbitrarily long period of time. Accordingly, the cat will remain calm and may not even awake from its usual slumberous state.

Tom and toastBy contrast, suppose that cat+toast falls rapidly. The resulting impact will occur over a very small duration. As we would expect from Heisenberg’s formulation, the cat will become really really angry and with strong probability will attack the researcher in a highly energetic manner.

From a theoretical standpoint therefore, we caution experimentalists to take proper precautions in preparing a laboratory system to test the paradox.

Next week – Getting more certain about Heisenberg

~~ Rich Olcott