quantum – Hard Science Ain't Hard

“Nice call, Sy.”

“Beg pardon?”

“Your post a couple weeks ago. You titled it ‘Everything Everywhere All At Once.’ That’s the movie that just won seven Oscars — Best Movie, Best Director, Best Actress and Best Supporting Actress… How’d you predict it?”

“I didn’t, Susan. I wasn’t even trying to. I knew the movie’s plot was based on the multiverse notion. That’s the theme for this post series so it seemed like a natural cultural reference. Besides, that post was about the Big Bang’s growth in a skillionth of a second from a Planck‑length‑size volume out to our ginormous Universe and all its particles. ‘Everything Everywhere All At Once‘ seemed like a nice description of what we think happened. A mug of my usual, Al, and I’m buying Susan’s mocha latte.”

“Sure, Sy. Nice call, by the way. Have a couple of scones, you two, on me.”

“Thanks, Al, and thanks, Sy. You know, I’ve noticed the multiverse idea cropping up a lot lately. They used it in the Spiderman franchise, and the recent Doctor Strange pic, and I just read it’ll be in the next Flash movie.”

“Oh, it’s an old writer’s ploy, Susan. Been around in one form or another since Aristophanes invented Cloudcuckooland for one of his Greek comedies. Small‑screen scifi uses it a lot — Star Trek used it back in the Kirk-Spock shows and DS9 based a whole story arc on the idea. Any time an author wants to move the action to a strange place or bring in some variation on a familiar character, they trot out the multiverse. Completely bogus, of course — they may sound all science‑y but none of them have anything to do with what we physicists have been arguing about.”

“You mean your anti-Universe won’t have an evil version of you in it?”

“I certainly don’t expect it to if it even exists. Suppose an anti‑Universe is out there. Think of all the contingencies that had to go just right during 13½ billion anti‑years of anti‑quark‑soup and anti‑atomic history before there’s an anti‑planet just like Earth in just the right environment around an anti‑star just like ours, all evolved to the level of our anti‑when, not to mention the close shaves our biological and personal histories would have had to scrape through. I’d be amazed if even anti‑humans existed there, let alone individuals anything like you and me. Talk about very low probabilities.”

“You’ve got a point. My folks almost didn’t survive the war back in Korea. A mine went off while they were working in our field — another few feet over and I wouldn’t be here today. But wait, couldn’t everything in the anti‑Universe play out in anti‑time exactly like things have in ours? They both would have started right next to each other with mirror‑image forces at work. It’d be like a pool table show by a really good trick‑shot artist.”

“If everything were that exactly mirror‑imaged, the anti‑me and I would have the same background, attitudes and ethics. The mirror people on those scifi shows generally have motives and moral codes that oppose ours even though the mirror characters physically are dead ringers for their our‑side counterparts. Except the male evil twins generally wear beards and the female ones use darker eye make‑up. No, I don’t think mirror‑imaging can be that exact. The reason is quantum.”

“How did quantum get into this? Quantum’s about little stuff, atoms and molecules, not the Universe.”

“Remember when the Universe was packed into a Planck‑length‑size volume? That’s on the order of 10^‑35 meter across, plenty small enough for random quantum effects to make a big difference. What’s important here, though, is everything that happened post‑Bang. The essence of quantum theory is that it’s not clockwork. With a few exceptions, we can only make statistical predictions about how events will go at microscopic scale. Things vary at random. Your chemical reactions are predictable but only because you’re working with huge numbers of molecules.”

“Even then sometimes I get a mess.”

“Well then. If you can’t reliably replicate reactions with gram‑level quantities, how can you expect an entire anti‑Universe to replicate its partner?”

“Then <singing> there can never be another you.”

~~ Rich Olcott

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.

By 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

Hard Science Ain't Hard

Tag: quantum

The Futile Search for Anti-Me

Buttered Cats — The QM perspective