Too Many Schrödingers

Cathleen takes back control of the conference software. “Thanks, Jim. OK, the final contestant in our online Crazy Theories contest is the winner of our last face-to-face event where she told us why Spock and horseshoe crabs both have green blood. You’re up, Amanda.”

“Thanks, and hello out there. I can’t believe Jim and I are both talking about parallel universes. It’s almost like we’re thinking in parallel, right?”

<Jim’s mic is muted so he makes gagging motions>

“We need some prep work before I can talk about the Multiverse. I’m gonna start with this heat map of North America at a particular time. Hot in the Texas panhandle, cool in British Columbia, no surprise. You can do a lot with a heat map — pick a latitude and longitude, it tells you the relative temperature. Do some arithmetic on the all numbers and you can get average temperature, highs and lows, front strength in degrees per mile, lots of stuff like that.

“You build this kind of map by doing a lot of individual measurements. If you’re lucky you can summarize those measurements with a function, a compact mathematical expression that does the same job — pick a latitude and longitude, it tells you the value. Three nice things about functions — they take up a lot less space than a map, you can use straightforward mathematical operations on them so getting statistics is less work than with a map, and you can form superpositions by adding functions together.”

Cathleen interrupts. “Amanda, there’s a question in the chat box. ‘Can you give an example of superposition?’

“Sure. You can superpose simple sine‑wave functions to describe chords for sound waves or blended colors for light waves, for instance.

“Now when we get to really small‑scale thingies, we need quantum calculations. The question is, what do quantum calculations tell us? That’s been argued about for a hundred years because the values they generate are iffy superpositions. Twenty percent of this, eighty percent of that. Everybody’s heard of that poor cat in Schrödinger’s box.

“Many researchers say the quantum values are relative probabilities for observing different results in an experiment — but most of them carefully avoid worrying about why the answers aren’t always the same. Einstein wanted to know what Bohr was averaging over to get his averages. Bohr said it doesn’t matter, the percentages are the only things we can know about the system and it’s useless to speculate further.

“Hugh Everett thought bigger. He suggested that the correct quantum function for an observation should include experiment and experimenter. He took that a step further by showing that a proper quantum function would need to include anyone watching the experimenter and so on. In fact, he proposed, maybe there’s just one quantum function for the entire Universe. That would have some interesting implications.

“Remember Schrödinger’s catbox with two possible experimental results? Everett would say that his universal quantum function contains a superposition of two component sub-functions — happy Schrödinger with a live kitty and sad Schrödinger with a disposal problem. Each Schrödinger would be quite certain that he’d seen the definite result of a purely random operation. Two Schrödingers in parallel universes going forward.

“But in fact there’d be way more than two. When Schrödinger’s eye absorbs a photon, or maybe doesn’t, that generates another pair of universes. So do the quantum events that occur as his nerve cells fire, or don’t. Each Schrödinger moves into the future embedded in a dense bundle of parallel universes.”

Cathleen interrupts. “Another question. ‘What about conservation of mass?‘”

“Good question, whoever asked that. Everett doesn’t address that explicitly in his thesis, but I think he assumed the usual superposition math. That always includes a fix‑up step so that the sum of all the pieces adds up to unity. Half a Schrödinger mass on one track and half on the other. Even as each of them splits again and again and again the total is still only one Schrödinger‑mass. There’s other interpretation — each Schrödinger’s universe would be independent of the others so there’s no summing‑up to generate a conservation‑of‑mass problem. Your choice.

“Everett traded quantum weirdness for a weird Universe. Not much of a trade-off, I think.”

~~ Rich Olcott

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