May 10, 2008
Not that I’m claiming I could have done better, if I’d been born into that time, instead of this one…
Macroscopic decoherence, a.k.a. many-worlds, was first proposed in a 1957 paper by Hugh Everett III. The paper was ignored. John Wheeler told Everett to see Niels Bohr. Bohr didn’t take him seriously.
Crushed, Everett left academic physics, invented the general use of Lagrange multipliers in optimization problems, and became a multimillionaire.
It wasn’t until 1970, when Bryce DeWitt (who coined the term “many-worlds”) wrote an article for Physics Today, that the general field was first informed of Everett’s ideas. Macroscopic decoherence has been gaining advocates ever since, and may now be the majority viewpoint (or not).
But suppose that decoherence and macroscopic decoherence had been realized immediately following the discovery of entanglement, in the 1920s. And suppose that no one had proposed collapse theories until 1957. Would decoherence now be steadily declining in popularity, while collapse theories were slowly gaining steam?
Imagine an alternate Earth, where the very first physicist to discover entanglement and superposition said, “Holy flaming monkeys, there’s a zillion other Earths out there!”
In the years since, many hypotheses have been proposed to explain the mysterious Born probabilities. But no one has yet suggested a collapse postulate. That possibility simply has not occurred to anyone.
One day, Huve Erett walks into the office of Biels Nohr…
“I just don’t understand,” Huve Erett said, “why no one in physics even seems interested in my hypothesis. Aren’t the Born statistics the greatest puzzle in modern quantum theory?”
Biels Nohr sighed. Ordinarily, he wouldn’t even bother, but something about the young man compelled him to try.
“Huve,” says Nohr, “every physicist meets dozens of people per year who think they’ve explained the Born statistics. If you go to a party and tell someone you’re a physicist, chances are at least one in ten they’ve got a new explanation for the Born statistics. It’s one of the most famous problems in modern science, and worse, it’s a problem that everyone thinks they can understand. To get attention, a new Born hypothesis has to be… pretty darn good.”
“And this,” Huve says, “this isn’t good?”
Huve gestures to the paper he’d brought to Biels Nohr. It is a short paper. The title reads, “The Solution to the Born Problem.” The body of the paper reads:
When you perform a measurement on a quantum system, all parts of the wavefunction except one point vanish, with the survivor chosen non-deterministically in a way determined by the Born statistics.
“Let me make absolutely sure,” Nohr says carefully, “that I understand you. You’re saying that we’ve got this wavefunction—evolving according to the Wheeler-DeWitt equation—and, all of a sudden, the whole wavefunction, except for one part, just spontaneously goes to zero amplitude. Everywhere at once. This happens when, way up at the macroscopic level, we ‘measure’ something.”
“Right!” Huve says.
“So the wavefunction knows when we ‘measure’ it. What exactly is a ‘measurement’? How does the wavefunction know we’re here? What happened before humans were around to measure things?”
“Um…” Huve thinks for a moment. Then he reaches out for the paper, scratches out “When you perform a measurement on a quantum system,” and writes in, “When a quantum superposition gets too large.”
Huve looks up brightly. “Fixed!”
“I see,” says Nohr. “And how large is ‘too large’?”
“At the 50-micron level, maybe,” Huve says, “I hear they haven’t tested that yet.”
Suddenly a student sticks his head into the room. “Hey, did you hear? They just verified superposition at the 50-micron level.”
“Oh,” says Huve, “um, whichever level, then. Whatever makes the experimental results come out right.”
Nohr grimaces. “Look, young man, the truth here isn’t going to be comfortable. Can you hear me out on this?”
“Yes,” Huve says, “I just want to know why physicists won’t listen to me.”
“All right,” says Nohr. He sighs. “Look, if this theory of yours were actually true—if whole sections of the wavefunction just instantaneously vanished—it would be… let’s see. The only law in all of quantum mechanics that is non-linear, non-unitary, non-differentiable and discontinuous. It would prevent physics from evolving locally, with each piece only looking at its immediate neighbors. Your ‘collapse’ would be the only fundamental phenomenon in all of physics with a preferred basis and a preferred space of simultaneity. Collapse would be the only phenomenon in all of physics that violates CPT symmetry, Liouville’s Theorem, and Special Relativity. In your original version, collapse would also have been the only phenomenon in all of physics that was inherently mental. Have I left anything out?”
“Collapse is also the only acausal phenomenon,” Huve points out. “Doesn’t that make the theory more wonderful and amazing?”
“I think, Huve,” says Nohr, “that physicists may view the exceptionalism of your theory as a point not in its favor.”
“Oh,” said Huve, taken aback. “Well, I think I can fix that non-differentiability thing by postulating a second-order term in the—”
“Huve,” says Nohr, “I don’t think you’re getting my point, here. The reason physicists aren’t paying attention to you, is that your theory isn’t physics. It’s magic.”
“But the Born statistics are the greatest puzzle of modern physics, and this theory provides a mechanism for the Born statistics!” Huve protests.
“No, Huve, it doesn’t,” Nohr says wearily. “That’s like saying that you’ve ‘provided a mechanism’ for electromagnetism by saying that there are little angels pushing the charged particles around in accordance with Maxwell’s equations. Instead of saying, ‘Here are Maxwell’s equations, which tells the angels where to push the electrons,’ we just say, ‘Here are Maxwell’s equations’ and are left with a strictly simpler theory. Now, we don’t know why the Born statistics happen. But you haven’t given the slightest reason why your ‘collapse postulate’ should eliminate worlds in accordance with the Born statistics, rather than something else. You’re not even making use of the fact that quantum evolution is unitary—”
“That’s because it’s not,” interjects Huve.
“—which everyone pretty much knows has got to be the key to the Born statistics, somehow. Instead you’re merely saying, ‘Here are the Born statistics, which tell the collapser how to eliminate worlds,’ and it’s strictly simpler to just say ‘Here are the Born statistics.’ ”
“But—” says Huve.
“Also,” says Nohr, raising his voice, “you’ve given no justification for why there’s only one surviving world left by the collapse, or why the collapse happens before any humans get superposed, which makes your theory really suspicious to a modern physicist. This is exactly the sort of untestable hypothesis that the ‘One Christ’ crowd uses to argue that we should ‘teach the controversy’ when we tell high school students about other Earths.”
“I’m not a One-Christer!” protests Huve.
“Fine,” Nohr says, “then why do you just assume there’s only one world left? And that’s not the only problem with your theory. Which part of the wavefunction gets eliminated, exactly? And in which basis? It’s clear that the whole wavefunction isn’t being compressed down to a delta, or ordinary quantum computers couldn’t stay in superposition when any collapse occurred anywhere—heck, ordinary molecular chemistry might start failing—”
Huve quickly crosses out “one point” on his paper, writes in “one part,” and then says, “Collapse doesn’t compress the wavefunction down to one point. It eliminates all the amplitude except one world, but leaves all the amplitude in that world.”
“Why?” says Nohr. “In principle, once you postulate ‘collapse,’ then ‘collapse’ could eliminate any part of the wavefunction, anywhere—why just one neat world left? Does the collapser know we’re in here?”
Huve says, “It leaves one whole world because that’s what fits our experiments.”
“Huve,” Nohr says patiently, “the term for that is ‘post hoc.’ Furthermore, decoherence is a continuous process. If you partition by whole brains with distinct neurons firing, the partitions have almost zero mutual interference within the wavefunction. But plenty of other processes overlap a great deal. There’s no possible way you can point to ‘one world’ and eliminate everything else without making completely arbitrary choices, including an arbitrary choice of basis—”
“But—” Huve says.
“And above all,” Nohr says, “the reason you can’t tell me which part of the wavefunction vanishes, or exactly when it happens, or exactly what triggers it, is that if we did adopt this theory of yours, it would be the only informally specified, qualitative fundamental law taught in all of physics. Soon no two physicists anywhere would agree on the exact details! Why? Because it would be the only fundamental law in all of modern physics that was believed without experimental evidence to nail down exactly how it worked.”
“What, really?” says Huve. “I thought a lot of physics was more informal than that. I mean, weren’t you just talking about how it’s impossible to point to ‘one world’?”
“That’s because worlds aren’t fundamental, Huve! We have massive experimental evidence underpinning the fundamental law, the Wheeler-DeWitt equation, that we use to describe the evolution of the wavefunction. We just apply exactly the same equation to get our description of macroscopic decoherence. But for difficulties of calculation, the equation would, in principle, tell us exactly when macroscopic decoherence occurred. We don’t know where the Born statistics come from, but we have massive evidence for what the Born statistics are. But when I ask you when, or where, collapse occurs, you don’t know—because there’s no experimental evidence whatsoever to pin it down. Huve, even if this ‘collapse postulate’ worked the way you say it does, there’s no possible way you could know it! Why not a gazillion other equally magical possibilities?”
Huve raises his hands defensively. “I’m not saying my theory should be taught in the universities as accepted truth! I just want it experimentally tested! Is that so wrong?”
“You haven’t specified when collapse happens, so I can’t construct a test that falsifies your theory,” says Nohr. “Now with that said, we’re already looking experimentally for any part of the quantum laws that change at increasingly macroscopic levels. Both on general principles, in case there’s something in the 20th decimal point that only shows up in macroscopic systems, and also in the hopes we’ll discover something that sheds light on the Born statistics. We check decoherence times as a matter of course. But we keep a broad outlook on what might be different. Nobody’s going to privilege your non-linear, non-unitary, non-differentiable, non-local, non-CPT-symmetric, non-relativistic, a-frikkin’-causal, faster-than-light, in-bloody-formal ‘collapse’ when it comes to looking for clues. Not until they see absolutely unmistakable evidence. And believe me, Huve, it’s going to take a hell of a lot of evidence to unmistake this. Even if we did find anomalous decoherence times, and I don’t think we will, it wouldn’t force your ‘collapse’ as the explanation.”
“What?” says Huve. “Why not?”
“Because there’s got to be a billion more explanations that are more plausible than violating Special Relativity,” says Nohr. “Do you realize that if this really happened, there would only be a single outcome when you measured a photon’s polarization? Measuring one photon in an entangled pair would influence the other photon a light-year away. Einstein would have a heart attack.”
“It doesn’t really violate Special Relativity,” says Huve. “The collapse occurs in exactly the right way to prevent you from ever actually detecting the faster-than-light influence.”
“That’s not a point in your theory’s favor,” says Nohr. “Also, Einstein would still have a heart attack.”
“Oh,” says Huve. “Well, we’ll say that the relevant aspects of the particle don’t existuntil the collapse occurs. If something doesn’t exist, influencing it doesn’t violate Special Relativity—”
“You’re just digging yourself deeper. Look, Huve, as a general principle, theories that are actually correct don’t generate this level of confusion. But above all, there isn’t any evidence for it. You have no logical way of knowing that collapse occurs, and no reason to believe it. You made a mistake. Just say ‘oops’ and get on with your life.”
“But they could find the evidence someday,” says Huve.
“I can’t think of what evidence could determine this particular one-world hypothesis as an explanation, but in any case, right now we haven’t found any such evidence,” says Nohr. “We haven’t found anything even vaguely suggestive of it! You can’t update on evidence that could theoretically arrive someday but hasn’t arrived! Right now, today, there’s no reason to spend valuable time thinking about this rather than a billion other equally magical theories. There’s absolutely nothing that justifies your belief in ‘collapse theory’ any more than believing that someday we’ll learn to transmit faster-than-light messages by tapping into the acausal effects of praying to the Flying Spaghetti Monster!”
Huve draws himself up with wounded dignity. “You know, if my theory is wrong—and I do admit it might be wrong—”
“If?” says Nohr. “Might?”
“If, I say, my theory is wrong,” Huve continues, “then somewhere out there is another world where I am the famous physicist and you are the lone outcast!”
Nohr buries his head in his hands. “Oh, not this again. Haven’t you heard the saying, ‘Live in your own world’? And you of all people—”
“Somewhere out there is a world where the vast majority of physicists believe in collapse theory, and no one has even suggested macroscopic decoherence over the last thirty years!”
Nohr raises his head, and begins to laugh.
“What’s so funny?” Huve says suspiciously.
Nohr just laughs harder. “Oh, my! Oh, my! You really think, Huve, that there’s a world out there where they’ve known about quantum physics for thirty years, and nobody has even thought there might be more than one world?”
“Yes,” Huve says, “that’s exactly what I think.”
“Oh my! So you’re saying, Huve, that physicists detect superposition in microscopic systems, and work out quantitative equations that govern superposition in every single instance they can test. And for thirty years, not one person says, ‘Hey, I wonder if these laws happen to be universal.’ ”
“Why should they?” says Huve. “Physical models sometimes turn out to be wrong when you examine new regimes.”
“But to not even think of it?” Nohr says incredulously. “You see apples falling, work out the law of gravity for all the planets in the solar system except Jupiter, and it doesn’t even occur to you to apply it to Jupiter because Jupiter is too large? That’s like, like some kind of comedy routine where the guy opens a box, and it contains a spring-loaded pie, so the guy opens another box, and it contains another spring-loaded pie, and the guy just keeps doing this without even thinking of the possibility that the next box contains a pie too. You think John von Neumann, who may have been the highest-g human in history, wouldn’t think of it?”
“That’s right,” Huve says, “He wouldn’t. Ponder that.”
“This is the world where my good friend Ernest formulates his Schrödinger’s Cat thought experiment, and in this world, the thought experiment goes: ‘Hey, suppose we have a radioactive particle that enters a superposition of decaying and not decaying. Then the particle interacts with a sensor, and the sensor goes into a superposition of going off and not going off. The sensor interacts with an explosive, that goes into a superposition of exploding and not exploding; which interacts with the cat, so the cat goes into a superposition of being alive and dead. Then a human looks at the cat,’ and at this point Schrödinger stops, and goes, ‘gee, I just can’t imagine what could happen next.’ So Schrödinger shows this to everyone else, and they’re also like ‘Wow, I got no idea what could happen at this point, what an amazing paradox.’ Until finally you hear about it, and you’re like, ‘hey, maybe at thatpoint half of the superposition just vanishes, at random, faster than light,’ and everyone else is like, ‘Wow, what a great idea!’ ”
“That’s right,” Huve says again. “It’s got to have happened somewhere.”
“Huve, this is a world where every single physicist, and probably the whole damn human species, is too dumb to sign up for cryonics! We’re talking about the Earth where George W. Bush is President.”