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Many Worlds, One Best Guess

If you look at many microscopic physical phenomena—a photon, an electron, a hydrogen atom, a laser—and a million other known experimental setups—it is possible to come up with simple laws that seem to govern all small things (so long as you don’t ask about gravity). These laws govern the evolution of a highly abstract and mathematical object that I’ve been calling the “amplitude distribution,” but which is more widely referred to as the “wavefunction.”

Now there are gruesome questions about the proper generalization that covers all these tiny cases. Call an object “grue” if it appears green before January 1, 2020 and appears blue thereafter. If all emeralds examined so far have appeared green, is the proper generalization, “Emeralds are green” or “Emeralds are grue”?

The answer is that the proper generalization is “Emeralds are green.” I’m not going to go into the arguments at the moment. It is not the subject of this essay, and the obvious answer in this case happens to be correct. The true Way is not stupid: however clever you may be with your logic, it should finally arrive at the right answer rather than a wrong one.

In a similar sense, the simplest generalizations that would cover observed microscopic phenomena alone take the form of “All electrons have spin 1/2” and not “All electrons have spin 1/2 before January 1, 2020” or “All electrons have spin 1/2 unless they are part of an entangled system that weighs more than 1 gram.”

When we turn our attention to macroscopic phenomena, our sight is obscured. We cannot experiment on the wavefunction of a human in the way that we can experiment on the wavefunction of a hydrogen atom. In no case can you actually read off the wavefunction with a little quantum scanner. But in the case of, say, a human, the size of the entire organism defeats our ability to perform precise calculations or precise experiments—we cannot confirm that the quantum equations are being obeyed in precise detail.

We know that phenomena commonly thought of as “quantum” do not just disappear when many microscopic objects are aggregated. Lasers put out a flood of coherent photons, rather than, say, doing something completely different. Atoms have the chemical characteristics that quantum theory says they should, enabling them to aggregate into the stable molecules making up a human.

So in one sense, we have a great deal of evidence that quantum laws are aggregating to the macroscopic level without too much difference. Bulk chemistry still works.

But we cannot directly verify that the particles making up a human have an aggregate wavefunction that behaves exactly the way the simplest quantum laws say. Oh, we know that molecules and atoms don’t disintegrate, we know that macroscopic mirrors still reflect from the middle. We can get many high-level predictions from the assumption that the microscopic and the macroscopic are governed by the same laws, and every prediction tested has come true.

But if someone were to claim that the macroscopic quantum picture differs from the microscopic one in some as-yet-untestable detail—something that only shows up at the unmeasurable 20th decimal place of microscopic interactions, but aggregates into something bigger for macroscopic interactions—well, we can’t prove they’re wrong. It is Occam’s Razor that says, “There are zillions of new fundamental laws you could postulate in the 20th decimal place; why are you even thinking about this one?”

If we calculate using the simplest laws which govern all known cases, we find that humans end up in states of quantum superposition, just like photons in a superposition of reflecting from and passing through a half-silvered mirror. In the Schrödinger’s Cat setup, an unstable atom goes into a superposition of disintegrating, and not-disintegrating. A sensor, tuned to the atom, goes into a superposition of triggering and not-triggering. (Actually, the superposition is now a joint state of [atom-disintegrated × sensor-triggered] + [atom-stable × sensor-not-triggered].) A charge of explosives, hooked up to the sensor, goes into a superposition of exploding and not exploding; a cat in the box goes into a superposition of being dead and alive; and a human, looking inside the box, goes into a superposition of throwing up and being calm. The same law at all levels.

Human beings who interact with superposed systems will themselves evolve into superpositions. But the brain that sees the exploded cat, and the brain that sees the living cat, will have many neurons firing differently, and hence many many particles in different positions. They are very distant in the configuration space, and will communicate to an exponentially infinitesimal degree. Not the 30th decimal place, but the 1030th decimal place. No particular mind, no particular cognitive causal process, sees a blurry superposition of cats.

The fact that “you” only seem to see the cat alive, or the cat dead, is exactly what the simplest quantum laws predict. So we have no reason to believe, from our experience so far, that the quantum laws are in any way different at the macroscopic level than the microscopic level.

And physicists have verified superposition at steadily larger levels. Apparently an effort is currently underway to test superposition in a 50-micron object, larger than most neurons.

The existence of other versions of ourselves, and indeed other Earths, is not supposed additionally. We are simply supposing that the same laws govern at all levels, having no reason to suppose differently, and all experimental tests having succeeded so far. The existence of other decoherent Earths is a logical consequence of the simplest generalization that fits all known facts. If you think that Occam’s Razor says that the other worlds are “unnecessary entities” being multiplied, then you should check the probability-theoretic math; that is just not how Occam’s Razor works.

Yet there is one particular puzzle that seems odd in trying to extend microscopic laws universally, including to superposed humans:

If we try to get probabilities by counting the number of distinct observers, then there is no obvious reason why the integrated squared modulus of the wavefunction should correlate with statistical experimental results. There is no known reason for the Born probabilities, and it even seems that, a priori, we would expect a 50/50 probability of any binary quantum experiment going both ways, if we just counted observers.

Robin Hanson suggests that if exponentially tinier-than-average decoherent blobs of amplitude (“worlds”) are interfered with by exponentially tiny leakages from larger blobs, we will get the Born probabilities back out. I consider this an interesting possibility, because it is so normal.

(I myself have had recent thoughts along a different track: If I try to count observers the obvious way, I get strange-seeming results in general, not just in the case of quantum physics. If, for example, I split my brain into a trillion similar parts, conditional on winning the lottery while anesthetized; allow my selves to wake up and perhaps differ to small degrees from each other; and then merge them all into one self again; then counting observers the obvious way says I should be able to make myself win the lottery (if I can split my brain and merge it, as an uploaded mind might be able to do).

In this connection, I find it very interesting that the Born rule does not have a split-remerge problem. Given unitary quantum physics, Born’s rule is the unique rule that prevents “observers” from having psychic powers—which doesn’t explain Born’s rule, but is certainly an interesting fact. Given Born’s rule, even splitting and remerging worlds would still lead to consistent probabilities. Maybe physics uses better anthropics than I do!

Perhaps I should take my cues from physics, instead of trying to reason it out a priori, and see where that leads me? But I have not been led anywhere yet, so this is hardly an “answer.”)

Wallace, Deutsch, and others try to derive Born’s Rule from decision theory. I am rather suspicious of this, because it seems like there is a component of “What happens to me?” that I cannot alter by modifying my utility function. Even if I didn’t care at all about worlds where I didn’t win a quantum lottery, it still seems to me that there is a sense in which I would “mostly” wake up in a world where I didn’t win the lottery. It is this that I think needs explaining.

The point is that many hypotheses about the Born probabilities have been proposed. Not as many as there should be, because the mystery was falsely marked “solved” for a long time. But still, there have been many proposals.

There is legitimate hope of a solution to the Born puzzle without new fundamental laws. Your world does not split into exactly two new subprocesses on the exact occasion when you see “absorbed” or “transmitted” on the LCD screen of a photon sensor. We are constantly being superposed and decohered, all the time, sometimes along continuous dimensions—though brains are digital and involve whole neurons firing, and fire/not-fire would be an extremely decoherent state even of a single neuron… There would seem to be room for something unexpected to account for the Born statistics—a better understanding of the anthropic weight of observers, or a better understanding of the brain’s superpositions—without new fundamentals.

We cannot rule out, though, the possibility that a new fundamental law is involved in the Born statistics.

As Jess Riedel puts it:

If there’s one lesson we can take from the history of physics, it’s that everytime new experimental “regimes” are probed (e.g. large velocities, small sizes, large mass densities, large energies), phenomena are observed which lead to new theories (Special Relativity, quantum mechanics, General Relativity, and the Standard Model, respectively).

“Every time” is too strong. A nitpick, yes, but also an important point: you can’t just assume that any particular law will fail in a new regime. But it’s possible that a new fundamental law is involved in the Born statistics, and that this law manifests only in the 20th decimal place at microscopic levels (hence being undetectable so far) while aggregating to have substantial effects at macroscopic levels.

Could there be some law, as yet undiscovered, that causes there to be only one world?

This is a shocking notion; it implies that all our twins in the other worlds— all the different versions of ourselves that are constantly split off, not just by human researchers doing quantum measurements, but by ordinary entropic processes—are actually gone, leaving us alone! This version of Earth would be the only version that exists in local space! If the inflationary scenario in cosmology turns out to be wrong, and the topology of the universe is both finite and relatively small—so that Earth does not have the distant duplicates that would be implied by an exponentially vast universe—then this Earth could be the only Earth that exists anywhere, a rather unnerving thought!

But it is dangerous to focus too much on specific hypotheses that you have no specific reason to think about. This is the same root error of the Intelligent Design folk, who pick any random puzzle in modern genetics, and say, “See, God must have done it!” Why “God,” rather than a zillion other possible explanations?—which you would have thought of long before you postulated divine intervention, if not for the fact that you secretly started out already knowing the answer you wanted to find.

You shouldn’t even ask, “Might there only be one world?” but instead just go ahead and do physics, and raise that particular issue only if new evidence demands it.

Could there be some as-yet-unknown fundamental law, that gives the universe a privileged center, which happens to coincide with Earth—thus proving that Copernicus was wrong all along, and the Bible right?

Asking that particular question—rather than a zillion other questions in which the center of the universe is Proxima Centauri, or the universe turns out to have a favorite pizza topping and it is pepperoni—betrays your hidden agenda. And though an unenlightened one might not realize it, giving the universe a privileged center that follows Earth around through space would be rather difficult to do with any mathematically simple fundamental law.

So too with asking whether there might be only one world. It betrays a sentimental attachment to human intuitions already proven wrong. The wheel of science turns, but it doesn’t turn backward.

We have specific reasons to be highly suspicious of the notion of only one world. The notion of “one world” exists on a higher level of organization, like the location of Earth in space; on the quantum level there are no firm boundaries (though brains that differ by entire neurons firing are certainly decoherent). How would a fundamental physical law identify one high-level world?

Much worse, any physical scenario in which there was a single surviving world, so that any measurement had only a single outcome, would violate Special Relativity.

If the same laws are true at all levels—i.e., if many-worlds is correct—then when you measure one of a pair of entangled polarized photons, you end up in a world in which the photon is polarized, say, up-down, and alternate versions of you end up in worlds where the photon is polarized left-right. From your perspective before doing the measurement, the probabilities are 50/50. Light-years away, someone measures the other photon at a 20° angle to your own basis. From their perspective, too, the probability of getting either immediate result is 50/50—they maintain an invariant state of generalized entanglement with your faraway location, no matter what you do. But when the two of you meet, years later, your probability of meeting a friend who got the same result is 11.6%, rather than 50%.

If there is only one global world, then there is only a single outcome of any quantum measurement. Either you measure the photon polarized up-down, or left-right, but not both. Light-years away, someone else’s probability of measuring the photon polarized similarly in a 20° rotated basis actually changes from 50/50 to 11.6%.

You cannot possibly interpret this as a case of merely revealing properties that were already there; this is ruled out by Bell’s Theorem. There does not seem to be any possible consistent view of the universe in which both quantum measurements have a single outcome, and yet both measurements are predetermined, neither influencing the other. Something has to actually change, faster than light.

And this would appear to be a fully general objection, not just to collapse theories, but to any possible theory that gives us one global world! There is no consistent view in which measurements have single outcomes, but are locally determined (even locally randomly determined). Some mysterious influence has to cross a spacelike gap.

This is not a trivial matter. You cannot save yourself by waving your hands and saying, “the influence travels backward in time to the entangled photons’ creation, then forward in time to the other photon, so it never actually crosses a spacelike gap.” (This view has been seriously put forth, which gives you some idea of the magnitude of the paradox implied by one global world!) One measurement has to change the other, so which measurement happens first? Is there a global space of simultaneity? You can’t have both measurements happen “first” because under Bell’s Theorem, there’s no way local information could account for observed results, etc.

Incidentally, this experiment has already been performed, and if there is a mysterious influence it would have to travel six million times as fast as light in the reference frame of the Swiss Alps. Also, the mysterious influence has been experimentally shown not to care if the two photons are measured in reference frames which would cause each measurement to occur “before the other.”

Special Relativity seems counterintuitive to us humans—like an arbitrary speed limit, which you could get around by going backward in time, and then forward again. A law you could escape prosecution for violating, if you managed to hide your crime from the authorities.

But what Special Relativity really says is that human intuitions about space and time are simply wrong. There is no global “now,” there is no “before” or “after” across spacelike gaps. The ability to visualize a single global world, even in principle, comes from not getting Special Relativity on a gut level. Otherwise it would be obvious that physics proceeds locally with invariant states of distant entanglement, and the requisite information is simply not locally present to support a globally single world.

It might be that this seemingly impeccable logic is flawed—that my application of Bell’s Theorem and relativity to rule out any single global world contains some hidden assumption of which I am unaware—

—but consider the burden that a single-world theory must now shoulder! There is absolutely no reason in the first place to suspect a global single world; this is just not what current physics says! The global single world is an ancient human intuition that was disproved, like the idea of a universal absolute time. The superposition principle is visible even in half-silvered mirrors; experiments are verifying the disproof at steadily larger levels of superposition—but above all there is no longer any reason to privilege the hypothesis of a global single world. The ladder has been yanked out from underneath that human intuition.

There is no experimental evidence that the macroscopic world is single (we already know the microscopic world is superposed). And the prospect necessarily either violates Special Relativity, or takes an even more miraculous-seeming leap and violates seemingly impeccable logic. The latter, of course, being much more plausible in practice. But it isn’t really that plausible in an absolute sense. Without experimental evidence, it is generally a bad sign to have to postulate arbitrary logical miracles.

As for quantum non-realism, it appears to me to be nothing more than a Get Out of Jail Free card. “It’s okay to violate Special Relativity because none of this is real anyway!” The equations cannot reasonably be hypothesized to deliver such excellent predictions for literally no reason. Bell’s Theorem rules out the obvious possibility that quantum theory represents imperfect knowledge of something locally deterministic.

Furthermore, macroscopic decoherence gives us a perfectly realistic understanding of what is going on, in which the equations deliver such good predictions because they mirror reality. And so the idea that the quantum equations are just “meaningless,” and therefore it is okay to violate Special Relativity, so we can have one global world after all, is not necessary. To me, quantum non-realism appears to be a huge bluff built around semantic stopsigns like “Meaningless!”

It is not quite safe to say that the existence of multiple Earths is as well-established as any other truth of science. The existence of quantum other worlds is not so well-established as the existence of trees, which most of us can personally observe.

Maybe there is something in that 20th decimal place, which aggregates to something bigger in macroscopic events. Maybe there’s a loophole in the seemingly iron logic which says that any single global world must violate Special Relativity, because the information to support a single global world is not locally available. And maybe the Flying Spaghetti Monster is just messing with us, and the world we know is a lie.

So all we can say about the existence of multiple Earths, is that it is as rationally probable as e.g. the statement that spinning black holes do not violate conservation of angular momentum. We have extremely fundamental reasons, having to do with the rotational symmetry of space, to suspect that conservation of angular momentum is built into the underlying nature of physics. And we have no specific reason to suspect this particular violation of our old generalizations in a higher-energy regime.

But we haven’t actually checked conservation of angular momentum for rotating black holes—so far as I know. (And as I am talking here about rational guesses in states of partial knowledge, the point is exactly the same if the observation has been made and I do not know it yet.) And black holes are a more massive regime. So the obedience of black holes is not quite as assured as that my toilet conserves angular momentum while flushing, which come to think, I haven’t checked either…

Yet if you make the mistake of thinking too hard about this one particular possibility, instead of zillions of other possibilities—and especially if you don’t understand the fundamental reason why angular momentum is conserved— then it may start seeming more and more plausible that “spinning black holes violate conservation of angular momentum,” as you think of more and more vaguely plausible-sounding reasons it could be true.

But the rational probability is pretty damned small.

Likewise the rational probability that there is only one Earth.

I mention this to explain my habit of talking as if many-worlds is an obvious fact. Many-worlds is an obvious fact, if you have all your marbles lined up correctly (understand very basic quantum physics, know the formal probability theory of Occam’s Razor, understand Special Relativity, etc.) It is in fact considerably more obvious to me than the proposition that spinning black holes should obey conservation of angular momentum.

The only reason why many-worlds is not universally acknowledged as a direct prediction of physics which requires magic to violate, is that a contingent accident of our Earth’s scientific history gave an entrenched academic position to a phlogiston-like theory that had an unobservable faster-than-light magical “collapse” devouring all other worlds. And many academic physicists do not have a mathematical grasp of Occam’s Razor, which is the usual method for ridding physics of invisible angels. So when they encounter many-worlds and it conflicts with their (undermined) intuition that only one world exists, they say, “Oh, that’s multiplying entities”—which is just flatly wrong as probability theory—and go on about their daily lives.

I am not in academia. I am not constrained to bow and scrape to some senior physicist who hasn’t grasped the obvious, but who will be reviewing my journal articles. I need have no fear that I will be rejected for tenure on account of scaring my students with “science-fiction tales of other Earths.” If I can’t speak plainly, who can?

So let me state then, very clearly, on behalf of any and all physicists out there who dare not say it themselves: Many-worlds wins outright given our current state of evidence. There is no more reason to postulate a single Earth, than there is to postulate that two colliding top quarks would decay in a way that violates Conservation of Energy. It takes more than an unknown fundamental law; it takes magic.

The debate should already be over. It should have been over fifty years ago. The state of evidence is too lopsided to justify further argument. There is no balance in this issue. There is no rational controversy to teach. The laws of probability theory are laws, not suggestions; there is no flexibility in the best guess given this evidence. Our children will look back at the fact that we were still arguing about this in the early twenty-first century, and correctly deduce that we were nuts.

We have embarrassed our Earth long enough by failing to see the obvious. So for the honor of my Earth, I write as if the existence of many-worlds were an established fact, because it is. The only question now is how long it will take for the people of this world to update.

Thou Art Physics




Science and Rationality