And the Winner is… Many-Worlds!

Eliezer Yudkowsky12 Jun 2008 6:05 UTC
28 points
12 comments9 min readLW linkArchive

This is one of several shortened indices into the Quantum Physics Sequence.

Macroscopic quantum superpositions, a.k.a. the “many-worlds interpretation” or MWI, was proposed in 1957 and brought to the general attention of the scientific community in 1970. Ever since, MWI has steadily gained in popularity. As of 2008, MWI may or may not be endorsed by a majority of theoretical physicists (attempted opinion polls conflict on this point). Of course, Science is not supposed to be an opinion poll, but anyone who tells you that MWI is “science fiction” is simply ignorant.

When a theory is slowly persuading scientists despite all academic inertia, and more and more graduate students grow up familiar with it, at what point should one go ahead and declare a temporary winner pending new evidence?

Reading through the referenced posts will give you a very basic introduction to quantum mechanics—algebra is involved, but no calculus—by which you may nonetheless gain an understanding sufficient to see, and not just be told, that the modern case for many-worlds has become overwhelming. Not just plausible, not just strong, but overwhelming. Single-world versions of quantum mechanics just don’t work, and all the legendary confusingness and mysteriousness of quantum mechanics stems from this essential fact. But enough telling—let me show you.

  • Quantum Explanations: Quantum mechanics doesn’t deserve its fearsome reputation. If you tell people something is supposed to be mysterious, they won’t understand it. It’s human intuitions that are “strange” or “weird”; physics itself is perfectly normal. Talking about historical erroneous concepts like “particles” or “waves” is just asking to confuse people; present the real, unified quantum physics straight out. The series will take a strictly realist perspective—quantum equations describe something that is real and out there.

  • Configurations and Amplitude: A preliminary glimpse at the stuff reality is made of. The classic split-photon experiment with half-silvered mirrors. Alternative pathways the photon can take, can cancel each other out. The mysterious measuring tool that tells us the relative squared moduli.

  • Joint Configurations: The laws of physics are inherently over mathematical entities, configurations, that involve multiple particles. A basic, ontologically existent entity, according to our current understanding of quantum mechanics, does not look like a photon—it looks like a configuration of the universe with “A photon here, a photon there.” Amplitude flows between these configurations can cancel or add; this gives us a way to detect which configurations are distinct.

  • Distinct Configurations: Since configurations are over the combined state of all the elements in a system, adding a sensor that detects whether a particle went one way or the other, becomes a new element of the system that can make configurations “distinct” instead of “identical”. This confused the living daylights out of early quantum experimenters, because it meant that things behaved differently when they tried to “measure” them. But it’s not only measuring instruments that do the trick—any sensitive physical element will do—and the distinctness of configurations is a physical fact, not a fact about our knowledge. There is no need to suppose that the universe cares what we think.

  • Where Philosophy Meets Science: In retrospect, supposing that quantum physics had anything to do with consciousness was a big mistake. Could philosophers have told the physicists so? But we don’t usually see philosophers sponsoring major advances in physics; why not?

  • Can You Prove Two Particles Are Identical?: You wouldn’t think that it would be possible to do an experiment that told you that two particles are completely identical—not just to the limit of experimental precision, but perfectly. You could even give a precise-sounding philosophical argument for why it was not possible—but the argument would have a deeply buried assumption. Quantum physics violates this deep assumption, making the experiment easy.

  • Classical Configuration Spaces: How to visualize the state of a system of two 1-dimensional particles, as a single point in 2-dimensional space. A preliminary step before moving into...

  • The Quantum Arena: Instead of a system state being associated with a single point in a classical configuration space, the instantaneous real state of a quantum system is a complex amplitude distribution over a quantum configuration space. What creates the illusion of “individual particles”, like an electron caught in a trap, is a plaid distribution - one that happens to factor into the product of two parts. It is the whole distribution that evolves when a quantum system evolves. Individual configurations don’t have physics; amplitude distributions have physics. Quantum entanglement is the general case; quantum independence is the special case.

  • Feynman Paths: Instead of thinking that a photon takes a single straight path through space, we can regard it as taking all possible paths through space, and adding the amplitudes for every possible path. Nearly all the paths cancel out—unless we do clever quantum things, so that some paths add instead of canceling out. Then we can make light do funny tricks for us, like reflecting off a mirror in such a way that the angle of incidence doesn’t equal the angle of reflection. But ordinarily, nearly all the paths except an extremely narrow band, cancel out—this is one of the keys to recovering the hallucination of classical physics.

  • No Individual Particles: One of the chief ways to confuse yourself while thinking about quantum mechanics, is to think as if photons were little billiard balls bouncing around. The appearance of little billiard balls is a special case of a deeper level on which there are only multiparticle configurations and amplitude flows. It is easy to set up physical situations in which there exists no fact of the matter as to which electron was originally which.

  • Decoherence: A quantum system that factorizes can evolve into a system that doesn’t factorize, destroying the illusion of independence. But entangling a quantum system with its environment, can appear to destroy entanglements that are already present. Entanglement with the environment can separate out the pieces of an amplitude distribution, preventing them from interacting with each other. Decoherence is fundamentally symmetric in time, but appears asymmetric because of the second law of thermodynamics.

  • The So-Called Heisenberg Uncertainty Principle: Unlike classical physics, in quantum physics it is not possible to separate out a particle’s “position” from its “momentum”. The evolution of the amplitude distribution over time, involves things like taking the second derivative in space and multiplying by i to get the first derivative in time. The end result of this time evolution rule is that blobs of particle-presence appear to race around in physical space. The notion of “an exact particular momentum” or “an exact particular position” is not something that can physically happen, it is a tool for analyzing amplitude distributions by taking them apart into a sum of simpler waves. This uses the assumption and fact of linearity: the evolution of the whole wavefunction seems to always be the additive sum of the evolution of its pieces. Using this tool, we can see that if you take apart the same distribution into a sum of positions and a sum of momenta, they cannot both be sharply concentrated at the same time. When you “observe” a particle’s position, that is, decohere its positional distribution by making it interact with a sensor, you take its wave packet apart into two pieces; then the two pieces evolve differently. The Heisenberg Principle definitely does not say that knowing about the particle, or consciously seeing it, will make the universe behave differently.

  • Belief in the Implied Invisible: If a spaceship goes over the cosmological horizon relative to us, so that it can no longer communicate with us, should we believe that the spaceship instantly ceases to exist?

  • Where Physics Meets Experience: Meet the Ebborians, who reproduce by fission. The Ebborian brain is like a thick sheet of paper that splits down its thickness. They frequently experience dividing into two minds, and can talk to their other selves. It seems that their unified theory of physics is almost finished, and can answer every question, when one Ebborian asks: When exactly does one Ebborian become two people?

  • Where Experience Confuses Physicists: It then turns out that the entire planet of Ebbore is splitting along a fourth-dimensional thickness, duplicating all the people within it. But why does the apparent chance of “ending up” in one of those worlds, equal the square of the fourth-dimensional thickness? Many mysterious answers are proposed to this question, and one non-mysterious one.

  • On Being Decoherent: When a sensor measures a particle whose amplitude distribution stretches over space—perhaps seeing if the particle is to the left or right of some dividing line—then the standard laws of quantum mechanics call for the sensor+particle system to evolve into a state of (particle left, sensor measures LEFT) + (particle right, sensor measures RIGHT). But when we humans look at the sensor, it only seems to say “LEFT” or “RIGHT”, never a mixture like “LIGFT”. This, of course, is because we ourselves are made of particles, and subject to the standard quantum laws that imply decoherence. Under standard quantum laws, the final state is (particle left, sensor measures LEFT, human sees “LEFT”) + (particle right, sensor measures RIGHT, human sees “RIGHT”).

  • The Conscious Sorites Paradox: Decoherence is implicit in quantum physics, not an extra law on top of it. Asking exactly when “one world” splits into “two worlds” may be like asking when, if you keep removing grains of sand from a pile, it stops being a “heap”. Even if you’re inside the world, there may not be a definite answer. This puzzle does not arise only in quantum physics; the Ebborians could face it in a classical universe, or we could build sentient flat computers that split down their thickness. Is this really a physicist’s problem?

  • Decoherece is Pointless: There is no exact point at which decoherence suddenly happens. All of quantum mechanics is continuous and differentiable, and decoherent processes are no exception to this.

  • Decoherent Essences: Decoherence is implicit within physics, not an extra law on top of it. You can choose representations that make decoherence harder to see, just like you can choose representations that make apples harder to see, but exactly the same physical process still goes on; the apple doesn’t disappear and neither does decoherence. If you could make decoherence magically go away by choosing the right representation, we wouldn’t need to shield quantum computers from the environment.

  • The Born Probabilities: The last serious mysterious question left in quantum physics: When a quantum world splits in two, why do we seem to have a greater probability of ending up in the larger blob, exactly proportional to the integral of the squared modulus? It’s an open problem, but non-mysterious answers have been proposed. Try not to go funny in the head about it.

  • Decoherence as Projection: Since quantum evolution is linear and unitary, decoherence can be seen as projecting a wavefunction onto orthogonal subspaces. This can be neatly illustrated using polarized photons and the angle of the polarized sheet that will absorb or transmit them.

  • Entangled Photons: Using our newly acquired understanding of photon polarizations, we see how to construct a quantum state of two photons in which, when you measure one of them, the person in the same world as you, will always find that the opposite photon has opposite quantum state. This is not because any influence is transmitted; it is just decoherence that takes place in a very symmetrical way, as can readily be observed in our calculations.

  • Bell’s Theorem: No EPR “Reality”: (Note: This post was designed to be read as a stand-alone, if desired.) Originally, the discoverers of quantum physics thought they had discovered an incomplete description of reality—that there was some deeper physical process they were missing, and this was why they couldn’t predict exactly the results of quantum experiments. The math of Bell’s Theorem is surprisingly simple, and we walk through it. Bell’s Theorem rules out being able to locally predict a single, unique outcome of measurements—ruling out a way that Einstein, Podolsky, and Rosen once defined “reality”. This shows how deep implicit philosophical assumptions can go. If worlds can split, so that there is no single unique outcome, then Bell’s Theorem is no problem. Bell’s Theorem does, however, rule out the idea that quantum physics describes our partial knowledge of a deeper physical state that could locally produce single outcomes—any such description will be inconsistent.

  • Spooky Action at a Distance: The No-Communication Theorem: As Einstein argued long ago, the quantum physics of his era—that is, the single-global-world interpretation of quantum physics, in which experiments have single unique random results—violates Special Relativity; it imposes a preferred space of simultaneity and requires a mysterious influence to be transmitted faster than light; which mysterious influence can never be used to transmit any useful information. Getting rid of the single global world dispels this mystery and puts everything back to normal again.

  • Decoherence is Simple and

  • Decoherence is Falsifiable and Testable: An epistle to the physicists. To probability theorists, words like “simple”, “falsifiable”, and “testable” have exact mathematical meanings, which are there for very strong reasons. The (minority?) faction of physicists who say that many-worlds is “not falsifiable” or that it “violates Occam’s Razor” or that it is “untestable”, are committing the same kind of mathematical crime as non-physicists who invent their own theories of gravity that go as inverse-cube. This is one of the reasons why I, a non-physicist, dared to talk about physics—because I saw (some!) physicists using probability theory in a way that was simply wrong. Not just criticizable, but outright mathematically wrong: 2 + 2 = 3.

  • Quantum Non-Realism: “Shut up and calculate” is the best approach you can take when none of your theories are very good. But that is not the same as claiming that “Shut up!” actually is a theory of physics. Saying “I don’t know what these equations mean, but they seem to work” is a very different matter from saying: “These equations definitely don’t mean anything, they just work!”

  • Collapse Postulates: Early physicists simply didn’t think of the possibility of more than one world—it just didn’t occur to them, even though it’s the straightforward result of applying the quantum laws at all levels. So they accidentally invented a completely and strictly unnecessary part of quantum theory to ensure there was only one world—a law of physics that says that parts of the wavefunction mysteriously and spontaneously disappear when decoherence prevents us from seeing them any more. If such a law really existed, it would be the only non-linear, non-unitary, non-differentiable, non-local, non-CPT-symmetric, acausal, faster-than-light phenomenon in all of physics.

  • If Many-Worlds Had Come First: If early physicists had never made the mistake, and thought immediately to apply the quantum laws at all levels to produce macroscopic decoherence, then “collapse postulates” would today seem like a completely crackpot theory. In addition to their other problems, like FTL, the collapse postulate would be the only physical law that was informally specified—often in dualistic (mentalistic) terms—because it was the only fundamental law adopted without precise evidence to nail it down. Here, we get a glimpse at that alternate Earth.

  • Many Worlds, One Best Guess: Summarizes the arguments that nail down macroscopic decoherence, aka the “many-worlds interpretation”. Concludes that many-worlds wins outright given the current state of evidence. The argument should have been over fifty years ago. New physical evidence could reopen it, but we have no particular reason to expect this.

  • Living in Many Worlds: The many worlds of quantum mechanics are not some strange, alien universe into which you have been thrust. They are where you have always lived. Egan’s Law: “It all adds up to normality.” Then why care about quantum physics at all? Because there’s still the question of what adds up to normality, and the answer to this question turns out to be, “Quantum physics.” If you’re thinking of building any strange philosophies around many-worlds, you probably shouldn’t - that’s not what it’s for.

Eliezer Yudkowsky12 Jun 2008 6:05 UTC
28 points
12 comments9 min readLW linkArchive