This is an inclusive guide to the series of posts on quantum mechanics that began on April 9th, 2008, including the digressions into related topics (such as the difference between Science and Bayesianism) and some of the preliminary reading.
You may also be interested in one of the less inclusive post guides, such as:
- An Intuitive Explanation of Quantum Mechanics (just the science, for students confused by their physics textbooks)
- Quantum Physics Revealed As Non-Mysterious (quantum physics does not make the universe any more mysterious than it was previously)
- And the Winner is... Many-Worlds! (the many-worlds interpretation wins outright given the current state of evidence)
- Quantum Mechanics and Personal Identity (the ontology of quantum mechanics, in which there are no particles with individual identities, rules out theories of personal continuity that invoke "the same atoms" as a concept)
My current plan calls for the quantum physics series to eventually be turned into one or more e-books.
- Probability is in the Mind: If you are uncertain about a phenomenon, this is a fact about your state of mind, not a fact about the phenomenon itself. There are mysterious questions but not mysterious answers. The map is not the territory.
- Reductionism: We build models of the universe that have many different levels of description. But so far as anyone has been able to determine, the universe itself has only the single level of fundamental physics - reality doesn't explicitly compute protons, only quarks.
- Joy in the Merely Real: If you can't take joy in things that turn out to be explicable, you're going to set yourself up for eternal disappointment. Don't worry if quantum physics turns out to be normal.
- Zombies! Zombies? and The Generalized Anti-Zombie Principle: Don't try to put your consciousness or your personal identity outside physics. Whatever makes you say "I think therefore I am", causes your lips to move; it is within the chains of cause and effect that produce our observed universe.
- 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?
Basic Quantum Mechanics:
- 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. Warning: Although a large faction of physicists agrees with this, it is not universally accepted. Stronger warning: I am not even going to present non-realist viewpoints until later, because I think this is a major source of confusion.
- 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. It is an experimentally testable fact that "Photon 1 here, photon 2 there" is the same configuration as "Photon 2 here, photon 1 there".
- 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.
- Identity Isn't In Specific Atoms, Three Dialogues on Identity: Given that there's no such thing as "the same atom", whether you are "the same person" from one time to another can't possibly depend on whether you're made out of the same atoms.
- 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.
- Which Basis Is More Fundamental?: The position basis can be computed locally in the configuration space; the momentum basis is not local. Why care about locality? Because it is a very deep principle; reality itself seems to favor it in some way.
- 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.
(At this point in the sequence, most of the mathematical background has been built up, and we are ready to evaluate interpretations of quantum mechanics.)
- 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, Decoherence is Falsifiable and Testable: (Note: Designed to be standalone readable.) 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.
(Now we depart from what is nailed down in standard physics, and enter into more speculative realms - particularly Julian Barbour's Machian timeless physics.)
- Mach's Principle: Anti-Epiphenomenal Physics: Could you tell if the whole universe were shifted an inch to the left? Could you tell if the whole universe was traveling left at ten miles per hour? Could you tell if the whole universe was accelerating left at ten miles per hour? Could you tell if the whole universe was rotating?
- Relative Configuration Space: Maybe the reason why we can't observe absolute speeds, absolute positions, absolute accelerations, or absolute rotations, is that particles don't have absolute positions - only positions relative to each other. That is, maybe quantum physics takes place in a relative configuration space.
- Timeless Physics: What time is it? How do you know? The question "What time is it right now?" may make around as much sense as asking "Where is the universe?" Not only that, our physics equations may not need a t in them!
- Timeless Beauty: To get rid of time you must reduce it to nontime. In timeless physics, everything that exists is perfectly global or perfectly local. The laws of physics are perfectly global; the configuration space is perfectly local. Every fundamentally existent ontological entity has a unique identity and a unique value. This beauty makes ugly theories much more visibly ugly; a collapse postulate becomes a visible scar on the perfection.
- Timeless Causality: Using the modern, Bayesian formulation of causality, we can define causality without talking about time - define it purely in terms of relations. The river of time never flows, but it has a direction.
- Timeless Identity: How can you be the same person tomorrow as today, in the river that never flows, when not a drop of water is shared between one time and another? Having used physics to completely trash all naive theories of identity, we reassemble a conception of persons and experiences from what is left. With a surprising practical application...
- Thou Art Physics: If the laws of physics control everything we do, then how can our choices be meaningful? Because you are physics. You aren't competing with physics for control of the universe, you are within physics. Anything you control is necessarily controlled by physics.
- Timeless Control: We throw away "time" but retain causality, and with it, the concepts "control" and "decide". To talk of something as having been "always determined" is mixing up a timeless and a timeful conclusion, with paradoxical results. When you take a perspective outside time, you have to be careful not to let your old, timeful intuitions run wild in the absence of their subject matter.
Rationality and Science:
(Okay, so it was many-worlds all along and collapse theories are silly. Did first-half-of-20th-century physicists really screw up that badly? How did they go wrong? Why haven't modern physicists unanimously endorsed many-worlds, if the issue is that clear-cut? What lessons can we learn from this whole debacle?)
- The Failures of Eld Science: A short story set in the same world as Initiation Ceremony. Future physics students look back on the cautionary tale of quantum physics.
- The Dilemma: Science or Bayes?: The failure of first-half-of-20th-century-physics was not due to straying from the scientific method. Science and rationality - that is, Science and Bayesianism - aren't the same thing, and sometimes they give different answers.
- Science Doesn't Trust Your Rationality: The reason Science doesn't always agree with the exact, Bayesian, rational answer, is that Science doesn't trust you to be rational. It wants you to go out and gather overwhelming experimental evidence.
- When Science Can't Help: If you have an idea, Science tells you to test it experimentally. If you spend 10 years testing the idea and the result comes out negative, Science slaps you on the back and says, "Better luck next time." If you want to spend 10 years testing a hypothesis that will actually turn out to be right, you'll have to try to do the thing that Science doesn't trust you to do: think rationally, and figure out the answer before you get clubbed over the head with it.
- Science Isn't Strict Enough: Science lets you believe any damn stupid idea that hasn't been refuted by experiment. Bayesianism says there is always an exactly rational degree of belief given your current evidence, and this does not shift a nanometer to the left or to the right depending on your whims. Science is a social freedom - we let people test whatever hypotheses they like, because we don't trust the village elders to decide in advance - but you shouldn't confuse that with an individual standard of rationality.
- Do Scientists Already Know This Stuff?: No. Maybe someday it will be part of standard scientific training, but for now, it's not, and the absence is visible.
- No Safe Defense, Not Even Science: Why am I trying to break your trust in Science? Because you can't think and trust at the same time. The social rules of Science are verbal rather than quantitative; it is possible to believe you are following them. With Bayesianism, it is never possible to do an exact calculation and get the exact rational answer that you know exists. You are visibly less than perfect, and so you will not be tempted to trust yourself.
- Changing the Definition of Science: Many of these ideas are surprisingly conventional, and being floated around by other thinkers. I'm a good deal less of a lonely iconoclast than I seem; maybe it's just the way I talk.
- Faster Than Science: Is it really possible to arrive at the truth faster than Science does? Not only is it possible, but the social process of science relies on scientists doing so - when they choose which hypotheses to test. In many answer spaces it's not possible to find the true hypothesis by accident. Science leaves it up to experiment to socially declare who was right, but if there weren't some people who could get it right in the absence of overwhelming experimental proof, science would be stuck.
- Einstein's Speed: Albert was unusually good at finding the right theory in the presence of only a small amount of experimental evidence. Even more unusually, he admitted it - he claimed to know the theory was right, even in advance of the public proof. It's possible to arrive at the truth by thinking great high-minded thoughts of the sort that Science does not trust you to think, but it's a lot harder than arriving at the truth in the presence of overwhelming evidence.
- That Alien Message: Einstein used evidence more efficiently than other physicists, but he was still extremely inefficient in an absolute sense. If a huge team of cryptographers and physicists were examining a interstellar transmission, going over it bit by bit, we could deduce principles on the order of Galilean gravity just from seeing one or two frames of a picture. As if the very first human to see an apple fall, had, on the instant, realized that its position went as the square of the time and that this implied constant acceleration.
- My Childhood Role Model: I looked up to the ideal of a Bayesian superintelligence, not Einstein.
- Einstein's Superpowers: There's an unfortunate tendency to talk as if Einstein had superpowers - as if, even before Einstein was famous, he had an inherent disposition to be Einstein - a potential as rare as his fame and as magical as his deeds. Yet the way you acquire superpowers is not by being born with them, but by seeing, with a sudden shock, that they are perfectly normal.
- Class Project: From the world of Initiation Ceremony. Brennan and the others are faced with their midterm exams.
- Why Quantum?: Why do a series on quantum mechanics? Some of the many morals that are best illustrated by the tale of quantum mechanics and its misinterpretation.