Monday, August 15, 2016
Quantum mechanics, determinism, and omniscience
by Daniel Ranard.
"Every choice we make is totally predetermined," you hear someone say, a little too loudly, from a nearby table at the coffee shop. "If we had a big enough supercomputer, and we knew the exact configuration of all the atoms that make up a person and their surroundings, we could calculate their future perfectly!" This sounds like an excited young scientist or amateur futurist. But imagine replacing "supercomputer" with "super-mind," and it sounds more like the French polymath Laplace, writing about determinism 200 years ago. In fact, as far back as antiquity, you can find philosophers speculating that all motion follows rules.
I imagine that humankind first witnessed the power of this idea when astronomers predicted the motion of the planets, leading to an image of the heavens as an orderly machine. Newton brought the laws of the heavens down to earth, positing that all matter follows the same rules, from celestial bodies to falling rocks. His theories made plausible the image of a clockwork universe, ticking in accordance with mechanical law. At the time, it was difficult or even ridiculous to imagine that living things followed the same rules, and many believed that life had its own spark or guiding force, apart from the mechanistic laws. But advances in biology and chemistry slowly convinced scientists that life is part of the clockwork, too. By the late 1800s, this idea permeated scientific circles and even literature–Dostoevsky's characters raged against the possibility that mathematics determined their decisions.
Since Laplace's time, our physical theories have changed, and our philosophical ideas have grown more sophisticated. With our new knowledge, what could we say to a nineteenth century thinker, existentially worried about living in a clockwork universe? What could we say, for example, to Dostoevsky's "Underground Man" in Notes from the Underground? He's concerned about a world where all human actions are "tabulated according to... laws, mathematically, like tables of logarithms." Phrasing the question in terms of free will and scientific determinism, many philosophers today declare that there's no need to pick between the two—free will and determinism are compatible. Other philosophers see the compatabilist argument as a mere redefinition of terms. But in addition to the philosophical question, there's also a more scientific question. According to modern scientific theories, is it true that the world behaves mechanistically and allows perfect prediction?
Two major ideas shape our new understanding of this question. The first is the phenomenon of chaos. As scholars like Laplace already understood, calculating the trajectory of a physical system can be extremely difficult. If you knew the positions and velocities of two planets in an otherwise empty sky, you could calculate their motion well into the future. But if you added just one more planet, the calculation becomes nearly impossible, even for a computer. You would need to know the initial positions with extraordinary precision, and any small error would become amplified to yield a wildly incorrect answer. Systems like this are called chaotic, and today we understand that chaotic systems abound in nature and within the human body.
In a sense, this discussion of chaos already answers the question. As a practical matter, it seems like we can't build a supercomputer or any other machine that predicts individual behavior with even modest accuracy. On the other hand, it might not be reassuring to know that such a machine is simply impractical. I imagine the Underground Man would still be concerned that all of his atoms follow mathematical equations, whether or not anyone will ever manage to work out the math.
The second major factor to shape our new understanding of determinism is quantum mechanics, which underpins all of modern physics. Here, physicists usually point out that quantum mechanics rarely makes exact predictions about the future, instead specifying only probabilities: there's a 90% chance the electron will go one way, and a 10% chance it will go the other way. So, strictly speaking, quantum mechanics is simply not deterministic. For me, though, this claim carries little philosophical impact. If we told the Underground Man that no matter how hard he tries to foil us, we could still predict whether he turns left or right 90% accuracy, I suspect he would remain unhappy.
However, if quantum mechanics is correct, there's more to say. Laplace already understood it would be difficult to gather enough information about a system to accurately predict its future. But what if there were a fundamental physical law revealing it's actually impossible to make good predictions, even probabilistic predictions, no matter our feats of engineering?
In order to predict the future of a system, first we need to know its current physical configuration – its state. In particular, the "quantum state" of a system specifies the quantum details of the state, dictating the probabilities for how the system will change over time. If you locked a person in an isolated room to remove the effect of outside influences, and you knew the exact quantum state of the person and the room, then you could hypothetically predict probabilities for everything that happens next.
The trouble is that quantum mechanics implies it's actually impossible to learn the exact quantum state of a system without changing or destroying it. In other words, there could never be a futuristic, Star Trek-like technology that performs a 3D scan of a room to discern the exact quantum state, without altering the state of the person and the room . The reason to care about whether we alter the room in the process is that, intuitively, it's "cheating" to make predictions about something by altering it. For instance, if you gave me a particular rock and asked me to determine its exact quantum state, it would be cheating for me to first throw out the rock, then create a new, slightly different rock with some specified state, and finally say: "Sorry, I modified the rock a bit. But now I know what the state is, so I can predict exactly how it ages over time" .
I doubt this is a large consolation to the Underground Man. Ultimately, modern physicists would claim his behavior is governed by equations. But perhaps it's a small comfort that he has a sort of unbreakable lock on the information about his exact internal state. No one could ever discern this information and use it to make predictions about him, at least not without altering the man himself .
This discussion comes with an odd caveat, though. It's impossible to learn the exact state of a system, assuming you don't already know the state. But if you were to design and build a system yourself, you could create it in some specified state. In other words, you would know the state of the system because you made it. If you built a machine that meticulously crafted a human being, cell by cell, in some specified configuration, then you really could know the exact quantum state of the person. No one else but you would know the state, unless you told them or they saw the design you used. You alone would know state, and you could use that knowledge to make ideal probabilistic predictions. So in a sense, the Underground Man only needs to worry about the knowledge of his maker.
It's a bit of a whimsical conclusion. It's also ironic, given the history of philosophy. Because before nineteenth century thinkers were worried about the conflict between physical law and free will, medieval philosophers like Anselm and Thomas Aquinas faced similar questions for different reasons. They wondered about the consequences of an omniscient God. If the Creator knew all that would happen, how could human beings be free? Maybe, ultimately, the Underground Man could confer with the old philosophers for his answer.
 I'm referring to the fact that you can't determine an unknown quantum state without destructive measurements, along with the no-cloning theorem, which implies you could not create a copy of a state in order to simulate it.
 Of course, there's some subtlety here I won't delve into. For instance, if you could learn the state of the rock and predict its future by giving it just a slight tap, barely altering the surface, would that count as predicting the future of the original rock?
 Again, there are many subtleties here. How much does quantum uncertainty actually affect behavior? And even if you can't directly learn the quantum state of a system, are there "classical records" elsewhere that reveal the state – as is the case, for instance, when someone prepares a system in a specific state and then writes down what the state is? Scott Aaronson explores this second question at length through a slightly different lens, in his wonderful article "The ghost in the quantum Turing machine."
Posted by Daniel Ranard at 12:35 AM | Permalink