The Ghost in the Quantum Turing Machine

The Ghost in the Quantum Turing Machine

Scott Aaronson

"The Universe is the interior of the Light Cone of Creation.

Science is a differential equation.

Religion is boundary condition."

  -Alan Turing

In honor of Alan Turing’s hundredth birthday, I unwisely set out some thoughts about one ofTuring’s obsessions throughout his life, the question of physics and free will. I focus relatively narrowly on a notion that I call “Knightian freedom”: a certain kind of in-principle physical un-predictability that goes beyond probabilistic unpredictability. Other, more metaphysical aspects of free will I regard as possibly outside the scope of science.I examine a viewpoint, suggested independently by Carl Hoefer, Cristi Stoica, and even Turing himself, that tries to find scope for “freedom” in the universe’s boundary conditions rather than in the dynamical laws. Taking this viewpoint seriously leads to many interesting conceptual problems. I investigate how far one can go toward solving those problems, and along the way, encounter (among other things) the No-Cloning Theorem, the measurement problem, decoherence, chaos, the arrow of time, the holographic principle, Newcomb’s paradox,Boltzmann brains, algorithmic information theory, and the Common Prior Assumption. I also compare the viewpoint explored here to the more radical speculations of Roger Penrose.The result of all this is an unusual perspective on time, quantum mechanics, and causation,of which I myself remain skeptical, but which has several appealing features. Among other things, it suggests interesting empirical questions in neuroscience, physics, and cosmology; and takes a millennia-old philosophical debate into some underexplored territory.

Summary based on Aaronson giving a talk ->

Aaronson on QM and Free Will

S.Esser

...Free will is then defined (for the purposes of his talk) as unpredictability (even in terms of probability distribution) by any actual or conceivable technologies. Aaronson describes a “prediction game” whereby a future computer analyzes one's entire brain/body/immediate environment, and predicts your answer to questions (actually the probability distribution of your answers).

Now, in assessing whether this will be possible, there is a key discovery we need to derive from science, which is: in a human brain, do quantum level states impact macroscopic (say, neuronal) behavior?...

...The next key point is that if this were to be true, then the quantum no-cloning theorem would prevent prediction of human behavior by any future technology (assuming quantum mechanics is true). We cannot replicate all the relevant physical states.

Then our behavior is described by “Knightian uncertainty”, i.e. uncertainty that one can’t even accurately quantify using probabilities. The prediction game is unwinnable.

Even if the prediction game is unwinnable in this way...the world would still be (stochastically) determined in spite of this result. It would just be that the computer couldn’t know the initial condition of the universe.

But here’s something weird. He says: “If the Prediction Game was unwinnable, then it would seem just as logically coherent to speak about our decisions determining the initial state, as about the initial state determining our decisions!” The situation could be something like this: “…there are qubits all over the world today which have been in states of Knightian uncertainty since the Big Bang. Maybe we should call them ‘willbits’. By making a decision, you can retroactively determine the quantum state of one of these willbits. But then once you determine it, that’s it! There’s no going back.”

For more context ->

PHYS771 Lecture 18: Free Will 

Aaronson

I have to rattle you up somehow, so let's throw quantum, relativity and free will all into the stew. There was a paper recently by Conway and Kochen called The Free Will Theorem, which got a fair bit of press. So what is this theorem? Basically, Bell's Theorem, or rather an interesting consequence of Bell's Theorem. It's kind of a mathematically-obvious consequence, but still very interesting. You can imagine that there's no fundamental randomness in the universe, and that all of the randomness we observe in quantum mechanics and the like was just predetermined at the beginning of time. God just fixed some big random string, and whenever people make measurements, they're just reading off this one random string. But now suppose we make the following three assumptions:

1. We have the free will to choose in what basis to measure a quantum state. That is, at least the detector settings are not predetermined by the history of the universe.
   
2. Relativity gives some way for two actors (Alice and Bob) to perform a measurement such that in one reference frame Alice measures first, and in another frame Bob measures first.
   
3. The universe cannot coordinate the measurement outcomes by sending information faster than light.
   

Given these three assumptions, the theorem concludes that there exists an experiment---namely, the standard Bell experiment---whose outcomes are also not predetermined by the history of the universe. Why is this true? Basically, because supposing that the two outcomes were predetermined by the history of the universe, you could get a local hidden-variable model, in contradiction to Bell's Theorem. You can think of this theorem as a slight generalization of Bell's Theorem: one that rules out not only local hidden-variable theories, but also hidden-variable theories that obey the postulates of special relativity. Even if there were some non-local communication between Alice and Bob in their different galaxies, as long as there are two reference frames such that Alice measures first in one and Bob measures first in the other, you can get the same inequality. The measurement outcomes can't have been determined in advance, even probabilistically; the universe must "make them up on the fly" after seeing how Alice and Bob set their detectors. I wrote a review of Steven Wolfram's book a while ago where I mentioned this, as a basic consequence of Bell's Theorem that ruled out the sort of deterministic model of physics that Wolfram was trying to construct. I didn't call my little result the Free Will Theorem, but now I've learned my lesson: if I want people to pay attention, I should be talking about free will! Hence this lecture.