Presentation on theme: "Scott Aaronson (MIT) Aharonov 80 th Birthday Conference, Anaheim, CA The Ghost in the Quantum Turing Machine 1011001 READ/ WRITE HEAD."— Presentation transcript:
Scott Aaronson (MIT) Aharonov 80 th Birthday Conference, Anaheim, CA The Ghost in the Quantum Turing Machine READ/ WRITE HEAD
Happy 81 st -to-Last Antibirthday, Yakir! Stuff I considered talking about: Postselection in quantum computing Quantum computing with closed timelike curves Psi-epistemic theories in quantum mechanics The information content of quantum states CRAZY FREE WILL TALK
The Universe is the interior of the light cone of the Creation. Science is a differential equation. Religion is a boundary condition In addition to Yakirs 80 th birthday, this year we celebrate Alan Turings 100 th Heres a postcard Turing sent Robin Gandy in March 1954, months before his death: Turing is best-known as the founder of computer science, but he also worried about many of the same issues Yakir does (including the foundations of QM)…
This Talk Building on previous ideas, Ill explore an unusual perspective on the ancient physics and free will debateone that really would put free will in the universes boundary conditions Determinist? Robot? No problem! Whenever I say free will, you can assume Im merely investigating some sort of effective free will Ill place a much higher premium on being interesting than on being right Thanks My version of free will will be stronger than the usual compatibilist kind, but compatibilists might still find much of what I have to say compatible with their views
What is free will? Whats determinism? Theres no free will, says the philosopher / To hang is most unjust. Theres no free will, assent the officers / We hang because we must. Ambrose Bierce Ill try to sidestep the moral, legal, and theological issues that have dominated the free-will debate for ~2500 years… Basic observation: If you stretch the notion of determination far enough, you can make anything trivially determined! (e.g., by Gods Encyclopedia, which only He can read) So I dont think determinism even merits scientific interest (or grows fangs, or constitutes a credible threat to anyone), unless it involves in-principle predictability by devices consistent with physical law Cf. the debate around Bell inequality and superdeterminism
A Turing Test for Free Will? AMT 1950: I propose to consider the question, Can machines think? … The original question … I believe to be too meaningless to deserve discussion. Turings revised question: Are there imaginable digital computers which would do well in the imitation game? Do humans have free will? Revised question: Is it physically possible to build a machine that, given some humans environmental stimuli as an input feed, predicts that humans future choices to any desired accuracy and arbitrarily far into the futureat least in the probabilistic sense that radioactive decay is predictable, and without killing or drastically altering the human? My position: If the answer to this revised question is no, then theres not much more science could possibly do toward showing the universe is hospitable to free will! Conversely, if the answer is yes, then theres not much more science could possibly do toward showing it isnt.
Even if this prediction game were winnable, why should we care? Even if someone could predict which finger Id flick a few seconds in advance (cf. Libet et al.), that doesnt seem very threatening! More like a conjuring trick. (Also, they obviously couldnt tell me their prediction beforehand, since then Id just do the opposite!) The problem arises from what I call the… Predictor Principle: Once a predictor of your choices becomes reliable enough, we ought to regard it as simply another copy of youwith all the sci-fi consequences that would entail
Going on a dangerous mountain-climbing trip? Remember to back up your brain first! Want to visit Mars? Just fax yourself! (And have the original you painlessly euthanized … or not) Most scientists: brain = computer program John Searle: brain computer programbecause brains have mysterious, unspecified causal powers that mere programs lack My view: If theres a difference, the best place to look for it is almost certainly in computer programs physical copyability (a property that isnt obviously shared by brain states!)
Knightian Uncertainty Lots of people have claimed that the randomness of quantum measurements, as chaotically amplified by brain activity, could already make humans physically unpredictable in the relevant way. Alas, those people are wrong! Economists fancy term for uncertainty that cant even be objectively quantified using probabilities (also shows up as nondeterminism in computer science) What wed need instead is
But where, in a law-governed universe, could Knightian uncertainty possibly be hiding? I think theres exactly one possibility that physics hasnt persuasively closed off… The No-Cloning Theorem What was the pure or mixed state at the Big Bang? What are the relevant indexical facts? (Where are you in the multiverse?) Lack of knowledge of the initial conditions + Illustrative applications: Quantum key distribution Quantum money Copy-protected quantum software
To make the issue as concrete as possible: BIG BANGTIME PMD Microscopic neural event (e.g., opening of a sodium-ion channel) Past macroscopic determinants (PMDs): observables that could have been non-invasively measured long before the event, and that influence its probability Can every event today be grounded in PMDs, from which we can use quantum mechanics to calculate its probability? Or do some causal chains go all the way back to the Big Bang without terminating at PMDs?
The Freedom from the Inside Out (FIO) Perspective (Hoefer 2002, Stoica 2008) The FIO Answer: Recall that the known equations of physics are all time-reversible, making forward-in-time causation seem just as incomprehensible as the opposite! On the modern view, causality is an emergent phenomenon, associated with the Second Law Look, isnt it anti-scientific insanity to imagine that our choices today could affect (or even be nontrivially correlated with) the universes microstate at the Big Bang? But if were talking about undecohered qubits left over the Big Bang, then theres no entropy increase anywayso why not annotate the static Block Universe with backwards causal arrows in those cases? BLOCK UNIVERSE ?
The Harmonization Problem Hoefer (2002) raised the obvious problem: Once we let causal arrows point backward in time, (say) from events today to the microstate at the Big Bang, how do know a globally-consistent solution even exists? How do we prevent causal cyclesi.e., closed timelike curves? In this account, the answer is simple: Macrofact: Whether a Stegosaurus kicked a particular rock 150 million years ago Microfact: The polarization state of some particular photon of the CMB radiation Retrocausal explanations are allowed only for microfacts, not for macrofacts. Together with No-Cloning, ensures CTCs dont arise
The Initial-State Objection Dont we know that the initial state at the Big Bang was basically thermal, and hence couldnt have encoded any interesting info? Quantum field theorists thought they knew black hole event horizons were thermal, but AdS/CFT suggests otherwise! More broadly, weve learned that many physical theories have both bulk and boundary formulations, and that the boundary picture can not only nontrivially encode everything that happens in the bulk, but even clarify issues that were obscure in the bulk picture (e.g., why is the entropy upper-bounded by the surface area?) Famously, the Second Law implies the Big Bang state must have been maximally far from thermal, for not-yet-understood reasons Inflation doesnt solve this problem unless Hilbert space dimension can grow 3 POSSIBLE RESPONSES:
The Gerbil Objection Why doesnt the following system have Knightian free will as discussed in this talk? If we say its because the gerbil and AI-program are separable, then why arent the brains Knightian noise and its cognitive information-processing similarly separable? Well, transferring a brain into silicon certainly seems more invasive than unhooking the gerbil box! But honestly I dont know AI PROGRAM ABLE TO PASS TURING TEST Gerbil in a box, whose movements provide Knightian indeterminism SENSORS USB LINK
The Many-Worlds Objection Consider an observer (e.g., Wigners friend) being asked lots of questions in superposition: Even if microscopic details of the initial state could somehow affect one observers answer, how could the same details affect all the Everett branches independently of one another? Conclusion: If we want to accept this account, then we have to assume that there exists irreversible decoherence (whatever its sourcegravity?), and that such decoherence is a necessary condition for free will
The Advertiser Objection (Generic objection to any account of free will) Humans are depressingly predictable in practiceadvertisers, salespeople, seducers, demagogues all take advantage of this On the other side of the intuitive ledger, we need to put the conspicuous failure of psychics, stock market analysts, pundits, etc. to predict what individuals or even entire populations will do Response: Its obvious that humans are somewhat predictable; the only question at issue is whether the prediction accuracy can approach that of physics (Of course, forecasters typically excel at explaining why whatever choices were made were inevitable!)
Penrose Lite The view Im discussing would affirm Roger Penroses core belief in a link between the mysteries of mind and those of modern physics, while denying almost all of the particulars… No appeal to Gödel, or to the Platonic perceptual abilities of human mathematicians No barrier to a digital computer passing the Turing Test (at most, a barrier to simulating a particular person) Nothing exotic supposed about the biology of the brain (e.g., no long-range entanglement or gravity-sensitive microtubules) No uncomputable quantum-gravity dynamics No attempt to explain consciousness (which incidentally seems logically impossible to me, regardless of what physics is assumed!)
Application to the Boltzmann Brain Problem On my account, a necessary condition for freely-willed observerhood would be having the right kind of causal relationship to the universes initial state. Boltzmann brains wouldnt count as observers because they wouldnt have that relationship I exist
Is This Picture Falsifiable? Predictions, if you want to take it seriously: Psychology will never become physics (the accuracy of brain- prediction wont asymptotically approach that of comet-prediction) (Ordinary) quantum uncertainty can indeed be chaotically amplified by brain activity on reasonable timescales Some of the relevant quantum states cant be grounded in PMDs, but only traced back to the early universe A quantum-gravitational description of the early universe wont reveal it to have a simply-describable pure or mixed state Irreversible decoherence, whatever its source, will forever prevent us from doing Wigners friend experiments on uncontroversially-conscious subjects
Conclusions David Deutschs momentous dichotomy: Either a given technology is possible, or else theres some principled reason why its not possible. When it comes to perfect brain-predictors, I think either horn of this dichotomy would have crazy consequences! In other words, theres no safe, conservative option Key question: To what extent can our decisions be probabilistically grounded in past macroscopic determinants? Reason for hope: This is an empirical question! Future discoveries in physics, biology, and other fields could very plausibly tell us more