Scott Aaronson (MIT)Aharonov 80th Birthday Conference, Anaheim, CA

The Ghost in the Quantum Turing Machine

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Happy 81st-to-Last Antibirthday, Yakir!

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Stuff I considered talking about:Postselection in quantum computingQuantum computing with closed timelike curvesPsi-epistemic theories in quantum mechanicsThe information content of quantum states

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“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 Yakir’s 80th birthday, this year we celebrate Alan Turing’s 100th

Here’s 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 TalkBuilding on previous ideas, I’ll explore an unusual perspective on the ancient “physics and free will” debate—one that really would put “free will” in the universe’s boundary conditions

Determinist? Robot? No problem! Whenever I say “free will,” you can assume I’m merely investigating some sort of “effective” free will

I’ll 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? What’s determinism?

There’s no free will, says the philosopher / To hang is most unjust.There’s no free will, assent the officers / We hang because we must.—Ambrose Bierce

I’ll 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 God’s Encyclopedia, which only He can read)

So I don’t 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.”

Turing’s 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 human’s environmental stimuli as an input feed, predicts that human’s future choices to any desired accuracy and arbitrarily far into the future—at 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 there’s not much more science could possibly do toward “showing the universe is hospitable to free will”! Conversely, if the answer is yes, then there’s not much more science could possibly do toward showing it isn’t.

My position: If the answer to this revised question is no, then there’s not much more science could possibly do toward “showing the universe is hospitable to free will”! Conversely, if the answer is yes, then there’s not much more science could possibly do toward showing it isn’t.

Even if this “prediction game” were winnable, why should we care?

Even if someone could predict which finger I’d flick a few seconds in advance (cf. Libet et al.), that doesn’t seem very threatening! More like a conjuring trick.

(Also, they obviously couldn’t tell me their prediction beforehand, since then I’d 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 you—with 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 program—because brains have mysterious, unspecified “causal powers” that mere programs lack

My view: If there’s a difference, the best place to look for it is almost certainly in computer programs’ physical copyability

(a property that isn’t 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 can’t even be objectively quantified using probabilities

(also shows up as nondeterminism in computer science)

willfree2 p

What we’d need instead is

But where, in a law-governed universe, could Knightian uncertainty possibly be hiding? I think there’s exactly one possibility that physics hasn’t 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 distributionQuantum money

Copy-protected quantum software

To make the issue as concrete as possible:

BIG BANG

TIM

E PMD

PMD 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, isn’t it anti-scientific insanity to imagine that our choices today could “affect” (or even be nontrivially correlated with) the universe’s microstate at the Big Bang?

But if we’re talking about undecohered qubits left over the Big Bang, then there’s no entropy increase anyway—so 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 cycles—i.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 don’t arise

The Initial-State ObjectionDon’t we know that the initial state at the Big Bang was basically thermal, and hence couldn’t have encoded any interesting info?

Quantum field theorists thought they knew black hole event horizons were thermal, but AdS/CFT suggests otherwise!

More broadly, we’ve 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 doesn’t solve this problem unless Hilbert space dimension can grow

3 POSSIBLE RESPONSES:

The Gerbil ObjectionWhy doesn’t the following system have “Knightian free will” as discussed in this talk?

If we say it’s because the gerbil and AI-program are “separable,” then why aren’t the brain’s “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 don’t know

AI PROGRAM ABLE TO PASS TURING TEST

Gerbil in a box, whose movements provide Knightian

indeterminism

SENSO

RS

USB LINK

The Many-Worlds ObjectionConsider an observer (e.g., Wigner’s friend) being asked lots of questions in superposition:

Even if microscopic details of the initial state could somehow affect one observer’s 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 source—gravity?), and that such decoherence is a necessary condition for ‘free will’

lsmicrodetai11 N

OqOq NN

The Advertiser Objection(Generic objection to any account of free will)

Humans are depressingly predictable in practice—advertisers, 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: It’s 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 I’m discussing would affirm Roger Penrose’s 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 universe’s initial state. Boltzmann brains wouldn’t count as observers because they wouldn’t 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 won’t 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 can’t be “grounded” in PMDs, but only traced back to the early universe

A quantum-gravitational description of the early universe won’t reveal it to have a simply-describable pure or mixed state

Irreversible decoherence, whatever its source, will forever prevent us from doing “Wigner’s friend” experiments on uncontroversially-conscious subjects

ConclusionsDavid Deutsch’s “momentous dichotomy”:

Either a given technology is possible, or else there’s some principled reason why it’s not possible.

When it comes to perfect brain-predictors, I think either horn of this dichotomy would have “crazy” consequences! In other words, there’s 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