“If the atoms never swerve so as to originate some newmovement that will snap the bonds of fate, the everlasting sequence of cause andeffect—what is the source of the free will possessed by living thingsthroughout the earth?”—Titus Lucretius Carus, Roman philosopher and poet, 99–55BC.
Human free will might seem like the squishiest ofphilosophical subjects, way beyond the realm of mathematical demonstration. Buttwo highly regarded Princeton mathematicians,John Conway and Simon Kochen, claim to have proven that if humans have even thetiniest amount of free will, then atoms themselves must also behaveunpredictably.
The finding won’t give many physicists a moment’s worry,because traditional interpretations of quantum mechanics embraceunpredictability already. the best anyone can hope to do, quantum theory says,is predict the probability that aparticle will behave in a certain way.
But physicists all the way back to Einstein have beenunhappy with this idea. Einstein famously grumped, “God does not play dice.”And indeed, ever since the birth of quantum mechanics, some physicists haveoffered alternate interpretations of its equations that aim to get rid of thisindeterminism. the most famous alternative is attributed to the physicist DavidBohm, who argued in the 1950s that the behavior of subatomic particles isentirely determined by “hidden variables” that cannot be observed.
Conway and Kochen say this search is hopeless, and theyclaim to have proven that indeterminacy is inherent in the world itself, ratherthan just in quantum theory. and to Bohmians and other like-minded physicists,the pair says: give up determinism, or give up free will. Even the tiniest bitof free will.
Their argument starts with a proof Kochen created with ErnstSpecker 40 years ago. Subatomic particles have a property called “spin,” whichoccurs around any axis. Experiments have shown that a type of subatomicparticle called a “spin 1 particle” has a peculiar property: Choose threeperpendicular axes, and prod the spin 1 particle to determine whether its spinaround each of those axes is 0. Precisely one of those axes will have spin 0and the other two will have non-zero spin. Conway and Kochen call this the1-0-1 rule.
Spin is one of those properties physicists can’t predict inadvance, before prodding. Still, one might imagine that the particle’s spinaround any axis was set before anyone ever came along to prod it. That’scertainly what we ordinarily assume in life. We don’t imagine, say, that afence turned white just because we looked at it — we figure it was white allalong.
But Kochen and Specker showed that this assumption — thatthe fence was white all along — can’t hold in the bizarre world of subatomicparticles. they used a pure mathematical argument to show that there is no waythe particle can choose spins around every imaginable axis in a way that isconsistent with the 1-0-1 rule. Indeed, there is a set of just 33 axes that areenough to force the particle into a paradox. it could choose spins around thefirst 32 axes that conform with the rule, but for the last, neither 0 nornon-zero would do. Choosing zero spin would create a set of three perpendicularaxes with two zeroes, and choosing non-zero spin would create a different setof three perpendicular axes with three non-zeroes, breaking the 1-0-1 ruleeither way.
This means that the particle cannot have a definite spin inevery direction before it’s measured, Kochen and Specker concluded. if it did,physicists would be able to occasionally observe it breaking the 1-0-1 rule,which never happens. Instead, it must “decide” which spin to have on the fly.
Conwaycompares the situation to the game “Twenty questions.” if you play the gamefairly, you decide upfront on a single object and honestly answer each of thequestions, hoping your opponent won’t deduce what you chose. But a cleverplayer could also cheat, changing the object partway through. In that case, hisanswers aren’t determined in advance. the particle, Kochen and Specker showed,is like a cheating player. they found it out by showing that no single objectsatisfies all the “questions” (or all 33 axes) at once.
But there’s another possible interpretation. Perhaps theparticle’s spin is completely determined — but depends on something else aboutthe state of the universe. That would be like a player in “Twenty Questions”who has decided his object is a donkey whenever his opponent starts a questionwith “Is,” and that his object a horse otherwise (or using any other arbitrarybut consistent rule). for example, if his opponent asked, “Is it something withbig ears?” he would say “yes,” but if his opponent asked, “Does it have bigears?” he’d say “no.” In that case, his answers are predetermined even thoughhe has no single object in mind.
Conway and Kochen say that they have now proven thatparticles’ responses can’t be pre-determined, even within this possibleinterpretation. “We can really prove that there’s no algorithm, no way that theparticle can give an answer that is unique and can be specified ahead of time,”Conway says.”I’m still amazed that we can actually manage to prove that.”
They concocted a thought experiment for their proof. it ispossible to entangle two spin 1 particles so that their spins are identicalalong every possible axis and will remain so, even if they are separated veryfar apart. Entangle two particles thisway, and then send a physicist named Alicewith one of them to Mars and leave the other with a physicist named Bob onEarth. That will prevent information from passing between the physicists or theparticles, according to relativity theory. Alice and Bob each prod theirparticles along some axis, which they freely choose. if Alice and Bob happen tochoose the same axis, they’ll get the same answer.
Now, imagine that the particles are like the “20 questions”player whose object is sometimes a donkey and sometimes a horse, with a fixedrule deciding when to answer with which animal. whatever the rule is, it appliesto each of the entangled particles and will cause them to have the same spins.It’s as if the “20 questions” player has been cloned, and both players areforced to give answers for the same animal.
But Conway and Kochen have shown this scenario is impossiblefor particles that are incommunicado. they invoked the old Kochen-Speckerparadox to show that if the spin 1 particle’s behavior is pre-determined sothat it isn’t allowed to “change its animal,” it won’t be able to give answersthat are consistent with the 1-0-1 rule. So if Alice and Bob are lucky in howthey choose their axes, they should be able to force the particles either todisagree or to violate the 1-0-1 rule — contrary to experimental evidence.
Kochen and Conway say the best way out of this paradox is toaccept that the particle’s spin doesn’t exist until it’s measured. But there’sone way to escape their noose: Suppose for a moment that Alice and Bob’s choiceof axis to measure is not a free choice. Then Nature could be conspiring toprevent them from choosing the axes that will reveal the violation of the rule.Kochen and Conway can’t rule that possibility out entirely, but Kochen says, “Aman on the street would say, ‘Don’t be ridiculous.’ a natural feeling is, ofcourse, that what we do, we do of our own free will. Not completely, butcertainly to the point of knowing we can choose what button to push in anexperiment.”
Ideally, a mathematical proof settles all uncertainty, butKochen and Conway haven’t yet managed to convince many of the physicists theyare addressing. “I’m not convinced,” says Sheldon Goldstein of RutgersUniversity, a Bohmian. he believes theargument implies nothing new, and he’s content with the notion that free willexists only effectively (not theoretically). he and his collaborators havespent many hours discussing these issues with the pair of mathematicians sinceKochen and Conwayfirst posted their result four years ago. their new version, posted onArxiv.org July 21, attempts to strengthen the result in light of criticisms.Still, mutual understanding has not yet come about. “It’s kind of depressingwhen people can’t communicate with each other,” Goldstein says. “We know that’strue in politics, but you’d think that wouldn’t be going on here.”
But Gerard ‘t Hooft of the University of Utrecht in theNetherlands, who won the Nobel Prize in physics in 1999, says the pair’sconclusions are legitimate — but he chooses determinism over free will. “As adetermined determinist I would say that yes, you bet, an experimenter’s choicewhat to measure was fixed from the dawn of time, and so were the properties ofthe thing he decided to call a photon,” ‘t Hooft says. “If you believe indeterminism, you have to believe it all the way. No escape possible. Conway andKochen have shown here in a beautiful way that a half-hearted belief inpseudo-determinism is impossible to sustain.”
