Zeeya Merali Is Science Compatible with Our Desire for Freedom? Barcelona meeting May 2010

What’s At Stake? Proof of the Free Will Theorem Implications: Deterministic Machines, Random Machines or Free Agents? Image:

Image: “It’s not the mathematics that loses other physicists. It’s the metaphysical worry about free will. Why worry at all about a notion as flimsy as ‘free will’ in a theory of physics?” – Gerard ’t Hooft

2006: John Conway and Simon Kochen publish their Free Will Theorem: If humans have free will, then so too do elementary particles. Bad news for deterministic alternatives to quantum mechanics – they rob us of free will. Is Science Compatible with Our Desire for Freedom? Barcelona 2010

Three axioms: SPIN, TWIN and FIN. SPIN: If you measure the spin of a particle along three perpendicular directions, you will always get 1, 0 and 1. TWIN: If Alice measures the spin for particle A along three perpendicular axes, then Bob will measure the same values if he performs the same measurement on twinned particle B, along the same axes. FIN: Information cannot travel faster than the speed of light. Is Science Compatible with Our Desire for Freedom? Barcelona 2010

Image courtesy of Jan -Åke Larsson The SPIN axiom can be broken down: Rule 1: Opposite directions (dots on the particle) always have the same spin value. Rule 2: Two perpendicular directions cannot both be 0. Rule 3: Three perpendicular directions cannot all be 1.

Is Science Compatible with Our Desire for Freedom? Barcelona 2010 Uses SPIN (1, 0, 1 rule) Proves that it is impossible to pre-assign consistent spin values along 33-axes passing through particle. Always hit a paradox.

Image courtesy of Jan -Åke Larsson Choose one of the axes to be green (spin 0). By Rule 2, all perpendicular axes are red (spin 1).

Image courtesy of Jan -Åke Larsson Choose one red axis on equator. Two directions on 45° latitude are perpendicular to this. Rule 2: One must be green. Set all perpendicular directions red.

Image courtesy of Jan -Åke Larsson Colour another axis green. All perpendicular directions are red.

Image courtesy of Jan -Åke Larsson Lather, rinse, repeat: Set another axis green and perpendicular axes red. Some red axes are now perpendicular to each other. Rule 3: Third perpendicular direction forced to be green (marked green/black)

Image courtesy of Jan -Åke Larsson Turn one green/black dot green. Rule 2: Another perpendicular direction turns red. Rule 3: Forces a new green direction (marked green/black).

Image courtesy of Jan -Åke Larsson Lather, rinse, repeat. Turn green/black axis green. New axis turns red. New axis turns green/black.

Image courtesy of Jan -Åke Larsson And again...

Image courtesy of Jan -Åke Larsson And again...

Image courtesy of Jan -Åke Larsson And again...

Image courtesy of Jan -Åke Larsson And again... Turn next green/black axis green. Forces the remaining green/black axis to be red. CONTRADICTION because red must also be green (here marked yellow/black!).

Is Science Compatible with Our Desire for Freedom? Barcelona 2010 K-S Paradox proves that you cannot simply pre- set spin values along all directions. Like playing 20 questions. Fine for QM “cheats”, setting spin on-the-fly. Bad news for “honest” deterministic theories. Nature’s conspiracy?!

Image: K-S paradox does not rule out a complex instruction booklet for assigning spin. Sneaky 20 Questions, where the order of questions matters.

Is Science Compatible with Our Desire for Freedom? Barcelona 2010

Carry out two TWINned K-S style experiments, one by Alice on Earth (measures three axes), one by Bob on Mars (measures one axis). Instruction booklet could potentially help us set pre- determined spin values for Bob’s particle. Complex instructions could be related to Alice’s choice of axes, Bob’s axis, order of Alice’s measurements... Want to prove this complex rulebook won’t help explain how Bob’s particle’s spin result could be predetermined. Is Science Compatible with Our Desire for Freedom? Barcelona 2010

FIN: Alice and Bob are so far apart that Alice’s choices can’t influence Bob’s results. So Bob’s result only depends on his axis. TWIN: If Bob chooses one of the same three axes that Alice measures, he’d get the same result she would. SPIN: Alice’s results must obey 1, 0, 1. By TWIN, Bob’s result is also constrained. K-S Paradox: Bob’s result cannot obey SPIN and be predetermined. Is Science Compatible with Our Desire for Freedom? Barcelona 2010

If an experimenter ’s choice of which particle axis to measure is not entirely predetermined by events in her past history, then the response of the particle is also not predetermined by events in its past history. Is Science Compatible with Our Desire for Freedom? Barcelona 2010

Free? OK Will?... “Quantum randomness as the basis for free will doesn't really give us control over our actions. We're either deterministic machines, or we're random machines. That's not much of a choice.” – Tim Maudlin Is Science Compatible with Our Desire for Freedom? Barcelona 2010

The opposite of determinism is not randomness. Both determinism and randomness sit in the same camp, neither gives moral responsibility. Can your “rules” be set ahead of time? Then not free.

No, according to Conway and Kochen. So too are particles. What does “free” mean? Define freedom to be the characteristic behaviour of quantum particles. On-the-fly as opposed to set ahead of time. Origin of free will and moral responsibility? Is Science Compatible with Our Desire for Freedom? Barcelona 2010