1. Newcomb’s problem in the light of Bell’s theorem Eric Cavalcanti Centre for Quantum Dynamics, Griffith University Eric Cavalcanti, Sydney, January 2009

2. Lewis: “They have their millions and we have our thousands. They think this goes to show the error of our ways, [but] we have no choice. The riches are reserved for the irrational”. 1Eric Cavalcanti, Sydney, January 2009

3. A picture of a Large Dinosaur Eric Cavalcanti, Sydney, January 20092

4. A picture of an Even Larger Comet 3Eric Cavalcanti, Sydney, January 2009

5. A picture of a turtle 4Eric Cavalcanti, Sydney, January 2009

6. Causation 5Eric Cavalcanti, Sydney, January 2009

7. Lewis: “They have their millions and we have our thousands. They think this goes to show the error of our ways, [but] we have no choice. The riches are reserved for the irrational”. 6Eric Cavalcanti, Sydney, January 2009

8. Newcomb’s problem You can pick A 1 ) just Box 1 A 2 ) both Predictor already put $1 Million in the box if and only if she predicted you were going to choose just Box 1 P(M|A 1 ) >> P(M|A 2 ) $ 1 M? $ 0 ? 12 $ 1 K Eric Cavalcanti, Sydney, January 2009

9. First solution: Bayesian (Evidential) Decision Theory Maximise expected conditional utility: In the Newcomb scenario: But Take one box only Eric Cavalcanti, Sydney, January 2009

10. On the other hand: principle of dominance No matter what’s in box 1, I’m better off taking both Critique: dominance isn’t an independent principle, but only a short-cut, and can only be used in case of no probabilistic dependence from actions to outcomes. Response: dominance should be used when the choices cannot causally influence the outcomes. Eric Cavalcanti, Sydney, January 2009

11. Nozick: paradox of rationality For Robert Nozick, Newcomb’s problem displayed a paradox for rationality. Both solutions have equal support; intuitions vary with the contents of the boxes. Eric Cavalcanti, Sydney, January 2009

12. Causal decision theory (CDT) Intuition behind the dominance argument is formalised in Causal Decision Theory. Conditional probabilities in expected utility should be causal (or counterfactual, under a causal reading of the counterfactual) In the Newcomb problem in particular: Take both boxes Eric Cavalcanti, Sydney, January 2009

13. Causal decision theory (CDT) Causal probabilities can be understood as an unconditional average over “dependency hypotheses” (Lewis) or “causal propensities” (Skyrms). Denoted by a set of variables ‘K’. As opposed to the actual conditional probability Eric Cavalcanti, Sydney, January 2009

14. Effective probabilities I’ll define “effective” probabilities as whatever you should use in your decisions. (What does the evidential pr. mean for the CDT’st if it doesn’t have any practical influence?) A Newcomb-type problem can be posed if and only if effective and evidential probabilities differ. 13 EDTCDT Effective Pr. = Evidential Pr.Effective Pr. = Causal Pr. ≠ Evidential Pr. Eric Cavalcanti, Sydney, January 2009

15. “Medical” Newcomb problems Gene (G) Smoking (S)Lung cancer (C) Eric Cavalcanti, Sydney, January 2009

16. “Medical” Newcomb problems Eric Cavalcanti, Sydney, January 2009

17. The “tickle” defence of EDT (Horgan) The action of the gene could only be through the agent’s beliefs and desires. She would feel a “tickle” T that tells her that she desires smoking. Conditional on T, cancer is screened off from the choice of smoking. A rational agent should take into account all available evidence Bayesian decision theory advises smoking as well. Eric Cavalcanti, Sydney, January 2009

18. Is CDT not even wrong? Horgan and others (e.g. Eells, Price) essentially argue that causal probabilities and evidential probabilities don’t actually come apart in problems such as the smoking gene. CDT – just an irrelevant complication? But what if in some cases they do come apart? Those defences are not general enough. Eric Cavalcanti, Sydney, January 2009

19. Regions of causal influence CDT needs an account of what’s “inside” and “outside” the causal influence of an action. Depends on the agent’s causal theory, or the “dependency hypotheses” K. E.g., according to relativity: –Inside: future light cone –Outside: everywhere else 18Eric Cavalcanti, Sydney, January 2009

20. Regions of causal influence b: any factors outside the agents’ causal influence a: any factors inside the agents’ causal influence Therefore when a decision situation depends on a and b CDT should use 19Eric Cavalcanti, Sydney, January 2009

21. The parallel with Bell’s theorem “Free will” / free conditionalisation / no-retrocausality Local causality Therefore Eric Cavalcanti, Sydney, January 2009

22. The parallel with Bell’s theorem Compare Eric Cavalcanti, Sydney, January 2009

23. 22 Bell (1964) No Local Hidden Variable model like that can explain the correlations predicted by Quantum Mechanics between certain entangled pairs of particles

24. Aspect (1980’s) 23 And what’s more, we’ve tested the predictions that Bell worked out, and found that quantum theory is accurate. Eric Cavalcanti, Sydney, January 2009

25. The Bell game Alice 1 RG 1 RG Bob Eric Cavalcanti, Sydney, January 2009

26. The Bell game Eric Cavalcanti, Sydney, January 2009

27. The Bell game Alice 1 RG 1 RG Bob Run 1: R A R B = -1 Run 2: G A R B = 1 Run 3: R A G B = 1 … Eric Cavalcanti, Sydney, January 2009

28. The Bell game Alice 1 RG 1 RG Bob B = + + - If B >= 2.8 you win $1 M If B < 2.8 you lose Eric Cavalcanti, Sydney, January 2009

29. The Bell game B = + + - If B >= 2.8 you win $1 M If B < 2.8 you lose $ 1 K Or you can just take home $1000… Eric Cavalcanti, Sydney, January 2009

30. Some possible causal hypotheses 1.Nonlocal causation: Some sort of nonlocal causation happens in Bell violations. Local causality is violated, and I have no reason to take space-like separated measurements to be outside my causal influence. 2.Acausal correlations: Bell correlations do not involve causation; 3.Superdeterminism: Local causality is never violated. Violations of Bell inequalities are due to the violation of the “free will” hypothesis. HVs in the past locally determine the choices of experiment as well as the outcomes of those experiments; 4.Loopholes: Bell inequalities are not really violated. Once we close all loopholes (detection efficiency, locality, etc) violations will disappear. 29Eric Cavalcanti, Sydney, January 2009

31. Analysis of the game: superdeterminism CDT should use the causal probabilities For each pair of Alice’s and Bob’s choices 30Eric Cavalcanti, Sydney, January 2009

32. Analysis of the game: superdeterminism Bob’s formula becomes QM predicts 31 CDT says take the thousand dollars; EDT says play the game Play: B >= 2.8 you win $1 M B < 2.8 you lose Or take the risk-free $1000 Eric Cavalcanti, Sydney, January 2009

33. Averaging over causal hypotheses To derive CDT’s prescription, we need to calculate the causal expectation values of the game according to each of the hypotheses and weigh each with their corresponding credences. = 2 P_3 + 2.83 (1 – P_3) < 2.83 For any finite P_3, we can choose an appropriate rule for the game such that the CDT will never play. 32 HypothesisCredenceCausal exp. value Nonlocal causationP_1<= 2.83 Acausal correlationsP_2<= 2.83 SuperdeterminismP_3<= 2 LoopholesP_4<=2.83 (small det. eff.) Eric Cavalcanti, Sydney, January 2009

34. The causal polytope In Bell inequalities, it is common to analyse the set of allowed LHV probabilities These live in a convex polytope Quantum probabilities can lie outside the causal polytope A CDTist will be constrained to have their effective probabilities in the polytope no matter what evidence is thrown at them Eric Cavalcanti, Sydney, January 2009

35. Possible objections (1) “The game is not exactly analogous to the original Newcomb problem”. No, but CDT should be applied in every decision situation. The important thing for a Newcomb-type problem is a disagreement between the evidential and causal probabilities. The advantage of this game is that you can actually do it. 34Eric Cavalcanti, Sydney, January 2009

36. Possible objections (2) “The money in the box is actually known by someone. But the hidden variables in QM are hidden even in principle. Suppose there’s a friend of mine looking at the closed box. Surely he would advise me to take both boxes?” Reply: Nothing in causal decision theory requires the posited causal factors to be known by someone (e.g., the gene). Your friend would advise you to take both boxes no matter what. He gives you no information. An agent’s choices can only depend on their information, not on someone else’s. The objection reveals a fragility of the original Newcomb scenarios, not of my argument…

37. Communicated vs. non-communicated predictions What makes the “tickle defences” work is that they argue that those are effectively cases of communicated prediction. However, the Predictor can know the effect of the communication on the prediction itself. She can’t always communicate a prediction and still keep it accurate! A way to guarantee that the prediction won’t be falsified is to guarantee that the knowledge simply won’t be available to the agent. HVs are inaccesible even in principle. Eric Cavalcanti, Sydney, January 2009

38. Possible objections (3) “The argument seems to depend on a ‘superdeterministic’ interpretation of the Bell correlations. What if I believe in non- local causality?”. Reply: there is no generally accepted way of explaining quantum correlations as causal correlations. Our best theory of causal structure is relativity. Why not get your causal probabilities from relativity? (It can’t be because it doesn’t give the right evidential probabilities!) Superdeterminism is a logically possible explanation, and it agrees with relativity as far as local causality is concerned. If you give this hypothesis any nonzero credibility, the argument holds. Eric Cavalcanti, Sydney, January 2009

39. Possible objections (4) “Alice does causally influence the correlations. It is her choice of a biased ensemble which causes the Bell violation to occur” –Reply: Alice doesn’t know, and cannot know, what the right choice is. As far as she is concerned, there is already a set of causal factors K responsible for the correlations. Averaging unconditionally over those, whatever she does, there can be no Bell violation. 38Eric Cavalcanti, Sydney, January 2009

40. Possible objections (4) “Alice does causally influence the correlations. It is her choice of a biased ensemble which causes the Bell violation to occur” –“Extended” Newcomb problem: Instead of one closed box, there are 100. Alice can choose to (a) take all of them and the extra thousand; or (b) open just one. As before, P(M|b) >> P(M|a) –It isn’t plausible to argue (under the usual forwards causality view) that it is Alice’s choice of which of the hundred boxes to take that causes the money to be there! 39Eric Cavalcanti, Sydney, January 2009

41. Lessons for physics? Possible defences from CDT camp: new loopholes in Bell’s theorem? More attention to the “no-retrocausality” / “free-will” assumption – e.g., retrocausal models of QM. Advantage: saves local causality. Introduce explicitly the agent’s choices of experiments in searches for information-theoretic principles for QM. Eric Cavalcanti, Sydney, January 2009

42. Summary of the argument It is logically possible that the world is “superdeterministic”; Assign credence p0; CDT needs some account of which of the contemplated outcomes are within the causal influence of each of the agent’s actions. Taking this into account, one can derive a Bell-type inequality for causal probabilities; CDT should, according to Lewis, Skyrms and others, give some weight to each causal hypothesis with a non-zero probability; In the usual Bell scenario, the superdeterminism hypothesis holds that the actions in space- like separated regions are outside the causal influence of an agent. This leads to Bell inequalities; Since this hypothesis has a nonzero credence, it will weigh down the violations of Bell inequalities. The maximal causal expectation value for a Bell violation will be B_QM – p0(B_QM – 2) < B_QM; Therefore a CDT’st will never have an expectation of observing the full quantum violation, but some smaller value. Although the difference is small, it can always be exploited with some finite data collection; Observing the quantum expectation value would not provide evidence that the superdeterminism causal hypothesis is false, just as observing a million dollars in Newcomb’s problem is not evidence that the causal hypothesis according to which you can’t affect the contents of the box is false. Therefore once the CDT’st states their credence in that hypothesis, they can be exploited forever in such a game; 41Eric Cavalcanti, Sydney, January 2009