Against the Empirical Viability of the DWE Approach to QM Richard Dawid and Karim Thebault

1. AgainsttheEmpiricalViabilityofthe DWE Approach to QM Richard Dawid and Karim Thebault • The Deutsch-Wallace-Everett Approach to QM • WhatisEmpiricalViability? • The Problem with DWE. • A lookattheapproachofGreavesandMyrvold

2. Everettian QM Canonical QM has the problem of the collapse of the wave function. Everettian QM: • No collapse. • Branches of the overall wavefunction decouple from each other due to decoherence. • Observer in one branch has epistemic access to her own branch only. • Each quantum ‘decision’ corresponds to branching. Everettian QM is a minimal account that relies only on the dynamics given by the Schrödinger equation.

3. The Born RuleQuestion ? CrucialQuestion: Can theEverettianapproachreproducetheobservedquantumstatistics? • Problem: noactualprobabilisticelement in branching. All branchesare ‚realized‘. • Itmay still work. A non-stochasticcharacteristicofthecausalstructureofthewavefunctionmayfrom an agent‘sperspectiveseemstochastic. • ‚Naive‘ idea: quantumstatisticsmaybeexplainedbybranchcounting. • But: branchcountingcannotreproducethe Born rule. ? Whatcanbedone?

4. The DWE Approach Subjective approach (Deutsch, Wallace): • Born rule is not implemented based on an ‘objective’ quality of the wave function at all. • Rather, it is extracted from constraints on rational reasoning of an agent in one branch. • Decision theoretic argument: • The agent is supposed to bet on outcomes of quantum measurements. • Based on a certain set of principles of rationality, the agent is forced to bet according to the Born rule. • Everettian QM thus is taken to ‘predict’ outcomes according to the Born rule.

5. EmpiricalViability ? Is DWE empirically viable? T1 meets T0´s standard of empirical viability only if: • it is not refuted by the collected data that confirms T0. • Data from past experiments that would have refuted T0 would also have refuted T1. DWE satisfies 1. But how about 2.? Would data that violates the Born rule refute DWE? • No objective basis for 2. • However, there is ‘prediction’ based on the decision theoretic argument.

6. The Crucial Question ? Does the decision theoretic ‘predictionD’ provide a basis for 2.? David Wallace claims it does (solve the ‘unknown theory problem’). Our claim: It does not. Why not? PredictionD is something very different than prediction.

7. Prediction The general point: • Predictions: are deduced from the theory T. => If data disagrees, either T or measurement theories are false. • PredictionsD: only rational betting behavior is deduced from T. => no logical inference leads from disagreement between rational betting and data to the falsity of T or measurement theories. It might just be that rational betting does not amount to betting on the most probable outcome. => If data contradicts predictionsD , that does not refute the theory.

8. ‘Pascal’s’ Wager An example of the disagreement between rational betting and probability: Afterlife Theory TA: • Chances for afterlife are 1/1000. • If afterlife, then • those who have betted on it get 1000E. • Those who betted against it get 1E. • The only rational betting behaviour is to bet on afterlife. ! Nevertheless, afterlife is highly improbable. => If, at the moment of death, god tells you “sorry, no afterlife”, don’t take that as a refutation of TA!

9. The QM Case Let us assume that recent data E contradicted statistical predictions of QM. How could it refute DWE? • We know that it could NOT be at variance with predictions deduced from Everettian structure. • It might be at variance with DWE’s principles of rational betting. But those principles are not empirical. So they cannot be refuted empirically. => no refutation of DWE took place at all. Everittian QM is not less probable than before and rational betting still implies betting according to the Born rule.

10. Ways out for the Everettian? • Onemightaddtotherationalityprinciples • P: rational betting must not disagreewithinductiveinference. But thatistoo strong andtooweakatthe same time. - in thepreviousexamplethebettingisclearly rational. - A scientistwould not abstainfrom ‚betting‘ in thefaceofdisagreementwithother DWE principles. • Onemighttrytore-introduceinductiveinferenceas an empiricalprincipleat a subjectivelevel. Greaves & Myrvold

11. The Greaves-Myrvold Approach • The Born ruleisinferredfromdata. • Born weightsareattributedtobranchesandgetmeaningonlyatat a subjectivelevel. • Decisiontheoryistakenas additional support. GM taketheirapproachtobecompatiblewith DWE. • The previousanalysisshowedthatthisis not so. • GM isbased on theprimateofinductiveinference. • DWE isbased on theprimateofitsrationalityprinciples. ! The twocandisagree.

12. Comparisonwith DWE + Unlike DWE, GME canbeempiricallyrefuted. • However, GWE loses an importantqualityofEvrettian QM: + Everettian QM does not addanythingtotheequationsof QM. - GM doesaddthe Born ruleas an empiricallyinferredpositthatmaybemotivatedbydecisiontheory but not deducedfromthetheory. • Moreover, the Born rulepositis not physicallyinteresteingwithout an objectivebasis. Itis not entrenched in thestructureofthetheory.

13. Conclusion • DWE isnoempiricallyviable form of QM. • GME is an empiricallyviable form of QM but sacrifices an importantelementofEverettian QM. • The subjectiveapproachseemsallownoescapefromthedilemmabetweenlosingempiricalviabilityandintroducingthe Born ruleas an ad-hoc positwithoutentrenchment in thetheory‘sstructure.