Against the Empirical Viability of the DWE Approach to QM

Richard Dawid and Karim Thebault

• The Deutsch-Wallace-Everett Approach to QM• What is Empirical Viability? • The Problem with DWE.• A look at the approach of Greaves and Myrvold

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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.

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The Born Rule Question

? Crucial Question: Can the Everettian approach reproduce the observed quantum statistics?

• Problem: no actual probabilistic element in branching. All branches are ‚realized‘.

• It may still work. A non-stochastic characteristic of the causal structure of the wave function may from an agent‘s perspective seem stochastic.

• ‚Naive‘ idea: quantum statistics may be explained by branch counting.

- But: branch counting cannot reproduce the Born rule.

? What can be done?

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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.

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Empirical Viability

? Is DWE empirically viable?

T1 meets T0´s standard of empirical viability only if:

1. it is not refuted by the collected data that confirms T0.

2. 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.

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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.

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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. 7

‘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.

Þ 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!

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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.

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Ways out for the Everettian?

• One might add to the rationality principleso P: rational betting must not disagree with inductive

inference.

But that is too strong and too weak at the same time.

- in the previous example the betting is clearly rational.

- A scientist would not abstain from ‚betting‘ in the face of disagreement with other DWE principles.

• One might try to re-introduce inductive inference as an empirical principle at a subjective level.

Greaves & Myrvold 10

The Greaves-Myrvold Approach

(1) The Born rule is inferred from data.

(2) Born weights are attributed to branches and get meaning only at at a subjective level.

(3) Decision theory is taken as additional support.

GM take their approach to be compatible with DWE.

- The previous analysis showed that this is not so. • GM is based on the primate of inductive inference.• DWE is based on the primate of its rationality principles.

! The two can disagree.

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Comparison with DWE

+ Unlike DWE, GME can be empirically refuted.

- However, GWE loses an important quality of Evrettian QM:+ Everettian QM does not add anything to the equations of QM.

- GM does add the Born rule as an empirically inferred posit that may be motivated by decision theory but not deduced from the theory.

- Moreover, the Born rule posit is not physically interesteing without an objective basis. It is not entrenched in the structure of the theory.

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Conclusion

• DWE is no empirically viable form of QM.

• GME is an empirically viable form of QM but sacrifices an important element of Everettian QM.

• The subjective approach seems allow no escape from the dilemma between losing empirical viability and introducing the Born rule as an ad-hoc posit without entrenchment in the theory‘s structure.

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