Entanglement swapping and retrocausation

Transcription

1 Entanglement swapping and retrocausation Juliusz Doboszewski UJ, Cracow Foundations of Quantum Mechanics and Relativistic Spacetime, Athens Juliusz Doboszewski (UJ, Cracow) Entanglement swapping and retrocausation / 14

2 Support Supported by: 1. Fundacja Studentów i Absolwentów Uniwersytetu Jagiellońskiego Bratniak 2. Philosophy of Science in European Perspective [RNP-ESF grant] Juliusz Doboszewski (UJ, Cracow) Entanglement swapping and retrocausation / 14

3 Outline What I am going to do: 1. Describe experiment which, depending on interpretation, may have some retrocausal flavour. 2. Practice some hair splitting about retrocausation. 3. Take a look three cases (interventionism, common cause principle, generalized manifolds). Juliusz Doboszewski (UJ, Cracow) Entanglement swapping and retrocausation / 14

4 Entanglement swapping Experiment first proposed by Peres [1999], here in Ma et al [2012] version. We are interested in polarisation measurements. Start with two EPR sources (I, II) emiting pairs of photons (12; 34). Alice gets one photon from the first source (1), Bob gets one photon from the second source (4), and they have three possible choices of the basis for the measurement: linear polarization, circular polarization, or linear polarization across 45 axis (note: Alice and Bob have the same basis in each round). Two remaining photons, one from each pair (23), are delayed and go to third party, Charlie. Charlie is placed in the future time-like region w.r.t. Alice and Bob, and chooses randomly between basis for his measurement: 1. separable state measurement on 23 (enanglement not swapped) 2. Bell state measurement on 23 (entanglement swaps to 14) Lots of rounds later, depending on Charlie s choice, we can sort Alice s and Bob s results into subsets, and see that the subsets behave as if they consisted of either entangled or separated pairs of photons (which have neither communicated nor interacted in the past). Juliusz Doboszewski (UJ, Cracow) Entanglement swapping and retrocausation / 14

5 Commentary Here s Ma et al [2012]: If one views the quantum state as a real physical object, one could get the seemingly paradoxical situation that future actions appear as having an influence on past and already irrevocably recorded events. However, there is never a paradox if the quantum state is viewed as to be no more than a catalogue of our knowledge. Then the state is a probability list for all possible measurement outcomes, the relative temporal order of the three observer s events is irrelevant and no physical interactions whatsoever between these events, especially into the past, are necessary to explain the delayed-choice entanglement swapping. Juliusz Doboszewski (UJ, Cracow) Entanglement swapping and retrocausation / 14

6 Ontic interpretation One may not be entirely satisfied with the catalogue of our knowledge explanation. Why? PBR theorem; some ideas concerning modalities, propensity interpretation of probability, or single case probability (branching space-times, Many Worlds, possibly others). So, suppose one is convinced that ontic interpretation is correct, i.e. quantum state of the single system is real or entanglement has modal aspect. Does one have to adopt retrocausation? And what kind of retrocausation would that be? Juliusz Doboszewski (UJ, Cracow) Entanglement swapping and retrocausation / 14

7 What is the retrocausation, again? Popular idea concerning causation: causes happen before their effects. Retrocausation: for two events e 1 and e 2, e 1 being earlier than e 2, it is possible that e 2 can, in some way, influence e 1. Best known example of retrocausation - closed timelike curves in GR. Juliusz Doboszewski (UJ, Cracow) Entanglement swapping and retrocausation / 14

8 Retrocausation in QM: so far Over the years, many authors tried to explain some quantum mechanical phenomena by resorting to retrocausation. 1. Double slit experiments - argument for retrocausation in QM usually depend on wave-particle duality. Ellerman [2011] argues that this kind of argument rests upon the separation fallacy - mistakening creation of an entangled superposition for a measurement. But here it looks different, because we are only speaking about results of measurements. 2. Bell-Aspect experiment and saving some version of hidden variables, cf. Price [2011]. But entanglement swapping is a prediction of QM, and (it looks like) we can consistently present the whole experiment without telling a story about hidden variables. Juliusz Doboszewski (UJ, Cracow) Entanglement swapping and retrocausation / 14

9 Very peculiar retrocausation here? Even if one claims that measurements have something to do with indeterminism and ontic interpretation of the quantum state, hypothetical retrocausation cannot be detected during single round of the experiment. In this sense, the effect is visible only statistically. But retrocausation appears precisely because one is convinced that one or another ontic interpretation of quantum state is the correct one. Funny. Juliusz Doboszewski (UJ, Cracow) Entanglement swapping and retrocausation / 14

10 Example 1: interventionism Intuition: causation is about us wiggling with the stuff around us. The paradigmatic assertion in causal relationships is that manipulation of a cause will result in the manipulation of an effect. (...) Causation implies that by varying one factor I can make another vary. Cook & Campbell (source: Woodward [2008]) Causation is about us being able to manipulate things this or that way. A causes B if and only if B would change if an appropriate manipulation on A were to be carried out. Woodward [2008] Juliusz Doboszewski (UJ, Cracow) Entanglement swapping and retrocausation / 14

11 Interventionism, cont d NO retrocausation! Because Charlie s choice has to be random for the experiment (if the choice wasn t random, we cannot exclude that the effect could be explained by photons knowing in advance what s going to happen), and in the (hardcore) interventionistic sense, Charlie isn t causing anything (the fact that Charlie is not an agent in interventionistic sense is irrelevant here). Juliusz Doboszewski (UJ, Cracow) Entanglement swapping and retrocausation / 14

12 Example 2: common causes Common cause principle: for every correlation between A and B there exists common cause - i.e. such an event C that conditional on C, A and B are no longer correlated. Of course, common causes have to satisfy certain principles, among them the common causes always in the past principle. Standard argument: no (physically reasonable - every probability space can be extended to a probability space containing common cause for each correlation) common causes for quantum correlations at distance. How about the situation here? Let us take a look at probability of, say, P(A + &B + ). Now, P(A + &B + C[1.]) P(A + &B + C[2.]). So what could be common cause lying in the past for correlations arising when Charlie is choosing [2.]? It looks like Charlie s choice is all there is. So again, there is no physically reasonable candidate for non-retrocausal common cause. Juliusz Doboszewski (UJ, Cracow) Entanglement swapping and retrocausation / 14

13 Example 3: generalized manifolds Suppose that one has a generalized manifold, and claims that quantum effects are responsible for (at least some of) the branching happening. That is, structure allowing for different branches, representing possible outcomes, with the choice of a given outcome interpreted as something modal / indeterministic. In the generalized manifold of this kind, one can represent e.g. Bell-Aspect or GHZ experiments, stochastic outcomes, etc. (cf. Placek [2009]). Main idea: experimenters choices are about choosing the appropriate probability space for a given setting, and from these choices appropriate (correlated or not) frequencies should arise. Problem: if the choice Charlie is making should be represented as a point in such a generalized manifold, can one represent delayed choice entanglement swapping experiment without resorting to existence of closed time-like curves? (possible way: Modal Funny Business?) Juliusz Doboszewski (UJ, Cracow) Entanglement swapping and retrocausation / 14

14 Bibliography 1. Ellerman [2011], A Very Common Fallacy in Quantum Mechanics: Superposition, Delayed Choice, Quantum Erasers, Retrocausality, and All That, arxiv: v1 [quant-ph] 2. Ma et al [2012], Experimental delayed-choice entanglement swapping, arxiv: v1 [quant-ph] 3. Peres [1999], Delayed choice for entanglement swapping, arxiv:quant-ph/ v1 4. Placek [2009], On propensity-frequentist models for stochastic phenomena; with applications to Bell s theorem, philsci-archive.pitt.edu/4920/ 5. Price [2011], Does Time-Symmetry Imply Retrocausality? How the Quantum World Says Maybe, arxiv: v3 [quant-ph] 6. Woodward [2008], Causation and Manipulability, plato.stanford.edu/entries/causation-mani/ Juliusz Doboszewski (UJ, Cracow) Entanglement swapping and retrocausation / 14