Chapman University Chapman University Digital Commons Mathematics, Physics, and Computer Science Science and Technology Faculty Articles and Faculty Articles and Research Research 2016 Accommodating Retrocausality with Free Will Yakir Aharonov Chapman University, [email protected] Eliahu Cohen Tel Aviv University Tomer Shushi University of Haifa Follow this and additional works at: http://digitalcommons.chapman.edu/scs_articles Part of the Quantum Physics Commons Recommended Citation Aharonov, Y., Cohen, E., & Shushi, T. (2016). Accommodating Retrocausality with Free Will. Quanta, 5(1), 53-60. doi:http://dx.doi.org/10.12743/quanta.v5i1.44 This Article is brought to you for free and open access by the Science and Technology Faculty Articles and Research at Chapman University Digital Commons. It has been accepted for inclusion in Mathematics, Physics, and Computer Science Faculty Articles and Research by an authorized administrator of Chapman University Digital Commons. For more information, please contact [email protected]. Accommodating Retrocausality with Free Will Comments This article was originally published in Quanta, volume 5, issue 1, in 2016. DOI: 10.12743/quanta.v5i1.44 Creative Commons License This work is licensed under a Creative Commons Attribution 3.0 License. This article is available at Chapman University Digital Commons: http://digitalcommons.chapman.edu/scs_articles/334 Accommodating Retrocausality with Free Will Yakir Aharonov 1;2, Eliahu Cohen 1;3 & Tomer Shushi 4 1 School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel. E-mail: [email protected] 2 Schmid College of Science, Chapman University, Orange, California, USA. E-mail: [email protected] 3 H. H. Wills Physics Laboratory, University of Bristol, Bristol, UK. E-mail: [email protected] 4 University of Haifa, Haifa, Israel. E-mail: [email protected] Editors: Kunihisa Morita, Danko Georgiev & Kelvin McQueen Article history: Submitted on September 22, 2015; Accepted on December 17, 2015; Published on January 11, 2016. etrocausal models of quantum mechanics add 1 Introduction further weight to the conflict between causality Rand the possible existence of free will. We an- Time-symmetric formulations of quantum mechanics are alyze a simple closed causal loop ensuing from the in- gaining growing interest. Using two boundary conditions teraction between two systems with opposing thermo- rather than the customary one, they offer novel twists dynamic time arrows, such that each system can fore- to several foundational issues. Such are the Wheeler– cast future events for the other. The loop is avoided Feynman electromagnetic absorber theory [1], Hoyle and by the fact that the choice to abort an event thus Narlikar’s theory of gravitation [2], and Cramer’s trans- forecasted leads to the destruction of the forecaster’s actional interpretation [3]. Among these, however, the past. Physical law therefore enables prophecy of fu- Aharonov–Bergmann–Lebowitz rule [4] and Aharonov’s ture events only as long as this prophecy is not re- two-state vector formalism [5] are distinct, in that they vealed to a free agent who can otherwise render it even predict some novel effects for a combination of for- false. This resolution is demonstrated on an earlier wards and backwards evolving wave functions. When per- finding derived from the two-state vector formalism, forming a complete post-selection of the quantum state, where a weak measurement’s outcome anticipates a otherwise counterfactual questions can be intriguingly an- future choice, yet this anticipation becomes appar- swered with regard to the state’s previous time evolution. ent only after the choice has been actually made. To These advances, however, might seem to come with quantify this assertion, weak information is described a price that even for adherents is too heavy, namely, dis- in terms of Fisher information. We conclude that an missing free will. While quantum indeterminism seemed already existing future does not exclude free will nor to offer some liberation from the chains imposed on our invoke causal paradoxes. On the quantum level, par- choices by classical causality, time-symmetric quantum ticles can be thought of as weakly interacting accord- mechanics somewhat undermines quantum indetermin- ing to their past and future states, but causality re- ism, as it renders future boundary conditions the missing mains intact as long as the future is masked by quan- source of possible causes. This might eventually reveal tum indeterminism. Quanta 2016; 5: 53–60. This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY-3.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Quanta j DOI: 10.12743/quanta.v5i1.44 January 2016 j Volume 5 j Issue 1 j Page 53 causality to be just as strict and closed as classical causal- quantum counterpart of these two paradoxes where inher- ity. If the future is, in some sense, already there to the ent indeterminism saves causality. We show that within point of being causally equal to the past, free will (which the two-state vector formalism, although both future and is defined in Section 2) might appear to be as illusory as it past states of the system are known, genuine freedom is has appeared within the classical framework. We aim to not necessarily excluded. We then define and quantify show this is not necessarily the case. The two-state vector weak information that is the kind of information coming formalism is no worse off than classical physics, or other from the future that can be encrypted in the past without formulations of quantum mechanics as it pertains to the violating causality. incorporation of free will. In other words, free will is not precluded even when discussing a quantum world having both past and future boundary. 3 Interaction between Two Systems In this special issue of Quanta, dedicated to Richard with Opposing Time-Arrows Feynman and discussing time-symmetry in quantum me- chanics, we examine what might seem to be a problem in To demonstrate the possibility of knowing one’s future these formulations, namely the notion of free will [6]. Dis- and its consequences, we discuss a highly simplified clas- cussion of this kind might at first be regarded as philosoph- sical gedanken experiment. Naturally, there are imme- ical in character, but we hope to formulate the problem diate difficulties with such a setup. For example, can rigorously enough to yield nontrivial physical insights. two regions in space have opposite time arrows to begin with? Can observers inside them communicate? These and other questions deserve further probing, but we focus 2 The Problem here only on what would happen if several conditions are met, rather than whether and how they can be achieved. Following Russell and Deery [6], we propose defining Consider, then, a universe comprised of only two free will as follows. Let a physical system be capable of closed, non-interacting laboratories located at some dis- initiating complex interactions with its environment, gain- tance from one another. Suppose further that their ther- ing information about it and predicting its future states, as modynamic time arrows are opposite to one another, such well as their effects on the system itself. This grants the that each system’s future time direction is the other’s past. system purposeful behavior, which nevertheless fully ac- Finally let each laboratory host a free agent, henceforth cords with classical causality. Now let there be more than Alice and Bob, capable of free choice. one course of action that the system can take in response It is challenging to create a communication channel to a certain event, which in turn lead to different future between two laboratories of this kind. An exchange of outcomes that the system can predict. Free will then de- signals is possible in the following form. A light beam is notes the system’s taking one out of various courses of sent from the exterior part of one laboratory to the other’s action, independently (at least to some extent) of past boundary, where a static message is posted. The beam is restrictions. This definition is very close in spirit to the then reflected back to its origin. If the labs are massive one employed in [7], i.e. the ability to make choices. It enough, the beam imparts only a negligible momentum should be emphasized that even in our time-symmetric transfer. context, free will means only freedom from the past, not The gedanken experiment proceeds as follows (Fig. 1): (b) from the future (see also [5]). t1 : Bob sends a light-beam (red arrow) to Alice’s lab. (b) In classical physics, conservation laws oblige any event t2 : He receives through his returning beam a message to be strictly determined by earlier causes. In our con- from Alice saying: “Let me know if you see this message” text, this might apparently leave only one course of action (dotted blue world-line). (b) for the system in question, and hence no real choices. t3 : Bob posts a confirmation saying: “I saw your When moving to the quantum realm, free will might be message” (red world-line). recovered [7], but then again, if one adds a final boundary Then there are the following events in Alice’s lab: (a) condition to the description of the quantum system, can t1 : Alice sends a light-beam (blue arrow) to Bob’s free will exist? We shall answer both classical and quan- lab. (a) tum questions on the affirmative, employing statistical t2 : Alice receives through her returning beam of par- and quantum fluctuations, respectively. ticles that scattered off Bob’s message, i.e. she gets the In what follows, we analyze a classical causal para- information from Bob through this beam reflected from dox avoided by the past’s instability.