Ruth E. Kastner Trinity College Cambridge 2014

1. TI (Transactional Interpretation) and TSVF (Time Symmetric Vector Formalism): A comparisonand some remarks about free will Ruth E. Kastner Trinity College Cambridge 2014

2. Part 1: Overview of TI, its newer version PTI, and comparison with TSVF First remark: PTI is a realist theory that proposes a novel ontology not based on beables or ‘elements of reality,’ where such beables/elements are determinate but unknown values of observables Instead: quantum objects are taken as physically real possibilities not contained in spacetime, but which can give rise to spacetime events.

3. Overview of TI • Based on the Wheeler/Feynman and Davies direct-action theories, in which the basic field propagation is time-symmetric and the response of the absorber plays a crucial role. • in TI, the usual quantum state, emanating from an emitter, is called an ‘offer wave’ (OW): |Y> • the absorber’s response to the offer wave is anegative energy (advanced) solution, called a ‘confirmation wave’ (CW): <F| • the interaction of OW and CW is like a ‘handshake’ that occurs outside spacetime (in my version, Possibilist TI) . In general, one OW generates several CW responses. Each of these sets up an incipient (possible) transaction. • One of these is actualized, whereupon a real transfer of energy occurs from emitter to ‘winning’ absorber in spacetime. The set of incipient transactions is the physical basis for von Neumann’s ‘process 1’ or measurement transition (pure state to mixed state); collapse is the transition from mixed state to a single outcome.

4. Offer and Confirmation Waves • According to the time-symmetric theory, any emission of a retarded offer wave (OW) is accompanied by an advanced wave. This is the time-symmetric propagator in Davies relativistic theory—each field is half strength. • absorbers are stimulated to respond with their own time-symmetric field, exactly out of phase with the offer wave: any confirmation wave (CW) is accompanied by a corresponding retarded wave • the advanced wave from the emitter and the retarded wave from the absorber are cancelled while the field between emitter and absorber are reinforced to full strength Courtesy of John G. Cramer (1986)

5. Completed transaction • The ‘transacted’ wave has a dual role: • superposition of retarded field and advanced field adds to an effective full strength real retarded field: ½( e-iwt + eiwt) = cos( wt) • the product of the amplitudes of the two components, *, provides a natural physical explanation for the Born Rule. Courtesy of John G. Cramer (1986)

6. Example of several absorber responses: a Mach-Zehnder interferometer: An OW |s> from the source encounters two possible absorbers C and D. The component absorbed by C is <c|s>|c> and the component absorbed by D is <d|s>|d>. Each absorption results in the advanced CW <s|c><c| and <s|d><d|, respectively (response of the absorber to the emitter). Thus the interaction of offer and confirmation for a particular absorber is represented by a weighted projection operator, e.g.: <c|s><s|c>|c><c|= |<c|s>|2 |c><c|, from which we can just read off the Born Rule, as well as gain a physical referent for the ubiquitous projection operators. C D  S

7. Von Neumann’s “process 1” • The preceding account leads to a weighted set of ‘competing’ potential transactions, each of which is called an ‘incipient transaction’ • Each incipient transaction is represented by a projection operator multiplied by the relevant squared amplitude (the Born Rule), so this weighted set of incipient transactions is just von Neumann’s “Process 1,” or heretofore mysterious measurement transition. • thus, it is the responses from absorbers x to the initial pure state |s> that gives the mixed state: Not all of these ‘incipient transactions’ can be actualized…..

8. What decides which transaction is actualized? The measurement basis is specified by what absorbers are available (‘Process 1’); but what ‘causes’ a particular transaction |x>< x| out of the weighted set ? Proposal (‘Possibilist TI’ or PTI): QM suggests that nature has a deeper kind of spontaneous symmetry breaking characterizing the transition from the potential to the actual; an analog of spontaneous symmetry breaking: Weighted SSB. This is an opening for volition at some level (Nature? Individual agents? Both?)

9. References on PTI • Kastner (2012) The Transactional Interpretation of Quantum Mechanics: The Reality of Possibility. Cambridge University Press • Kastner (2012) “The Possibilist Transactional Interpretation and Relativity”, Foundations of Physics: Vol42, Issue 8, Page 1094-1113 [http://arxiv.org/abs/1204.5227] • Kastner (2010) “The Quantum Liar Experiment in Cramer's Transactional Interpretation ,” SHPMP: Vol41, Issue 2, May 2010, 86-92 ) [arXiv:0906.1626]

10. The first two references (cf. http://arxiv.org/abs/1204.5227) provide an account for the micro/macro divide, and the emergence of classicality, in terms of the likelihood of the emission of offers and confirmations and resulting actualized transactions. These considerations involve the relativistic level. Concerning the emergence of classicality, I recently observed that ‘Quantum Darwinism’ in an Everettianapproach, i.e., ‘decoherence’ and ‘einselection’ in a unitary-only dynamics, does not work as advertised: Kastner (2014) 'Einselection' of Pointer Observables: The New H-Theorem? Forthcoming in SHPMP, arXiv:1406.4126

11. Now, the comparison between PTI and TSVF

12. Areas of commonality • Both TI and TSVF involve ‘something more’ beyond the one-state formulation of QM • Both TI and TSVF make use of advanced states, although in different ways • TI and TSVF are both empirically equivalent to standard QM.* The founders of TSVF have said: “…Does it mean that the TSVF has different predictions than the standard quantum approach? No, the two formalisms describe the same theory with the same predictions.” (Aharonov and Vaidman, “The Two-State Vector Formalism:AnUpdated Review,” www.tau.ac.il/~yakir/yahp/yh165.pdf #3 is why I object to claims that various experiments allegedly support TSVF as opposed to standard QM: that is not possible, since they both yield exactly the same observable predictions. (Argument from simplicity is unreliable; specifics given later if time allows.) Note that I don’t claim that any particular experiment (at the nonrelativistic level*) corroborates TI, since all such experiments also corroborate standard QM. What I do claim is that TI provides a better explanation for certain peculiarities of the formalism (e.g. Born Rule), as well as the physical nature of ‘measurement’ and collapse. It does so by providing physical referents for crucial but ad hoc formal machinery in the theory (e.g. Born Rule, V.N. ‘Process 1’.) *There is a possible deviation between PTI and standard QED at the relativistic level (see Kastner 2013, arXiv:1312.4007)

13. Another commonality that, on further reflection, is actually just PTI with itself…. TI in its possibilist form (PTI) agrees with A. Elitzur that the past is ‘empty’ pending a measurement result; measurements bring about certain aspects of the past. However, arguably this picture is not consistent with the TSVF, since it treats an emitted quantum as existing for some time without a post-selection measurement; i.e., as a single forward-directed state (offer wave in TI). That is the only way that the past could ever be ‘empty.’ But in TSVF, quanta are always described by TSV, not by single states. This is indicated by E.C. and L.V.’s references to ‘future measurements’ as existing and having influences on the present and past. Therefore, by assumption in TSVF, the past can never be ‘empty.’ Perhaps what A.E. has in mind is really the transactional picture and not TSVF?

14. Areas of divergence • In TI the advanced state is a separate entity, the ‘confirmation wave’ : <F| • In PTI, both offers and confirmations are pre-spacetime entities.* It is only an actualized transaction that establishes spacetime events. In contrast, TSVF takes two-state vectors as spacetime entities (see also below). • Two-state vectors are essentially offer wave components, i.e., the different components of the OW reaching different absorbers; so they are not the whole story according to the transactional picture • TI gives a straightforward account of the Born Rule, while TSVF must assume it. • PTI involves pre-spacetime, sub-empirical retrocausation only, while TSVF asserts that retrocausation occurs within spacetime • In PTI there is a growing universe, whereas TSVF implies a block universe: all future measurements must be assumed to exist as events in spacetimein order to define the basic quantum states, which always include post-selection. *So are microscopic emitters and absorbers such as individual atoms.

15. 7. It is inconsistent with the relevant direct-action theories (such as Wheeler-Feynman (1945, 1949) and Davies (1971, 1972)) to combine the retarded state |y> and advanced state <f| into a single hybrid entity, <f||y>. The advanced and retarded solutions are fundamentally distinct entities, even though they can and do interact and function to produce phenomena

16. Isn’t the transactional interpretation ‘retrocausal’? Only at the sub-empirical, pre-spacetime level. . • In possibilist TI (PTI), offers and confirmations bring about spacetime events from a pre-spacetime domain of possibilities. Thus any ‘retrocausality’ in PTI is not a causal influence within spacetime. Rather, it is part of the process by which ST events are created. (cf. Kastner 2012, Chapter 8) • PTI therefore does not have explicit retrocausal effects within spacetime, nor does it imply a block world picture.

17. Part 2: Free Will

18. Basic definitions • Compatibilism: free will is compatible with determinism (and/or a block world) • Incompatibilism: free will is incompatible with determinism; also incompatible with indeterministic block world • Agent-causal libertarianism: a form of incompatibilism asserting that we do have free will; agents are the irreducible causes of their willed actions

19. Ginet’s formulation of incompatibilism: ‘Consequence Argument’ (1966) • “No one has power over the facts of the past and the laws of nature. • No one has power over the fact that the facts of the past and the laws of nature entail every fact of the future (i.e., determinism is true). • Therefore, no one has power over the facts of the future.” Thus, Ginet’s argument acts as a refutation of compatibilism. If in addition the future is already determinate (as in a block world picture), no one has power over the facts of the past, present, and future, regardless of laws. Being ignorant of choices we are fated (and thus compelled) to make is not equivalent to having free will.

20. another way to look at it • the spirit behind the preceding principle is that if the laws governing events require those events given certain conditions not dependent on the agent, and those conditions are met, then the agent is not the free cause of those events. • In this sense, a block world picture rules out free will, because it specifies laws and conditions, all of which obtain without any input from an agent participating in the events. This applies also to an indeterministic block world; in such a world, all events already exist without any input, external to those events, from the agent . • (Possible exception: agents are seen as bringing about the spacetime events from outside spacetime—an account would be needed)

21. None of the dominoes has any say in its behavior (simple determinism); if in the future each is already fallen, doubly so. None of them needs to be consulted on whether it will fall or not.

22. Incompatibilist libertarian • Argues that events are neither deterministic nor fated, and that we do have free will permitted by this fundamental indeterminism. • Various demands for an adequate libertarian account – a few preliminary comments about that • Various objections to this view; I’ll focus on a specific one that is arguably the most important

23. the ‘common thesis’ contra libertarianism • The idea that libertarians are necessarily committed to anomic or ‘lawless’ human action, i.e. that human choices are not subject to any law • This is certainly questionable; e.g.: Balaguer 2010, Kane 1996, and O'Connor 2000. Clarke 2003, chaps. 8-10 also takes libertarianism to be compatible with comprehensive natural laws.

24. In this context, some libertarians have attempted to give an account of free choice in terms of reasons for the choice…. • Many accounts of free will implicitly assume Principle of Sufficient Reason (PSR). These kinds of considerations often lead to difficulties (e.g. the ‘problem of luck, which replaces volition with ‘luck’ without justification) • The characterization of libertarianism as requiring ‘anomic’ or ‘lawless’ action (e.g. Pereboom 2005) is an implicit adoption of PSR: it effectively equates basic indeterminism with ‘lawlessness’ • However: PSR not at all required for a free choice. In fact, it is a key element of free choice that an agent need not have any reason--or even desire-- for the choice, but makes it out of pure volition.

25. Example of a free choice lacking a sufficient reason: Buridan’s Ass Would a donkey starve to death because he has no specific reason to choose one bundle of hay over another? Probably not. A political cartoon (ca. 1900) satirizing U.S. Congress’ inability to choose between a canal through Panama or Nicaragua, by reference to Buridan’s Ass. [Wiki Open Source; public domain]

26. Volition… • The ability and power to make a completely arbitrary choice. [Example: The arbitrary and capricious choice of the evil Centauri Emperor Cartagia on ‘Babylon 5’] • No reason, desire, or asymmetrical cause of any kind required for that choice. • Well-known example in physics: spontaneous symmetry breaking--the actualization of one of a set of equally legitimate solutions, where there is no reason at all to prefer the one selected. This phenomenon is certainly not ‘anomic,’ even if it is underdetermined.

27. Objection to free will even if the world is indeterministic Pereboom (2013): “…it might be that if we were undetermined agent causes – if we as substances had the power to cause decisions without being causally determined to cause them – we would then have…free will. But although our being undetermined agent causes has not been ruled out as a coherent possibility, it is not credible given our best physical theories.“He is referring to Sider’s argument: (Sider 2005: “agent causation [is] a slave to quantum mechanical probabilities") Specifically: if a class of choices is governed by quantum statistical laws, this places a constraint on free choices that some have taken as ruling out free will. The argument: it would take a ‘miracle’ for all the freely chosen actions, out of a class of actions, to conform to the statistical constraints.

28. A counterargument… • Clarke (2010): argues that an agent can freely choose even under a probabilistic constraint; there is no inconsistency • In what follows, we develop his argument further. To do so, we need to journey to…

29. The Land of the Quantum Dominoes

30. The God of the Quantum Dominoes I decree that whenever one of my Subjects is struck, he has a free choice of whether to fall or not. However, each has a 50% chance of falling, and they must collectively demonstrate that by a frequency of 50%. Therefore, if all my Subjects are struck, only half of them should fall.

31. the paradox… • if each domino has a free choice of whether to fall, doesn’t this imply that they could all fall if they so chose, thus violating the God’s decree? I.e., isn’t the God’s decree self-refuting? (This is Sider’s objection.) • on the other hand, if each just happened to freely choose so as to conform to the collective statistics, wouldn’t that be a miracle?

32. Not if the dominoes’ volitional choices are subject to quantum influences—’steering’ Nominally, each domino has an objectively indeterminate 50% chance, and therefore a free choice, of whether to fall or not. Suppose ‘Yes’ means it chooses to fall and ‘No’ means it chooses not to fall. We could model the state of each by the superposition |Y> = (1/√2) [|Y> + |N>], where the choice options instantiate a physically well-defined ‘computational basis’ Model them by a collective quantum state. Toy example: 3 dominoes

33. 3-domino state (Y=falls; N=does not fall) |Y> = (1/2√2) {|YYY> + |YYN> + |YNY> + |YNN> + |NYY> |NYN> + |NNY> + |NNN>} Suppose the first two dominoes make their choices.* The third domino is ‘steered’ more toward one choice than another, based on the choices of his fellows. This constrains the exercise of his will, but does not eliminate it. Significantly: who said that exercise of the will need be effortless? In fact, it usually takes an ‘effort of will’ to carry out certain morally correct actions (such as taking back the library book that you insisted you had returned 10 years ago, but just found in your basement). Thus, exercising free will under contrary pressures is certainly an empirically valid experience. *This need not imply a preferred frame. QM constraints apply atemporally in TI (see Kastner 2012, Chapter 5)

34. Specifically, |Y> = (1/2√2){|YYY> + |YYN> + |YNY> + |YNN> + |NYY> |NYN> + |NNY> + |NNN>} Probability that 3rd domino will choose to fall: applicable states are 1,3,5,7. If the 1st and the 2nd domino choose to fall, the 3rd has only a 25% chance (term #1). But if at least one of the others chooses not to fall (terms #3,#5, and #7), 3rd has a 75% chance of falling. Thus, 3rd is steered away from falling based on choices of the others to fall. It is still perfectly possible for 3rd to choose to fall; however, it requires a ‘stronger effort of will’. In this way, the decree of the God of the QM Dominoes is satisfied.

35. Conclusion QM constraints are no obstacle to free will, but they can be seen as influencing the likelihood of an agent’s making a particular choice, in effect requiring different amounts of effort required to make various choices. The influence can be seen as a collective effect arising from an ‘entanglement’ of wills of individual agents. Reminiscent of Jung’s ‘collective unconscious’? Or Aboriginal ‘Dreamtime’? “Dreamtimeis a place beyond time and space……” and “[Aboriginals] believe that every person essentially exists eternally in the Dreaming. This eternal part existed before the life of the individual begins, and continues to exist when the life of the individual ends.” [http://www.crystalinks.com/dreamtime.html]

36. Recap: PTI explains the Born Rule and measurement process, including the physical basis for Von Neumann’s “Process 1,” the transition from a pure to mixed state. • PTI involves a limited and subtle form of sub-empirical retrocausation • In that sense, it has overlap with A. Elitzur’s notion of ‘filling in the empty past’ • However it lacks the tension of the TSVF which invokes explicit retrocausality while implying a block world ontology. • PTI has room for a robust form of free will, whereas TSVF does not. • PTI is based on well-developed time-symmetric field theories, while TSVF deviates from those theories in an ad hoc way.

37. Available down the street at the CUP bookstore… Kastner (2012) The Transactional Interpretation of Quantum Mechanics: The Reality of Possibility

38. supplemental material & references • for reference specifics, contact the author via transactionalinterpretation.org

39. remarks on weak values and retrocausality in a block world • As Silberstein, Stuckey et al have pointed out, a block world certainly has relations between events, but it is acausal in a dynamical sense. If all events already exist in spacetime, nothing within spacetime is required to bring them about. Causality is superfluous in this picture. (One could still consider creation of events from beyondspacetime, as in Sorkin’s causal set approach allowing for the creation of events from a pre-spacetime ontology) • Two-state vector formalism implies a block world, since all future measurements must be assumed to exist in order to define the states. So there is tension between the idea that we can have well-defined, spacetime two-state vectors and that they also involve causation, in either direction. • In any case, weak values in themselves, as elements of the standard QM formalism (basically matrix elements or two-time transition amplitudes), have nothing to say about the ontology of the world or causal flow. In particular, they do not imply retrocausation within spacetime. To see this, consider the parable of…

40. Weak SHOE Values and the DRUNKEN Shoe Factory Alice owns a shoe factory. On Thursday night, her workers party too hard, and the shoes they make on Friday have a high rate of defects. In contrast, on Sunday night the workers are all in a state of repentance and abstention, and their performance on Monday is exemplary. Bob owns a retail shoe store and is one of Alice’s customers. When receiving shipments of shoes (preselection state |A>), he sorts them into two piles, one for ‘ready to sell’ (|S>) and another for ‘return due to defects’ (|D>) . The observable in question is the day of the week each shoe was made. Compare the (unnormalized) weak values of Monday and Friday for the “two-state vector “ <D||A> : <D|M|A> << <D|F|A>

41. Weak SHOE Values and the DRUNKEN Shoe Factory Alice owns a shoe factory. On Thursday night, her workers party too hard, and the shoes they make on Friday have a high rate of defects. In contrast, on Sunday night the workers are (of course) all in a state of repentance and abstention, and their craftsmanship on Monday is exemplary. Bob owns a retail shoe store and is one of Alice’s customers. When receiving shipments of shoes (preselection state |A>), he sorts them into two piles, one for ‘ready to sell’ (<S|) and another for ‘return due to defects’ (<D|) . The observable in question is the day of the week each shoe was made. Compare the (unnormalized) weak values of Monday and Friday for the “two-state vector “ <D||A> : <D|M|A> << <D|F|A> Do we conclude that Bob’s selection of a defective shoe retrocausally influences that shoe to have been more likely made on a Friday? No. This is no different from ordinary statistical inference, i.e., a defective shoe is simply more likely to have been made on a Friday. In standard QM terms, the states |F> and |D> have a large overlap, whereas the states |M> and |D> are almost orthogonal.

42. Thus, causation is underdetermined in the context of ‘weak values’: The expression <D|M|A> << <D|F|A> in this example simply reflects the fact that most of the defective shoes are coming from the Friday production. The post-selection sorts the process into different ensembles, each with its own characteristics; but retrocausation is neither implied, nor necessary, nor the most natural explanation of the phenomena. It is entirely superfluous. There is nothing about quantum entities (as opposed to classical objects like shoes) that escapes these conclusions; they can apply also to electrons in a Stern-Gerlach apparatus. Weak values are simply normalized transition amplitudes, and as such do not themselves imply anything about the direction of causal influences, or even whether there are any causal influences. For example, in an explicitly acausal block world such as that proposed by Silberstein & Stuckey, these sorts of statistical correlations would express only acausal relations; there need be no explicit causal flow even in the future direction! Nevertheless: the directionality of causation is of course an interesting and highly nontrivial question, and PTI does have things to say about that (see Kastner 2012 and Kastner (forthcoming): Understanding Our Unseen Reality: Resolving Quantum Riddles, Imperial College Press).

43. Further consideration—weak pointer measurement and system post-selection could be spacelike separated • Model system/apparatus as an EPR pair: there is a frame in which post-selection occurs before weak pointer measurement (pointer could be a poorly localized photon) • In this case, the system’s post-selection can be viewed as steering the pointer in the forward time direction

44. Conclusions re retrocausation in a weak values context • Retrocausation is a metaphysical assumption not implied or required by the QM formalism or by weak values • Of course, it’s not ruled out by the formalism either, but the construction of a ‘two-state vector’ and attendant calculations of weak values (which do not require a two-state vector for their construction in any case) does not constitute an argument that retrocausality obtains, or even that it is a better way to understand what’s going on. • What about the ‘argument from simplicity’?

45. Argument from simplicity favors retrocausal effects even from Bob’s straightforwardly classical, future-directed shoe selection process. Thus, the argument may well be overrated. It is certainly simpler for Bob to assume that his selection of each shoe as either defective or not retrocausally influences on which day it was crafted: |A> → |F><F| ← <D|, or |A> → |M><M| ← <S| As opposed to the less simple account: |S> |D> |M><M| → |A> → |F><F| → |D> |S> But we know that the latter accurately describes what happened in this case : the projection of Monday-crafted shoes on the state |D> is very small, while the projection of Friday-crafted shoes on the state |D> is very large. "Make everything as simple as possible, but not simpler.“ - Albert Einstein

46. argument from simplicitycan amount to a logical fallacy: specifically, correlation demonstrates causation Simplest explanation for data: pirates cause global warming? Or global warming causes pirates? Which is it? Both? Or are there other things going on here, and should we take them into account for a more accurate--even if less simple--story? [http://en.wikipedia.org/wiki/Flying_Spaghetti_Monster#mediaviewer/File:PiratesVsTemp%28en%29.svg]

47. 3-box experiment demystified Weak measurement of box C for given pre- and post-selection is a projection of the pointer onto an x value when it is in the state -1/3 |sort of yes> + 2/3 |sort of no>, where ‘sort of yes’ and ‘sort of no’ states are not orthogonal, i.e. <x|sort of yes> ~ exp[(x-1)2/D] (x=1 corresponds to a definite ‘yes’ and D >> 1) <x|sort of no> ~ exp[(x)2/D] (x=0 corresponds to a definite ‘no’) Avg. value of pointer reading turns out to be -1. This does not necessarily translate to any property of the system such as negative mass or momentum.Measurements of the apparatus in a strange superposition are not measurements of the system. Rather, the apparatus is steered to an exotic state through the given pre- and post-selection states of the system, which confer on it the necessary phase relationships to attain strange x values.

48. superposed weak pointer state with mean value x = -1