*The non-technical presentation of this material is available in my new book for the general reader, available here and as a Kindle version here.*

**The Possibilist Transactional Interpretation:**

**A Unified Account of Relativistic and Non-Relativistic Quantum Theory **

**that Solves the Problem of Measurement**

Ruth E. Kastner

17 February 2015

1 Introduction

The transactional interpretation of quantum mechanics (TI) was initially proposed by John G. Cramer in the 1980s. His most comprehensive exposition is found in Cramer (1986). This time-symmetric interpretation of quantum mechanics gives rise to a physical basis for the Born Rule for the probability of an event. The Born Rule specifies that the probability of an outcome is given by the square of the wave function corresponding to that outcome.

TI was inspired by the Wheeler-Feynman (WF) time-symmetric or ‘direct action’ theory of classical electrodynamics (Wheeler and Feynman 1945, 1949). In the WF theory, radiation is a time-symmetric process. A charge emits a field in the form of half-retarded, half-advanced solutions to the wave equation; the response of absorbers then gives rise to a radiative process that transfers energy from an emitter to an absorber. In this picture, the usual quantum state is called an ‘offer wave’ (OW) and the advanced response from the absorber is called the ‘confirmation wave’ (CW). In terms of state vectors, the OW is represented by a ket, |Y>, and the CW by a dual state vector or ‘brac,’ <F|.

The basic transactional picture has been extended by this author, in a ‘possibilist’ ontology, to the relativistic domain. This version of the interpretation is referred to as ‘Possibilist Transactional Interpretation’ or PTI (Kastner 2012). A theoretical basis can be found in the Davies application of the direct-action picture of fields to quantum electrodynamics (Davies 1971, 1972). However, PTI departs from the Davies treatment in two ways: (i) virtual particles are clearly distinguished from real particles (see also Kastner 2014a) and (ii) the coupling amplitude is identified as the amplitude for generation of an offer or confirmation wave, in a transactional account. These developments allow the interpretation to provide a smooth transition between the non-relativistic and the relativistic domains. The latter can be viewed as the ‘birthplace’ of offer waves, in a physically well-defined (although fundamentally stochastic) manner. These points will be discussed in Sections 3 and 4.

It should also be noted that the direct-action theory of fields provides an elegant and effective escape from Haag’s Theorem, a famously vexing result showing that the interaction picture of the standard quantized fields does not exist. This point is discussed in Kastner (2015).

- How TI explains von Neumann’s Measurement Process and the Born Rule

John von Neumann formulated in precise terms an account of measurement which, despite its practical utility, remains mysterious in any interpretation except TI. To review, von Neumann delineated two different processes that take place in quantum systems. The second of these, which he called ‘Process 2’, is the unitary evolution described by the Schrödinger Equation. The first of these, called ‘Process 1’, is the transition of a quantum system from a pure state to a mixed state upon measurement, i.e.:

The coefficients |c_{n}|^{2} are the probabilities given by the Born Rule for each of the outcomes *y** _{n}*.

Von Neumann noted that this transformation is acausal , nonunitary, and irreversible, yet he was unable to explain it in physical terms. He himself spoke of this transition as dependent on an observing consciousness. However, we need not view the measurement process as observer-dependent. If we take into account the advanced responses of absorbers, then for an OW described by |Y>, we have for a collection of numbered absorbers:

In the above diagram, an initial offer wave from emitter **E** passes through some measuring apparatus that separates it into components <y_{n}|Y> |y _{n}>, each reaching a different absorber *n*. Each absorber responds with an advanced (adjoint) confirmation <y_{n}| <Y|y_{ n}>. In TI, these OW/CW encounters are called *incipient transactions*. They are described in probabilistic terms by the product of the OW and CW, which gives a weighted projection operator: <y_{n}|Y><Y|y_{n}> |y _{n}><y _{n }| = |c_{n}|^{2} |y _{n}><y _{n }|. If we add all the incipient transactions, we clearly have the density operator representation of ‘Process 1”.

Thus, by including the advanced responses of absorbers, we have a physical account of measurement as well as a natural explanation of the Born Rule and Von Neumann’s ‘Process 1’. The response of absorbers is what creates the irreversible act of measurement and breaks the linearity of the basic deterministic propagation of the quantum state. Since the conserved physical quantities can only be delivered to one absorber, there is an indeterministic collapse into one of the outcomes y* _{k}* with a probability given by the weight |c

_{k}|

^{2 }of the associated projection operator |y

_{k}><y

_{k }|. This is called an

*actualized transaction*, and it consists in the delivery of energy, momentum, angular momentum, etc., to absorber

*k*. That absorber that figuratively wins the incipient transaction ‘lottery’ is called the ‘receiving absorber’ in PTI. The process of collapse precipitated in this way by absorber response(s) can be understood as a form of spontaneous symmetry breaking (this is discussed in Chapter 4 of Kastner 2012a).

- The Possibilist Ontology and why it is necessary

If the system under consideration consists only of a single quantum, its associated state vector has only 3 spatial degrees of freedom. In that case, one can think of the wave function as inhabiting spacetime. However, any composite system of N quanta has 3N spatial degrees of freedom, and therefore cannot be considered a spacetime object. Any realist interpretation of the quantum state must take this fact into account. As a realist interpretation, the transactional picture describes real objects that inhabit a realm described not by 3+1 spacetime dimensions but by the 3N dimensions of the relevant Hilbert space (in addition to any spin degrees of freedom). If we think of the spacetime realm as the realm of concrete, actualized events, then the quantum entities described by state vectors must have a different ontological status. In PTI they are viewed as physical possibilities. The latter are precursors to any actualized spacetime event. In view of quantum indeterminism, they are necessary but not sufficient conditions for observable events. The necessary condition is the emission of an offer wave and confirming response(s) to that offer wave from one or more absorbers. This sets up a set of incipient transactions as described in the previous section. At that point we have non-unitary collapse, and only one of the set is actualized to become a spacetime interval with well-defined emission and absorption endpoints—that is the sufficient condition. Thus, not all OW/CW exchanges will result in actualized transactions corresponding to spacetime events.

- The relativistic domain as the birthplace of offer waves

Nonrelativistic quantum mechanics describes a constant number of particles emitted at some locus and absorbed at another. However, in the relativistic domain we are dealing with interactions among various coupling fields, and the number and types of quanta are generally in great flux. Such interactions are described in terms of scattering. The internal connections –i.e., virtual particles– are characterized at each scattering vertex by the coupling amplitude (in the case of QED, the elementary charge *e*) and are neither offers nor confirmations according to relativistic PTI. These are ‘internal lines’ in which the direction of propagation is undefined; i.e., there is no fact of the matter concerning which current ‘emitted’ and which ‘absorbed’ the virtual quantum. In that case, as shown by Davies (1971), the Feynman propagator *D _{F}* of standard QED can be replaced by the time-symmetric propagator in the direct-action theory.

According to PTI, the field coupling amplitudes, which are not present in the non-relativistic case, represent *the amplitude for an offer or confirmation to be generated*. This is a feature of the interpretation appearing only at the relativistic level, in which the number and type of particles can change. It is a natural step, in view of the fact that in standard QED the coupling amplitude is the amplitude for a real photon to be emitted. In PTI, a ‘real photon’ corresponds to an offer wave.[1] So we can think of virtual particles as necessary but not sufficient conditions for real particles, which correspond to offer waves in PTI. We see that the relativistic level brings with it a subtler form of the uncertainty associated with the nonrelativistic form of the theory, i.e., the amplitudes of quantum states themselves.

Thus, in PTI we have a clear distinction between virtual and real particles: virtual particles are not offer waves. Rather, they are *precursors* to offers or confirmations that do not rise to that level. In general, they are not on the mass shell. In the direct-action theory underlying the transactional picture, they are represented by time-symmetric propagators, not Fock space states. On the other hand, real particles correspond to offer waves, which are on the mass shell and are represented by Fock space states. In the direct action picture, offer waves are always responded to by confirmations, so the term ‘real photon’ (in the context of QED) can refer either to a Fock space state |*k*> (i.e., an OW) or to the projection operator |**k**><**k**| (where **k** is 3-momentum), depending on the context.

One of the criticisms of the original Cramer theory was that it took emitters and absorbers as primitive. PTI overcomes this limitation by providing well-defined physical conditions for the generation of OW and CW: both have their origins in the incessant virtual particle activity that is the coupling between fields, such as between the Dirac field and the electromagnetic field. When the interacting photons are on the mass shell and satisfy energy conservation, they are capable of achieving OW status, which in turn generates a CW response from eligible interacting fermionic currents. This is an inherently indeterministic process, since it is described by two factors of the coupling amplitude—i.e., the fine structure constant for QED (as well as the square of the relevant transition amplitude between the initial and final states, with satisfaction of energy conservation). The two factors of the coupling amplitude correspond to the two vertices that are involved in each scattering interaction.

Details of the conditions for the emission of an offer wave instead of an internal process (i.e. a propagator linking two vertices) are given in Kastner (2014a), along with a discussion of how this picture can shed light on the computations necessary to obtain atomic decay rates. The latter are spontaneous emission processes in which virtual photon exchange is spontaneously elevated to a real photon offer and confirmation. Such elevations must of course satisfy energy conservation. That is the only way a would-be virtual photon becomes a real photon—only those photons satisfying the mass shell condition and the energy conservation requirements are eligible to be elevated in this way.

One way to visualize the new level of uncertainty presented in the relativistic domain is in terms of a coin flip. In the nonrelativistic theory, the coin flip has two outcomes: (1) an offer wave |Y> is emitted; (2) no offer wave is emitted. So we either have an offer wave or we don’t. Of course, if we do have an offer wave, it is characterized by its amplitudes <x|Y> for reaching various absorbers X. (If we have an offer wave, we also have confirming responses <x| to that offer, so the two always go hand-in-hand.) This is what made the notion of emitter and absorber in the original TI seem primitive or arbitrary: at what point do we call something an emitter or absorber? However, this problem is remedied at the relativistic level. At that level it is as if the coin becomes much thicker, and a third option becomes available: the coin lands on its side. This in-between, ‘sideways’ outcome corresponds to the virtual quantum. This result has a well-defined probability to yield an emitted offer and confirming response(s) (subject also to the satisfaction of conservation laws as noted above). That probability is the square of the coupling amplitude—i.e., the fine structure constant for QED. So we have two levels of probability amplitudes: (i) the usual, nonrelativistic amplitude of a quantum state <x|Y> corresponding to a particular outcome X; and (ii) the relativistic amplitude for a virtual quantum to become a real quantum representable by a quantum state |Y>.

- Spacetime as the growing set of actualized events

It is often claimed that relativity implies a block world – that is, an ever-present spacetime in which all past, present and future events exist in an equally robust sense. The main argument used in support of that claim is termed ‘chronogeometrical fatalism’ (cf. Stein 1991, pp. 148-9). However, that argument rests on certain assumptions, such as the ontological status of ‘lines of simultaneity’, and a substantival view of spacetime as a ‘container’ for events, that do not necessarily hold. (See Kastner 2012a, §8.1.4 for a rebuttal of chronogeometrical fatalism. See also Sorkin (2007) for a rebuttal to this common but erroneous assumption that a ‘block world’ is necessarily implied by relatibity.)

A different model, of a growing spacetime, is perfectly viable; one such model is the ‘causal set’ approach as proposed by Bombelli et al (1987) (see also Sorkin (2003) and Marolf and Sorkin (2006)). A causal set (causet) C is a locally finite partially ordered set of elements on which is defined a binary relation < . The following properties apply to the causet:

(i) transitivity: (∀x, y, z ∈ C)(x ≺ y ≺ z ⇒ x ≺ z)

(ii) irreflexivity: (∀x ∈ C)(x ~< x)

(iii) local finiteness: (∀x, z ∈ C) (cardinality {y ∈ C | x ≺ y ≺ z} < ∞)

Properties (i) and (ii) imply that the elements are acyclic, while (iii) dictates that the elements form a discrete rather than continuous set. The result is a well-defined causal order of distinct events that can be associated with a spacetime manifold possessing a temporal direction defined by that causal order. As new elements are introduced into the causet, its growth describes a growing, temporally unidirectional spacetime.

The actualized transactions of PTI can readily function as the dynamics underlying the process of ‘sprinkling’ new events into the causal set that is the spacetime manifold. An introduction to the basic concepts involved can be found in Kastner (2014b). The addition of new events to the spacetime causal set must be a Poissonian process in order to preserve relativistic covariance. Interestingly, the generation of offer waves is just such a process, since (as noted in the previous section) these are governed by Poissonian decay rates for the bound states, such as atoms, that give rise to those offer waves.

Offers are always responded to by confirmations, one of which will result in the actualization of a transaction that defines a spacetime interval in terms of its corresponding emission and absorption event. The absorption event of such an actualized transaction defines the present for that receiving absorber, while the emission event is actualized in the timelike (or lightlike) past relative to that absorption. The transferred quantum of energy constitutes a link between the two events that establishes their temporal relationship. It is this linking process between actualized events that establishes spacetime intervals and provides a clearly defined structure of the spacetime ‘fabric’, including its naturally oriented temporal direction towards the unactualized future. In this picture, the present is a strictly local property and cannot be extended along a ‘line of simultaneity’ into the spacelike ‘elsewhere’. Rather, events that are unrelated by the partial ordering of the transactional links have no temporal relationship.

- Conclusion

This article has reviewed the essential concepts of the ‘Possibilist Transactional Interpretation’ (PTI) of quantum theory. It has been argued that PTI can provide a solution to the notorious problem of measurement, as well as providing a unified account of nonrelativistic and relativistic quantum theory. At the nonrelativistic level, we deal only with pre-existent offer waves |Y> and their confirmations from one or more absorbers indexed by X, which correspond to dual states <Y|x> <x|. The confirming response constitutes the onset of the measurement process, where the collapse to a particular outcome |x><x| concludes the measurement process. The collapse is not a process that occurs within spacetime, and that is why it has been so notoriously difficult to give a spacetime account of collapse (cf. Aharonov and Albert (1981) and Kastner (2012, §6.7). Rather, collapse corresponds to the creation of spacetime events from the quantum substratum. That substratum is composed of physical possibilities described by quantum states and of the virtual processes, described by time-symmetric propagators, which are the precursors to those states. The two events created via an actualized transaction are (i) the emission and (ii) the absorption of real energy. That transfer of real energy from the emitter to the receiving absorber defines a spacetime interval and a temporal direction, the emitter defining the past and the absorption defining the present for that absorber. Thus we gain deep physical meaning corresponding to the mathematical fact that energy is the generator of time translation.

At the relativistic level, we take into account virtual processes and their couplings with candidate emitters and absorbers. Such virtual processes are necessary but not sufficient conditions for the generation of offers and confirmations. The latter occur on a stochastic basis, where the probabilities for their occurrence correspond to decay rates. Thus, while the transactional picture of measurement involves objective uncertainty, that uncertainty is precisely quantifiable both at the nonrelativistic and relativistic levels..

References

Aharonov, Y. and Albert, D. (1981) . “Can we make sense out of the measurement process in relativistic quantum mechanics?” *Physical Review D 24*, 359- 370.

Bombelli, L., J. Lee, D. Meyer and R.D. Sorkin (1987). “Spacetime as a causal set”, *Phys. Rev. Lett. *59: 521-524.

Cramer J. G. (1986). “The Transactional Interpretation of Quantum Mechanics.” *Reviews of Modern Physics 58*, 647-688.

Davies, P. C. W. (1971).”Extension of Wheeler-Feynman Quantum Theory to the Relativistic Domain I. Scattering Processes,” *J. Phys. A: Gen. Phys. 6*, 836

Davies, P. C. W. (1972).”Extension of Wheeler-Feynman Quantum Theory to the Relativistic Domain II. Emission Processes,” *J. Phys. A: Gen. Phys. 5*, 1025-1036.

Kastner, R. E. (2012). *The Transactional Interpretation of Quantum Mechanics: The Reality of Possibility.* Cambridge University Press.

Kastner, R. E. (2014a). “On Real and Virtual Photons in the Davies Theory of Time-Symmetric Quantum Electrodynamics,” *Electronic Journal of Theoretical Physics* *11*, 75–86. Preprint version: http://arxiv.org/abs/1312.4007

Kastner, R. E. (2014b). “The Emergence of Spacetime: Transactions and Causal Sets,” to appear in Ignazio Licata, ed.*, The Algebraic Way. *Springer.

Kastner, R. E. (2015). “Haag’s Theorem as a Reason to Reconsider Direct-Action Theories,” to appear in *International Journal of Quantum Foundations*. Preprint version: http://arxiv.org/abs/1502.03814

Marolf, D. and R.D. Sorkin,”Geometry from order: causal sets ” in: *Einstein Online* **Vol.** **02** (2006), 1007.

Sorkin, R. D. (2003) “*Causal Sets: Discrete Gravity (Notes for the Valdivia Summer School)*,” In Proceedings of the Valdivia Summer School, edited by A. Gomberoff

Sorkin, R. D. (2007). “Relativity theory does not imply that the future already exists: a counterexample,” in Vesselin Petkov (editor), *Relativity and the Dimensionality of the World*. Springer. Preprint version: http://arxiv.org/abs/gr-qc/0703098

Wheeler, J.A. and R. P. Feynman, “Interaction with the Absorber as the Mechanism of Radiation,” *Reviews of Modern Physics*, 17, 157–161 (1945)

Wheeler, J.A. and R. P. Feynman, “Classical Electrodynamics in Terms of Direct Interparticle Action,” *Reviews of Modern Physics*, 21, 425–433 (1949).

[1] The term ‘real photon’ can also be applied to an actualized transaction, depending on the context. The term is really a conflation of two different physical situations in the standard approach which can be clearly disambiguated in the transactional approach.

If a spacetime metric M doesn’t exist, how can PTI explain a theory of gravity (Solely as exchange of virtual gravitons?)? Do real gravitons exist or only virtual gravitons (if so what are the transitions that produce real gravitons?) Are OW-CW transactions of gravitons what constitutes gravitational waves?

As a non-physicist (engineer) I’ll assume that gravity resembles CW (confirmation wave) to other types of interactions (https://en.wikipedia.org/wiki/Orchestrated_objective_reduction). What if the Copenhagen interpretation, the transactional interpretation, and Orch-OR (but not Many Worlds) are all legit interpretations? That’s something I assumed here: http://www.igi-global.com/book/rethinking-machine-ethics-age-ubiquitous/125523 and the outcome resembles this (I might have made some major flaws along the way): https://en.wikipedia.org/wiki/Ludwig_von_Bertalanffy#General_system_theory

Thanks, I’ll take a look. But in PTI, gravity is not a quantum field like the ‘real’ forces, so there are no OW/CW for gravity. It is simply the structure of the emergent spacetime manifold. See my reply to the other comment here concerning the spacetime metric.

I can’t reply to a reply, so I’ll write here.

Len Troncale (http://lentroncale.com/?page_id=100) and David Rousseau (http://systemology.org/publications1.html) are individuals that I met as I was asking people for an opinion. Len Troncale claims (but not in his publications) that the Theory of Everything might actually be the General Systems Theory (although we still don’t know any of these). He even had back in the day a conversation with Kip Thorne that the General Systems Theory might be beyond or behind space-time.

This year has an extra 366th day so I think that it will be more than enough time for me to either move forward with that or move on. It was both fun and exhausting.

Sorry, I may not have replied to this yet. In PTI a spacetime metric does exist, but it applies to the ‘extruded’ spacetime set only–not to any ‘future’ events which are not components of spacetime–not yet emergent. The metric is established through actualized transactions, in the sense that those are connected spacetime intervals. The ‘connections’ are the actualized transferred quanta and the endpoints are the emission and absorption respectively. In this picture gravity is not a quantum field–it is just the structure of the emergent spacetime manifold which is perfectly in keeping with GR.

I came up with a version of TI that doesn’t require collapse. In short, I am making the assumption that a particular OW doesn’t collapse into a transaction, but makes *all* transactions simultaneously, but dispersed over (space)time! That is, one absorber absorbs at t0, and another at t1, and yet another at t2, equivalent with being simultaneous. For instance, in the case of an interference pattern there is correlation between the shape of the wave and the frequency of transactions at the various positions on the screen, built up over time. The transactions have to balance each other out in the form of an interference pattern. In other words, there is no random collapse, but a balancing out of transactions of space and time. It’s a deterministic approach if we take the whole universe into account.

I don’t like the concept of collapse. It brings many paradoxes.

However, it may be impossible to prove. The building up of an interference pattern (or any pattern) can be run over again, but we won’t get the exact same impacts of the particles. It might be possible to prove if we are able to exactly reproduce the boundary conditions. I can’t imagine how though.

If I’m making any sense to you, what do you think?

I think that would violate energy conservation, because then one quantum (say a photon) emitted would have to be absorbed by many absorbers, turning one quantum of energy into N quanta. Collapse can make sense if we see it as the indeterministic emergence of spacetime events in a single spacetime.

Indeed, I was sloppy. I don’t know anything about the definition of ‘fields’ in QFT, but I should have said that a particular *emitter* emits a field of a certain amplitude, emitting several quanta, that then get absorbed one by one in a pattern. ;)

“recreate the boundary conditions” – my apologies

Is the TI compatible with dBB theory?

TI denies the basic assumption of dBB that there is a little material particle being guided by a wave. The ‘guiding wave’ is just the offer wave. TI also takes into account the confirmation wave which is missing in dBB. The ‘particle’-aspect is the just the actualized transaction.

Reading past the middle I increasingly got struck by the notion that this writing is stroke of genius. Pity I don’t understand a word of it. However, I’m very much convinced (like you?) that (P)TI is just the answer. I find you writing comprehensively.

Well you’re very kind. But I’m sure you can understand it. In any case my 2015 book “Understanding Our Unseen Reality” is a non-technical presentation of the concepts. I invite you to take a look and see if you find it more accessible.

Hi, Ruth. I’ve been exploring your new blog format and noticed I hadn’t read this piece before. I actually understood it! :) It seems to me you’re overall interpretation of physics deserves more attention. I do, however, have a slightly unrelated (likely dunce-level) question–but as you were discussing the Born Rule here, anyway, I thought I may as well ask it here. It involves Many Worlds–which I don’t believe and which seems refuted in a number of ways. Yet there’s something I’ve never understood about MWI which might be relevant to QM in general. The question is this: even if one were somehow able to set the Born Rule aside (as Everettians attempt to do), how could all outcomes be essentially equally likely given a single set of physical laws? This seems to me like it would be a problem independent of the Born Rule. What I was really wondering–and the part of my question that maybe relates to QM in general–is whether the uncertainty of various properties of existence–position/momentum energy/time–means that all possible outcomes could be equally likely given one set of natural laws. But then it seems to me that one would have to assume that the physical properties (position, momentum, etc.), due to uncertainty, have multiple values which are all equally likely–and aren’t those properties in some sense related to the natural laws, which would make some of their values more likely than others? I guess what I’m asking is, if one assumes that multiple outcomes are possible (which all but hidden variable interpretations do) don’t some HAVE to be likelier than others, given the laws of physics? This seems like it would be yet another problem for Many Worlds, even if they could somehow prove the Born Rule to be an ‘illusion’.

Thanks Eric, glad this made some sense for you! Re your question, actually, whether certain outcomes are more likely than others depends on the specific situation. For example if you have a prepared state of an electron with spin ‘up along x’, then its outcomes of ‘up’ or ‘down’ for z are indeed equally likely. So there is a state-dependence of these probabilities over and above the basic laws of physics.

Question 1: I realize that SOME things are 50-50–that in fact QM is the only place where you could have a true coin-toss! I was just thinking that, given one set of basic natural laws, and also the same SITUATION, at least SOME outcomes should be likelier than others–and that this poses problems for a vision of every possible outcome in the universe occurring without probability. Is this true?

Question 2 (on a completely different note): I happened to notice that you’ve published your William Byrd screenplay. Is that the same as what you sent me last spring, or have you converted it to book-form now? I enjoyed it and was glad to see you’ve published it (though I guess this means it’s not becoming a miniseries). ;)

I think I may have been asking a broader, more philosophical (but still probably dunce-like) ;) question than you realized. I know there are 50-50 ‘coin-tosses’ in QM–but in Many Worlds, everything would be happening with probability of 1 or 0–it would happen or be impossible. That makes sense in classical mechanics, but I’ve always thought that, in a situation where more than one outcome is usually possible (and where in the Big Picture a huge number of outcomes are ultimately possible), it starts to seem like there aren’t laws of physics. ‘Maverick’ universes outnumber ‘normal’ ones, without any real probability. I was thinking, isn’t that a problem above and beyond the Born Rule–or am I missing something?

Have a great Labor Day Weekend!!!

Well (if I understand your question) of course the problem with MWI is that all possible outcomes happen, each one in some world with some version of ‘the observer’. So it’s a notorious problem to make sense of the Born probabilities in that context, and a lot of the literature on this problem ends trying to base the probabilities on what a ‘rational agent’ would want or do–i.e. a subjectivist notion of probability. It’s also a notorious problem trying to relate all the descendant ‘observers’ to ‘the observer’ in the present. A very extravagant and ill-defined ontology IMHO. (People think my ontology is extravagant, but by comparison with MWI it is much simpler!)

Thanks, Ruth. I think you answered my question. I wasn’t doing a good job of wording it (and I’m a writer!). Maybe a better way of putting it is this: as you know, many interpretations (including Copenhagen, but not yours) see the Born Rule as something that must be assumed because it can’t be explained away, but they can produce no physical reason for it. As you state in the piece above, the formalism of TI seems to provide a reason for it. The murky question I was asking was, aren’t probabilities implied (regardless of an interpretation’s formalism) simply by assuming that there are multiple possible outcomes within a single set of physical laws? Incidentally, I think another reason Many Worlds is wrong is that it can’t explain consciousness. We never become aware of splitting, which implies there is no conscious action, yet the brain is aware that consciousness exists. Further, sense of self seems global in the brain (there is only one ‘I’), yet MWI is local and reductionistic; it shouldn’t allow even the illusion of a self to exist. On the other hand, your idea of the mind in some sense existing outside space-time works quite well with regard to consciousness!

Good points here.In my CUP book I give a quote (I don’t have the book with me now, it may have been a former MWI proponent who has now left the field–will try to follow up and get this) about how MWI makes the whole notion of probability meaningless. In fact, one could say that MWI is actualism run amok: in denying that these are possible (but not actual) outcomes, it ends up with a nondenumerable set of continually splitting ‘actual’ worlds. If there is only one actual world, but many possibilities, that is avoided–and of course we also get the Born Rule out of it in a physical way. Stu Kauffman and I (and another researcher) are currently working on a paper on this very point–the idea that quantum theory implies that possibilities are real (at least as quantum possibilities).

Interesting idea you present also re the mind and Self. MWI’ers might quibble–Albert for a while had a ‘Many Minds’ version of MWI but I think that fails on the basis ambiguity problem (discussed in my post on why splitting can’t really happen).

All of this got me to thinking–you’ve told me before that you are skeptical of the existence of singularities. Yet the usual way of resolving them involves quantum gravity, which you don’t believe exists. What I was wondering is–do you think singularities can’t happen because a confirmation wave couldn’t be sent back from them? And would this mean only that singularities can’t ACTUALLY happen, in space-time, but that they ‘happen’ or ‘exist’ in the substratum? A second question–you mentioned basis ambiguity, and how you’ve pretty well refuted Einselection for smuggling classicism into quantum states. But what I was wondering is, does it also smuggle in that notion of probability we’ve been discussing? Isn’t Einselection supposed to work because some states are overwhelmingly more LIKELY than others? Doesn’t that imply meaningful probability somewhere in QM? I was wondering if Zurek might be tacitly assuming the Born Rule, too?

We have to be careful here. I don’t recall exactly what you’re referring to here as far as what I said about singularities, but I don’t think that spacetime has singularities. The quantum interactions, remember, are not in spacetime–they’re in the substratum. Offers and confirmations are always sent between emitters and absorbers–these are QP (quantum possibilities). It’s only an actualized transaction that leads to the emergence of a spacetime interval, and that is always finite, so we never get a spacetime singularity in the transactional picture. Re the 2nd part of your question: yes, all unitary-only researchers have to just assume the Born Rule as a given.

I was just thinking that at some point as a star collapses you get to a point where nothing further can happen (?), where no more possibilities can be actualized, and it isn’t a singularity, really–but nothing else happens in space-time. Because there’s evidence that the things we call black holes exist (though they might not result in singularities), and I was thinking that at some point something that falls into one of them might be ‘permanently’ in the substratum? Or maybe you think black holes eventually rebound back outward?–I know that theory exists, too.

I’m WAY out of my depth here, I know! ;)

Well, black holes are specifically a prediction of the classical theory of gravitation, just as an electron radiating away all its energy and crashing into the nucleus is a prediction of classical electromagnetic theory. We know that the latter does not really happen. But yes, there is evidence for black holes and I think most astrophysicists think they do exist. I don’t claim the expertise in this area (astrophysics/cosmology) to express an opinion one way or the other. But I think that if they do exist, they don’t really correspond to spacetime singularities (as you suggest here).

Thanks, Ruth. Re the source of my question–I was referring to a question I asked last year, about whether the innermost part of a black hole might be in the substratum, and you told me that you’d once considered the same idea, but that you didn’t believe singularities actually existed. And I just got to thinking that maybe the ‘singularity’ isn’t a singularity because it doesn’t exist in spacetime, but is merely the ‘point’ where nothing more can be actualized. In which case it might be like your conception of vacuum energy–vacuum energy exists, but in the substratum, not ’empty space’. A ‘singularity’ might exist, yet it wouldn’t be a spacetime singularity, being rather a ‘place’ in Quantumland where nothing more can be actualized. Things that fall into a black hole eventually fall into Quantumland, in the form of offer waves that never get confirmed. And I don’t know–would Hawking Radiation and black hole sublimation be things that take place largely in the substratum, with the ‘singularity’ eventually ‘disappearing’ from the substratum as new particles appear? I admit this sounds a bit wacky.

Oh, by the way–I mentioned above your Harmony of that Heavenly City screenplay, and it sounded like I was cracking a joke. But I really was pleased to see you’d published it and wondered if it was the same version you sent me in March (or April) of 2016. I enjoyed it (and still have it on my computer) and would definitely tune in if it ever becomes a miniseries. :)

Thanks! Yes, essentially the same version. I sure wish somebody would produce it…IMHO a story that would be timely and worthwhile (as well as a fantastic soundtrack!)

I was thinking about your position on gravity being just part of the emergent spacetime structure. One thing that always gave me trouble with this was the idea of gravitational waves being transmitted between separate locales. But then I thought, the G-waves aren’t transmitted across a vacuum–other energy is traveling with them, establishing the space-time manifold in which gravity is expressed. Is that right?

Yes, the effects of G-waves are part of spacetime emergence, which in my proposal is mediated by transactions (usually involving the em field).

Another thing I’ve always been curious about–if gravity only emerges classically, and vacuum energy is something that takes place in the substratum, what does this say about the theory that vacuum energy has a repulsive gravitational force that helps account for accelerating cosmic expansion?

Do you mean ‘dark energy’? IMHO there is no such thing. It’s an artifact of the emergence process. See: https://arxiv.org/abs/1708.02907