The Relativistic Transactional Interpretation of Quantum Mechanics

The Transactional Interpretation of Quantum Mechanics attempts to resolve the apparent paradoxes left unsatisfactorily unraveled by other interpretations. One of its appealing qualities is its compatibility with and usefulness in making sense of experimental evidence without the introduction of hidden variables or conscious observers. By dispensing with these contrivances TIQM demystifies concepts that are glossed over or needlessly complicated by competing attempts to construe the quantum formalism. Ruth Kastner’s version of TIQM, the Possibilist Transactional (Possibilist has since been swapped with Relativist) Interpretation (RTI/PTI), differs in some key respects from John Cramer’s original proposal. Besides resolving causal loop challenges posed by Contingent Absorber Experiments, PTI also readily lends itself to explaining how spacetime arises and to the long-awaited reconciliation of quantum mechanics with general relativity.

Wheeler-Feynman absorber theory was initially formulated to make sense of electrodynamics by proposing all radiation sources emit half-advanced and half-retarded waves in a time symmetric fashion. WF fell out of favor, however, because it was believed a radiation source could not interact with its own field. It was later found that phenomena like Lamb Shift require self-interaction. In TI an absorber generates confirmation waves (CWs) in response to offer waves (OWs). Emitters and absorbers, as their names suggest, are entities that absorb or emit quanta. They are also field currents that can couple with other fields The Born Rule is a method of determining the probability of a given result in a quantum system. According to Landsman its meaning in each framework “hinges on some interpretation of probability.” In TI The Born Rule is just the product of the amplitudes of the OW and CW components. In PTI it is a crucial source of asymmetry and indeterminism.

Although the scaffolding for TIQM came from WH absorber theory, Cramer’s flash of insight came while discussing Einstein’s Bubble Paradox with a group of undergraduates. In this thought experiment a central source surrounded by detectors emits a sphere of light. When a photon localizes in space the bubble “pops” and the wave function collapses. What interested Einstein was how the entire globe knew this had happened. Heisenberg, toeing the Copenhagen line, dismissed the gedankenexperiment on the grounds that the resulting collapse can only be conceived of in terms of observer knowledge. How then should the instantaneous disappearance of the bubble be understood? The transactional process involves an emission, which acts as an offer wave, followed by a reply from the receiver in the form of a confirmation wave. In PTI a wave is an offer and a particle, like a photon appearing at a detection site, is an actualized transition. The quantum formalism, the same body of knowledge all interpretations strive to be consistent with, suggests there are multiple outcomes, but it does not tell us how or why only one has been realized.

The two slit experiment may have, in Feynman’s words, the “heart of quantum mechanics,” but there are few animals or thought experiments in the annals of science as iconic as Schrodinger’s Cat. From the vantage point of the ethically challenged experimentalist who has yet to open the box the cat can be considered partially dead, but it is obvious that something cannot be be partially dead or, more precisely, certain events cannot be partially completed. The particle has been emitted or it has not; the confirmation wave has been accepted or rejected. This all might seem considerably less exciting than narratives that bring consciousness to the postmortem (my apologies to the (1/2 )| alive⟩+ (1/2) | dead⟩ kitty for my poor word choice), but is it necessary? Moreover, when does the wave function collapse? Is it when the material decays, the Geiger counter is alerted, the box is opened or the paper is published? The Geiger Counter itself is a set of actualized transactions, not a quantum object. Applying tools from one level of analysis to another, not surprisingly, can lead to confusion.

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Scientists of the 19th century took Young’s experiment as proof of the wavelike nature of light because it exhibited diffraction, by bending through the slits, and interference, as evinced by the pattern left at the detection sites. In 1909 a low-intensity trial conducted by Sir Geoffrey Taylor showed the same interference pattern is obtained when it is formed one photon at a time. How does a single photon go through both slits at once and interfere with itself? After going through the single slit at point A, then through the two slits at B, the constructive and destructive interference patterns are formed after passing through C. Visualizing subatomic entities as tiny balls of energy can lead to confusion. This is graphically illustrated by Archibald Wheeler’s Delayed Choice Experiment, a variation of Young’s demonstration, wherein the removal of the screen determines whether the photon passes through only one or both slits. Making one measurement instead of another seems to affect the photon’s “decision” retroactively. The absorber sites on the screen responds with confirmation waves. This confusing state of affairs does not phase PTI because all parts of the OW go through both slits and so, mirroring them, all CWs do the same. The sudden removal of the screen does not change the course of the OW, but it does change the replies made by the CW, which will be returned by one of the two telescopes watching their respective slits. The OW can remain indeterminate until a confirmation is received, including one that comes, from our perspective, from the past.

This strangeness is not peculiar to photons and electrons. De Broglie won the Nobel Prize in 1929 for showing that other types of particles lead the same kind of double life. It is not easy to find the exact place to make the mark. Above it objects obey familiar classical laws, below it fall under the dictates of the minute. The Heisenberg Cut asks where the Schnitt between the classical realm and the wave function collapse – one where superposition is the norm, the other where it is unknown – is located. Fullerene, a molecule composed of 60 carbon atoms, can also find itself in a superposition between slits A and B. Functionalized porphyrin, C284.H190.F320.N4.S12, is the largest molecule thus far found to demonstrate diffraction and interference. Heisenberg himself called the Bohr, Slater, and Kramer’s probability wave a “quantitative version” of Aristotelian potentia, “a strange kind of physical reality just in the middle between possibility and reality.”

Where and how does TI make the Schnitt? There is no obvious place to put the area of material transmogrification, only a vast transitional mesoscopic continuum. More absorbers and means macroscopic laws are more likely to come into play. Having a large number of receivers and absorbers makes certain events almost unavoidable, thus endowing the world of everyday experience with solidity. Take the photoelectric effect as an example: the coupling of a photon with an electron is quite low, but given the sheer number of electrons in a single cubic centimeter of metal, about 1023, it is bound to happen. Unlike De Broglie waves, objects in spacetime – the observable actualizations of transactions – are always represented by real numbers. In quantum field theory the vacuum state is maximally nonlocal and has no spacetime arguments. The “spooky action at a distance” Einstein found so disturbing, largely thanks to the work of Freedman and Clauser, was shown to be as real as acceleration, time dilation, tables, and tangerines. If two entangled electrons are sent to opposite sides of the galaxy to have their spin measured by a Stern-Gerlach device one particle would know instantly if its sister’s spin changes.

Imaginary numbers are used to analyze De Broglie waves, which are used to describe quantum systems. For Descartes and his contemporaries the adjective “imaginary” was a term of abuse. Leonhard Euler called them “neither nothing, nor greater than nothing,” making them “imaginary or impossible. Yet no living physicist or electrical engineer would dispute their usefulness. Wrapping one’s mind around PTI requires a few heroic leaps outside of the commonplace, but similar leaps have been made by several pivotal figures in the history of modern physics. Niels Bohr asserted that quantum jumps “[transcend] the frame of space and time.” Minkowski space, which counterintuitively contains 3 + 1 dimensions, was found to be a logical consequence of special relativity. The Bohmians introduce hidden variables and the Everettians are perfectly at ease, William of Ockham be damned, with the endless creation of diverging universes. Given what its competitors resort to, and the unusual phenomena to be explained – which surely are not constrained by what human beings or any other organism considers “sensible” – PTI’s use of Hilbert Space, where each relevant variable has its own dimension, does not seem farfetched. Unlike Cramer, who views it is an unnecessary accoutrement which may not have a basis in reality, Kastner claims the atemporal domain of the very small may be best described with Hilbert Space, which reflects the “infinitely expansive ambiguity” of the quantum world, where classical phase space is “only one of an infinite number of ways to provide coordinationization.”

The original version of TI was compatible with relativity. This is just as true, if not more so, for PTI. How do the interactions of infinitesimal atoms give rise to the vast, stable, and fairly predictable universe with which we are familiar? Shimony asserts, in accordance with the PTI programme, the “domain governed by relativistic locality is the domain of actuality, while potentialities have ‘careers’ in spacetime which modify and even violate the restrictions that spacetime imposes upon actual events.” The ephemeral Electron Possibility Cloud gives rise to steel, granite, and bone. The Pauli Exclusion Principle tells us no two electrons can have the same quantum state, meaning their OWs have different amounts of energy and momentum. The Heisenberg Uncertainty Principle, although it applies to a number of different inequalities, is best known as a reminder of a precision trade off when trying to measure a particle’s momentum and position.In practice these two related concepts give electrons their incompressibility.

Parallels have been drawn between quantum collapse and spontaneous symmetry breaking. The background Higgs field can alter the ground state of an electron field. It has an infinite number of possible choices, but can select only one. The lack of, to borrow Leibniz’s phrase, a “sufficient cause” behind this selection conjures the dilemma of Buridan’s Ass, who stands between two stacks of equally delicious hay. Since there are no differences between the two it cannot pick just one, and so it starves. As evinced by the fact particles have mass, it is safe to say choices are made by the Higgs Mechanism and analogous processes in spite of a lack of a “sufficient cause.” Stewart and Golubitsky note that nature is overflowing with examples of spontaneously broken symmetries and situations in “choices” made for no discernible reason. PTI’s picture of nature is, at its core, fundamentally unbounded.

While PTI is not incompatible with the Block World conception of spacetime, where the order of events – past, present, and future – are arbitrary and exist together at once, its vision of time and space are quite different.Time is the byproduct of these “irreducibly stochastic” transactions. Although related to one another, time and space are not interchangeable in PTI. They are woven together by the transactions of entities in Hilbert space. The knitting is not done in time, but it creates space. The familiar rhythms of the natural world are the result of these events. This asymmetrical exchange, the fact there are more absorbers than emitters, is what creates the forward direction of time. Borrowing a phrase from Borges, Kastner calls the sort of unfettered selection that come about the emission of each offer waves“the garden of forking paths.” It can be seen in the motion of dust particles, which are nudged to and fro by the genuinely random perturbations of heat acting on the air.

Tim Maudlin claimed to have found“causal loop” issues with TIQM and, for a time, his thought experiment was widely seen as a refutation. Absorber B is placed behind A, which is to the right of the emitter. Absorber B will only swing around to the left side of the source if A fails to detect an emission.This means only A can return a CW and B can only return one if A does not, in which case it will certainly do so – but B’s probability has an amplitude of ½. His second criticism is of the failure of Cramer’s pseudotime account to make sense of the outcome because the transaction is decided without input from absorber B. This was quite valid because before introduction of hierarchical selection it was assumed all confirmations waves are received by the emitter at the same time. Kastner, however, does not believe hierarchical selection solves the problem of causal loops because such a scheme requires “clearly defined spacetime intervals.” Lastly, the ontologically indeterminate situations that arise in Contingent Absorber Experiment are a part of standard quantum mechanics, meaning that their existence cannot be considered a shortcoming of an interpretation.

Sider contends free will does not exist because conscious agents cannot extricate themselves from the Born Rule. Let’s say that there is a 99.999% chance Sally will eat a the warm chocolate chip cookie on the counter and a 0.001% chance she will swallow a clump of mud from her garden. Even in a less ridiculous situation the basic premise of the argument remains flawed. The Born Rule is applicable to clearly defined systems with clearly defined observables, in other words, systems that are astronomically less complex than the human brain. Kastner writes: “there is no justification for assuming that the agent would be in the same quantum state over any extended period of time, in particular the time interval in which repeated choices would be presented…one is dealing with an enormously complex and underdefined system.” Maybe the brain can alter the relevant microstates to utilize the indeterminacy of our unseen reality.

In The Quantum Handshake John Cramer notes that very few graduate level textbooks invite their readers to do anything but learn to calculate and accept the quantum formalism. Rightly or wrongly, they are primarily concerned with giving students the tools to solve problems in quantum mechanics and believe, rightly or wrongly, that addressing the whys? lurking underneath the formalism is extraneous, distracting, or of dubious benefit.

But on occasion it is natural and, dare I say, potentially productive to ask “well, what is it – really?”

Note by Dr. Kastner: "Regarding the Maudlin experiment, this is now nullified by the relativistic developments in PTI: https://arxiv.org/abs/1610.04609"

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