quantum mechanics phd thesis

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Excerpts from the dissertation which Paul A. M. Dirac wrote in order to obtain his Ph. D. from the University of Cambridge. Dirac's dissertation on quantum mechanics includes his notes; a preface; a table of contents; and topics such as algebraic axioms, quantum numbers, and the motion of a particle within a central field.

Dissertation

72 p. : ill.

463297204 353070 FSDT353070 fsu:641

Quantum theory.

Paul A.M. Dirac Papers, 1788-1999

http://purl.fcla.edu/fsu/MSS_1989-009

Special Collections & Archives, Florida State University Libraries, Tallahassee, Florida.

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Quantum Mechanics, PhD Dissertation by Paul Adrien Maurice Dirac b19020808 d19841020 [192605]

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The Historical and Physical Foundations of Quantum Mechanics

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5 Further steps to quantum mechanics: Louis de Broglie and the world’s most important PhD thesis

Published: February 2023
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Working on his Ph.D. thesis, Louis de Broglie asked himself this question: If light, thought to be a wave motion because of observed interference and diffraction effects, could behave like a particle, might particles exhibit some wave-like properties? He justified this idea with several arguments which are highly relevant to an understanding of quantum theory. Among these was the fact that the Bohr-Sommerfeld condition can be derived from the association of a wave with particle motion. This was a critically significant step in the development of quantum mechanics. This work was presented in a relatively short Ph.D. dissertation.

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Philipp Köhler, PhD Thesis University of Vienna (2022): " Towards Quantum Experiments on Gravitating Objects "

Lorenzo Magrini, PhD Thesis University of Vienna (2021): “ Quantum measurement and control of mechanical motion at room temperature ”

Claus-Markus Gärtner, PhD Thesis University of Vienna (2020): Advanced membrane architectures for multimode opto-mechanics

Uros Delic, PhD Thesis University of Vienna (2019): Cavity cooling by coherent scattering of a levitated nanosphere in vacuum

Julian Fesel, PhD Thesis University of Vienna (2019): Molcular anions as a coolant for antimatter experiments

Ramon Moghadas Nia, PhD Thesis Universität Wien/Leibniz Universität Hamburg (2018): Multimode optomechanics in the strong cooperativity regime - Towards optomechanical entanglement with micromechanical membranes

Ralf Riedinger, PhD Thesis Universität Wien (2018): Single Phonon Quantum Optics - An experimental exploration of a silicon photonics quantum memory

David Grass, PhD Thesis Universität Wien (2018): Levitated optomechanics in vacuum using hollow core photonic crystal fibers and optical cavities

Jason Hoelscher-Obermaier, PhD Thesis Universität Wien (2017): Generation and Detection of Quantum Entanglement in Optomechanical Systems

Jonas Schmöle, PhD Thesis Universtät Wien (2017): Development of a micromechanical proof-of-principle experiment for measuring the gravitational force of milligram masses

Sebastian Hofer, PhD Thesis Universität Wien (2015): Quantum Control of Optomechanical Systems

Michael Vanner, PhD Thesis Universität Wien (2013): Continuous and Pulsed Cavity Quantum Optomechanics

Simon Gröblacher, PhD Thesis, Universität Wien (2010): Quantum opto-mechanics with micromirrors: combining nano-mechanics with quantum optics

Hannes Rene Böhm, PhD Thesis, Universität Wien (2007): Radiation Pressure Cooling of a Mechanical Oscillator

Master/Diploma Theses

Livia Egyed, Master Thesis, Universität Wien (2022): Light induced dipole dipole interactions between optically levitated nanoparticles

Constanze Bach, Master Thesis, Universität Wien (2021): Detection of a levitated particle's mechanical motion close to the Heisenberg limit

Klemens Winkler, Master Thesis, Universität Wien (2018): An analytical and computational approach to steady-state optomechanical systems by quantum Langevin equations

Manuel Reisenbauer, Master Thesis, Universität Wien (2018): Dissipative Optomechanics on a Levitated Microresonator

Martin Siegele, Master Thesis, Universität Wien (2017): Particle synthesis, preparation, and loading for cavity optomechanics

Hans Hepach, Master Thesis, Universität Wien (2015): Design and Characterisation of a Low-Noise, Audio-Band Photodetector at 100mW Optical Power

Julian Fesel, Master Thesis, Universität Wien (2014): Position readout of an optically trapped nano sphere in a hollow core photonic crystal fiber as a step towards parametric feedback cooling

Ralf Riedinger, Master thesis, Universität Marburg/Universität Wien (2013): Optomechanical State Reconstruction and Optical Noise Reduction for Cavity Optomechanical Experiments

Uroš Delić, Master thesis, Universität Wien (2013): Optical readout and control of a levitated dielectric sphere inside a high-finesse cavity

David Grass, Master thesis, Universität Wien (2013): Optical Trapping and Transport of Nanoparticles with Hollow Core Photonic Crystal Fibers

Jonas Schmöle, Master thesis, Universität Wien (2011): Towards magnetic levitation in optomechanics

Dilek Demir, Diploma thesis, Universität Wien (2011): A table-top demonstration of radiation pressure

Alexey Trubarov, Diploma thesis, Universität Wien (2010): Measurement of thermal bath of a harmonic oscillator

Katharina Gugler, Diploma thesis, Universität Wien (2008): Aufbau eines Faser-Interferometers zur Charakterisierung von mikromechanischen Spiegeln

Florian Blaser, Diploma thesis, Université de Neuchâtel (2008): Mechanical FEM Analysis and Optical Properties of micromirrors for radiation-pressure experiments

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Quantum Physics

Title: non-classical correlations in quantum mechanics and beyond.

Abstract: Is entanglement an exclusive feature of quantum systems, or is it common to all non-classical theories? And if this is the case, how strong is quantum mechanical entanglement as compared to that exhibited by other theories? The first part of this thesis deals with these questions by considering quantum theory as part of a wider landscape of physical theories, collectively called general probabilistic theories (GPTs). Among the other things, this manuscript contains a detailed introduction to the abstract state space formalism for GPTs. We start with a comprehensive review of the proof of a famous theorem by Ludwig that constitutes one of its cornerstones (Ch. 1). After explaining the basic rules of the game, we translate our questions into precise conjectures and present our progress toward a full solution (Ch. 2). In Ch. 3 we consider entanglement at the level of measurements instead of states, focusing on one of its main implications, i.e. data hiding. We determine the maximal data hiding strength that a quantum mechanical system can exhibit, and also the maximum value among all GPTs, finding that the former scales as the square root of the latter. In the second part of this manuscript we look into quantum entanglement. In Ch. 4 we discuss the entanglement transformation properties of a class of maps that model white noise acting either locally or globally on a bipartite system. In Ch. 5 we employ matrix analysis tools to develop a unified approach to Gaussian entanglement. The third part of this thesis concerns more general forms of non-classical correlations in bipartite continuous variable systems. In Ch. 6 we devise a general scheme that allows to consistently classify correlations of bipartite Gaussian states into classical and quantum ones. Finally, Ch. 7 explores some problems connected with a certain strong subadditivity matrix inequality.

Comments:	PhD thesis, 377 pages, 8 figures
Subjects:	Quantum Physics (quant-ph); Mathematical Physics (math-ph); Functional Analysis (math.FA)
Cite as:	[quant-ph]
	(or [quant-ph] for this version)
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Doctoral dissertation and first publication of his formulation of quantum mechanics (1957)

On March 1, 1957, Everett submitted his 36-page doctoral dissertation, "On the Foundations of Quantum Mechanics", in a footnote to which he writes that it would be too much to hope that the revised wording avoids every misunderstanding or ambiguity [37] . Bryce DeWitt later published [44] the background of how Wheeler sat down with Everett and told him precisely what to omit from the manuscript of 1956. So when the article "'Relative State' Formulation of Quantum Mechanics" [45] was published, there was published with it an assessment by Wheeler [46] . This article of Everett's differed from his 1957 dissertation only by minor stylistic changes. In comparison with the 1956 paper, however, it is practically new text (no more than 20-30 percent of the texts coincide and the sequence of parts differs). Fortunately, DeWitt, known for his refined courtesy, found time to shed additional light on this history. He has stated that Everett himself re-wrote the "large" thesis (Urwerk) into a "small" one based on Wheeler's instructions. Wheeler, according to DeWitt, was motivated in part by his wish not to spoil his relations with Bohr [38] .

John Wheeler, in his autobiography [24a, copy kindly provided by Kenneth Ford on behalf of John Wheeler] , provides more evidence about this story. On pp. 268-271, Wheeler recalls that he could sense the depth of Everett's dissertation (the draft version of January 1956, the version that DeWitt later called the Urwerk), yet "found the draft barely comprehensible. I knew that if I had that much trouble with it, other faculty members on his committee would have even more trouble. They not only would find it incomprehensible; they might find it without merit. So Hugh and I worked long hours at night in my office to revise the draft. Even after that effort, I decided the thesis needed a companion piece, which I prepared for publication with his paper. My real intent was to make his thesis more digestible to his other committee members". [24a, p. 268] (This interaction with Everett came just after Wheeler's extremely productive period, 1954-56, when he achieved some of his most important results, including the ideas of geons-which were never accepted by Einstein-and of quantum foam. [24a, pp. 237-263] )

On March 10, 1957, Everett and Wheeler started to dispatch preprints of their articles, and during the next two days Everett participated in a large conference on game theory at Princeton [22] . In a copy of their mailing list it is marked that answers came from Petersen, Groenewald, and Norbert Wiener [47] . (In the cover letter it is mentioned that the articles are intended for publication in Reviews of Modern Physics as part of the Proceedings of "the recent Chapel Hill Conference." That conference, on the subject of "The Role of Gravitation in Modern Physics," was held at the beginning of March at the University of North Carolina, Chapel Hill. Among the conference participants was Richard Feynman [48] , but, according to the conference organizer, Cecile DeWitt-Morette, Everett did not attend [49] .)

On April 15 1957, Everett formally presented his dissertation for defense. Wheeler and his faculty colleague V. Bargmann wrote in their assessment that Everett's formulation of the problem and his solution were almost completely original, and suggested that the thesis "may be a significant contribution to our understanding of the foundations of quantum theory." Accordingly, they recommended acceptance of the dissertation [50] . The oral examination took place on April 23. The principal examiners-Wheeler, Bargmann, H. W. Wyld, and R. H. Dicke-concluded: "The candidate passed a very good examination. He dealt with a very difficult subject and defended his conclusions firmly, clearly, and logically. He shows marked mathematical ability, keenness in logic analyses, and a high ability to express himself well." [51] .

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Paul Dirac’s PhD Thesis: the First Ever Written on Quantum Mechanics

Physics , Short but Cool!
June 12, 2023

Paul Dirac is real-life Sheldon Cooper. And Dirac’s PhD thesis is an unparalleled masterpiece in the field of science. At the incredibly young age of 24, Dirac submitted a revolutionary dissertation laying the foundational ideas of the general theory of quantum mechanics, considered one of the most significant breakthroughs in science. The thesis is like no other, combining a child’s tidy writing and an extraterrestrial’s complex symbols. It is a fascinating work that is significant for its intellectual depth and the exceptional thought process and research that went into it. It continues to inspire and challenge scientists to this day.

The world of quantum mechanics has always been a topic of fascination for many people, including young scientists. One of the brightest minds to ever grace this field is Paul A. M. Dirac, who wrote his Ph.D. thesis on the subject at the University of Cambridge. Dirac’s dissertation is notable for being the first-ever written on quantum mechanics, making it an important milestone in the field.

Paul Dirac’s PhD thesis: Quantum Mechanics

Paul Dirac’s PhD thesis, titled “Quantum Mechanics,” was a significant contribution to the field of quantum physics. The dissertation delved deep into the mathematical foundations of quantum mechanics and explored topics such as algebraic axioms, quantum numbers, and the motion of a particle within a central field. His dissertation was more remarkable because it was primarily based on his research rather than just a summary of past research and experiments. This was one of the reasons why Dirac’s dissertation was seen as an important piece of work.

One of the most interesting aspects of Paul Dirac’s PhD thesis is the handwritten notes that he included in it. The notes give us a glimpse into Dirac’s thought processes and how he worked through complex problems. One example is the page where he wrote out the equations of motion for a particle under the influence of a central force. After several iterations, he finally arrived at the correct formula, later known as the Dirac equation. It is fascinating to see how he arrived at such a significant equation through his notes.

Another interesting thing about Dirac’s handwritten notes is that they are filled with notations and symbols that only he could understand. He used his unique notation system for algebraic expressions, making it easier to work through problems. While it might be challenging for someone unfamiliar with his system to read through his notes, they are a testament to the fact that he was a genius who saw mathematics in a different light.

Aside from his handwritten notes, Dirac’s preface was also notable. In it, he acknowledged the work of several other scientists who were also exploring the field of quantum mechanics. He also explained his research in a way that was accessible to his peers and the general public. Dirac’s writing style was clear and concise, making his dissertation enjoyable for anyone interested in the subject.

Paul Dirac’s handwritten notes for his Ph.D. thesis testify to his brilliance and contributions to the quantum mechanics field. His dissertation was an essential milestone in the field, and the handwritten notes he included in it are a fascinating insight into his thinking process. Dirac’s research on quantum mechanics opened up new avenues of thought and sparked creative thinking in many scientists. Today, his legacy lives on, inspiring new scientists to explore the fascinating world of quantum mechanics.

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PAWS Princeton Advanced Wireless Systems

Phd thesis: quantum and quantum-inspired computation for mimo communications in wireless networks.

A central design challenge for future generations of wireless networks is to meet users’ ever-increasing demand for capacity, throughput, and connectivity. Recent advances in the design of wireless networks to this end, including the NextG efforts underway, call in particular for the use of Large and Massive multiple input multiple output (MIMO) antenna arrays to support many users near a base station. These techniques are coming to fruition, yielding significant performance gains, spatially multiplexing information streams concurrently. To fully realize MIMO’s gains, however, the system requires sophisticated signal processing to disentangle the mutually-interfering streams from each other. Currently deployed linear filters have the advantage of low computational complexity, but suffer from rapid throughput degradation for more parallel streams. Theoretically optimal Maximum Likelihood (ML) processing can significantly improve throughput over such linear filters, but soon becoming infeasible due to its computational complexity and limitations in processing time. The base station’s computational capacity is thus becoming one of the key limiting factors on performance gains in wireless networks. Quantum computing is a potential tool to address this computational challenge. It exploits unique information processing capabilities based on quantum mechanics to perform fast calculations that are intractable by traditional digital methods. This dissertation presents four design directions of quantum compute-enabled wireless systems to expedite the ML processing in MIMO systems, which would unlock unprecedented levels of wireless performance: (1) quantum optimization on specialized hardware, (2) quantum-inspired computing on classical computing platforms, (3) hybrid classical-quantum computational structures, and (4) scalable and elastic parallel quantum optimization. We introduce our prototype systems (QuAMax, ParaMax, IoT-ResQ, X-ResQ) that are implemented on real-world analog quantum processors, experimentally demonstrating their substantial achievable performance gains in many aspects of wireless networks. As an initial guiding framework, this dissertation provides system design guidance with underlying principles and technical details and discusses future research directions based on the current challenges and opportunities observed.

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Everettian Quantum Mechanics

Hugh Everett III proposed solving the quantum measurement problem by adopting pure wave mechanics, the theory one gets by dropping the collapse dynamics from the standard von Neumann formulation of quantum mechanics. Everett’s relative state formulation consists in pure wave mechanics supplemented with a distinction between absolute and relative states, a model of situated observation, and a standard of typicality. His aim was to recapture the predictions of the standard collapse theory by showing that the relative records of a typical situated observer will satisfy the standard quantum statistics. We will consider his theory and several quite different ways of understanding it.

1. Introduction

2. the measurement problem, 3.1 determinate records, 3.2 probabilities, 4. empirical faithfulness, 5.1 experience is found in the relative memory records of observers, 5.2 pure wave mechanics predicts that one would not ordinarily notice that there are alternative relative records, 5.3 the surplus structure of pure wave mechanics is in principle detectable and hence isn’t surplus structure at all, 5.4 a typical relative sequence of measurement records exhibits the standard quantum statistics, 6. empirical faithfulness and empirical adequacy, 7. many worlds, 8.1 the bare theory, 8.2 many minds and hidden variables.

8.3 Many Histories

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Related entries.

Everett developed his relative-state formulation of quantum mechanics while a graduate student in physics at Princeton University. The short version of his doctoral thesis (1957a) was accepted in March 1957 and a paper (1957b) covering essentially the same material was published in July of the same year. The short version of his thesis was revised from a longer draft thesis that Everett had given John Wheeler, his Ph.D. adviser, in January 1956 under the title “Wave Mechanics Without Probability”. DeWitt and Graham (1973) later published a version of the long thesis in an anthology of papers on Everett’s theory. While Everett always favored the description of the theory as presented in the long thesis, in part because of Bohr’s disapproval of Everett’s critical approach, Wheeler insisted on the revisions that led to the much shorter version that Everett ultimately defended.

Everett took a job outside academics as a defense analyst in the spring of 1956. Subsequent notes and letters indicate that he continued to be interested in the conceptual problems of quantum mechanics and in the reception of his theory, but he did not take an active role in the debates surrounding either. Everett died in 1982. See Byrne (2007) and (2010) for further biographical details and Barrett and Byrne (2012) for an annotated collection of Everett’s papers, notes, and letters regarding quantum mechanics. See also Osnaghi, Freitas, Freire (2009) for an excellent introduction to the history of Everett’s formulation of quantum mechanics.

Everett’s relative state formulation was a direct reaction to the measurement problem faced by the standard von Neumann collapse formulation of quantum mechanics. Everett understood the measurement problem in the context of his own version of the Wigner’s Friend story, a version published four years before Wigner’s (1961). In brief, Everett’s solution to the problem was to drop the collapse postulate from the standard formulation of quantum mechanics then deduce the empirical predictions of the standard collapse theory as the subjective experiences of observers who were themselves modeled as physical systems in the theory. The result was his relative-state interpretation of pure wave mechanics.

In order to understand Everett’s solution to the quantum measurement problem, it is helpful first to understand just what he took the problem to be. We will start with this, then consider his presentation of the relative-state formulation of pure wave mechanics and the sense in which he took it to solve the quantum measurement problem. We will then consider how one might get a theory that provides a richer account of determinate quantum records and probabilities.

Everett presented the relative-state formulation of pure wave mechanics as a way of avoiding the conceptual problems encountered by the standard von Neumann collapse formulation of quantum mechanics. Everett took the chief problem to be that the standard theory required observers to be treated as external to the system described by the theory. One consequence of this, he thought, was that the theory consequently fails to provide a consistent description the physical universe. Everett distinguished between the standard von Neumann formulation of quantum mechanics and Bohr’s Copenhagen interpretation. He believed that the latter was in an important sense yet less satisfactory as it did not even aim to provide a consistent description of the process of observation (1956, 152–3). We will follow the main argument of Everett’s long thesis starting with the measurement problem as encountered by the standard collapse theory.

The standard collapse formulation of quantum mechanics, as Everett understood it, is based on the following principles (von Neumann, 1955):

Representation of States : The state of a physical system $S$ is represented by an element of unit length in a Hilbert space, a complex-valued vector space with an inner product.
Representation of Observables : Every physical observable $O$ is represented by a Hermitian operator $\boldsymbol{O}$ on the Hilbert space representing states, and every Hermitian operator corresponds to some physical observable. Equivalently, the observable $O$ can be thought of as being represented by the orthonormal basis consisting of the eigenvectors of $\boldsymbol{O}$.
Standard Interpretation of States : A system $S$ has a determinate value for an observable $O$, and hence determinately has the corresponding physical property, if and only if the state of $S$ is represented by an eigenvector of $\boldsymbol{O}$. If so, then one would with certainty get the corresponding eigenvalue as the result of measuring $O$ of $S$.
Two Dynamical Laws : (a) If no measurement is made, then a system $S$ evolves in a continuous deterministic way according to the linear dynamics, which depends only on the energy properties of the system. (b) If a measurement is made of $S$, then the system instantaneously and randomly jumps to an eigenstate of the observable being measured. The probability of each possible post-measurement state is equal to the norm squared of the projection of the initial state onto the final state.

Everett referred to the standard von Neumann theory as the “external observation formulation of quantum mechanics” and discussed it in both the long (1956) and short (1957) versions of his thesis (beginning on pages 73 and 175 respectively). While he believed that the standard collapse theory was ultimately unacceptable, he used it as the starting point for his presentation of pure wave mechanics. The latter theory he characterized as the standard collapse theory but without the collapse dynamics (rule 4b). We will briefly consider the roles played by rule (4a) and (4b) and the measurement problem then consider Everett’s discussion of the Wigner’s Friend story and his proposal for replacing the standard theory with pure wave mechanics.

The linear dynamics (rule 4a) plays an essential role in the standard collapse theory. It explains how a system might come to be in a superpositions of different classical states and how two systems may come to be quantum-mechanically entangled, which in turn explains quantum inference effects and quantum nonlocality. But given the standard interpretation of states (rule 3), the linear dynamics cannot on its own explain how measurements yield determinate measurement records that exhibit the standard quantum probabilities. For most initial states, the linear dynamics predicts that a measurement interaction would produce a physical record in an entangled superposition of recording mutually incompatible measurement results, something like state $\boldsymbol{E}$ below). On the standard interpretation of states, this is not a state where there is any determinate physical record at all. Hence, the collapse dynamics (rule 4b) is apparently essential to how the standard theory explains determinate physical records, and in doing so it also explains why one should expect each physically possible record with the usual quantum probabilities.

The deterministic linear dynamics (rule 4a), then, describes how a system evolves when there is no measurement , and the stochastic nonlinear dynamics (rule 4b) describes how a system evolves when there is a measurement . Note that the term measurement occurs in the theory as an undefined primitive term. Without saying what it takes for an interaction to count as a measurement, the theory is at best incomplete since it does not indicate when each dynamical law obtains. Further, if one supposes that observers and their measuring devices are physical systems like any other (and why wouldn’t they be?), they must also evolve in a continuous deterministic way, and nothing like the random, discontinuous evolution described by rule 4b can ever occur. In this case, stipulating a collapse on measurement yields an immediate contradiction. This is the quantum measurement problem. See Barrett (2020) and the section on the measurement problem in the entry on philosophical issues in quantum theory for further discussions.

Everett took the standard formulation of quantum mechanics to be logically inconsistent, and hence untenable, because it did not allow one to provide a consistent account of nested measurement. He illustrated the problem in the context of an “amusing, but extremely hypothetical drama” (1956, 74–8), a story that was famously retold by Eugene Wigner (1961) a few years later.

Everett’s version of the Wigner’s Friend story involved an observer $A$ who knows the state function of some system $S$, and knows that it is not an eigenstate of the observable he is about to measure of it, and an observer $B$ who is in possession of the state function of the composite system $A{+}S$. Observer $A$ believes that the outcome of her measurement on $S$ will be randomly determined by rule 4b, hence $A$ attributes to $A{+}S$ a post-measurement state describing $A$ as having a determinate measurement record and $S$ as having collapsed to the corresponding state. Observer $B$, however, attributes the state function of the room after $A$’s measurement according to the rule 4a, hence $B$ attributes to $A{+}S$ an entangled state where, according to rule 3, neither $A$ nor $S$ even has a determinate quantum-mechanical state of its own. Everett held that since $A$ and $B$ make incompatible state attributions to $A{+}S$, the standard collapse theory commits one to a straightforward contradiction.

It would be extraordinarily difficult in practice to isolate and control a composite system like $A{+}S$ in such a way that $B$ would be able even to calculate how its state evolves. This is one of the reasons Everett referred to the drama as “extremely hypothetical”. But he was also careful to explain why this practical difficulty was irrelevant to the conceptual problem faced by the standard theory. Indeed, he explicitly rejected that one might simply “deny the possibility that $B$ could ever be in possession of the state function of $A{+}S$.” Rather, he argued, that “no matter what the state of $A{+}S$ is, there is in principle a complete set of commuting operators for which it is an eigenstate, so that, at least, the determination of these quantities will not affect the state nor in any way disrupt the operation of $A$,” nor, he added, are there “fundamental restrictions in the usual theory about the knowability of any state functions.” And he concluded that “it is not particularly relevant whether or not $B$ actually knows the precise state function of $A{+}S$. If he merely believes that the system is described by a state function, which he does not presume to know, then the difficulty still exists. He must then believe that this state function changed deterministically, and hence that there was nothing probabilistic in $A$’s determination” (1956, 76). And, Everett argued, $B$ is right in so believing.

It is a key feature of both Everett’s understanding of the measurement problem and how his own formulation of quantum mechanics worked that $B$ might in principle show by means of an interference measurement that the state resulting from $A$’s interaction with $S$ was in fact the entangled superposition of incompatible records predicted by the linear dynamics (a state like $\boldsymbol{E}$ below). Indeed, that it is always in principle possible to make such a measurement is why Everett held every element of the superposition to be real: “It is … improper to attribute any less validity or ‘reality’ to any element of a superposition than any other element, due to this ever present possibility of obtaining interference effects between the elements. All elements of a superposition must be regarded as simultaneously existing” (1956, 150).

That Everett took the Wigner’s Friend story, which involves an experiment that would be virtually impossible to perform because of environmental decoherence effects, to pose the central conceptual problem for quantum mechanics is essential to understanding how he thought of the measurement problem and what it would take to solve it. In particular, he held that one only has a satisfactory solution to the quantum measurement problem if one can account for nested measurement in a consistent way. Being able to tell the Wigner’s Friend story in one’s theory is a necessary condition for a satisfactory resolution of the quantum measurement problem.

3. Everett’s Deduction

In order to solve the measurement problem, Everett proposed dropping the collapse dynamics (rule 4b) from the standard collapse theory and taking the resulting theory to provide a complete and accurate description of all physical systems at all times. He called the resultant theory pure wave mechanics . Everett believed that he could deduce the standard statistical predictions of quantum mechanics, the predictions that depend on rule 4b in the standard collapse formulation, in terms of the subjective experiences of observers who are themselves treated as ordinary physical systems within pure wave mechanics. We will discuss how this deduction was supposed to work in some detail.

Everett sketched the outline of his deduction in the long thesis:

We shall be able to introduce into [pure wave mechanics] systems which represent observers. Such systems can be conceived as automatically functioning machines (servomechanisms) possessing recording devices (memory) and which are capable of responding to their environment. The behavior of these observers shall always be treated within the framework of wave mechanics. Furthermore, we shall deduce the probabilistic assertions of Process 1 [rule 4b] as subjective appearances to such observers, thus placing the theory in correspondence with experience. We are then led to the novel situation in which the formal theory is objectively continuous and causal, while subjectively discontinuous and probabilistic. While this point of view thus shall ultimately justify our use of the statistical assertions of the orthodox view, it enables us to do so in a logically consistent manner, allowing for the existence of other observers (1956, 77–8).

More specifically, Everett’s goal was to show that the relative records of a typical observer in pure wave mechanics would exhibit the statistical properties predicted by the collapse dynamics. In order to so, he needed to supplement pure wave mechanics with a small handful of background assumptions.

Expressed in the language of his Wigner’s Friend story, Everett insisted on three things: (1) there are no collapses of the quantum-mechanical state, hence observer $B$ is correct in attributing to $A{+}S$ a state where observer $A$ is in an entangled superposition of having recorded mutually incompatible results, (2) there is a sense in which $A$ nevertheless gets a perfectly determinate measurement record, and (3) typical sequences of such records will satisfy the standard quantum statistics.

The main task in understanding what Everett had in mind is in figuring out precisely how the correspondence between the predictions of the standard collapse theory and those of pure wave mechanics was supposed to work. One problem is that the former theory is stochastic with fundamentally chance events while the latter is deterministic with no mention of probabilities whatsoever. Another is that since an observer like $A$ will typically fail to have any determinate record on the standard interpretation of states, one needs a new way of understanding the post-measurement state of the composite system $A{+}S$, a way that provides a sense in which $A$ might be said to have a determinate measurement record.

Consider measuring the $x$-spin of a spin-½ system. Such a system will be found to be either “$x$-spin up” or “$x$-spin down”. Suppose that $J$ is a good observer. For Everett, being a good $x$-spin observer meant that $J$ has the following two dispositions, where the arrows below represent the time-evolution of the composite system as described by rule 4a:

So if $J$ measures a system that is determinately $x$-spin up, then $J$ will determinately record “$x$-spin up”; and if $J$ measures a system that is determinately $x$-spin down, then $J$ will determinately record “$x$-spin down”. And in each case we will suppose that the spin of the object system $S$ is undisturbed by the interaction.

Now consider what happens when $J$ observes the $x$-spin of a system that begins in a superposition of $x$-spin eigenstates:

The initial state of the composite system is:

Here $J$ is determinately ready to make an $x$-spin measurement, but the object system $ S$, according to rule 3, has no determinate $x$-spin. Given $J$’s two dispositions and the fact that the deterministic dynamics (rule 4a) is linear, the state of the composite system after her $x$-spin measurement will be:

Call this state $\boldsymbol{E}$ . On the standard formulation of quantum mechanics, at some point during the measurement interaction the state collapses resulting in either

each with probability 1/2. In the former case, $J$ ends up with the determinate measurement record “spin up”, and in the later she ends up with the determinate measurement record “spin down”.

In contrast, no such collapse occurs on Everett’s proposal. Rather, the post-measurement state of the composite system is $\boldsymbol{E}$, the state resulting from the linear dynamics alone, an entangled superposition of $J$ recording the result “spin up” and $S$ being $x$-spin up and $J$ recording “spin down” and $S$ being $x$-spin down. On the standard interpretation of states (rule 3), $\boldsymbol{E}$ is not a state where $J$ determinately records “spin up” nor is it a state where $J$ determinately records “spin down”. Indeed, it is not even a state where $J$ has a determinate state to call her own as the state of the composite system does not factor.

Further, Everett held that one might, at least in principle, show by means of a Wigner’s Friend interference experiment that the post-measurement state is in fact $\boldsymbol{E}$. Consider an observable $\boldsymbol{A}$ of the composite system $J{+}S$ that has state $\boldsymbol{E}$ as an eigenstate corresponding to eigenvalue +1 and the orthogonal state

as an eigenstate corresponding to eigenvalue $-1.$ If Everett is right and $\boldsymbol{E}$ is in fact the post-measurement state, then an observation of $\boldsymbol{A}$ would always yield $+1.$ But if a collapse occurs in the interaction between $J$ and $S,$ then an $\boldsymbol{A}$-measurement might yield $+1$ or $-1,$ each with probability 1/2 since the post-measurement collapsed states are at 45 degree angles to the rays containing the eigenstates of $\boldsymbol{A}$.

By insisting that $\boldsymbol{E}$ was in fact the post-measurement state of the composite system, Everett faced two problems. The determinate-record problem required him to explain how this state is compatible with observer $J$ having a determinate measurement record. And the probability problem required him to recover, in some sense, the standard quantum probabilities for such determinate records.

Everett appealed to a principle he called the fundamental relativity of states to distinguish between absolute and relative states:

There does not, in general, exist anything like a single state for one subsystem of a composite system. Subsystems do not possess states that are independent of the states of the remainder of the system, so that the subsystem states are generally correlated with one another. One can arbitrarily choose a state for one subsystem, and be led to the relative state for the remainder. Thus we are faced with a fundamental relativity of states , which is implied by the formalism of composite systems. It is meaningless to ask the absolute state of a subsystem—one can only ask the state relative to a given state of the remainder of the subsystem. (1956, 103; 1957, 180)

The distinction between absolute and relative states allows for a richer interpretation of states than that provided by rule 3 alone. Namely, it provides a relative state in the post-measurement absolute state on which a relative observer’s determinate measurement record might supervene.

While the absolute state $\boldsymbol{E}$ is one where $J$ has no determinate absolute record and $S$ has no determinate absolute $x$-spin, $J$ records “$x$-spin up” relative to $S$ being $x$-spin up and $J$ records “$x$-spin down” relative to $S$ being $x$-spin down. Everett associates an observer’s experience with her relative records:

Let one regard an observer as a subsystem of the composite system: observer + object-system. It is then an inescapable consequence that after the interaction has taken place there will not, generally, exist a single observer state. There will, however, be a superposition of the composite system states, each element of which contains a definite observer state and a definite relative object-system state. Furthermore, as we shall see, each of these relative object system states will be, approximately, the eigenstates of the observation corresponding to the value obtained by the observer which is described by the same element of the superposition. Thus, each element of the resulting superposition describes an observer who perceived a definite and generally different result, and to whom it appears that the object-system state has been transformed into the corresponding eigenstate. (1956, 78).

Each relative observer then has a determinate relative record. That is, each element or branch of $\boldsymbol{E}$ describes a relative observer with a corresponding determinate relative measurement record. The sense in which this accounts for our experience is given by Everett’s notion of empirical faithfulness, something we will discuss after laying the groundwork for his account for quantum probabilities.

Everett sought to address the probability problem by showing that a typical sequence of relative records will exhibit the standard quantum statistics. To show that records in typical branches exhibit the standard quantum statistics he needed a typicality measure over branches, something that is not given by pure wave mechanics itself. As he put the point, “In order to make quantitative statements about the relative frequencies of the different possible results of observation which are recorded in the memory of a typical observer we must have a method of selecting a typical observer” (1956, 124).

Everett introduced his typicality measure by imposing a sequence of formal constraints until a measure was uniquely determined. In particular, he required that the typicality measure $m$ (1) satisfy the standard axioms for being a probability measure, (2) be a positive function of the complex-valued coefficients associated with the branches of the superposition, and (3) satisfy a sub-branch additivity condition to ensure that the sum of the measures on branches are equal to the measure on the initial ancestor branch before branching. Together, he took these constraints to determine $m$ to be the norm-squared-amplitude measure over branches. See Everett (1956, 123–8) and (1957, 188–93) and Barrett and Byrne (2012, 274–5) for his description of his typicality measure, how he justified it, and how he intended for it to work in his account of quantum statistics.

Consider state $\boldsymbol{E}$ above. Here $m$ assigns measure 1/2 to the first branch and measure 1/2 to the second branch. While $m$ assigns a measure to each branch equal to the probability that would be assigned to the corresponding outcome on the standard collapse theory, $m$ is a typically measure and hence says nothing whatsoever regarding the probability of the alternative measurement outcomes. Indeed, inasmuch as he took all branches to be equally actual, Everett took the probability associated with each branch to be one. While the typicality measure is across branches , the subjective appearance of quantum probabilities was to be explained by the sequence of records within a typical branch .

The setup for Everett’s argument went as follows. Consider a measuring device M that is ready to make and record an infinite series of measurements on each of an infinite series of systems $S_k$ each in state:

Suppose that M interacts with each system in turn and perfectly correlates its $k$th memory register with the $x$-spin of system $S_k$ by the linear dynamics. This will produce an increasingly complicated entangled superposition of different sequences of measurement outcomes. After one measurement, the state of M and $S_1$ will be:

After two measurements, the state of M, $S_1$, and $S_2$ will be

Here there are four branches, and again the typically measure for each branch is the norm-squared of the associated amplitude. After $k$ measurements in the present case there will be $2^k$ terms representing all possible sequences of records.

Within this framework, Everett argued that in the limit as the number of measurements gets large, almost all branches in measure $m$ will describe sequences of measurement records that are randomly distributed with the standard quantum statistics. While he just sketched the corresponding results, one can show that:

Randomness : The sum of the norm-squared of the amplitude associated with each branch where the sequence of relative records satisfies any standard criterion for being random goes to one as the number of measurements gets large. This result holds for any criterion of randomness that classifies at most a countable number of $\omega$-length binary sequences as nonrandom.

See Hartle (1968), Farhi, Goldstone, and Gutmann (1989), Barrett (1999), and Barrett and Goldbring (2022) for proofs of the first limiting result and the last two references for proofs of the second.

It is an immediate consequence that the records of a typical relative observer, in the special measure $m$ sense of typical, will exhibit the standard quantum statistics as the number of measurements gets large. As Everett put it:

In the language of subjective experience, the observer which is described by a typical element … of the superposition has perceived an apparently random sequence of definite results for the observations.… It will thus appear to the observer which is described by a typical element of the superposition that each initial observation on a system caused the system to “jump“ into an eigenstate in a random fashion and thereafter remain there for subsequent measurements on the same system. Therefore, qualitatively, at least, the probabilistic assertions of Process 1 [the collapse of the state under rule 4b] appear to be valid to the observer described by a typical element of the final superposition. (1956, 123)

More generally, he concluded that “the memory sequence of a typical element of [the superposition] has all the characteristics of a random sequence, with individual, independent … probabilities“ (1956, 127). Hence, a typical sequence of relative measurement records will exhibit the standard quantum statistics and thus appear to have been produced by Process 1 (rule 4b). And that is Everett’s full deduction of quantum probabilities as subjective appearances to a typical relative observer.

Everett was careful to explain that the typicality measure over branches involved no reference to probability (1956, 79). While he sometimes used the language of probability theory, he explained that this was only for ease of exposition, and he repeatedly instructed the reader that all talk of probabilities should be translated back to talk of typicalities (1956, 127 and 1957, 193). That he did not aim to deduce probabilities over branches corresponding to alternative measurement outcomes is something that distinguishes Everett’s approach from most other formulations of quantum mechanics, including those of many Everettians.

Why showing that a typical sequence of relative measurement records will exhibit the standard quantum statistics is supposed to be enough to explain our experience turns on Everett’s understanding of empirical faithfulness.

When the physicist Bryce DeWitt read Everett’s description of pure wave mechanics in the long version of his PhD thesis, DeWitt objected on the grounds that the surplus structure of the theory made it too rich to represent the world we experience. In his 7 May 1957 letter to Everett’s advisor John Wheeler, DeWitt wrote

I do agree that the scheme which Everett sets up is beautifully consistent; that any single one of the [relative memory states of an observer] … gives an excellent representation of a typical memory configuration, with no causal or logical contradictions, and with “built-in” statistical features. The whole state vector …, however, is simply too rich in content, by vast orders of magnitude, to serve as a representation of the physical world. It contains all possible branches in it at the same time. In the real physical world we must be content with just one branch. Everett’s world and the real physical world are therefore not isomorphic. (Barrett and Byrne 2012, 246–7)

The worry was that the richness of pure wave mechanics indicated an empirical flaw in the theory because we do not notice other branches. As DeWitt put it:

The trajectory of the memory configuration of a real observer … does not branch. I can testify to this from personal introspection, as can you. I simply do not branch. (Barrett and Byrne 2012, 246)

Wheeler showed Everett the letter and told him to reply. In his 31 May 1957 letter to DeWitt, Everett began by summarizing his understanding of the proper cognitive status of physical theories:

First, I must say a few words to clarify my conception of the nature and purpose of physical theories in general. To me, any physical theory is a logical construct (model), consisting of symbols and rules for their manipulation, some of whose elements are associated with elements of the perceived world. If this association is an isomorphism (or at least a homomorphism) we can speak of the theory as correct, or as faithful . The fundamental requirements of any theory are logical consistency and correctness in this sense. Barrett and Byrne (2012, 253)

In a subsequent version of the long thesis, Everett further explained that “[t]he word homomorphism would be technically more correct, since there may not be a one-one correspondence between the model and the external world” (1956, 169). The map is a homomorphism because (1) there may be elements of the theory that do not directly correspond to experience and because (2) a particular theory may not seek to explain all of experience. As indicated by the italicized some in the quotation above, the first point is particularly important in the case of pure wave mechanics. Specifically, that the relative records on the vast majority of branches of the absolute state do not correspond with our experience did not worry Everett at all, even when these records represent empirical structure.

Everett further described how he understood the aim of physical inquiry in his letter to DeWitt, “There can be no question of which theory is ‘true’ or ‘real’ — the best that one can do is reject those theories which are not isomorphic to sense experience” Barrett and Byrne (2012, 253). In all, Everett’s position was in some ways strikingly similar to Bas van Fraassen’s (1980) later constructive empiricism except that most of the empirical structure of pure wave mechanics is irrelevant to one’s actual experience. See Barrett (2011a) for an extended discussion of Everett’s notion of faithfulness.

For Everett, then, the relative-state formulation of pure wave mechanics is empirically faithful because there is a particular sort of homomorphism between its model and the world as experienced. Namely, it is because one can find a modeled observer’s experience in a typical relative sequence of her physical records. But the sense in which he finds finds an observer’s experience in his model of pure wave mechanics is such that it makes it difficult to judge the theory as empirically adequate over quantum probabilities. We will review four distinct features of empirical faithfulness which Everett argued for then return to the question of empirical adequacy.

5. Four Arguments for the Faithfulness of Pure Wave Mechanics

The relative state formulation of pure wave mechanics clearly satisfies Everett’s condition of logical consistency. There are four lines of argument that explain why he also took it to be empirically faithful and hence empirically acceptable.

Everett held that one can find our actual experience in the model of pure wave mechanics as relative measurement records associated with observers modeled as ordinary physical systems. In the state $\boldsymbol{E}$ above, since $J$ has a different relative measurement record in each branch and since these relative records span the space of possible outcomes, regardless of what result is in fact experienced, one will be able to find that experience as a relative record of the modeled observer in the post-measurement state.

Further, if one performs a sequence of measurements, it follows from the linearity of the dynamics and Everett’s physical model of an observer that every physically possible sequence of determinate measurement results will be represented in the entangled post-measurement state as a relative sequence of determinate measurement records. This is also true if one only relatively, rather than absolutely, makes a sequence of observations. In this precise sense, then, it is possible to find our experience as sequences of relative records in the model of pure wave mechanics.

Everett took such relative records to be sufficient to explain the subjective appearances of observers because, at least for an ideal measurement, every post-measurement relative state will be one where the observer in fact has, and, as we will see in the next section, would report that she has, a fully determinate, repeatable measurement record that agrees with the records of other ideal observers. As he explained the point, the system states observed by a relative observer are typically eigenstates of the observable being measured (1957, 188). For further discussion of this point see Everett (1956, 129–30), (1955, 67), (1956 121–3 and 130–3), and (1957, 186–8 and 194–5).

Note that he did not require a physically preferred basis to show that pure wave mechanics was empirically faithful. The principle of the fundamental relatively of states explicitly allows for arbitrarily specified decompositions of the absolute universal state into relative states. Given his understanding of empirical faithfulness, all he needed to explain a particular actual record was to show that is that there is some decomposition of the state that represents the modeled observer with the corresponding relative record. It is there that he finds the records corresponding to an observer’s experience in his model.

Everett believed that he could also explain why the surplus empirical structure of pure wave mechanics would go unnoticed. In his reply to DeWitt, he claimed that pure wave mechanics “is in full accord with our experience (at least insofar as ordinary quantum mechanics is) … just because it is possible to show that no observer would ever be aware of any ‘branching,’ which is alien to our experience as you point out” Barrett and Byrne (2012, 254).

There are two arguments that Everett may have had in mind.

The first is not one that Everett highlighted, but he clearly recognized the point. One would only notice macroscopic splitting if one had access to records of macroscopic splitting events. Specifically, one would need to show that there are branches where one’s macroscopic measurement devices have different macroscopic measurement records for the same measurement. This would require one to perform something akin to a Wigner’s Friend interference measurement on a macroscopic system in an entangled superposition of record states that shows that it is. But as Everett indicated in his characterization of his Wigner Friend drama as “extremely hypothetical,” such an experiment would be extraordinarily difficult. The upshot is that, while not impossible, one should not expect to find reliable interference records indicating that there are branches corresponding to alternative macroscopic measurement records.

The second is a point to which Everett repeatedly returned in his deductions of the subjective experience of modeled observers in both the long and short thesis. Namely, it follows directly from the linear dynamics that it would appear to an ideal agent that she had fully determinate measurement results. Albert and Loewer (1988) presented a dispositional version of this line of argument in their presentation of the bare theory, a version of pure wave mechanics, as a way of understanding Everett’s formulation of quantum mechanics.

The idea is that if there is no collapse of the quantum-mechanical state, an ideal modeled observer like $J$ would have the sure-fire disposition falsely to report and hence to believe that she had a perfectly ordinary, fully sharp and determinate measurement record. The trick is to consider not what result the observer got, but rather whether she believes that she got some specific determinate result. If the post-measurement state was:

then $J$ would report “I got a determinate result, either spin up or spin down” and presumably so believe. And she would make precisely the same report and believe that she got a determinate result if she ended up in the post-measurement state:

So, by the linearity of the dynamics, $J$ would falsely report “I got a determinate result, either spin up or spin down” and believe that she got a determinate result when in post-measurement state $\boldsymbol{E}$:

Thus, insofar as her beliefs agree with her sure-fire dispositions to report that she got a fully determinate result, it would seem to $J$ that she got a perfectly determinate ordinary measurement result even when she did not. That is, she does not determinately believe that she got “spin up”, and she does not determinately believe that she got “spin down”, but she does determinately believe that she got “ either spin up or spin down.”

So, while which result $J$ got in state $\boldsymbol{e}$ is a relative fact, that it would appear to $J$ that she got some determinate result is an absolute fact. See Everett (1956, 129–30), (1955, 67), (1956, 121–3 and 130–3), and (1957, 186–8 and 194–5), Albert and Loewer (1988), Albert (1992), and Barrett (1999) and (2020) for further details. We will return to a discussion of the bare theory later in this article and consider that theory on its own terms. For present purposes, the determinate result property illustrates why an observer would not report or notice that she had branched.

Everett insisted that alternative relative states, even relative states of macroscopically distinct records, were always at least in principle detectable by means of something like the Wigner’s Friend $A$-measurement discussed above. This was Everett’s point in insisting that “due to the ever present possibility of obtaining interference effects between the elements, all elements of a superposition must be regarded as simultaneously existing” (1956, 150). So while extremely difficult to detect, alternative relative records are all equally real since the linear dynamics requires that it be always in principle possible to measure an observable that would detect other branches. And since they are in principle detectable, they do not represent surplus structure.

Note that this does not mean that only the branches in a single physically preferred basis are real. It means that every branch in every decomposition of a the state of a system is real in precisely the same sense as its presence entails in principle observational consequences. That Everett considered alternative branches of the universal wave function to be always in principle detectable represents a significant difference between his formulation of quantum mechanics and a many-worlds theory where worlds are supposed to be causally isolated.

Everett did not solve the probability problem by finding probabilities in pure wave mechanics. Rather, he repeatedly insisted that there were no probabilities and took this to be an essential feature of the theory. What he did, rather, was to show that a typical relative sequence of a modeled observer’s measurement records will exhibit the standard quantum statistics.

As we saw above, Everett got this result in two steps. First, he found a suitable measure of typicality over relative states $m$ whose value is fully determined by the model of pure wave mechanics. Then he showed that, in the limit as the number of measurement interactions gets large, almost all relative sequences of measurement records, in the sense of almost all given by $m$, will exhibit the standard quantum statistics. While the typicality measure $m$ is across branches , he explained the subjective appearance of quantum probabilities by the sequence of records within a typical branch .

Everett summarized his strategy and main result to a group a physicists at a conference on the foundations of quantum mechanics at Xavier University in October of 1962:

Now, I would like to assert that, for a “typical” branch, the frequency of results will be precisely what is predicted by ordinary quantum mechanics. Even more strongly, I would like to assert that, as the number of observations goes to infinity, almost all branches will contain frequencies of results in accord with ordinary quantum theory predictions. To be able to make a statement like this requires that there be some sort of a measure on the superposition of states. What I need, therefore, is a measure that I can put on a sum of orthogonal states. There is one consistency [criterion] which would be required for such a thing. Since my states are constantly branching, I must insist that the measure on a state originally is equal to the sum of the measures on the separate branches after a branching process. Now this consistency criterion can be shown to lead directly to the squared amplitude of the coefficient, as the unique measure which satisfies this. With this unique measure, deduced only from a consistency condition, I can then assert: indeed, for almost all (in the measure theoretical sense) elements of a very large superposition, the predictions of ordinary quantum mechanics hold. (Barrett and Byrne 2012, 274–75)

Importantly, it is usually not the case that most relative sequences by count will exhibit the standard quantum statistics. This is why the norm squared coefficient measure $m$ is essential to Everett’s account.

Regarding Everett’s summary of his project, there are two closely related points worth noting. First, his sub-branch additivity condition is not required for simple consistency. This can be seen by the fact that a proportional counting measure over descendent branches would have been perfectly consistent. It just wouldn’t have entailed that a typical branch will exhibit the standard quantum statistics. Second, as he acknowledged in this thesis, he needed more than just sub-branch additivity to get the squared amplitude measure $m$. He also needed $m$ to be a positive linear function of the complex-valued coefficients associated with each branch, and he needed to suppose that $m$ satisfied the standard axioms for being a probability measure. See Everett (1956, 120–30) and (1957, 186–94) and Barrett (2017) and (2020) for discussions of typicality and quantum statistics in pure wave mechanics.

It is an immediate consequence of Everett’s deduction that that if one were to further assume that one should expect one’s records to be typical in the sense provided by measure $m$, then one should expect one’s records to exhibit the standard quantum statistics. Were such an assumption added to his formulation of pure wave mechanics, something that Everett himself never proposed, then one would be able to explain why one should expect to find oneself at each time with records that appear to have been generated by a random process like rule 4b. But one cannot get even this, let alone standard forward-looking quantum probabilities, without supplementing pure wave mechanics with auxiliary assumptions that tie the measure $m$ to one’s probabilistic expectations. Such auxiliary assumptions would clearly represent significant additions to pure wave mechanics.

For his part, Everett just argued that the sequence of records in a typical branch, in his specified sense of typical, would satisfy the standard quantum statistics. And it was this that he took to establish that his relative-state formulation of pure wave mechanics was empirically faithful and hence empirically acceptable.

Everett took pure wave mechanics to empirically faithful because (1) one can find an observer’s experience in the relative records of the observer as modeled in the theory and (2) pure wave mechanics provides something that one can take as a typicality measure over relative states such that a typical relative sequence of measurement records in that measure will exhibit the standard quantum statistics. The first is Everett’s resolution of the determinate record problem, and the second is his resolution of the probability problem. That said, one might want more than empirical faithfulness from a satisfactory formulation of quantum mechanics.

That empirical faithfulness is a weak standard of empirical adequacy is illustrated in what Everett’s formulation of pure wave mechanics does not explain about our experience. It does not explain what it is about the physical world that makes it appropriate to expect one’s relative sequence of records to be typical in the norm-squared-coefficient sense, or in any other sense, at a time. Nor does it explain why one should expect alternative future measurement results with the standard quantum probabilities. The lack of both synchronic and forward-looking probabilities means that Everett did not deduce the probabilistic predictions of rule 4b as subjective appearances to his modeled observers. It also illustrates the need for relatively strong auxiliary assumptions in order to derive anything like the standard quantum predictions from pure wave mechanics.

The upshot is that while the relative state formulation of pure wave mechanics is logically consistent and empirically faithful in a sense that Everett thought sufficient, it does not make the standard probabilistic predictions of quantum mechanics for even simple experiments and, hence, fails to be empirically adequate in any standard sense. There is a long tradition of supplementing pure wave mechanics with yet stronger auxiliary assumptions in order to get a theory that one might take to be straightforwardly empirically adequate. This is the aim of the various many-worlds reconstructions of Everett’s relative state formulation.

While he was initially skeptical of Everett’s project, DeWitt became an ardent proponent of the many-worlds interpretation, a theory that DeWitt presented as the EWG interpretation of quantum mechanics (named after Everett, Wheeler, and DeWitt’s graduate student R. Neill Graham). In his description of the many-worlds interpretation, DeWitt (1970) emphasized that its central feature was the metaphysical commitment to physically splitting worlds. DeWitt’s description subsequently became the most popular understanding of Everett’s theory. See Barrett (2011b) for a discussion of Everett’s historical attitude toward DeWitt and the many-worlds interpretation. See Lewis (2016), Saunders, Barrett, Kent, and Wallace (eds) (2010), Vaidman (2012), Wallace (2010a) (2010b) (2012), Sebens (2015), Sebens and Carroll (2018), and the entry many-worlds interpretation of quantum mechanics for discussions of a number of quite different many-worlds interpretations.

DeWitt described his theory in the context of the Schrödinger’s cat thought experiment.

The animal [is] trapped in a room together with a Geiger counter and a hammer, which, upon discharge of the counter, smashes a flask of prussic acid. The counter contains a trace of radioactive material—just enough that in one hour there is a 50% chance one of the nuclei will decay and therefore an equal chance the cat will be poisoned. At the end of the hour the total wave function for the system will have a form in which the living cat and the dead cat are mixed in equal portions. Schrödinger felt that the wave mechanics that led to this paradox presented an unacceptable description of reality. However, Everett, Wheeler and Graham’s interpretation of quantum mechanics pictures the cats as inhabiting two simultaneous, noninteracting, but equally real worlds. (1970, 31)

DeWitt took this view to follow from “the mathematical formalism of quantum mechanics as it stands without adding anything to it.” More specifically, he claimed that EWG had proven a metatheorem that the mathematical formalism of pure wave mechanics interprets itself:

Without drawing on any external metaphysics or mathematics other than the standard rules of logic, EWG are able, from these postulates, to prove the following metatheorem: The mathematical formalism of the quantum theory is capable of yielding its own interpretation. (1970, 33)

He gave Everett credit for the metatheorem, Wheeler credit for encouraging Everett, and Graham credit for clarifying the metatheorem. DeWitt and Graham later described Everett’s formulation of quantum mechanics as follows:

[It] denies the existence of a separate classical realm and asserts that it makes sense to talk about a state vector for the whole universe. This state vector never collapses and hence reality as a whole is rigorously deterministic. This reality, which is described jointly by the dynamical variables and the state vector, is not the reality we customarily think of, but is a reality composed of many worlds. By virtue of the temporal development of the dynamical variables the state vector decomposes naturally into orthogonal vectors, reflecting a continual splitting of the universe into a multitude of mutually unobservable but equally real worlds, in each of which every good measurement has yielded a definite result and in most of which the familiar statistical quantum laws hold (1973, v).

The metaphysics of splitting worlds immediately addresses the determinate result problem. As DeWitt notes, after an observer makes a measurement, each resultant copy of the observer will inhabit a physical world described by a branch of the global state and endowed with with a fully determinate physical record. But inasmuch as the pre-measurement observer can expect to find herself in each post-measurement world, there remains a problem accounting for the standard quantum probabilities. It appears that the forward-looking probability of each possible measurement result is precisely one. We will return to this issue in a moment.

There is a conceptual cost in getting determinate measurement records by stipulating splitting worlds. DeWitt conceded that he had found the constant splitting of worlds whenever the states of systems become correlated to be strongly counterintuitive:

I still recall vividly the shock I experienced on first encountering this multiworld concept. The idea of $10^{100}$ slightly imperfect copies of oneself all constantly splitting into further copies, which ultimately become unrecognizable, is not easy to reconcile with common sense. Here is schizophrenia with a vengeance (1973, 161).

That said, DeWitt promoted the theory at every turn, and Everett’s views quickly came to be identified with DeWitt and Graham’s many-worlds interpretation. It is instructive to consider how DeWitt’s views differ from Everett’s.

To begin, since purely mathematical postulates entail only purely mathematical theorems, one cannot deduce any metaphysical commitments whatsoever regarding the physical world from the mathematical formalism of pure wave mechanics alone. The formalism of pure wave mechanics might entail the sort of commitments that DeWitt envisioned but only if supplemented with sufficiently strong auxiliary assumptions. For his part, Everett seems to have clearly understood this this point. Concerning DeWitt’s claim that pure wave mechanics somehow interprets itself by way of a metatheorem that Everett proved, there is nothing answering to DeWitt’s description of this metatheorem in either Everett’s long or short thesis.

Further, contrary to what DeWitt, Graham, and others have supposed, Everett was never committed to “mutually unobservable worlds.” In contrast, as we have seen, Everett held that it is always in principle possible for branches to interact. In this regard, he argued that “no matter what the state of [the observer in Everett’s version of the Wigner’s Friend story] is, there is in principle a complete set of commuting operators for which it is an eigenstate, so that, at least, the determination of these quantities will not affect the state nor in any way.” He also denied that there are fundamental restrictions about the “knowability of any state functions.” And he believed that the sense in which all branches of the global state are equally actual is given by the ever present possibility of interaction between branches.

In identifying Everett’s theory with Graham’s many-world reconstruction there is good reason to believe that DeWitt simply failed to understand Everett. We know what Everett thought of DeWitt and Graham’s formulation of the theory. In his personal copy of DeWitt’s description of the many-worlds interpretation, Everett wrote the word “bullshit” next to the passage where DeWitt presented Graham’s discussion of the branching process and Everett’s typicality measure. See Barrett and Byrne 2012, 364–6 for scans of Everett’s handwritten marginal notes.

Finally, Everett carefully avoided the metaphysical talk of worlds. Rather, his understanding of the reality of branches was operational. For Everett there was no canonical basis. Given how he understood branches and their role in determining the empirical faithfulness of the theory, he had no need of a physically preferred basis. He believed that it was sufficient if one could find our experience in a modeled observer’s typical relative records. In contrast, DeWitt seems to have had in mind a canonically preferred basis that would determine what worlds there are and their state.

While Everett himself did not do so, one might designate a special set of branches of the global absolute state to represent worlds, or emergent worlds, or approximate emergent worlds. But there are many ways one might do this, and how one understands such worlds cannot be determined solely by the mathematical formalism of pure wave mechanics alone. Easily the most popular sort of many-worlds theory at present characterizes approximate emergent worlds in terms of decoherence conditions.

In contrast with DeWitt, who appears to have taken worlds to be basic entities described by the global absolute state, David Wallace (2002, 2010a, 2010b, and 2012) takes the global quantum state as basic, then seeks to characterize worlds as emergent entities represented in its structure. The analogy he gives is that pure wave mechanics describes the quantum state just as classical field theory describes physical fields (2010a, 69). Worlds are understood as physically real but contingently emergent entities that are identified with approximate substructures of the quantum state, or as Wallace puts it, “mutually dynamically isolated structures instantiated within the quantum state, which are structurally and dynamically ‘quasiclassical’” (2010a, 70). Since the fundamental theory is supposed to be pure wave mechanics, such emergent worlds will be more or less well-defined and more and less well-isolated on the linear dynamics depending on details of the physical situation and the level of description one considers.

On Wallace’s account, there is no simple matter of fact concerning what, or even how many, emergent worlds there are. Such questions depend on one’s level of description and on how well-isolated one requires worlds to be for the explanatory considerations at hand. That said, the decohering worlds approach provides something that is characterized by the evolution of the global state on which alternative measurement records might supervene. In this case, one need not stipulate a physically preferred basis as it is decoherence conditions that individuate alternative quasi-determinate worlds at a given level of description. One gets a determinate measurement result because, at a level of description appropriate for characterizing the properties of macroscopic systems, one in fact inhabits an emergent world containing a determinate record.

There remains, however, the problem of accounting for standard quantum probabilities. Taking the decision-theoretic approach of David Deutsch (1997, 1999) as a starting point, Wallace (2010b) proves a representation theorem from ten constraints on the preferences of a rational agent in the context of a world described by pure wave mechanics. If an agent acts as required by these constraints, she will act as if she expects future events with the standard quantum probabilities. Wallace understands these constraints as basic principles of reason, but inasmuch as they only make sense in the context of pure wave mechanics, they are perhaps best understood as auxiliary assumptions that, in conjunction with pure wave mechanics, explain why an agent might act as if the standard quantum probabilities held when in fact every physically possible outcome of her actions is fully realized. There is, of course, nothing wrong with supplementing pure wave mechanics with whatever auxiliary assumptions one needs to derive a suitable version of the standard quantum probabilities. See Wallace (2003, 2006, 2007, 2010b, and 2012) and Greaves (2006) for further discussions of quantum probabilities and epistemology on a decision-theoretic approach to pure wave mechanics.

Granting such auxiliary assumptions, making sense of standard forward looking quantum probabilities requires further care. Before making an observation, an observer knows that every physically possible measurement result will certainly occur. One wants to say that she will expect to find herself in each resulting world with the standard quantum probabilities after the measurement interaction, but if there is just one pre-measurement observer, then inasmuch as she gets any result at all, she will get every possible result. One way around this is to suppose that for every post-measurement observer there is already a corresponding pre-measurement observer. Each of these pre-measurement observers is unsure which post-measurement observer is her future self. Forward looking quantum probabilities represent this epistemic uncertainty. On this strategy, then, one seeks to add auxiliary assumptions to pure wave mechanics sufficient to provide standard forward-looking quantum probabilities as epistemic self-location probabilities concerning which full history characterizes one’s experience. If one is successful, the resultant theory might be taken to be empirically adequate in a perfectly ordinary sense. Saunders and Wallace’s (2008a, 2008b) divergent worlds account and Barrett’s (1999) many-threads theory seek to exploit this strategy. See Lewis (2016) for a critical examination of the divergent worlds approach to forward looking probabilities. See Saunders, Barrett, Kent, and Wallace (2010) and the entry on the many-worlds interpretation of quantum mechanics for other approaches to getting synchronic and, in some cases, forward-looking self-location probabilities.

8. The Bare Theory and Extensions

The bare theory is pure wave mechanics with the standard interpretation of states (rule 3). This approach takes seriously Everett’s proposal of simply dropping the collapse dynamics (rule 4b) from the standard theory then try to derive the standard theory’s predictions as subjective experiences from the resulting theory. Inasmuch as the bare theory is arguably identical to pure wave mechanics, studying it is a good way to assess the virtues and vices of Everett’s proposal. It is also a good first step in figuring out what auxiliary assumptions are needed in order to get a straightforward account of determinate records and forward-looking quantum probabilities starting from pure wave mechanics. See Albert and Loewer (1988), Albert (1992), and Barrett (1994) for a description of the bare theory and Geroch (1984) for a similar reading of Everett.

On the bare theory there is no distinction between absolute and relative states nor is there any special notion of typicality. Rather, one uses Everett’s model of an idealized observer to argue that it would appear to such observers that they had the perfectly determinate measurement outcomes predicted by the collapse dynamics when they in fact did not. The thought is that this is one way of capturing Everett’s goal of deducing the standard predictions of quantum mechanics as the subjective appearances of observers who are themselves treated within the theory. We have already seen the basic argument in section 5.2. We will start by briefly reviewing how it goes in a slightly more general setup.

Since $J$ would report that she had a determinate result in post-measurement state:

and would report that she had a determinate result in post-measurement state:

$J$ would, by the linearity of the dynamics, also report that she got a perfectly determinate result, either spin up or spin down, in the post-measurement state $J$ gets when observing $S$ in state

Assuming that she perfectly correlates her record with the $x$-spin of $S$ in a way that does not disturb its spin, then on the linear dynamics (rule 4a), the resultant post-measurement state in this case is

If asked in this state $J$ would be in a superposition of reporting “I got a determinate result, either spin up or spin down” in the first branch and reporting “I got a determinate result, either spin up or spin down” in the second branch, which is an eigenstate of reporting “I got a determinate result, either spin up or spin down.” Hence, if we assume that her reports are in fact true of her experience, it would appear to $J$ that she got a perfectly determinate ordinary measurement result even when she did not determinately get “spin up” and she did not determinately get “spin down”. One might think of this as a disjunctive experience . The disjunctive experience is not an experience of either ordinary determinate result, but it is one where the observer is convinced that her result is “determinately spin up or determinately spin down”.

One can similarly argue from the linear dynamics and the properties of an ideal observer that if $J$ repeats her spin measurement, then she will end up with the sure-fire disposition to report that she got the same result for the second measurement as for the first, even when she did not in fact get an ordinary determinate result for either. As a result, it will appear to her that there has been a collapse of the quantum-mechanical state when in fact there has been no collapse, splitting of worlds, or anything else that would produce an ordinary determinate measurement record. The subjective appearance of a collapse here is an illusion produced by the linear dynamics. It represents her inability to distinguish between ordinary and disjunctive experience.

The linear dynamics also entails intersubjective agreement between different observers. If a second observer were to check $J$’s measurement result, the second observer would end up believing that his result agreed with her result, even when neither observer in fact has an ordinary determinate measurement record. In this sense, there is subjective agreement on the apparent result of the apparent collapse.

Finally, one can show that an observer who repeats a measurement on an infinite sequence of systems in the same initial state will approach a state where she has the sure-fire dispositions to report that her measurement results were randomly distributed with the standard quantum statistics, even when she in fact got no ordinary results for any of her measurements. This follows from the relative frequency and randomness results in section 3.2. Hence she will end up believing that she got a determinate measurement result to each measurement and that these results were distributed precisely as one would expect on the standard collapse dynamics. See Everett (1956, 129–30), (1955, 67), (1956, 121–3 and 130–3), and (1957, 186–8 and 194–5) for his discussions of these formal properties of pure wave mechanics.

While the bare theory has a number of suggestive properties, there are at least two serious problems. To begin, it is not empirically coherent. If the bare theory were true, it would be impossible to have empirical evidence for accepting it as true given the radical sort of illusions it predicts. See Barrett (1996) for a discussion of empirical coherence in the context of the bare theory and John Bell’s (1981, 133–7) Everett (?) theory. Another is that if the bare theory were true, one would most likely fail to have any determinate beliefs at all since, on the linear dynamics, one would expect the global state to almost never be an eigenstate of any particular observer being sentient or even existing. For a further discussion of how experience is supposed to work in the bare theory and some the problems it encounters see Albert (1992), Bub, Clifton, and Monton, (1998), and Barrett (1999 and 2020).

Everett held that on his formulation of quantum mechanics “the formal theory is objectively continuous and causal, while subjectively discontinuous and probabilistic” (1956, 77). Albert and Loewer (1988) aimed to capture this feature in their many-minds theory. In doing so, they show one way that one might add auxiliary assumptions to pure wave mechanics that yield both determinate records and standard forward-looking quantum probabilities.

The many-minds theory distinguishes between an observer’s physical state and her mental state . Her physical state is given by pure wave mechanics, and associated with her physical state is a continuously infinite set of minds. The observer’s physical state, like all other physical systems, always evolves in the usual deterministic way according to rule 4a, but each mind associated with the observer jumps randomly to a mental state corresponding to one of the Everett branches that is produced in each measurement-like interaction. The probability that a particular mind will experience a given Everett branch is equal to the norm squared of the amplitude associated with that branch.

On this dynamics, then, if a measurement interaction between $J$ and $S$ produces post-measurement state

then one should expect $|\alpha|^2$proportion of $J$’s minds to end up associated with the result “spin up” (the first term of the expression) and $|\beta|^2$proportion of $J$’s minds to end up associated with the result “spin down” (the second term of the expression). We will also suppose that the mental dynamics is memory-preserving so that once a mind is associated with a particular branch it remains associated with the descendants of that branch. See Barrett 1995 for a discussion of the dynamics.

While the many-minds theory involves a strong mind-body dualism, it has several salient virtues. First, there is no need for a physically preferred basis. One must choose a preferred basis in order to specify the mental dynamics completely but this choice has nothing to do with physical facts. Rather, it is just characterizes how mental states supervene on physical states. Second, the determinate result problem is immediately solved since each mind always has a fully determinate set of measurement records. Third, the probability problem is addressed by how mental states evolve. Unlike many-worlds theories where an observer is copied into each post-measurement world, one gets the standard forward-looking quantum probabilities here as predictions for the future experiences of a particular mind. Finally, the many-minds theory is one of the few formulations of quantum mechanics that is (with decohering worlds and GRWf) arguably compatible with the constraints of special relativity. See Hemmo and Pitowsky (2003) and Barrett (2020) for discussions.

The many-minds formulation of quantum mechanics can be thought of as a hidden-variable theory much like Bohmian mechanics. See below and the entry on Bohmian mechanics . But here, instead of making particle positions determinate and then assuming that determinate particle will provide observers with determinate measurement records, one simply stipulates that the mental states of the observers are always determinate. While this strategy is clearly ad hoc, it is also effective. It immediately provides observers with fully determinate measurement records, and with a suitable stochastic dynamics, it yields the standard forward-looking quantum probabilities.

The many-minds formulation also illustrates the close relationship between pure wave mechanics and no-collapse hidden-variable theories. One way to get ordinary determinate measurement outcomes and forward looking probabilities is to add a parameter to pure wave mechanics that represents the observer’s records then to give a suitable dynamics for that parameter. We will consider another way this might work in the next section.

8.3 Many Histories and Bohmian Mechanics

On the standard sort of many-worlds theory, worlds are taken to split over time as new branches are produced in measurement-like interactions. As we have seen, inasmuch as each possible measurement outcome is in fact recorded by some future copy of the observer one of the post-measurement branches, one problem with this is that the forward-looking probability of an observer getting each quantum-mechanically possible outcome for a measurement is simply one. One way to get the right forward-looking probabilities, the standard probabilistic predictions of quantum mechanics, is to postulate worlds are characterized by complete histories and never branch. If one inhabits such a world, then one simply experiences its history.

The idea is closely related to many-history tradition. Gell-Mann and Hartle (1990) characterized Everett’s theory as one that describes many, mutually decohering, histories. On this sort of theory, one might think of each physically possible trajectory through the Everett branches as a thread that defines a world. See Dowker and Kent (1996) for critical examination of the consistent histories approach and Barrett (1999) for a characterization of such “many-threads” theories as a type of hidden-variable theory.

One can see how a many-threads theory might provide ordinary forward-looking probabilities by considering how one might construct such a theory from the many-minds theory. For each full trajectory that a particular mind might take through the Everett branches, associate a single, non-splitting world that implements the events experienced along that trajectory. What the mind would see, then, is what in fact happens in the corresponding world. In this way each mind determines the history of a non-branching world.

Now consider the probability measure over the set of all such worlds determined by the many-minds probability associated with each full history. A many-threads theory would stipulate this measure as the prior epistemic probability of each possible non-branching world in fact being ours. These prior probabilities are then updated as we learn more about the actual history of the world we inhabit. Since such worlds and everything in them have perfectly ordinary trans-temporal identities, there is no problem accounting for forward-looking probabilities. The forward-looking probability for a future event is just the epistemic probability that the event in fact occurs in the world we inhabit.

A no-collapse hidden-variable theory like Bohmian mechanics can also be thought of as a many-threads theory. The close relationship between such hidden variable theories and this sort of many-world theory is instructive.

On Bohmian mechanics the wave function always evolves in the usual deterministic way, but particles are taken to always have fully determinate positions. For an $N$-particle system, the particle configuration can be thought of as being pushed around in $3N$-dimensional configuration space by the flow by the probability associated with the wave function just as a massless particle would be pushed around by a compressible fluid. Here both the evolution of the wave function and the evolution of the particle configuration are fully deterministic. Quantum probabilities are the result of the distribution postulate. The distribution postulate sets the initial prior probability distribution equal to the norm squared of the wave function for an initial time. One learns what the new effective wave function is from one’s measurement results, but one never knows more than what is allowed by the standard quantum statistics. Indeed, Bohm’s theory always predicts the standard quantum probabilities for particle configurations, but it predicts these as epistemic probabilities. Bohm’s theory is supposed to give determinate measurement results in terms of determinate particle configurations (say the position of the pointer on a measuring device). See the entry on Bohmian mechanics and Barrett (2020) for further details.

If one chooses configuration as the preferred physical observable and adopts the particle dynamics of Bohm’s theory, then one can construct a many-threads theory by fixing the initial wave function and the Hamiltonian and then considering every possible initial configuration of particles to correspond to a different full history for a possible world. Here the prior probabilities are given by the distribution postulate in Bohm’s theory, and the updated epistemic probabilities yield the effective Bohmian wave function. On this view, the only difference between Bohm’s theory and the associated many-threads theory is that the many-threads theory treats all possible Bohmian worlds as actual and quantum probabilities as epistemic self-location probabilities over these worlds. A many-threads theory might be constructed for virtually any determinate physical quantity just as one would construct a hidden-variable or a modal theory. See the entry on entries on Bohmian mechanics and modal interpretations of quantum mechanics and Vink (1993).

The upshot is that if one takes the account of determinate records and quantum probabilities in pure wave mechanics alone to be inadequate, adding hidden variables provides a sure-fire way to get ordinary records and forward-looking probabilities. That said, there is good historical reason to suppose that Everett did not have a hidden-variable theory in mind.

Everett explicitly discussed Bohmian mechanics in two places in his long thesis (1956, 75, 153–5). His complaint was that Bohm’s theory was “more cumbersome than the conceptually simpler theory based on pure wave mechanics.” Even so, he took Bohmian mechanics to be of “great theoretical importance” because it “showed that ‘hidden variable’ theories are indeed possible” contrary to received wisdom. Concerning hidden-variable theories like Bohm’s, Everett further acknowledged that “[i]t cannot be disputed that these theories are often appealing and might conceivably become important should future discoveries indicate serious inadequacies in the present scheme [pure wave mechanics] (i.e. they might be more easily modified to encompass new experience)” (1956, 155). While Everett thought that he could adequately explain (or better, explain away) quantum probabilities, given the subsequent difficulty in understanding forward-looking quantum probabilities in pure wave mechanics, that Bohmian mechanics and other many-threads theories treat quantum probability in an entirely straightforward way is a manifest virtue, one that may ultimately be useful in finding a satisfactory extension of pure wave mechanics.

Everett took his version of the Wigner’s Friend story to reveal an inconsistency in the standard collapse formulation of quantum mechanics and the incompleteness of the Copenhagen interpretation. On his understanding, the quantum measurement problem was that neither theory could account for the sort of nested measurement that occurs in the Wigner’s Friend story. Pure wave mechanics clearly provides a consistent dynamical account of how the state of the composite system evolves in the context of nested measurement. Everett’s task then was to explain a sense in which pure wave mechanics might be taken to be empirically faithful over determinate measurement records that exhibit the standard quantum-mechanical statistics.

Everett’s relative-state formulation of pure wave mechanics has a number of salient virtues. It eliminates the collapse dynamics and hence immediately resolves the potential conflict between the standard theory’s two dynamical laws. It is logically consistent, applicable to all physical systems, and arguably as simple as a formulation of quantum mechanics can be. And it is empirically faithful in the sense that relative sequences of records exhibiting the standard quantum statistics are typical.

The empirical problems with the relative state formulation of pure wave mechanics are illustrated by the fact that it provides neither probabilistic predictions nor expectations for one’s records at a time or in the future. There are now a number reconstructions of pure wave mechanics that add auxiliary assumptions in order to provide a richer account of both determinate records and quantum probability. The methodological goal is to add as little as possible to get a satisfactory empirical theory given one’s explanatory demands.

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Further steps to quantum mechanics: Louis de Broglie and the world's
Collapse 5 Further steps to quantum mechanics: Louis de Broglie and the world's most important PhD thesis 5.1 Introduction 5.1 ... This was a critically significant step in the development of quantum mechanics. This work was presented in a relatively short Ph.D. dissertation.
PDF Formal Analysis of Quantum Optics
Quantum optics is an essential branch of quantum mechanics, where the particle-nature of light is considered; typically, these particles are called photons. Based on this concept, quantum optics investigates new properties and phenomena about light, especially light beams with a low number of photons [56]. This investigation allows a
PDF Rethinking causality in quantum mechanics
in quantum mechanics Christina Giarmatzi M.Sc. A thesis submitted for the degree of Doctor of Philosophy at ... where the events are described by quantum mechanics, there is a di erent description of the ... I thank the person that gave me the opportunity to do my PhD in this wonderful place: we all know him, we all love to see him, and we ...
Theses
PhD Theses. Philipp Köhler, PhD Thesis University of Vienna (2022): "Towards Quantum Experiments on Gravitating Objects "Lorenzo Magrini, PhD Thesis University of Vienna (2021): " Quantum measurement and control of mechanical motion at room temperature " Claus-Markus Gärtner, PhD Thesis University of Vienna (2020): Advanced membrane architectures for multimode opto-mechanics
Non-classical correlations in quantum mechanics and beyond
The third part of this thesis concerns more general forms of non-classical correlations in bipartite continuous variable systems. In Ch. 6 we devise a general scheme that allows to consistently classify correlations of bipartite Gaussian states into classical and quantum ones. Finally, Ch. 7 explores some problems connected with a certain ...
Feynman's Thesis
Feynman's Thesis — A New Approach to Quantum Theory. Richard Feynman's never previously published doctoral thesis formed the heart of much of his brilliant and profound work in theoretical physics. Entitled "The Principle of Least Action in Quantum Mechanics," its original motive was to quantize the classical action-at-a-distance ...
PDF Many lives in many worlds
Everett's PhD thesis, the shortened official version of which celebrates its 50th birthday this year, is buried in the out-of-print book The Many-Worlds Interpretation of Quantum Mechanics. I remember my excitement on finding it in a small Berkeley book store back in grad school, and still view it as one of the
PDF The Many-Worlds Interpretation of Quantum Mechanics
OF QUANTUM THEORY by John A. Wheeler 151 QUANTUM MECHANICS AND REALITY by Bryce S.DeWitt ,..155 THE MANY-UNIVERSES INTERPRET ATION OF QUANTUM MECHANICS by Bryce S.DeWitt 167 ONTHE INTERPRETATION OF MEASUREMENT WITHIN THE QUANTUM THEORY by Leon N. Cooper and Deborah van Vechten 219 THE MEASUREMENT OFRELATIVE FREQUENCY byNeill Graham 229
Feynman's Thesis: A New Approach to Quantum Theory
For the energy expression, classically y (σ) = q̇ (σ). The formula (60) can be deduced from (70) most simply by writing for y i the f44 Feynman's Thesis — A New Approach to Quantum Theory % i+1 −qi qi −qi−1 & + form, yi = 21 qti+1 −ti ti −ti−1 in the case that the coordinates are rectangular.
[PDF] Geometry of quantum mechanics
Quantum mechanics is formulated on the true space of physical states—the projective Hilbert space. It is found that the postulates of quantum mechanics assume an intrinsically geometric form. In particular, observables are represented by real‐valued functions, the Lie bracket on the space of observables is given by a Poisson structure, and the Schrodinger evolution is equivalent to the ...
Doctoral dissertation and first publication of his formulation of
Doctoral dissertation and first publication of his formulation of quantum mechanics (1957) On March 1, 1957, Everett submitted his 36-page doctoral dissertation, "On the Foundations of Quantum Mechanics", in a footnote to which he writes that it would be too much to hope that the revised wording avoids every misunderstanding or ambiguity [37].Bryce DeWitt later published [44] the background of ...
Paul Dirac's PhD Thesis: the First Ever Written on Quantum Mechanics
June 12, 2023. Paul Dirac is real-life Sheldon Cooper. And Dirac's PhD thesis is an unparalleled masterpiece in the field of science. At the incredibly young age of 24, Dirac submitted a revolutionary dissertation laying the foundational ideas of the general theory of quantum mechanics, considered one of the most significant breakthroughs in ...
THE PRINCIPLE OF LEAST ACTION IN QUANTUM MECHANICS
A generalization of quantum mechanics is given in which the central mathematical concept is the analogue of the action in classical mechanics. It is therefore applicable to mechanical systems whose equations of motion cannot be put into Hamiltonian form. It is only required that some form of least action principle be available.
PhD Thesis: Quantum and Quantum-Inspired Computation for MIMO
PhD Thesis: Quantum and Quantum-Inspired Computation for MIMO Communications in Wireless Networks. Author. ... Quantum computing is a potential tool to address this computational challenge. It exploits unique information processing capabilities based on quantum mechanics to perform fast calculations that are intractable by traditional digital ...
PDF Quantum Computation: Theory and Implementation
quantum computation, to demonstrate how to extract the necessary design criteria for a functioning tabletop quantum computer, and to report on the construction of a portable NMR spectrometer which can characterize materials and hopefully someday perform quantum computation. This thesis concentrates on the digital and system-level issues.
Everettian Quantum Mechanics
When the physicist Bryce DeWitt read Everett's description of pure wave mechanics in the long version of his PhD thesis, DeWitt objected on the grounds that the surplus structure of the theory made it too rich to represent the world we experience. ... ---, 1999, The Quantum Mechanics of Minds and Worlds, Oxford: Oxford University Press ...
PhD Theses of Recently Graduating Research Students
PhD thesis : Bridges Between Quantum and Classical Mechanics: Directed Polymers, Flocking and Transitionless Quantum Driving; Completed his PhD in summer 2017 Left to become a Postdoctoral Fellow in the Department of Physics at Syracuse University D. Zeb Rocklin. PhD thesis : Directed-Polymer Systems Explored Via Their Quantum Analogs ...