The consistent histories, also known as decoherent histories, approachto quantum interpretation is broadly compatible with standard quantummechanics as found in textbooks. However, the concept ofmeasurement by which probabilities are introduced in standardquantum theory no longer plays a fundamental role. Instead,all quantum time dependence is probabilistic (stochastic),with probabilities given by the Born rule or its extensions. Byrequiring that the description of a quantum system be carried outusing a well-defined probabilistic sample space (called a“framework”) this approach resolves many well-knownquantum paradoxes of quantum foundations. In particular, quantummechanics is local and consistent with special relativity. Classicalmechanics emerges as a useful approximation to the more fundamentalquantum mechanics under suitable conditions. The price to be paid forthis is a set of rules for reasoning resembling, but very much simplerthan, those of quantum logic. An important philosophical implicationis the absence of a single universally-true state of affairs at eachinstant of time. However, there is a correspondence limit in which thenew quantum logic becomes standard logic in the macroscopic world ofeveryday experience, and the laws of classical mechanics emerge as agood approximation to an underlying, and in principle more exact,quantum description.
QBism: Quantum Theory as a Hero's Handbook
This paper represents an elaboration of the lectures delivered by one of us (CAF) during "Course 197 -- Foundations of Quantum Physics" at the International School of Physics "Enrico Fermi" in Varenna, Italy, July 2016. Much of the material for it is drawn from arXiv:1003.5209, arXiv:1401.7254, and arXiv:1405.2390. However there are substantial additions of original material in Sections 4, 7, 8 and 9, along with clarifications and expansions of the older content throughout. Topics include the meaning of subjective probability; no-cloning, teleportation, and quantum tomography from the subjectivist Bayesian perspective; the message QBism receives from Bell inequality violations (namely, that nature is creative); the import of symmetric informationally complete (SIC) quantum measurements for the technical side of QBism; quantum cosmology QBist-style; and a potential meaning for the holographic principle within QBism.
Jacob Barandes | Quantum Theory as a New Kind of Stochastic Process
Jacob Barandes | Quantum Theory as a New Kind of Stochastic Process
Jacob Barandes - “A Deflationary Account of Quantum Theory & Implications for the Complex Numbers”
Collapse Theories
Quantum mechanics, with its revolutionary implications, has posedinnumerable problems to philosophers of science. In particular, it hassuggested reconsidering basic concepts such as the existence of aworld that is, at least to some extent, independent of the observer,the possibility of getting reliable and objective knowledge about it,and the possibility of taking (under appropriate circumstances) atleast some properties to be objectively possessed by physical systems.It has also raised many others questions which are well known to thoseinvolved in the debate on the interpretation of this pillar of modernscience. One can argue that most of the problems are not only due tothe intrinsic revolutionary nature of the phenomena which have led tothe development of the theory. They are also related to the fact that,in its standard formulation and interpretation, quantum mechanics is atheory which is excellent (in fact it has an unprecedented success inthe history of science) in telling us everything about what weobserve, but it meets with serious difficulties in telling uswhat there is. We are making here specific reference to thecentral problem of the theory, usually referred to as themeasurement problem, which is accompanying quantum theory sinceits birth. It is just one of the many attempts to overcome thedifficulties posed by this problem that has led to the development ofCollapse Theories, i.e., to the Dynamical ReductionProgram (DRP). As we shall see, this approach consists inaccepting that the dynamical equation of the standard theory should bemodified by the addition of stochastic and nonlinear terms. The nicefact is that the resulting theory is capable, on the basis of a singledynamics which is assumed to govern all natural processes, to accountat the same time for all well-established facts about microscopicsystems as described by the standard theory, as well as for theso-called postulate of wave packet reduction (WPR), which accompaniesthe interaction of a microscopic system with a measuring device. As iswell known, such a postulate is assumed in the standard scheme just inorder to guarantee that measurements have outcomes but, as weshall discuss below, it meets with insurmountable difficulties if onetries to derive it by assuming the measurement itself to be a processgoverned by the linear laws of the theory. Finally, the collapsetheories account in a completely satisfactory way for the classicalbehavior of macroscopic systems.
Putting Paradoxes to Work: Contextuality in Measurement-Based Quantum Computation
We describe a joint cohomological framework for measurement-based quantum computation (MBQC) and the corresponding contextuality proofs. The central object in this framework is an element $$[\beta _\Psi ]$$[βΨ]in the second cohomology group of the chain complex describing a given MBQC. $$[\beta _\Psi ]$$[βΨ]contains the function computed therein up to gauge equivalence, and at the same time is a contextuality witness. The present cohomological description only applies to temporally flat MBQCs, and we outline an approach for extending it to the temporally ordered case.
The Kochen-Specker Theorem
The Kochen-Specker theorem is an important and subtle topic in the foundations of quantum mechanics (QM). The theorem demonstrates the impossibility of a certain type of interpretation of QM in terms of hidden variables (HV) that naturally suggests itself when one begins to consider the project of interpretating QM.We here present the theorem/argument and the foundational discussion surrounding it at different levels. The reader looking for a quick overview should read the following sections and subsections: 1, 2, 3.1, 3.2, 4, and 6. Those who read the whole entry will find proofs of some non-trivial claims in supplementary documents.
‘Shut up and calculate’ does a disservice to quantum mechanics | Aeon Essays
The cliché has it that the Copenhagen interpretation demands adherence without deep enquiry. That does physics a disservice
A Cryptography Engineer’s Perspective on Quantum Computing Timelines
The risk that cryptographically-relevant quantum computers materialize within the next few years is now high enough to be dispositive, unfortunately.
The Causal Axioms of Algebraic Quantum Field Theory: A Diagnostic
This paper examines the axioms of algebraic quantum field theory (AQFT) that aim to characterize the theory as one that implements relativistic causation. I suggest that the spectrum condition (SC), microcausality (MC), and primitive causality axioms (PC), taken individually, fall short of fulfilling this goal against what some philosophers have claimed. Instead, I will show that the “local primitive causality” (LPC) condition captures each axiom’s advantages. However, this is only the case because SC, MC, and PC, taken together, imply LPC, as I will show from a construction by Haag and Schroer (1962).
A Post-Quantum Future for Let's Encrypt
Let’s Encrypt is committed to a post-quantum-safe Web PKI. The path we’re planning to take is Merkle Tree Certificates (“MTCs”), a new approach that adds post-quantum authentication to the web without sacrificing the speed and reliability that have made TLS universal. This post is about these plans and why we believe MTCs are worth pursuing as a key to a post-quantum future. An increasingly urgent problem For much of the last several years, the conversation about post-quantum cryptography has been a conversation about encryption. The reasoning was straightforward: an attacker who records encrypted traffic today might be able to decrypt it years from now once quantum computers can break the underlying math. Authentication, the part of TLS that indicates a server is who it says it is, has been a less urgent problem. A quantum computer needs to forge a signature in real time, not retroactively, so threats to authentication hinge on the existence of a cryptographically relevant quantum computer (CRQC).
Bayesian Thinking in Everyday Life
More than 200 years ago, Thomas Bayes came up with a brilliant idea that has helped shape the world today, called Bayes Theorem. This…
Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity
Out of Nowhere is the monograph co-authored by Nick Huggett and Christian Wüthrich, which appeared in 2025 from Oxford University Press. Selected chapters are posted here. (Our publication agreemen…
Local Causation
The counterfactual and regularity theories are universal accounts of causation. I argue that these should be generalized to produce local accounts of causation. A hallmark of universal accounts of causation is the assumption that apparent variation in causation between locations must be explained by differences in background causal conditions, by features of the causal-nexus or causing-complex. The local account of causation presented here rejects this assumption, allowing for genuine variation in causation to be explained by differences in location. I argue that local accounts of causation are plausible, and have pragmatic, empirical and theoretical advantages over universal accounts. I then report on the use of presheaves as models of local causation. The use of presheaves as models of local variation has precedents in algebraic geometry, category theory and physics; they are here used as models of local causal variation. The paper presents this idea as stemming from an approach using presheaves as models of local truth. Finally, I argue that a proper balance between universal and local causation can be assuaged by moving from presheaves to fully-fledged sheaf models.
Causality
Written by one of the preeminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, economics, philosophy, cognitive science, and the health and social sciences. Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations. Cited in more than 2,100 scientific publications, it continues to liberate scientists from the traditional molds of statistical thinking. In this revised edition, Judea Pearl elucidates thorny issues, answers readers' questions, and offers a panoramic view of recent advances in this field of research. Causality will be of interest to students and professionals in a wide variety of fields. Dr Judea Pearl has received the 2011 Rumelhart Prize for his leading research in Artificial Intelligence (AI) and systems from The Cognitive Science Society.
