Quantum entanglement and ‘the measurement problem’

An increasingly popular interpretation of quantum mechanics holds that in any genuinely chancy situation, all possible outcomes occur.1 For example, if the spin of a typical electron is measured in a given direction, then both 'up' and 'down' results will be registered. (True, 'up' and 'down' won't occur within the same 'branch of reality', for that would be inconsistent. Rather, the idea is that reality comes to contain two elements, with 'up' registered relative to one, and 'down' registered relative to the other.) This kind of 'many worlds' or 'many minds' interpretation of quantum mechanics has advantages and disadvantages. The main advantage is that it avoids any 'collapse of the wave function' and so avoids the measurement problem, mysterious non-local interactions, and the like. The most obvious disadvantage is that its burgeoning world of duplicate histories seems repugnant to common sense. Some commentators think that there is another disadvantage. They argue that this interpretation undermines itself by destroying any notion of objective probability. Quantum mechanics is, if anything, a theory which specifies the objective probabilities of certain results. But in what sense is there an objective probability for 'up' and 'down' in a spin measurement, if both results always happen? (Albert [1]; Albert and Loewer [3], [4]; Healey [5]; Squires [9]; Stein [8].) This looks like a good objection. But I shall show in this note that it is not. The proposed interpretation does leave objective probability as a rather mysterious notion. But it is no more mysterious on the proposed interpretation than on the conventional view of the world. This is not the place to go into details about the 'many minds'2 interpretation of quantum mechanics, but one point may help readers. If both the 'up' and 'down' results occur, why do we experience only one?

Although this book is about the implications for social science of a quantum approach to the mind, much of that potential stems from its ability to integrate consciousness – a particular aspect of the mind – into a naturalistic worldview. And when it comes to the hard problem, quantum brain theory is only a necessary condition for such integration, not sufficient. Necessary, because it would enable the body to exploit for macro-level purposes a physical but non- material space for consciousness at the quantum level – collapse of the wave function – that does not exist in classical physics. Insufficient, however, because quantum brain theory embodies an objective, third-person standpoint and as such can tell us no more than classical brain theory can about why brains have a subjective, first-person point of view in the first place. The explanatory gap is still there, in other words, only now pushed down into quantum theory. To cross this gap, therefore, in addition to a new physics of the brain we will need a new meta -physics as well. As I argue in this chapter, it is this metaphysics that does the real work in solving the mind–body problem. Most social scientists have an instinctive aversion to ‘metaphysics,’ which in our world connotes wooly-headed and speculative thinking that has no place in science. Yet in moving onto this terrain the situation is both worse and better than that. It is worse because we have no choice. The Neuron Doctrine itself is based on a metaphysic, materialism, which looks increasingly unlikely to ever explain consciousness; and in thinking about the meaning of quantum theory metaphysical debate can hardly be avoided, precisely because physics provides little guidance for choosing among its interpretations. So the only question is whether to change our metaphysics of the brain from classical to quantum.

Quantum mechanics, randomness, and deterministic reality

It has been proven that universal quantum computers based on qubits and classical analog networks both have superTuring capabilities. It is a grand challenge to computer science to prove that the combination of the two, in analog (continuous variable) quantum computing, offers supersuperTuring capability, the best we can achieve. Computing with continuous spins is now the most promising path AQC. Two papers at SPIE2014 described unbreakable quantum codes using continuous spins beyond what traditional qubits allow. To make this real, we must first develop a realistic ability to model and predict the behavior of networks of spin gates which act in part as polarizers. Last year I proposed a triphoton experiment, where three entangled photons go to linear polarizers set to angles θ_a, θ_b and θ_c. Assuming a “collapse of the wave function” yields predictions for the coincidence detection rate, R₃/R₀(θ_a, θ_b, θ_c) significantly different from the prediction of a new family of models based on classical Markov Random Fields (MRF) across space time, even though both yield the same correct prediction in the two-photon case. We cannot expect to predict systems of 100 entangled photons correctly if we cannot even predict three yet. Yanhua Shih is currently performing this experiment, as a first step to demonstrating a new technology to produce 100 entangled photons (collaborating with Scully) and understanding larger systems. I have also developed continuous-time versions of the MRF models and of “collapse of the wave function”, so as to eliminate the need to assume metaphysical observers in general.

In this paper, the physical explanation of all quantum phenomena such as wave function, wave function collapse, wave-particle duality, single-electron double-slit interference, uncertainty relation, tunneling effect and quantum entanglement is given by using the new etheric theory, and a new uncertainty relation which is consistent with the latest experimental results is given.

The Wave Function Collapse (WFC) algorithm is a widely used tile-based algorithm in procedural content generation, including textures, objects, and scenes. However, the current WFC algorithm and related optimized algorithms based on it lack the ability to generate commercial-scale or infinite content due to constraint conflicts and high time complexity. This paper proposes the Nested WFC (N-WFC) algorithm framework to reduce time complexity. To avoid conflict and backtracking problems, we offer a complete and sub-complete tileset preparation strategy, which requires only a small number of tiles to generate infinite, aperiodic, and deterministic content. We use Mario and Carcassonne as two game examples to describe their application and discuss potential research value. Our contribution addresses WFC's challenge in massive content generation and provides a theoretical basis for implementing concrete games.

This paper introduces a groundbreaking synthesis of fundamental quantum mechanics with the Advanced Observer Model (AOM), presenting a unified framework that reimagines the construction of reality. AOM highlights the pivotal role of the observer in shaping reality, where classical notions of time, space, and energy are reexamined through the quantum lens. By engaging with key quantum equations—such as the Schrödinger equation, Heisenberg uncertainty principle, and Dirac equation—the paper demonstrates how AOM unifies the probabilistic nature of quantum mechanics with the determinism of classical physics. Central to this exploration is the Sequence of Quantum States (SQS) and Constant Frame Rate (CFR), which align with concepts like quantum superposition, entanglement, and wave function collapse. The model’s implications extend to how observers perceive reality, proposing that interference patterns between wave functions form the foundation of observable phenomena. By offering a fresh perspective on the interplay between determinacy and indeterminacy, AOM lays a robust theoretical foundation for future inquiry into quantum physics and the philosophy of consciousness.

Because the validity of mathematics is premised on self‐reference avoidance, the validity or authenticity of the physical world must also be based on self‐reference avoidance. Based on this belief, this article explores the fundamental question of whether the collapse of the wave function is triggered by consciousness from the perspective of self‐reference avoidance. This article analyzes and points out that the real physical world (i.e., quantum systems) is self‐referential, and it contains uncomputable mathematical prohibitions, which are the essence of superposition. To avoid the paradox brought by self‐reference, quantum systems collapse from the superposition state to a definite state, which is the wave function collapse. In other words, the wave function collapse is essentially the spontaneous avoidance of self‐reference by the quantum system. Although this is related to the observer's consciousness, it is not directly triggered by consciousness, because, as part of an inseparable quantum system, the observer and the quantum system are inherently entangled. When the observer identifies themselves from the quantum system in an instant, they subconsciously avoid self‐reference, thereby gaining certainty.

According to a procedure previously introduced from Y. Ilamed and N. Salingaros, we start giving proof of two existing Clifford algebras, the Si that has isomorphism with that one of Pauli matrices and the Ni,±1 where Ni stands for the dihedral Clifford algebra. The salient feature is that we show that the Ni,±1 may be obtained from the Si algebra when we attribute a numerical value (+1 or −1) to one of the basic elements (e1,e2,e3) of the Si. We utilize such result to advance a criterium under which the Si algebra has as counterpart the description of quantum systems that in standard quantum mechanics are considered in absence of observation and quantum measurement while the Ni,±1 attend when a quantum measurement is performed on such system with advent of wave function collapse. The physical content of the criterium is that the quantum measurement with wave function collapse induces the passage in the considered quantum system from the Si to Ni,+1 or to the Ni,−1 algebras, where each algebra has of course its proper rules of commutation. After a proper discussion on the difference between decoherence and wave function collapse, we re-examine the von Neumann postulate on quantum measurement, and we give a proper justification of such postulate by using the Si algebra. Soon after we study some applications of the above mentioned criterium to some cases of interest in standard quantum mechanics, analyzing in particular a two state quantum system, the case of time dependent interaction of such system with a measuring apparatus and finally the case of a quantum system plus measuring apparatus developed at the order n=4 of the considered Clifford algebras and of the corresponding density matrix in standard quantum mechanics. In each of such cases examined, we find that the passage from the algebra Si to Ni,±1, considered during the quantum measurement of the system, actually describes the collapse of the wave function. Therefore we conclude that the actual quantum measurement has as counterpart in the Clifford algebraic description, the passage from the Si to the Ni,±1 Clifford algebras, reaching in this manner the objective to reformulate von Neumann postulate on quantum measurement and proposing a self-consistent formulation of quantum theory.

Wave function collapse as a nonlocal quantum effect

Review of: "Relation Between Quantum Jump and Wave Function Collapse"

This chapter provides a brief introduction to some key concepts of quantum theory that are contrasted with their classical analogs. By means of simple examples, the aim is to develop an intuition for notions such as quantum state, observables, superposition, Born’s rule, collapse of the wave function, Schrödinger’s equation, quantum interference, Heisenberg uncertainty, and incompatibility of observables. The hope is to provide a readable account on these core ideas of quantum theory that is accessible to readers from disciplines other than physics. The mathematical framework is developed from scratch, but some familiarity with basic linear algebra and probability theory will be assumed.

The Wave Function Collapse (WFC) algorithm is a new algorithm that can generate procedural patterns from a sample image. It is especially fascinating for game designers, allowing them to draw their ideas rather than coding them by hand. This article discusses what kinds of output images WFC can generate with an implementation in the Python programming language.

Virtual cities as background scenarios can be used for many 3D video game genres like action. However, the procedural generation of virtual cities for specific video game genres is an on-going research problem. In this paper, we seek to establish a grounding for future work into city generation for specific game genres by exploring how game designers approach existing generation tool-sets. Firstly, we look at the video game city Skara Brae from the party-based role-playing game The Bard's Tale and try to replicate it using the Wave Function Collapse (WFC) approach to procedural generation. We show in two experimental conditions which parameters for WFC are suitable for replicating the city. Secondly, a pilot user study with eight users shows how they approach creating different video game cities after they preselect a video game genre. The users' video game level ideas are then discussed, and different output levels are generated using WFC.

The collapse of the wave function has recently reemerged as a subject of extensive discussion in the quantum mechanical literature. In the present paper, wave function collapses occuring during the irreversible evolution of complex quantum systems, including those involved in measurement procedures, are described.