It is shown that the non-associative operators in a non-associative quantum theory are unobservables. The observable quantity may be presented only by the elements of some associative subalgebra. It is shown that the elements of the associative subalgebra are extended objects that can be similar to strings. It is assumed that the non-associative quantum field theory can be applied to the quantization of strongly interacting fields. The method for obtaining field equations in a non-associative case is given.
Toy models of a non-associative quantum mechanics are presented. The Heisenberg equation of motion is modified using a non-associative commutator. Possible physical applications of a non-associative quantum mechanics are considered. The idea is discussed that a non-associative algebra could be the operator language for the non-perturbative quantum theory. In such approach the non-perturbative quantum theory has observables and unobservables quantities.
It is shown that the supersymmetric quantum mechanics has an octonionic generalization. The generalization is based on the inclusion of quaternions into octonions. The elements from the coset octonions/quaternions are unobservables bacause they cannot be considered as quantum operators as a consequence of their non-associative properties. The idea that the octonionic generalization of the supersymmetric quantum mechanics describes an observable particle formed with unobservable ``particles'' is presented.
The paper argues that far from challenging - or even refuting - Bohm's quantum theory, the no-hidden-variables theorems in fact support the Bohmian ontology for quantum mechanics. The reason is that (i) all measurements come down to position measurements and (ii) Bohm's theory provides a clear and coherent explanation of the measurement outcome statistics based on an ontology of particle positions, a law for their evolution and a probability measure linked with that law. What the no-hidden-variables theorems teach us is that (i) one cannot infer the properties that the physical systems possess…
The interpretation of quantum theory known as QBism argues that many elements of the formalism have a subjective interpretation. At the same time, QBism claims to be a broadly realist program. This implies that reality in QBism must be somehow founded upon an agent's subjective experiences (measurement outcomes). To make this idea more precise, we propose to interpret QBism's "experiences" as synonymous with the concept of "perceived phenomena" in phenomenology. This suggests an approach to ontology in which objects can only be physically real if they are in principle observable. But what does…
State representations summarize our knowledge about a system. When unobservable quantities are introduced the state representation is typically no longer unique. However, this non-uniqueness does not affect subsequent inferences based on any observable data. We demonstrate that the inference-free subspace may be extracted whenever the quantity's unobservability is guaranteed by a global conservation law. This result can generalize even without such a guarantee. In particular, we examine the coherent-state representation of a laser where the absolute phase of the electromagnetic field is believ…
The associators/antiassociators for the product of four non-associative operators are deduced. By analogy with SU(3) gauge theory the notion of colorless (white) operators is introduced. Some properties of white operators are considered. It is hypothesized that white operators do not give any contribution to corresponding associators/antiassociators. It is suggested that the observables in a non-associative quantum theory correspond to the white operators only.
We investigate the propagation of information through one-dimensional quantum chains in fluctuating external fields. We find that information propagation is suppressed, but in a quite different way compared to the situation with static disorder. We study two settings: (i) a general model where an unobservable fluctuating field acts as a source of decoherence; (ii) the XX model with both observable and unobservable fluctuating fields. In the first setting we establish a noise threshold below which information can propagate ballistically and above which information is localised. In the second se…
Recently authors of a paper (arXiv:2105.04407) claim that quantum energy teleportation is unobservable due to a time-energy uncertainty relation. In this short note, I will point out that their argument is wrong. They misuse the uncertainty relation.
The brain is composed of electrically excitable neuronal networks regulated by the activity of voltage-gated ion channels. Further portraying the molecular composition of the brain, however, will not reveal anything remotely reminiscent of a feeling, a sensation or a conscious experience. In classical physics, addressing the mind-brain problem is a formidable task because no physical mechanism is able to explain how the brain generates the unobservable, inner psychological world of conscious experiences and how in turn those conscious experiences steer the underlying brain processes toward des…
The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to non-associative algebras. Their quantum physics has remained obscure. This letter presents the first derivation of potentially testable physical results in non-associative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.
It is shown that the observability of a large class of operations on mixed states is fundamentally limited. We consider trace preserving, unital operations. This class includes unitary and perfect premeasurement operations. An upper bound on the trace distance between an untransformed state and a state transformed by one of these operations is derived. The bound is dependent only on the purity of the state. In the case of maximal mixedness, the bound implies all operations of this class are unobservable.
The quantum-to-classical transition is considered from the point of view of contractions of associative algebras. Various methods and ideas to deal with contractions of associative algebras are discussed that account for a large family of examples. As an instance of them, the commutative algebra of functions in phase space, corresponding to classical physical observables, is obtained as a contraction of the Moyal star-product which characterizes the quantum case. Contractions of associative algebras associated to Lie algebras are discussed, in particular the Weyl-Heisenberg and $SU(2)$ groups …
The human mind is constituted by inner, subjective, private, first-person conscious experiences that cannot be measured with physical devices or observed from an external, objective, public, third-person perspective. The qualitative, phenomenal nature of conscious experiences also cannot be communicated to others in the form of a message composed of classical bits of information. Because in a classical world everything physical is observable and communicable, it is a daunting task to explain how an empirically unobservable, incommunicable consciousness could have any physical substrates such a…
We consider the reversible processes between two one-to-one correlated measurement outcomes which underly both problem-solving and quantum nonlocality. In the former case the two outcomes are the setting and the solution of the problem, in the latter those of measuring a pair of maximally entangled observables whose subsystems are space separate. We argue that the quantum description of these processes mathematically describes the correlation but leaves the causal structure that physically ensures it free, also of violating the time-symmetry required of the description of a reversible process.…
We introduce a new hybrid quantum-classical adversarial machine learning architecture called a quantum-classical associative adversarial network (QAAN). This architecture consists of a classical generative adversarial network with a small auxiliary quantum Boltzmann machine that is simultaneously trained on an intermediate layer of the discriminator of the generative network. We numerically study the performance of QAANs compared to their classical counterparts on the MNIST and CIFAR-10 data sets, and show that QAANs attain a higher quality of learning when evaluated using the Inception score …
The quantization of time-reparametrization invariant systems such as general relativity is plagued by an ambiguity relating to the role of time in the theory. If one parametrizes observables by the (unobservable) time, and then relies on the existence of an approximate "clock" degree of freedom to give physical meaning to the observables, one finds multiple quantum states that yield the same predictions yet interfere with each other.
The recently proposed ER=EPR correspondence postulates the existence of wormholes (Einstein-Rosen bridges) between entangled states (such as EPR pairs). Entanglement is famously known to be unobservable in quantum mechanics, in that there exists no observable (or, equivalently, projector) that can accurately pick out whether a generic state is entangled. Many features of the geometry of spacetime, however, are observables, so one might worry that the presence or absence of a wormhole could identify an entangled state in ER=EPR, violating quantum mechanics, specifically, the property of state-i…
Physics explains the laws of motion that govern the time evolution of observable properties and the dynamical response of systems to various interactions. However, quantum theory separates the observable part of physics from the unobservable time evolution by introducing mathematical objects that are only loosely connected to the actual physics by statistical concepts and cannot be explained by any conventional sets of events. Here, I examine the relation between statistics and dynamics in quantum theory and point out that the Hilbert space formalism can be understood as a theory of ergodic ra…
Invertible maps from operators of quantum obvservables onto functions of c-number arguments and their associative products are first assessed. Different types of maps like Weyl-Wigner-Stratonovich map and s-ordered quasidistribution are discussed. The recently introduced symplectic tomography map of observables (tomograms) related to the Heisenberg-Weyl group is shown to belong to the standard framework of the maps from quantum observables onto the c-number functions. The star-product for symbols of the quantum-observable for each one of the maps (including the tomographic map) and explicit re…
The conservation of physical quantities under coordinate transformations, known as gauge invariance, has been the foundation of theoretical frameworks in both quantum and classical theory. The finding of gauge-invariant quantities has enabled the geometric and topological interpretations of quantum phenomena with the Berry phase, or the separation of quark and gluon contributions in quantum chromodynamics. Here, with an example of quantum geometric quantities-Berry connection, phase, and curvature-we extract a new gauge-invariant quantity by applying a "weak value picture". By employing differ…
Quantum physics can only make statistical predictions about possible measurement outcomes, and these predictions originate from an operator algebra that is fundamentally different from the conventional definition of probability as a subjective lack of information regarding the physical reality of the system. In the present paper, I explore how the operator formalism accommodates the vast number of possible states and measurements by characterizing its essential function as a description of causality relations between initial conditions and subsequent observations. It is shown that any complete…
A commonly adopted relational account of time evolution in generally-covariant systems, and more specifically in quantum cosmology, is argued to be unsatisfactory, insofar as it describes evolution relative to observed readings of a clock that does not exist as a bona fide observable object. A modified strategy is proposed, in which evolution relative to the proper time that elapses along the worldline of a specific observer can be described through the introduction of a `test clock', regarded as internal to, and hence unobservable by, that observer. This strategy is worked out in detail in th…
I point out that if one defines the operator $U_R(t)$ as done by M. Znojil in his reply [arXiv:0711.0514v1] to my comment [arXiv:0711.0137v1] and also accepts the validity of the defining relation of $U_R(t)$ as given in his paper [arXiv:0710.5653v1], one finds that the time-evolution of the associated quantum system is not governed by the Schrödinger equation for the Hamiltonian operator $H$ but an operator $H'$ which differs from $H$ if the metric operator is time-dependent. In the latter case this effective Hamiltonian $H'$ is not observable. This is consistent with the conclusions of my pa…
Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing "unobservable" elements in their descriptions. Since our aim is physics where the choice between finite and infinite descriptions can not have any empirical consequences, we consider the problem in the finite background. Besides, there are many indications from observations - from the lepton mixing data, for example - that finite groups underly phenomena in particl…
