General Quantum Theory Research Articles

Complementarity of subjective and objective realities: An experimental investigation of variations of subjective self-reported intelligence data when objective data are erased or not-erased

The Complementarity Principle (CP), introduced by Nils Bohr, described the wave-particle duality of quantum phenomena and its dependence on the measurement setup exploring the quantum states. In general, this principle summarized the fact that two mutually exclusive and contradictory states of quantum events can be reconciled as a measurement-dependent occurrence of these states. Originally, the CP was postulated only for the realm of quantum mechanics, but recently the Generalized Quantum Theory (GQT) extended its area of applicability to the macroscopic domain. According to GQT complementarity relations are also hypothesized to exist between macroscopic objective and subjective measurements of the same concept. This implies objective measurement-dependent variations of subjective experience. To test this hypothesis, seven studies were conducted in which individual variations in subjective intelligence ratings were tested in relation to the availability or non-availability of corresponding objective individual intelligence data. Only one pre-registered study (Study 2) showed strong Bayesian evidence for H1 (BF10 > 10), indicating, as predicted, higher subjective intelligence ratings when objective data were erased compared to a condition in which objective data were available within a male sample. This effect could not be replicated in direct replication attempts, nor did a moderator search in subsequent studies find any robust systematic variation in the data. The results seem to question the validity of the macroscopic complementarity conjecture derived from the GQT. On the other hand, they could also be interpreted as the “effect and decline” data pattern that the Model of Pragmatic Information would predict when conducting empirical confirmations of macroscopic complementarity relations. Possible future research strategies to clarify these different interpretations are discussed.

Modified Friedmann equations and fractal Black Hole thermodynamics

The general relativity unification and quantum theory is a significant open problem in theoretical physics. This problem arises from the fact that these two fundamental theories, which describe gravity and the behavior of particles at the microscopic level, respectively, are currently incompatible. The unification of these theories is crucial for a complete comprehension of the fundamental forces and the nature of the universe. In this regard, the quantum properties of a Black Hole result in fundamental importance. By analyzing such properties in quantum field theory, in the first step, the gravity enters as a classical background. In semi-classical approximation, Black Holes will emit Hawking radiation with an almost thermal spectrum, while Black Hole’s entropy is proportional to the Black Hole’s horizon. Besides, Hawking’s temperature and Black Hole entropy should follow the first law of Black Hole thermodynamics. Also, Jacobson [Thermodynamics of spacetime: The Einstein equation of state, Phys. Rev. Lett. 75 (1995) 1260, doi:10.1103/PhysRevLett.75.1260] showed shown that there is a connection between Black Hole thermodynamics and Einstein’s equation that opens the root of a potential thermodynamic nature of gravity. This issue opened a new impressive research framework in which the Einstein field equation can be expressed as a form of the first law of thermodynamics and vice versa. In this study, it is assumed that the universe has a fractal structure. Accordingly, modified Friedmann’s equations and the Black Holes thermodynamics in a fractal universe have been examined. The fractal framework shows what features and changes occur in the description of the universe, particularly in studying the thermodynamics of a Black Hole. However, the paper strategy is organized as follows: in the beginning, we consider the first thermodynamic law in a fractal universe. Then, we investigate the Friedmann equation of the fractal universe in the form of the entropy balance, this means [Formula: see text], where [Formula: see text] and [Formula: see text] are the thermal energy and horizon temperature. We consider the entropy [Formula: see text] have two terms; (1) obeys the usual area law and (2) the entropy production term due to the non-equilibrium thermodynamics of a fractal universe. Therefore, in a fractal universe, a term with non-equilibrium thermodynamics of spacetime may be needed. Also, we study the generalized second law of thermodynamics in a fractal universe. When the temperature of the apparent horizon and the temperature of the matter fields inside the horizon are equal, i.e. [Formula: see text], the second law of generalized thermodynamics can be obtained according to the state parameter range equation, which is consistent with the recent observations. Finally, in Sec. 6, based on the mathematical calculations, we study the various cosmological parameters such as the Hubble parameter, scale factor, deceleration parameter and equation of state parameter.

An Effective Refutation of General Relativity and Quantum Theories

It is briefly shown that all physical theories that rely on a mathematical application of the circle number as an irrational dimensionless number are irrational and flawed in their explanatory content, since they place the physical dimensions of space (L) [length] and time (T) in an inaccurate and irrational relationship. Albert Einstein's most important postulate (speed of light in a vacuum = constant) is thus refuted and shown that there π are no natural constants in nature – apart from the circle number π

Generalized stimulated Raman scattering with nonlocal effects

We present a generalized quantum theory of stimulated Raman scattering, which is based on coupled Heisenberg–Langevin equations. Analytical solutions in previous models neglect the effects of the frequency dispersion, assume far-off resonance and only consider slowly varying terms in the atomic operator. In obtaining the more general theory, we have derived partial integro-differential equation containing polarization kernels that include all the temporal nonlocal effects using systematic integral method over time. Analytical solutions of the Stokes field with greater generality for arbitrary spatial-temporal laser fields have been obtained using Laplace transform in the retarded space frame with minimal approximations made. The solutions are very general and potentially useful for studying systems in which highly accurate modeling is required such as quantum memories of a wide range of Raman systems.

General quantum theory of Thomson scattering

It is well known that the interaction of radiation with matter can be described using classical or quantum physics in relation to three systems: incoming radiation, matter, and scattered radiation. Currently, there is no general non-perturbative theory of electromagnetic wave scattering by free electrons, which describes the scattering process using quantum physics. In this paper, such a non-relativistic theory is presented, where statistics and the number of incoming photons is taken into account, and in scattering, statistics with the number of scattered photons is obtained. This theory is completely analytical, considering an arbitrary number of electrons in the system and, in a particular case, goes over into the previously known theory of scattering as the number of incident photons tends to infinity. It is shown that this theory can differ greatly from the previously known theory of Thomson scattering in the non-perturbative case and at relatively small numbers of incident photons. In addition, this theory is applicable to the scattering of ultrashort pulses by free electrons. This theory has good prospects for application in quantum optics, since it fully takes into account the quantum nature of the incident and scattered radiation when interacting with an arbitrary number of free electrons, including in the non-perturbative case.

The Open Systems View and the Everett Interpretation

It is argued that those who defend the Everett, or ‘many-worlds’, interpretation of quantum mechanics should embrace what we call the general quantum theory of open systems (GT) as the proper framework in which to conduct foundational and philosophical investigations in quantum physics. GT is a wider dynamical framework than its alternative, standard quantum theory (ST). This is true even though GT makes no modifications to the quantum formalism. GT rather takes a different view, what we call the open systems view, of the formalism; i.e., in GT, the dynamics of systems whose physical states are fundamentally represented by density operators are represented as fundamentally open as specified by an in general non-unitary dynamical map. This includes, in principle, the dynamics of the universe as a whole. We argue that the more general dynamics describable in GT can be physically motivated, that there is as much prima facie empirical support for GT as there is for ST, and that GT could be fully in the spirit of the Everett interpretation—that there might, in short, be little reason for an Everettian not to embrace the more general theoretical landscape that GT allows one to explore.

Experimental simulation of loop quantum gravity on a photonic chip

The unification of general relativity and quantum theory is one of the fascinating problems of modern physics. One leading solution is Loop Quantum Gravity (LQG). Simulating LQG may be important for providing predictions which can then be tested experimentally. However, such complex quantum simulations cannot run efficiently on classical computers, and quantum computers or simulators are needed. Here, we experimentally demonstrate quantum simulations of spinfoam amplitudes of LQG on an integrated photonics quantum processor. We simulate a basic transition of LQG and show that the derived spinfoam vertex amplitude falls within 4% error with respect to the theoretical prediction, despite experimental imperfections. We also discuss how to generalize the simulation for more complex transitions, in realistic experimental conditions, which will eventually lead to a quantum advantage demonstration as well as expand the toolbox to investigate LQG.

M-Theory and F-Theory over Theoretical Analysis on Cosmic Strings and Calabi-Yau Manifolds Subject to Conifold Singularity with Randall-Sundrum Model

String theory always comes with heavy mathematical rigor as it questions the most significant and impossible attempt to make a scale-invariant phenomenology between general relativity and quantum theory. Thus, steps have been taken to simplify the theory a bit thereby making it accessible to general yet enthusiastic readers of physics. However, as there is numerous mathematics involved in the modeling of this theory, thus, any chance to make a purely non-mathematical approach towards strings would prove vacuous and intimidating making the pathway of this marvelous theory chocked with unnecessary assumptions resulting in false analogies (or hopes) relating to this theory. Thus, where it’s almost impossible to proceed without any equations, we have given a few just to wipe out some logical confusion arising to the first readers of strings. Few necessary diagrams are included along with intense theory and least mathematics for making this significant approach of theoretical physicists accessible to general learners or readers.
 Topics: Bosonic string theory, supersymmetric string theory, M – theory, F – theory, dualities and interconnectedness, viability, Randall – Sundrum model for tackling the hierarchy problem of particle physics, conifold singularities, Branes, Bulks, Extremal black holes, Ekpyrotic cosmology, topological aspects of Calabi – Yau (CY) manifolds, A and B models, Mirror Symmetries; AdS/CFT, cosmic strings, all in a way accessible to every reader.
 Methods: Theoretical analogies, deductions, principles behind the origin, development along with the probable conclusion of this theory, the roots of its origin, the necessary difficulty for detecting those strings, and approaches done by theorists to work out the pathway of achieving Einstein’s dream of unification irrespective of several hindrances.
 Results: String theory itself is not a complete theory. Rather it’s in the process of further development through the increment of time resulting in more applications of mathematics by developing or incorporating them in due needs. Thus, without stating any concrete results, the theory has been tackled in this paper with a viable hypothesis based on the current understanding, and previous attempts are stated to have been made for its success.

Noncausal Page-Wootters circuits

One of the most fundamental open problems in physics is the unification of general relativity and quantum theory to a theory of quantum gravity. An aspect that might become relevant in such a theory is that the dynamical nature of causal structure present in general relativity displays quantum uncertainty. This may lead to a phenomenon known as indefinite or quantum causal structure, as captured by the process matrix formalism. Due to the generality of that framework, however, for many process matrices there is no clear physical interpretation. A popular approach towards a quantum theory of gravity is the Page-Wootters formalism, which associates to time a Hilbert space structure similar to spatial position. By explicitly introducing a quantum clock, it allows to describe time-evolution of systems via correlations between this clock and said systems encoded in history states. In this paper we combine the process matrix framework with a generalization of the Page-Wootters formalism in which one considers several agents, each with their own discrete quantum clock. We describe how to extract process matrices from scenarios involving such agents with quantum clocks, and analyze their properties. The description via a history state with multiple clocks imposes constraints on the implementation of process matrices and on the perspectives of the agents as described via causal reference frames. While it allows for scenarios where different definite causal orders are coherently controlled, we explain why certain noncausal processes might not be implementable within this setting.

Towards Unification of General Relativity and Quantum Theory: Dendrogram Representation of the Event-Universe.

Following Smolin, we proceed to unification of general relativity and quantum theory by operating solely with events, i.e., without appealing to physical systems and space-time. The universe is modelled as a dendrogram (finite tree) expressing the hierarchic relations between events. This is the observational (epistemic) model; the ontic model is based on p-adic numbers (infinite trees). Hence, we use novel mathematics: not only space-time but even real numbers are not in use. Here, the p-adic space (which is zero-dimensional) serves as the base for the holographic image of the universe. In this way our theory is connected with p-adic physics; in particular, p-adic string theory and complex disordered systems (p-adic representation of the Parisi matrix for spin glasses). Our Dendrogramic-Holographic (DH) theory matches perfectly with the Mach’s principle and Brans–Dicke theory. We found a surprising informational interrelation between the fundamental constants, h, c, G, and their DH analogues, h(D), c(D), G(D). DH theory is part of Wheeler’s project on the information restructuring of physics. It is also a step towards the Unified Field theory. The universal potential V is nonlocal, but this is relational DH nonlocality. V can be coupled to the Bohm quantum potential by moving to the real representation. This coupling enhances the role of the Bohm potential.

Modified general relativity and quantum theory in curved spacetime

With appropriate modifications, the multi-spin Klein–Gordon (KG) equation of quantum field theory can be adapted to curved space–time for spins 0, 1, 1/2. The associated particles in the microworld then move as a wave at all space–time coordinates. From the existence in a Lorentzian space–time of a line element field [Formula: see text], the spin-1 KG equation [Formula: see text] is derived from an action functional involving [Formula: see text] and its covariant derivative. The spin-0 KG equation and the KG equation of the outer product of a spin-1/2 Dirac spinor and its Hermitian conjugate are then constructed. Thus, [Formula: see text] acts as a fundamental quantum vector field. The symmetric part of the spin-1 KG equation, [Formula: see text], is the Lie derivative of the metric. That links the multi-spin KG equation to Modified General Relativity (MGR) through its energy–momentum tensor of the gravitational field. From the invariance of the action functionals under the diffeomorphism group Diff(M), which is not restricted to the Lorentz group, [Formula: see text] can instantaneously transmit information along [Formula: see text]. That establishes the concept of entanglement within a Lorentzian formalism. The respective local/nonlocal characteristics of MGR and quantum theory no longer present an insurmountable problem to unify the theories.

Entropic uncertainty relations in a class of generalized probabilistic theories

Entropic uncertainty relations play an important role in both fundamentals and applications of quantum theory. Although they have been well-investigated in quantum theory, little is known about entropic uncertainty in generalized probabilistic theories (GPTs). The current study explores two types of entropic uncertainty relations, preparation and measurement uncertainty relations, in a class of GPTs which can be considered generalizations of quantum theory. Not only a method for obtaining entropic preparation uncertainty relations but also an entropic measurement uncertainty relation similar to the quantum one by Buscemi et al (2014 Phys. Rev. Lett. 112 050401) are proved in those theories. These results manifest that the entropic structure in the uncertainty relations is not restricted to quantum theory and therefore is universal one. Concrete calculations of our relations in GPTs called the regular polygon theories are also demonstrated.

How dynamics constrains probabilities in general probabilistic theories

We introduce a general framework for analysing general probabilistic theories, which emphasises the distinction between the dynamical and probabilistic structures of a system. The dynamical structure is the set of pure states together with the action of the reversible dynamics, whilst the probabilistic structure determines the measurements and the outcome probabilities. For transitive dynamical structures whose dynamical group and stabiliser subgroup form a Gelfand pair we show that all probabilistic structures are rigid (cannot be infinitesimally deformed) and are in one-to-one correspondence with the spherical representations of the dynamical group. We apply our methods to classify all probabilistic structures when the dynamical structure is that of complex Grassmann manifolds acted on by the unitary group. This is a generalisation of quantum theory where the pure states, instead of being represented by one-dimensional subspaces of a complex vector space, are represented by subspaces of a fixed dimension larger than one. We also show that systems with compact two-point homogeneous dynamical structures (i.e. every pair of pure states with a given distance can be reversibly transformed to any other pair of pure states with the same distance), which include systems corresponding to Euclidean Jordan Algebras, all have rigid probabilistic structures.

Repainting the Rabbithole: Law, Science, Truth and Responsibility

An exploration of the connections between law, science, and truth, this paper argues that ‘truth’ is an evolving, rather than fixed, concept. It is a human creation, and the processes, or standards, by which it has been evaluated have changed over time. Currently knowledge production is anchored in the natural sciences but reproduced and validated by philosophical rationalisation. There are two problems with this technique of knowledge verification (or ‘veridiction’). First, the natural sciences are not, in fact, practiced according to their ideal forms; and second, the Queen of Sciences, physics, underwent two fundamental paradigm shifts in the early nineteenth century. General relativity and quantum theory entered the scene, sending ripples throughout science, and the social sciences. These changes too have been slowly absorbed by philosophy, giving rise in part to the postmodernist and deconstructivist movements. I chart this gradual evolution of truth and knowledge production in physics and in law and analyse the resistance it has faced from both classical law and classical physics. Finally I argue that this resistance could be overcome, if legal theory, and especially legal positivism, would embrace a more accurate and up-to-date understanding of the science it purports to examine and emulate.

Thermal behaviors of the sharp zero–phonon luminescence lines of NV center in diamond

The nitrogen–vacancy (NV) center in diamond has quickly emerged as a promising solid–state candidate for single-photon emitters, quantum bits or qubits, and ultrasensitive sensors in recent years. At the same time, it may also provide an excellent molecule–like platform for exploiting the fundamental principles of quantum mechanics, such as quantum entanglement mechanism. Therefore, it is of both scientific and technological significance to have an in-depth investigation on NV center, especially on the optoelectronic processes and optical properties of NV center. In this study, the temperature dependence of the sharp zero–phonon lines (ZPL) of luminescence of NV center with neutral and negative charge states in a CVD–grown diamond crystal is measured in the range from 5 K to 300 K. It is shown that the experimental data, including the temperature induced broadening, peak shift and even intensity quenching of the two sharp ZPL lines of NV0 and NV−1, all on the whole support a generalized quantum theory in spite of in which Franck–Condon, harmonic and Debye approximations were assumed. In particular, the thermal quenching tendency of the integrated intensities can be described by Debye–Waller factor in the theory of the Mössbauer effect. The study sheds some light on the challenging issue, the temperature dependence of the so–called zero-phonon luminescence of NV center in diamond.

Efficient Simulation of Loop Quantum Gravity: A Scalable Linear-Optical Approach

The problem of simulating complex quantum processes on classical computers gave rise to the field of quantum simulations. Quantum simulators solve problems, such as boson sampling, where classical counterparts fail. In another field of physics, the unification of general relativity and quantum theory is one of the greatest challenges of our time. One leading approach is loop quantum gravity (LQG). Here, we connect these two fields and design a linear-optical simulator such that the evolution of the optical quantum gates simulates the spin-foam amplitudes of LQG. It has been shown that computing transition amplitudes in simple quantum field theories falls into the bounded-error quantum polynomial time class, which strongly suggests that computing transition amplitudes of LQG are classically intractable. Therefore, these amplitudes are efficiently computable with universal quantum computers, which are, alas, possibly decades away. We propose here an alternative special-purpose linear-optical quantum computer that can be implemented using current technologies. This machine is capable of efficiently computing these quantities. This work opens a new way to relate quantum gravity to quantum information and will expand our understanding of the theory.

General quantum theory—unification of classical and modal quantum theories

Inspired by classical (‘actual’) quantum theory over and modal quantum theory (MQT), which is a model of quantum theory over certain finite fields, we introduce general quantum theory as a quantum theory—in the København interpretation—over general division rings with involution, in which the inner product ‘is’ a (σ, 1)-Hermitian form φ. This unites all known such approaches in one and the same theory, and we show that many of the known results such as no-cloning, no-deleting, quantum teleportation and super-dense quantum coding, which are known in classical quantum theory over and in some MQTs, hold for any general quantum theory. Our approach is totally different (and more general) than Hardy’s axiomatic approach [], and generalized probability theories. On the other hand, in many general quantum theories, a geometrical object which we call ‘quantum kernel’ arises, which is invariant under the unitary group U(V, φ), and which carries the geometry of a so-called polar space. This object cannot be seen in classical quantum theory over , but it is present, for instance, in all known MQTs. We use this object to construct new quantum (teleportation) coding schemes, which mix quantum theory with the geometry of the quantum kernel (and the action of the unitary group). We also show that in characteristic 0, every general quantum theory over an algebraically closed field behaves like classical quantum theory over at many levels, and that all such theories share one model, which we pin down as the ‘minimal model,’ which is countable and defined over . Moreover, to make the analogy with classical quantum theory even more striking, we show that Born’s rule holds in any such theory. So all such theories are not modal at all. Finally, we obtain an extension theory for general quantum theories in characteristic 0 which allows one to extend any such theory over algebraically closed fields (such as classical complex quantum theory) to larger theories in which a quantum kernel is present. In this sense, these singular objects are always virtually around in abundance.

Operational Restrictions in General Probabilistic Theories

The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the usual no-restriction hypothesis, the set of accessible meters within a given theory can be limited for different reasons, and this raises a question of what restrictions on meters are operationally relevant. We argue that all operational restrictions must be closed under simulation, where the simulation scheme involves mixing and classical post-processing of meters. We distinguish three classes of such operational restrictions: restrictions on meters originating from restrictions on effects; restrictions on meters that do not restrict the set of effects in any way; and all other restrictions. We fully characterize the first class of restrictions and discuss its connection to convex effect subalgebras. We show that the restrictions belonging to the second class can impose severe physical limitations despite the fact that all effects are accessible, which takes place, e.g., in the unambiguous discrimination of pure quantum states via effectively dichotomic meters. We further demonstrate that there are physically meaningful restrictions that fall into the third class. The presented study of operational restrictions provides a better understanding on how accessible measurements modify general probabilistic theories and quantum theory in particular.

STEPHEN HAWKING: SPACE, TIME AND QUANTA

A brief introduction to the scientic work of Stephen Hawking and to his contributions to our understanding of the interplay between general relativity and quantum theory.

Spin-rotation coupling observed in neutron interferometry

Einstein’s theory of general relativity and quantum theory form the two major pillars of modern physics. However, certain inertial properties of a particle’s intrinsic spin are inconspicuous while the inertial properties of mass are well known. Here, by performing a neutron interferometric experiment, we observe phase shifts arising as a consequence of the spin’s coupling with the angular velocity of a rotating magnetic field. This coupling is a purely quantum mechanical extension of the Sagnac effect. The resulting phase shifts linearly depend on the frequency of the rotation of the magnetic field. Our results agree with the predictions derived from the Pauli–Schrödinger equation.