Gravitation and quantum mechanics of macroscopic objects

In cosmological special relativity theory, we study Maxwell equations, electromagnetic wave equations and functions. In the cosmological special theory of relativity, we study energy-momentum relations, the Klein-Gordon equation and wave functions. If we solve the Klein-Gordon equation, we obtain the Yukawa potential in the cosmological inertial frame. We derive the Schrodinger equation from Klein-Gordon free particle’s wave function in the cosmological special theory of relativity. We derive the uncertainty principle in cosmological quantum mechanics in cosmological special relativity theory. The Dirac equation is a one order wave equation. The wave function is used as a probability amplitude in quantum mechanics. We derive the Dirac equation from the wave function, Type A in the cosmological inertial frame. The Dirac equation satisfies the Klein-Gordon equation in the cosmological inertial frame. We found equations of complex scalar fields and electromagnetic fields on the interaction of complex scalar fields and electromagnetic fields in Klein-Gordon-Maxwell theory from Type A of the wave function and Type B of the expanded distance in the cosmological inertial frame. In the cosmological special theory of relativity, we quantized the Klein-Gordon scalar field. We treat the Lagrangian density and Hamiltonian in a quantized Klein-Gordon scalar field. We address the particle’s force and kinetic energy in the cosmological special theory of relativity. In the expanded universe, we found the gravity field equation and solution. We found the Schwarzschild solution and Kerr-Newman solution in an expanded universe. Hence, we found a new general relativity theory-the Cosmological General Theory of Relativity (CGTR).

The strong and singular interaction between nucleons, makes the nuclear many body theory very complicated. Still, nuclei exhibit simple and regular features which are simply described by the shell model. Wave functions of individual nucleons may be considered just as model wave functions which bear little resemblance to the real ones. There is, however, experimental evidence for the reality of single nucleon wave functions. There is a simple method of constructing such wave functions for valence nucleons. It is shown that this method can be improved by considering the polarization of the core by the valence nucleon. This gives rise to some rearrangement energy which affects the single valence nucleon energy within the nucleus.

Quantum information technology mainly includes quantum communication, quantum radar, quantum computer these three aspects, in recent years, rapid development, many countries invested heavily in development. The awarding of the Nobel Prize in Physics in 2022 to three scientists for their work in quantum informatics has further stimulated people's interest in quantum theory, which has been studied and discussed. This paper not only reviews the historical situation, but also thinks and innovates in theory. The main contents of this paper are as follows: It is pointed out that there are fundamental contradictions between relativity and quantum mechanics; The wave function, quantum statistics and uncertainty principle are discussed in detail. The hidden variable theory is reviewed and the Bell inequality is discussed. The Aspect two-photon experiment was analyzed. The rationality of Bohm experiment scheme is discussed. The development of Bell type experiment is discussed. It is pointed out that the entangled state is not acting at a distance but propagating faster than the speed of light. Reviews the Copenhagen interpretation of quantum mechanics; Quantum communication and Wootters theorem are discussed. etc. This paper holds that quantum mechanics has been finalized from 1926 to 1928, and its basic content has not changed much. But for some of the accusations, it is necessary to answer them theoretically. For example, we believe that the Copenhagen interpretation fundamentally changes our understanding of nature and marks a profound revolution in physics. And no other theory has since emerged that has such a profound understanding and wide application of microscopic phenomena as this interpretation. Another example is Bohm's two-particle correlation spin scheme in quantum entanglement experiments, which has been proved to be effective in a series of experiments, which is an important contribution in Bohm's life. This paper holds that the so-called quantum field theory is a failure, and the original quantum mechanics should still be advocated today. Current theoretical research should pay great attention to quantum entangled states, because its nature is still unclear. Understanding this "first mystery of the physical world" not only has scientific significance, but also has great philosophical significance for understanding the universe.

In this paper we incorporate different strengths of the centrifugal potential into a single partial wave function of the WKB approach in different spatial regions. By a suitable choice of these regions and strengths, the WKB wave functions can be made bounded and smooth everywhere as well as compatible with quantum mechanics both close to and far from the origin. This modified WKB approximation becomes exact in the strong-coupling limit. Moreover, by iteration, it develops an absolute convergent series expansion of the correct scattering wave function at fixed coupling constants.

An unconditionally energy-stable and orthonormality-preserving iterative scheme for the Kohn-Sham gradient flow based model

Bohr and Heisenberg suggested that the thermodynamical quantities of temperature and energy are complementary in the same way as position and momentum in quantum mechanics. Roughly speaking their idea was that a definite temperature can be attributed to a system only if it is submerged in a heat bath, in which case energy fluctuations are unavoidable. On the other hand, a definite energy can be assigned only to systems in thermal isolation, thus excluding the simultaneous determination of its temperature. Rosenfeld extended this analogy with quantum mechanics and obtained a quantitative uncertainty relation in the form ΔU Δ(1/T) ≥ k, where k is Boltzmann's constant. The two “extreme” cases of this relation would then characterize this complementarity between isolation (U definite) and contact with a heat bath (T definite). Other formulations of the thermodynamical uncertainty relations were proposed by Mandelbrot (1956, 1989), Lindhard (1986), and Lavenda (1987, 1991). This work, however, has not led to a consensus in the literature. It is shown here that the uncertainty relation for temperature and energy in the version of Mandelbrot is indeed exactly analogous to modern formulations of the quantum mechanical uncertainty relations. However, his relation holds only for the canonical distribution, describing a system in contact with a heat bath. There is, therefore, no complementarily between this situation and a thermally isolated system.

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.

This chapter explores the intricate dynamics between medium-sized and large enterprises in EU candidate countries through the lens of Bohm's interpretation of Bohr's complementarity principle and Heisenberg's uncertainty principle which are two fundamental concepts in quantum theory. By drawing parallels between quantum mechanics and economic behavior, the research posits that the growth trajectories of these enterprises are interrelated, exhibiting complementary relationships under uncertainty that reflect the principles of quantum duality. Employing a robust research methodology, the chapter presents empirical evidence showcasing the correlation between capital concentration and growth rates of medium-sized and large enterprises across various regions. Statistical analyses, including Pearson coefficients, reveal significant relationships that support the hypothesis of a higher share of medium enterprises correlating with an increased presence of large enterprises revalidating complementariness. Furthermore, the findings highlight important policy implications for regional economic development, emphasizing the need for tailored strategies that foster the growth of both enterprise sizes under uncertain conditions. By integrating quantum theory with economic dynamics, this chapter contributes a novel perspective to the discourse on entrepreneurship and regional growth, encouraging further exploration of interdisciplinary approaches in econophysics research.

We construct the novel Clifford-Yang algebra which is an extension of the Yang algebra in noncommutative phase spaces. The Clifford-Yang algebra allows us to write down the commutators of the [Formula: see text] polyvector-valued coordinates and momenta which are compatible with the Jacobi identities, the Weyl–Heisenberg algebra, and paves the way for a formulation of quantum mechanics (QM) in noncommutative Clifford spaces. We continue with a detailed study of the isotropic 3D quantum oscillator in noncommutative spaces and find the energy eigenvalues and eigenfunctions. These findings differ considerably from the ordinary quantum oscillator in commutative spaces. We find that QM in noncommutative spaces leads to very different solutions, eigenvalues, and uncertainty relations than ordinary QM in commutative spaces. The generalization of QM to noncommutative Clifford (phase) spaces is attained via the Clifford-Yang algebra. The operators are now given by the generalized angular momentum operators involving polyvector coordinates and momenta. The eigenfunctions (wave functions) are now more complicated functions of the polyvector coordinates. We conclude with some important remarks.

Quantum physics is a linear theory, so it is somewhat puzzling that it can underlie very complex systems such as digital computers and life. This paper investigates how this is possible. Physically, such complex systems are necessarily modular hierarchical structures, with a number of key features. Firstly, they cannot be described by a single wave function: only local wave functions can exist, rather than a single wave function for a living cell, a cat, or a brain. Secondly, the quantum to classical transition is characterised by contextual wave-function collapse shaped by macroscopic elements that can be described classically. Thirdly, downward causation occurs in the physical hierarchy in two key ways: by the downward influence of time dependent constraints, and by creation, modification, or deletion of lower level elements. Fourthly, there are also logical modular hierarchical structures supported by the physical ones, such as algorithms and computer programs, They are able to support arbitrary logical operations, which can influence physical outcomes as in computer aided design and 3-d printing. Finally, complex systems are necessarily open systems, with heat baths playing a key role in their dynamics and providing local arrows of time that agree with the cosmological direction of time that is established by the evolution of the universe.

Quantum mechanics, heredity and the origin of life

It is customary to introduce students to quantum mechanics with the Schrödinger equation because the single-component wave function is easy to handle mathematically. However, the Schrödinger equation is not consistent with special relativity, nor does it describe spin angular momentum. We propose that the Dirac equation provides a better introduction because (1) it is consistent with the laws of physics, (2) it describes spin angular momentum, and (3) it is easily derived from the classical physics model of an ideal elastic solid. The resultant description of classical wave mechanics shares many features of relativistic quantum mechanics.  These include Lorentz invariance, bispinor wave functions, half-integer azimuthal quantum numbers, standing waves with circular wave propagation, particle classifications similar to fermions and bosons, operators for physical quantities including spin angular momentum, Pauli exclusion principle, and interaction via potentials. The Schrödinger equation approximates the evolution of a single wave function component.

The uncertainty relation is considered to be one of key features of quantum mechanics which distinguishes quantum and classical systems. Recently, we developed a new formulation of the uncertainty relation based on the generalized scheme of variational principle, the stochastic variational method (SVM). In this method, the uncertainty relation is related to the nondifferentiability of observables and thus can be obtained even in classical stochastic systems. This new formulation resolves the famous paradox in quantum mechanics, the angular uncertainty relation without introducing artificial assumptions. In this paper, we show that the fluctuations of position and momentum for a nonrelativistic viscous fluid element satisfies the uncertainty relation analogous to the corresponding quantum mechanical one. Such a fluctuation is sensitive to the temperature gradient at the freezeout surface and can affect the collective flow anisotropy in relativistic heavy‐ion collisions.

The three main points of this article are: 1. Quantum mechanical data differ from conventional data: for example, joint distributions usually cannot be defined conventionally; 2. rigorous methods have been developed for analyzing such data; the methods often use quantum-consistent analogs of classical statistical procedures; 3. with these procedures, statisticians, both data-analytic and more theoretically oriented, can become active participants in many new and emerging areas of science and biotechnology. In the physical realm described by quantum mechanics, many conventional statistical and probabilistic assumptions no longer hold. Probabilistic ideas are central to quantum theory but the standard Kolmogorov axioms are not uniformly applicable. Studying such phenomena requires an altered model for sample spaces, for random variables and for inference and decision making. The appropriate decision theory has been in development since the mid-1960s. It is both mathematically and statistically rigorous and conforms to the requirements of the known physical results. This article provides a tour of the structure and current applications of quantum-consistent statistical inference and decision theory. It presents examples, outlines the theory and considers applications and open problems. Certain central concepts of quantum theory are more clearly apprehended in terms of the quantum-consistent statistical decision theory. For example, the Heisenberg uncertainty principle can be obtained as a consequence of the quantum version of the Cramer-Rao inequality. This places concepts of statistical estimation and decision theory, and thus the statistician, at the center of the quantum measurement process. Quantum statistical inference offers considerable scope for participation by the statistical community, in both applications and foundational questions.

The Nature of Space and Time is a seven and a half hour long video that comes in a three tape set. Professors Hawking and Penrose are shown giving a series of one hour lectures at the Isaac Newton Institute. The topics of their talks range from the structure of space-time to the quantum theory of gravitation. They are organized along three main lines. Both speakers first discuss the singularities of space and time within the framework of classical general relativity, that is, as deduced from Einstein's equations. After giving arguments in favour of the existence of closed trapped surfaces (collapsing stars, black holes), Hawking draws a parallel between thermodynamic irreversibility and the loss of information coming from gravity trapped surfaces. Instead, Penrose insists on the mathematical structure of the singularities, using in particular the Weyl curvature to characterize them. From his analysis two classes of singularities emerge: those from which matter comes out (big bang) and those in which matter comes in (big crunch, black holes). The classical setting being recalled, the speakers turn to quantum theory. Hawking's second talk is concerned with the quantum theory of black holes. In order to account for quantum effects, he introduces a path-integral formulation over Euclideanized metrics, Armed with this tool, the validity of which he merely assumes, he proves that black holes actually radiate so that he renders fully consistent the thermodynamic analogy, entropy being replaced by the area event horizon, and statistical fluctuations by quantum fluctuations. Basing his analysis upon an interpretation in terms of information theory, there exists, Hawking asserts, a new level of unpredictability. Penrose prefers not to expand on Hawking's interpretations and starts building upon quantum mechanics (analysis of the EPR experiment) and the density matrix formalism to stress the problems caused by the nonlocality of energy. In his last lecture Hawking comes back in great detail over the definition of his integration measure over all compact Euclidean metrics and discusses the issue of boundary conditions, summarizing the difficulty of the procedure by `Gravity determines the topology of the manifold on which it lives'. As a conclusion he insists on the predictive power of his theory. He also explains the classical appearance of space-time as a decoherence effect due to the fact that only part of it is seen. Penrose develops twistor theory on a constructive basis from functions on 1D complex manifolds and shows how twistors can describe quantum particles. The wave function has become a complex function on twistor space. Quantum field theory is to be replaced by a twistor quantum field theory. The formalism has the advantage of incorporating in a natural fashion features described by conformal field theory. That twistor theory allows the recovery of existing results is not but a prerequisite, and Penrose remains elusive as to what new concrete results it could bring. Research is in progress. In the last hour, Hawking and Penrose debate the most speculative parts of their talks and how to interpret or to understand the results. The viewer should not be misled by the beautiful red apple swallowed by a black hole that is shown on the front cover of the package: it must be emphasized that the talks are highly technical and the authors assume the audience are researchers in the field. Hawking's less mathematical approach might be more accessible to some, who however could find his tendency to over-interpretation somewhat irritating. Others might be delighted by the mathematical beauty of Penrose's description, though it is undoubtedly much more opaque to the mathematically ignorant. The controversies between the two lie on choices of the interpretation, often rooted in their personal philosophical beliefs. As suggested by questions from the floor, another debate, perhaps not as easy to enclose on a videotape, would have involved other approaches such as superstrings. Be that as it may, whether a researcher or not, the viewer watched half of the time a close shot, under two different angles, of a motionless protagonist, whose personal charisma is certainly not best conveyed through the vibrations of his voice synthesizer. Apart from the obvious intrinsic interest of the topic, nice summarizing transparencies along with puns scattered here and there are not enough to hold the concentration. Of course Penrose's style is livelier by far, though the viewer is given no chance to read the content of his numerous (hand-written) transparencies (shot from the back of the lecture hall), which would be compulsory to follow him in his formal approach. The tapes should at least have been accompanied by a copy of the speaker's documents. Some European viewers will be spared due to a technical point: the tapes are distributed in the American NTSC format.