Shape dynamics is a theory first proposed by Julian Barbour which states that physics happen uniquely in the reduced configuration space of a theory. So far, studies in the area have focused on gravitational systems. Here we first contemplate on the implications of this idea on quantum mechanics. We summarize the idea of shape dynamics and then give physical configurations of multi qubit systems. It is observed that inclusion of the spacetime curvature introduces a new qubit degree of freedom. This is a novel effect of general relativity on a quantum system. Our aim in the grand picture, is to initiate a research program translating classical shape dynamics to quantum realm.
Shape dynamics is a theory first proposed by Julian Barbour which states that physics happen uniquely in the reduced configuration space of a theory. So far, studies in the area have focused on gravitational systems. Here we first contemplate on the implications of this idea on quantum mechanics. We summarize the idea of shape dynamics and then give physical configurations of multi qubit systems. It is observed that inclusion of the spacetime curvature introduces a new qubit degree of freedom. This is a novel effect of general relativity on a quantum system. Our aim in the grand picture, is to initiate a research program translating classical shape dynamics to quantum realm.
This paper introduces Quantum State Curvature Response Theory (QSCRT), a novel framework proposing that curvature within Hilbert space induces measurable physical responses in quantum systems. The core concept is expressed as [Rψ → Fψ], drawing an analogy to Einstein's theory of General Relativity, where spacetime curvature dictates gravitational effects. QSCRT posits that changes in the curvature of the quantum state space—represented by the curvature tensor Rψ—will generate a corresponding force Fψ. This theory suggests a dynamic nature of Hilbert space itself, moving beyond a purely geometric description. The research explores various parameter spaces of quantum systems to investigate this curvature response and its potential implications. The work aims to establish a foundation for understanding the inherent dynamics of quantum space and its influence on quantum phenomena, with potential implications for future research and theoretical advancements. ---
We study kinematics of atoms and molecules in quantum shape dynamics. We analyzed a model universe where there is only electrical force between protons and electrons. In ref. \cite{sd-prl} a similar model where there is only gravitational attraction between masses is investigated. Our results is an expansion of the ideas there. We found that hydrogen atoms can form when they are entangled in singlet pairs. On the other hand if there is single hydrogen atom in the universe, it occupies the entire universe. What is more, in the investigation of hydrogen molecule, we found that absolute spacetime emerges by coarse graining the quantum degrees of freedom. It may be that spacetime only exists because of the presence of quantum degrees of freedom. This is especially important from the quantum gravity perspective.
Quantum mechanics successfully predicts microscopic phenomena through themathematical formalism of the wavefunction, operators, and probabilistic measurement.General Relativity successfully describes gravitation through spacetime geometry, whileclassical electromagnetism employs electric and magnetic fields governed by Maxwell'sequations. Although each framework is extraordinarily successful within its domain, eachbegins from different primitive physical entities.Space-Phase (SP3) theory proposes a different hierarchy. Rather than treating thewavefunction, electromagnetic fields, or spacetime curvature as fundamental, SP3proposes that the primary physical quantity is the adaptive coherence state of a structuredspace-phase medium. The familiar quantum state, electric field, magnetic field, andgravitational organization are interpreted as observable manifestations of this deepercoherence potential.This paper outlines a conceptual framework in which quantum behavior emerges naturallyfrom coherence organization within space-phase. The proposal remains speculative andrequires quantitative development but suggests a unified research program connectingquantum mechanics, electromagnetism, and gravitation through a common constitutiveprinciple.
This short document presents no new results. It is a collection of related ideas that may lead to a way of quantizing gravity. To achieve this it may be relevant to use my recent new approach to quantum theory, which is based on quantum events. Given that most standard quantum texts do not define a mathematical object which corresponds to a physical event, the definition of a quantum event is motivated and discussed in detail. This in turn leads to the idea that the mathematical object that contains enough quantum events for describing a quantum system is a von Neumann algebra. The next idea is that the kinematics of special relativity (as embodied in flat Minkowski space) should be quantized as a first step in the program of the quantization of general relativity, that is, quantizing Einstein's equation. It must be emphasized that the events of special relativity are viewed as part of the kinematics, rather than of the dynamics of that theory. The same holds for general relativity. Similarly, I am viewing quantum events as part of the kinematics of quantum theory, even though some find this to be counterintuitive. An Appendix shows how ``collapse'' is easily understood in this new approach to quantum theory.
Abstract In general relativity, the dynamics of objects is governed by the curvature of spacetime, which is caused by the presence of matter and energy. In contrast, in quantum mechanics, the dynamics is governed by the wavefunction, which completely describes the behavior of the particles. There is an ongoing effort to explore analogs of space and spacetime curvature in the context of quantum mechanics. Such analogies may reveal a deeper structure of quantum reality and its possible relations with Einstein’s theory of gravity. In this note, by coupling the non-relativistic Schrödinger equation with the heat equation and using the hydrodynamical formulation of quantum mechanics, we find that the dynamics of the particle is fully characterized by the normalized curvature of the wavefunction’s amplitude. Such a curvature obtains an analogy to the Ricci curvature of curved space in a Riemannian manifold. The proposed geometric correspondence provides a new pathway to explore quantum dynamics through the lens of differential geometry, the language of general relativity.
Every vertex of the magic cube of physics discussed so far introduced a major element in the development of physics and the whole of science. Mechanics introduced the basic concept of equations of motion, or time-evolution of a physical system given certain initial condition and the associated idea of determinism, even with its generalization in the form of chaos, the dependence of the outcomes of the temporal evolution on the initial conditions. These concepts taken for many particles, or elements of a physical system, led to the probabilistic description of many particle systems, in the realm of statistical physics and thermodynamics, whereby the averages over time of various observable quantities were related to the ensemble averages, that involve classical, so-called Kolmogorov, probability measures, at least for certain “equilibrium” situations. The second law of thermodynamics introduced the concept of entropy and its probabilistic increase, the first truly emergent, probabilistic law in physics (temperature and pressure, being other emergent quantities, apart from entropy, the measure of disorder of a statistical system). In the context of Newtonian gravity, one gets, at least in retrospect the geometric description of gravity in non-relativistic, Galilean spacetime. Galilean relativity, based on the asymmetric mixing of space and time, with the absolute, universal time, true for all observers, gets generalized in special theory of relativity to observer dependent space and observer dependent time, viewed as “slices” of a new concept of spacetime, with the new concept of causal structure, that distinguish timelike, null and spacelike events. This in turn is made into a full dynamical geometric structure of spacetime with a relativistic description of gravity stemming from curvature of spacetime, and a dynamical causal structure, tied to gravity. In our next story, the story of quantum theory, we will encounter fundamental, intrinsic probabilities, that can interfere, unlike the classical probabilities of statistical thermodynamics, and which are consistent with equations of motion of individual elements, and not, as in statistical thermodynamics, with temporal averages over the time evolution of many elements. This is the big new lesson of quantum theory, that transcends the lessons of classical spacetime physics.