arXiv subjects

M. J. Luo

Publications and source records attributed to M. J. Luo.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Mechanics Relative to a Quantum Reference System: a Relative State Approach

This paper proposes an intrinsic or background-independent quantum framework based on entangled state rather than absolute quantum state, it describes a quantum relative state between the under-study quantum system and the quantum measuring apparatus as a quantum reference system, without relying on any external absolute parameter. The paper focuses on a simple example, in which a quantum object's one-dimensional position as an under-study quantum system, and a quantum clock as a quantum reference system or quantum measuring apparatus. The evolution equation of the state of the quantum object's position with respect to the state of the quantum clock is given coming from the Ricci-flat Kaehler-Einstein equation. In a linear and non-relativistic approximation, the framework recovers the equation of the standard quantum mechanics, in which an intrinsic potential related to some "inertial force" is automatically incorporated in the covariant derivative. A physical relative probability interpretation and a geometric non-trivial fiber bundle interpretation of the entangled state in this intrinsic quantum framework are given. Furthermore, some non-inertial effects, such as the "inertial force", coming from the general covariance of the intrinsic quantum framework are also discussed. Compared with the functional integral approach which is more easily to generalize the quantum clock to the quantum spacetime reference frame and study quantum gravity, the relative state approach as a canonical description is more suitable for conceptually demonstrating the connections to the standard formalism and interpretation of the quantum mechanics.

quant-ph↗

arXiv2026

MOND from Second-Order Moment Modified Acceleration and Quantum Equivalence Principle

This paper proposes a novel non-inertial quantum effect wherein particle spectra show second-order moment extra Gaussian broadening due to local short-time (non-uniform) acceleration, as well as in a deSitter spacetime background. Although the effect is too small to be detected, it provides a mechanism for the cosmological constant to enter the local kinematics of particles in the form of acceleration. The acceleration composition relation of a proper motion acceleration and the cosmological constant playing the role of a background acceleration, which is required in the Modified Newtonian Dynamics (MOND). The origin of acceleration discrepancies lies in the importance of the intrinsic second moment quantum fluctuations in the deSitter background, so that the mean value of derivative (modified effective acceleration) does not equal to the derivative of mean value (the first moment acceleration given by the unmodified Newtonian gravity). Such an interpretation of MOND as a second moment effect necessitates a quantum equivalence principle as its physical foundation, that is, extending the classical equivalence at the level of mean values (first-order moments) to the quantum equivalence at the level of second moment quantum fluctuations. The effective distance quadratic form, effective curvature and effective acceleration, etc., modified by the universal second moments all behave as if they were real geometrical or physical quantities. This effect also offers a unified framework for understanding the accelerated expansion of the universe and the anomalies in galactic rotation curves or radial acceleration.

gr-qc↗

arXiv2025

Well-posedness of Ricci Flow in Lorentzian Spacetime and its Entropy Formula

This paper attempts to construct monotonic entropy functionals for four-dimensional Lorentzian spacetime under physical boundary conditions, as an extension of Perelman's monotonic entropy functionals constructed for three-dimensional compact Riemannian manifolds. The monotonicity of these entropy functionals is utilized to prove the well-posedness of applying Ricci flow to four-dimensional Lorentzian spacetime for a long flow-time, particularly for the timelike modes which would seem blow up and ill-defined. The general idea is that the Ricci flow of a Lorentzian spacetime metric and the coupled conjugate heat flow of a density on the Lorentzian spacetime as a whole turns out to be the gradient flows of the monotonic functionals for a long flow-time, so the superficial "blow-up" in the individual Ricci flow system or the conjugate heat flow system contradicts the boundedness of the monotonic functionals within finite flow interval, which gives a semi-global control to the whole coupled system. The physical significance and applications of these monotonic entropy functionals in real gravitational systems are also discussed.

gr-qc↗

arXiv2025

Second-Order Moment Quantum Fluctuations and Quantum Equivalence Principle

The second-order moment quantum fluctuations or uncertainties are mass-dependent, and the incompatibility between the quantum uncertainty principle and the equivalence principle is at the second-order moment (variation) level, but not the first-order moment (mean) level. To reconcile the two fundamental principles, we find that the second-order moment quantum fluctuations are actually distinguished into two parts: a dynamic part and a geometric part. The dynamic part is indeed mass-dependent and governed by a non-zero Hamiltonian in a non-general-covariant inertial frame, and the geometric part is mass-independent and comes from coarse-graining and/or geometric effects. The dynamic part is coordinate dependent, it can be canceled away by a coordinate transformation, and hence it plays no role in general covariant theories whose Hamiltonian automatically vanishes. However, the geometric part is valid for general coordinate, and it can not be eliminated by a coordinate transformation. On the contrary, the geometric part of second-order moment fluctuation of quantum spacetime leads to coordinate transformation anomaly, which induces an effective Einstein's gravity theory. The geometric part is mass-independent and universal, so it is only this part measures the universal second-order moment quantum fluctuation of the spacetime, while the dynamic part plays no role in the general covariant description. The observation generalizes the classical equivalence principle to the quantum level. And according to the principle, a general covariant theory with only geometric part quantum fluctuation, i.e. a non-linear sigma model, is proposed as a theory of a material quantum reference frame system. The effects of the universal second-order moment quantum fluctuations in the material quantum reference system and its implications to an effective gravity theory are also discussed.

gr-qc↗

arXiv2024

Local Short-Time Acceleration induced Spectral Line Broadening and Possible Implications in Cosmology

The paper proposes an acceleration effect that a local short-time acceleration produces an additional broadening to spectral line, while the central value of the line remains unaffected. The effect can be considered as a local and non-uniform generalization of Unruh effect. Although the acceleration-induced line broadening effect is too small to be measured in ordinary lab setup, it may offer us a key concept to gain a simple and unified perspective on the cosmic acceleration and the radial acceleration discrepancy of rotating galaxies. We find that the measurement of the acceleration of the cosmic expansion by fitting the distance-redshift relation is essentially the measurement of the line or redshift broadening, and the cosmic acceleration induced line broadening also plays a crucial role in the acceleration discrepancy at the outskirt of rotating galaxies. Possible predictions of the effect are also discussed.

gr-qc↗

arXiv2023

The Ricci Flow and the Early Universe

A framework of quantum spacetime reference frame is proposed and reviewed, in which the quantum spacetime at the Gaussian approximation is deformed by the Ricci flow. At sufficient large scale, the Ricci flow not only smooths out local small irregularities making the universe a homogeneous and isotropic Friedmann-Robertson-Walker metric, but also develops a local singularity at the physical-time origin. Due to the phenomenological suppression of the non-Gaussian primordial perturbations, we assume the validity of the Ricci flow applying to the high curvature region near the local singularity of the early universe. The no-local-collapsing theorem of Perelman ensures the existence of a canonical neighborhood around the large curvature pinching point, which resembles a gradient shrinking Ricci soliton (GSRS) solution of the Ricci flow. Without any inflaton field, the GSRS naturally reproduces an exact inflationary deSitter universe near the singularity at the leading order. Without any rolling-down behavior of inflaton, the deviation from exact deSitter described by the "slow roll parameters" can be calculated by a small deviation from the singular flow-time via the Ricci flow, and the primordial perturbations can also be studied on the GSRS background, the power spectrum of the scalar perturbation agrees with present observations, and the one of the tensor perturbation is predicted too small to be detectable than the standard inflation. The previous treatment of the cosmological constant and the effective gravity are also briefly reviewed in the framework. So we argue that the Ricci flow provides us a possible unified view and treatment of the late epoch accelerating expansion and early epoch inflation of the universe without introducing dark energy or inflaton (dark energy of the second kind).

gr-qc↗

arXiv2023

Quantum Modified Gravity at Low Energy in the Ricci Flow of Quantum Spacetime

Quantum treatment of physical reference frame leads to the Ricci flow of quantum spacetime, which is a quite rigid framework to quantum and renormalization effect of gravity. The theory has a low characteristic energy scale described by a unique constant: the critical density of the universe. At low energy long distance (cosmic or galactic) scale, the theory modifies Einstein's gravity which naturally gives rise to a cosmological constant as a counter term of the Ricci flow at leading order and an effective scale dependent Einstein-Hilbert action. In the weak and static gravity limit, the framework gives rise to a transition trend away from Newtonian gravity and similar to the MOdified Newtonian Dynamics (MOND) around the characteristic scale. When local curvature is large, Newtonian gravity is recovered. When local curvature is low enough to be comparable with the asymptotic background curvature corresponding to the characteristic energy scale, the transition trend produces the baryonic Tully-Fisher relation. For intermediate general curvature around the background curvature, the interpolating Lagrangian function yields a similar transition trend to the observed radial acceleration relation of galaxies. When the baryonic matter density is much lower than the critical density at the outskirt of a galaxy, there may be a universal "acceleration floor" corresponding to the acceleration expansion of the universe, which differs from MOND at its deep-MOND limit. The critical acceleration constant $a_0$ introduced in MOND is related to the low characteristic energy scale of the theory. The cosmological constant gives a universal leading order contribution to it and the flow effect gives the next order scale dependent contribution, which equivalently induces the "cold dark matter" to the theory. $a_0$ is consistent with galaxian data when the "dark matter" is about 5 times the baryonic matter.

gr-qc↗

arXiv2023

A Statistical Fields Theory underlying the Thermodynamics of Ricci Flow and Gravity

The paper proposes a statistical fields theory of quantum reference frame underlying the Perelman's analogies between his formalism of the Ricci flow and the thermodynamics. The theory is based on a d=4-ε quantum non-linear sigma model, interpreted as a quantum reference frame system which a to-be-studied quantum system is relative to. The statistic physics and thermodynamics of the quantum frame fields is studied by the density matrix obtained by the Gaussian approximation. The induced Ricci flow of the frame fields and the Ricci-DeTurck flow of the frame fields associated with the density matrix is deduced. In this framework, the diffeomorphism anomaly of the theory has a deep thermodynamic interpretation. The trace anomaly is related to a Shannon entropy in terms of the density matrix, which monotonically flows and achieves its maximal value at the flow limit, called the Gradient Shrinking Ricci Soliton (GSRS), corresponding to a thermal equilibrium state of spacetime. A relative Shannon entropy w.r.t. the maximal entropy gives a statistical interpretation to Perelman's partition function, which is also monotonic and gives an analogous H-theorem to the statistical frame fields system. A temporal static 3-space of a GSRS 4-spacetime is also a GSRS in lower 3-dimensional, we find that it is in a thermal equilibrium state, and Perelman's analogies between his formalism and the thermodynamics of the frame fields in equilibrium can be explicitly given in the framework. Extending the validity of the Equivalence Principle to the quantum level, the quantum frame fields theory at low energy gives an effective theory of gravity, a scale dependent Einstein-Hilbert action plus a cosmological constant is recovered. As a possible underlying microscopic theory of gravity, the theory is also applied to understand the thermodynamics of the Schwarzschild black hole.

gr-qc↗

arXiv2022

Local Conformal Instability and Local Non-Collapsing in the Ricci flow of Quantum Spacetime

It is known that the conformal instability or bottomless problem rises in the path integral method in quantizing the general relativity. Does quantum spacetime itself really suffer from such conformal instability? If so, does the conformal instability cause the collapse of local spacetime region or even collapse the whole spacetime? The problems are studied in the framework of the Quantum Spacetime Reference Frame (QSRF) and induced spacetime Ricci flow. We find that if the lowest eigenvalue of an operator, associated with the F-functional in a local compact (closed and bounded) region, is positive, the local region is conformally unstable and will tend to volume-shrinking and curvature-pinching along the Ricci flow-time t; if the eigenvalue is negative or zero, the local region is conformally stable up to a trivial rescaling. However, the local non-collapsing theorem in the Ricci flow proved by Perelman ensures that the instability will not cause the local compact spacetime region collapse into nothing. The total effective action is also proved positive defined and bounded from below keeping the whole spacetime conformally stable, which can be considered as a generalization of the classical positive mass theorem of gravitation to the quantum level.

gr-qc↗

arXiv2021

Trace Anomaly, Perelman's Functionals and the Cosmological Constant

The trace anomaly and the cosmological constant problem are two typical breakdowns when applying the quantum principle to a general covariant or gravitational system. A quantum theory of spacetime reference frame is proposed and reviewed. We study the theory by functional method, and show that the trace anomaly of the theory is closely related to some of the Perelman's functionals. The functionals may provide us possible links between the trace anomaly and the cosmological constant. We find that to cancel the trace anomaly at the lab's scale up to very high energy, a cosmological constant is required which is consistent with observations. In the framework, an effective theory of gravity and possible observational effect are also discussed.

gr-qc↗

arXiv2021

Ricci Flow Approach to The Cosmological Constant Problem

In order to resolve the cosmological constant problem, the notion of reference frame is re-examined at the quantum level. By using a quantum non-linear sigma model (Q-NLSM), a theory of quantum spacetime reference frame (QSRF) is proposed. The underlying mathematical structure is a new geometry endowed with intrinsic 2nd central moment (variance) or even higher moments of its coordinates, which generalizes the classical Riemannian geometry based on only 1st moment (mean) of its coordinates. The 2nd central moment of the coordinates directly modifies the quadratic form distance which is the foundation of the Riemannian geometry. At semi-classical level, the 2nd central moment introduces a flow which continuously deforms the Riemannian geometry driven by its classical Ricci curvature, which is known as the Ricci flow. A generalized equivalence principle of quantum version is also proposed to interpret the new geometry endowed with at least 2nd moment. As a consequence, the spacetime is stabilized against quantum fluctuation, and the cosmological constant problem is resolved within the framework. With an isotropic positive curvature initial condition, the long flow time solution of the Ricci flow exists, the accelerating expansion universe at cosmic scale is an observable effect of the spacetime deformation of the normalized Ricci flow. A deceleration parameter -0.67 consistent with measurement is obtained by using the reduced volume method introduced by Perelman. Effective theory of gravity within the framework is also discussed.

physics.gen-ph↗

arXiv2018

The Cosmological Constant Problem and Quantum Spacetime Reference Frame

This paper is a generalization of earlier papers [Nucl. Phys. B 884, 344 (2014) (arXiv:1312.2759) and JHEP 6, 63 (2015) (arXiv:1401.2488)]. We generalize the idea of quantum clock time to quantum spacetime reference frame via physical realization of a reference system by quantum rulers and clocks. Omitting the internal degrees of freedom (such as spins) of the physical rulers and clocks, only considering their metric properties, the spacetime reference frame is described by a bosonic non-linear sigma model (NLSM). We study the quantum behavior of the system under approximations, and obtain (1) a cosmological constant valued $(2/π)ρ_{c0}$ ($ρ_{c0}$ the critical density at near current epoch) which is very close to the observations; (2) an effective Einstein-Hilbert term; (3) the ratio of variance to mean-squared of spacetime interval tends to a universal constant $2/π$ in the infrared region. This effect is testable by observing a linear dependence between the inherent quantum variance and mean-squared of the redshifts from cosmic distant spectral lines. The proportionality is expected to be the observed percentage of the dark energy. The equivalence principle is also generalized to the quantum level.

gr-qc↗

arXiv2017

Quark-Gluon Plasma and Topological Quantum Fields Theory

Based on an analogy with topologically ordered new state of matter in condensed matter systems, we propose a low energy effective field theory for a parity conserving liquid-like quark-gluon plasma (QGP) around critical temperature in quantum chromodynamics (QCD) system. It shows that below a QCD gap which is expected several times of the critical temperature, the QGP behaves like topological fluid. Many exotic phenomenon of QGP near the critical temperature discovered at RHIC are more readily understood by the suggestion that QGP is a topologically ordered state.

hep-ph↗

arXiv2015

Dark Energy from Quantum Uncertainty of Distant Clock

The observed cosmic acceleration was attributed to an exotic dark energy in the framework of classical general relativity. The dark energy behaves very similar with vacuum energy in quantum mechanics. However, once the quantum effects are seriously taken into account, it predicts a completely wrong result and leads to a severe fine-tuning. To solve the problem, the exact meaning of time in quantum mechanics is reexamined. We abandon the standard interpretation of time in quantum mechanics that time is just a global parameter, replace it by a quantum dynamical variable playing the role of physical clock. We find that synchronization of two spatially separated clocks can not be precisely realized at quantum level. There is an intrinsic quantum uncertainty of distant clock time, which implies an apparent vacuum energy fluctuation and gives an observed dark energy density $ρ_{de}=\frac{6}πL_{P}^{-2}L_{H}^{-2}$ at tree level approximation, where $L_{P}$ and $L_{H}$ are the Planck and Hubble scale cutoffs. The fraction of the dark energy is given by $Ω_{de}=\frac{2}π$, which does not evolve with the internal clock time. The "dark energy" as a quantum cosmic variance is always seen comparable with the matter energy density by an observer using the internal clock time. The corrected distance-redshift relation of cosmic observations due to the distant clock effect are also discussed, which again gives a redshift independent fraction $Ω_{de}=\frac{2}π$. The theory is consistent with current cosmic observations.

physics.gen-ph↗

arXiv2014

Gauge Systems with Finite Chemical Potential in 2+1 Dimensions by Bosonization

We present a bosonization method to study generic low energy behavior of gauge systems with finite chemical potential in 2+1 dimensions. Benefit from the existence of gap (e.g. Gribov gap) in gauge systems at low energy, the fermion fields can be explicitly bosonized by new gauge fields. When chemical potential of the gauge systems is introduced, we find that topological terms (such as Chern-Simons term in 2+1D) as constraints inevitably emerge at low energy. The fermion sign problem at finite chemical potential and its deep connection to the Chern-Simons theories are discussed. The Wilson's criteria of confinement in pure gauge theories is generalized to finite chemical potential case. The chemical potential dependence of physical quantities at strong coupling are explicitly calculated, including the expectation value of the Wilson loop, the confining potential and the confined/deconfined transition temperature. The bosonization puts discussions on chiral symmetry breaking and confined/deconfined transition on an equal footing, so it is suitable for the study of the subtle interplay between them. We find that the chiral symmetry breaking is a necessary (not sufficient) condition for the confinement in 2+1D, and argue that the confined/deconfined phases are not characterized by any local symmetries but distinguished by their non-local topologies. The low energy modes of the strongly coupled gauge systems in a non-symmetry breaking phase is also discussed. The results of the paper can be widely applied to real strongly coupled gauge systems, e.g. high-temperature superconductor and quantum chromodynamical systems in 2+1 dimensions.

cond-mat.str-el↗

arXiv2014

The Cosmological Constant Problem and Re-interpretation of Time

We abandon the interpretation that time is a global parameter in quantum mechanics, replace it by a quantum dynamical variable playing the role of time. This operational re-interpretation of time provides a solution to the cosmological constant problem. The expectation value of the zero-point energy under the new time variable vanishes. The fluctuation of the vacuum energy as the leading contribution to the gravitational effect gives a correct order to the observed "dark energy". The "dark energy" as a mirage is always seen comparable with the matter energy density by an observer using the internal clock time. Conceptual consequences of the re-interpretation of time are also discussed.

physics.gen-ph↗

arXiv2013

Anomalous Local Criticality in Heavy Fermion Metals from Holography

We propose a holographic theory to explain numbers of anomalous critical phenomena observed in certain heavy-fermion metals, e.g. $\mathrm{CeCu_{5.9}Au_{0.1}}$ and $\mathrm{YbRh_{2}(Si_{0.95}Ge_{0.05}})_{2}$, which are incompatible with any conventional spin-density-wave quantum critical point theory. We show that the non-Gaussian nature of the fixed point from holography plays an essential role in the physics of these materials near a quantum critical point, which is not in the same universality class of the spin-density-wave type fixed point. The critical spin fluctuations at the non-Gaussian fixed point are strongly anisotropic, localized in spatial directions and critical in temporal direction with critical exponent 2/3 in frequency over temperature dependence at low temperature. The local critical exponent tends to unity which leads to a constant spin relaxation rate in the quantum critical regime at high temperature. The stability of the fixed point is also discussed.

cond-mat.str-el↗

arXiv2012

Dynamic Critical Scaling of the Holographic Spin Fluctuations

Criticality with strong coupling is described by a theory in the vicinity of a non-Gaussian fixed point. The holographic duality conjectures that a theory at a non-Gaussian fixed point with strong coupling is dual to a gravitational theory. In this paper, we present a holographic theory in treating the strongly coupled critical spin fluctuations in quasi-2-dimension. We show that a universal frequency over temperature scaling law is a rather general property of the critical ac spin susceptibility at strongly coupled limit. Explicit results for the dynamic scaling of spin susceptibility are obtained in large-N and large 't Hooft limit. We argue that such critical scaling are in good agreement with a number of experiments, some of which can not be explained by any perturbative spin-density-wave theory. Our results strongly suggest that the anomalous behavior of non-Fermi liquids in materials is closely related to the spin fluctuations described through the non-Gaussian fixed point. The exotic properties of non-Fermi liquids can be viewed as the Fermi liquids coupling to strongly coupled critical spin fluctuations.

hep-th↗