Limits on inflationary models of the universe

It is shown that there are severe limits on any model in which the universe undergoes a period of exponential expansion in the early stages. If one requires that the exponential expansion is long enough to account for the spatial flatness of the universe and that it should not create larger density fluctuations than are observed, it follows that the Hubble constant during the exponential expansion cannot be greater than 6 × 10^?5 of the Planck mass. This rules out all models in which the Hubble constant is of the order of the Planck mass. It is shown that one can satisfy the limits with a model containing a massive scalar field if the mass of the field is less than about 10¹⁴ GeV.     

谈普朗克质量

简要介绍了普朗克于1912年提出的三个基本物理量：普朗克质量、普朗克长度和普朗克时间，它们巳被列入1986和1998年基本物理常数表，该文只讨论普朗克质量，假定原子核内存在量子化的核力场，命名其场量子为“引斥子”，其质量推算出恰好等于普朗克质量，由此可用4个耦合常数定量地描述四种相互作用的强度比，从而还可找到一种测定G的新方法。     

Relativistic Quantum Mechanics as a Consequence of the Planck Mass Plasma Conjecture

The Planck mass plasma conjecture is the hypothesis that the vacuum of space is a kind of plasma composed of positive and negative Planck mass particles interacting by the Planck force over a Planck length, repulsive for equal and attractive for unequal Planck masses. The hypothesis permits to derive quantum mechanics and Lorentz invariance as asymptotic approximations for energies small compared to the Planck energy. Besides a spectrum of elementary particles greatly resembling the particles of the standard model, the hypothesis gives a value of the fine structure constant at the energy where the strong, the weak, and electromagnetic interaction become equal.     

Can Quantum Gravity be Exposed in the Laboratory?

I propose an experiment that may be performed, with present low temperature and cryogenic technology, to reveal Wheeler’s quantum foam. It involves coupling an optical photon’s momentum to the center of mass motion of a macroscopic transparent block with parameters such that the latter is displaced in space by approximately a Planck length. I argue that such displacement is sensitive to quantum foam and will react back on the photon’s probability of transiting the block. This might allow determination of the precise scale at which quantum fluctuations of space–time become large, and so differentiate between the brane-world and the traditional scenarios of spacetime.     

Does the planck mass run on the cosmological-horizon scale?

Einstein's theory of general relativity contains a universal value of the Planck mass. However, one may envisage that in alternative theories of gravity the effective value of the Planck mass (or Newton's constant), which quantifies the coupling of matter to metric perturbations, can run on the cosmological-horizon scale. In this Letter, we study the consequences of a glitch in the Planck mass from subhorizon to superhorizon scales. We show that current cosmological observations severely constrain this glitch to less than 1.2%.     

Black-Hole Thermodynamics and Electromagnetism

We show a strong parallel between the Hawking-Bekenstein black-hole thermodynamics and electromagnetism: When the gravitational coupling constant transforms into the electromagnetic coupling constant, the Schwarzchild radius, the Bekenstein temperature, the Bekenstein decay time and the Planck mass transform to respectively the Compton wavelength, the Hagedorn temperature, the Compton time and a typical elementary particle mass. The reasons underlying this parallalism are then discussed in detail.     

On the relation of the Methagalaxy mass to the gravitation constant. 1. from Einstein’s theory to the Einstein–Cartan theory

The notion of the dimensionless gravitational charge defined through the Planck mass and the fundamental constants specifying this mass itself is introduced. The Big Bang is related to the unified physical interaction decay and the drop of Newton’s gravitational constant by 40.67 orders of magnitude in comparison with the electromagnetic constant taken as unity. This causes an increase in theMetagalaxy curvature radius by the same value and a decrease in the average density of space–time curvature sources by 122 orders of magnitude: from the maximum allowable Planck density to the observed critical density. The microphysics appears naturally related to cosmology.     

Instability of flatspace and the origin of conformal fluctuations

It is shown that conformal fluctuations in the metric can be initiated by the vacuum fluctuations of a scalar field with mass greater than the Planck mass. Flatspace is unstable against such fluctuations.     

Nonsingular Collapse of a Perfect Fluid Sphere Within a Dilaton-Gravity Reformulation of the Oppenheimer Model

A generic four-dimensional dilaton gravity is considered as a basis for reformulating the paradigmatic Oppenheimer–Synder model of a gravitationally collapsing star modelled as a perfect fluid or dust sphere. Initially, the vacuum Einstein scalar-tensor equations are modified to Einstein–Langevin equations which incorporate a noise or micro-turbulence source term arising from Planck scale conformal, dilaton fluctuations which induce metric fluctuations. Coupling the energy-momentum tensor for pressureless dust or fluid to the Einstein–Langevin equations, a modification of the Oppenheimer–Snyder dust collapse model is derived. The Einstein–Langevin field equations for the collapse are of the form of a Langevin equation for a non-linear Brownian motion of a particle in a homogeneous noise bath. The smooth worldlines of collapsing matter become increasingly randomised Brownian motions as the star collapses, since the backreaction coupling to the fluctuations is non-linear; the input assumptions of the Hawking–Penrose singularity theorems are then violated. The solution of the Einstein–Langevin collapse equation can be found and is non-singular with the singularity being smeared out on the correlation length scale of the fluctuations, which is of the order of the Planck length. The standard singular Oppenheimer–Synder model is recovered in the limit of zero dilaton fluctuations.     

介观电子谐振腔量子能谱与能量的量子涨落

针对介观电子谐振腔模型,在由电荷算符本征态构成的新Fock空间中,假设系统具有变换的对称性,通过求解Hamilton算符的本征值方程,给出系统的量子能谱关系.在电荷算符的Fock态下计算能量的量子涨落,分析和研究电子谐振腔的量子能谱性质.结果表明:类似于电荷的量子性,能谱明显地呈现出离散性,其大小决定于谐振腔的电参量、形状因子及栅极所加偏压等因素;而能量的量子涨落却仅与电荷量子、Planck常数以及系统自感有关.     

Mass exchange and angular distribution in a dynamical treatment of heavy ion collisions

We present a first numerical computation of the absolute value of the double differential cross section as a function of mass asymmetry and detection angle including a dynamical coupling between relative motion and mass asymmetry. We apply it to the⁶³Cu+¹⁹⁷Au experiment at two different energies. The equation of motion used is a Fokker Planck equation for the distribution function in classical phase space. The coefficients needed are those known from classical model calculations, besides a friction coefficient introduced for the mass asymmetry degree. We find encouraging agreement between the calculated and experimental curves.     

Surface tension and the cosmological constant

One of the few predictions from quantum gravity models is Sorkin's observation that the cosmological constant has quantum fluctuations originating in the fundamental discreteness of spacetime at the Planck scale. Here we present a compelling analogy between the cosmological constant of the Universe and the surface tension of fluid membranes. The discreteness of spacetime on the Planck scale translates into the discrete molecular structure of a fluid membrane. We propose an analog quantum gravity experiment which realizes Sorkin's idea in the laboratory. We also notice that the analogy sheds light on the cosmological constant problem, suggesting a mechanism for dynamically generating a vanishingly small cosmological constant. We emphasize the generality of Sorkin's idea and suggest that similar effects occur generically in quantum gravity models.     

Under what kind of parametric fluctuations is spatiotemporal regularity the most robust?

It was observed that the spatiotemporal chaos in lattices of coupled chaotic maps was suppressed to a spatiotemporal fixed point when some fractions of the regular coupling connections were replaced by random links. Here we investigate the effects of different kinds of parametric fluctuations on the robustness of this spatiotemporal fixed point regime. In particular we study the spatiotemporal dynamics of the network with noisy interaction parameters, namely fluctuating fraction of random links and fluctuating coupling strengths. We consider three types of fluctuations: (i) noisy in time, but homogeneous in space; (ii) noisy in space, but fixed in time; (iii) noisy in both space and time. We find that the effect of different kinds of parametric noise on the dynamics is quite distinct: quenched spatial fluctuations are the most detrimental to spatiotemporal regularity; spatiotemporal fluctuations yield phenomena similar to that observed when parameters are held constant at the mean value, and interestingly, spatiotemporal regularity is most robust under spatially uniform temporal fluctuations, which in fact yields a larger fixed point range than that obtained under constant mean-value parameters.     

Quantum synchronization

Using the methods of quantum trajectories we study numerically a quantum dissipative system with periodic driving which exhibits synchronization phenomenon in the classical limit. The model allows to analyze the effects of quantum fluctuations on synchronization and establish the regimes where the synchronization is preserved in a quantum case (quantum synchronization). Our results show that at small values of Planck constant ħ the classical devil's staircase remains robust with respect to quantum fluctuations while at large ħ values synchronization plateaus are destroyed. Quantum synchronization in our model has close similarities with Shapiro steps in Josephson junctions and it can be also realized in experiments with cold atoms.     

Planck Mass Plasma Analog of String Theory

In recent years there had been a growing interest in analog models of general relativity, with certain superfluid solutions simulating black hole solutions of Einstein's gravitational field equation. The quantization of a superfluid, composed of discrete particles (helium atoms), treated as a nonrelativistic many body problem does not lead to divergencies as the quantization of Einstein's field equations. Quantization of gravity is possible in string theory, but only if one introduces the daring hypothesis of higher dimensions. But if the gravitational field is made up of discrete elements as superfluid helium is made up of helium atoms, then gravity can be quantized without difficulty in three space and one time dimension. Such a hypothesis, of course, implies that Lorentz invariance is a dynamic symmetry caused by real rod and clock deformations, as it was assumed in the pre-Einstein theory of relativity by Lorentz and Poincaré, which required the existence of an aether. Making the hypothesis that this aether is a kind of superfluid plasma made up of positive and negative Planck mass particles interacting with the Planck force over a Planck length, one obtains an analog of the standard model, including gravity, which can be quantized as a nonrelativistic many body problem. In this model nonrelativistic vortex rings in three space dimensions and one time dimension simulate the relativistic theory of closed strings in ten space-time dimensions. But because in the vortex lattice, one obtains a large dimensionless number conceivably advancing our understanding of the finestructure constant.     

The Planck Aether model for a unified theory of elementary particles

A dense assembly of an equal number of two kinds of Planck masses, one having positive and the other one negative kinetic energy, described by a nonrelativistic nonlinear Heisenberg equation with pointlike interactions, is proposed as a model for a unified theory of elementary particles. The dense assembly of Planck masses leads to a vortex field below the Planck scale having the form of a vortex lattice, which can propagate two types of waves, one having the property of Maxwell's electromagnetic and the other one the property of Einstein's gravitational waves. The waves have a cutoff at a wavelength equal to the vortex lattice constant about 10³ times larger than the Planck length, reproducing the GUT scale of elementary particle physics. The vortex lattice has a resonance energy leading to two kinds of quasiparticles, both of which have the property of Dirac spinors. Depending on the resonance energy, estimated to be 10⁷ times smaller than the Planck energy, the mass of one of these quasiparticles is about equal to the electron mass. The mass of the other particle is much smaller, making it a likely candidate for the much smaller neutrino mass. Larger spinor masses occur as internal excitations, with a maximum of four such excitations corresponding to a maximum of four particle families. Other vortex solutions may describe the quark-lepton symmetries of the standard model. All masses, with the exception of the Planck mass particles, are quasiparticles for which Lorentz invariance holds, with the Galilei invariance at the Planck scale dynamically broken into Lorentz invariance below this scale. The assumed equal number of Planck masses with positive and negative kinetic energy makes the cosmological constant exactly equal to zero.     

Noncommutative gravity, a ‘no strings attached’ quantum-classical duality, and the cosmological constant puzzle

There ought to exist a reformulation of quantum mechanics which does not refer to an external classical spacetime manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which follows is that the ‘weakly quantum, strongly gravitational’ dynamics of a relativistic particle whose mass is much greater than Planck mass is dual to the ‘strongly quantum, weakly gravitational’ dynamics of another particle whose mass is much less than Planck mass. The masses of the two particles are inversely related to each other, and the product of their masses is equal to the square of Planck mass. This duality explains the observed value of the cosmological constant, and also why this value is nonzero but extremely small in Planck units. Second Award in the 2008 Essay Competition of the Gravity Research Foundation.     

A New Proposal to Redefine Kilogram by Measuring the Planck Constant Based on Inertial Mass

A novel method to measure the Planck constant based on inertial mass is proposed here, which is distinguished from the conventional Kibble balance experiment which is based on the gravitational mass. The kilogram unit is linked to the Planck constant by calculating the difference of the parameters, i.e. resistance, voltage, velocity and time, which is measured in a two-mode experiment, unloaded mass mode and the loaded mass mode. In principle, all parameters measured in this experiment can reach a high accuracy, as that in Kibble balance experiment. This method has an advantage that some systematic error can be eliminated in difference calculation of measurements. In addition, this method is insensitive to air buoyancy and the alignment work in this experiment is easy. At last, the initial design of the apparatus is presented.     

On geometrically unified fields and universal constants

We consider the Cartan extension of Riemann geometry as the basis upon which to build the Sciama–Kibble completion of Einstein gravity, developing the most general theory in which torsion and metric have two independent coupling constants: the main problem of the ESK theory was that torsion, having the Newton constant, was negligible beyond the Planck scale, but in this $\mathrm {ESK}^{2}$ theory torsion, with its own coupling constant, may be relevant much further Planck scales; further consequences of these torsionally-induced interactions will eventually be discussed.     

The Operator Formulation of Classical Mechanics and Semiclassical Limit

The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing h ₀. For the later of these two extreme values, introduced operator algebra becomes equivalent to the algebra of observables of quantum mechanical system defined in the standard manner by operators in the Hilbert space. For the vanishing Planck constant, the generalized algebra gives the operator formulation of classical mechanics since it is equivalent to the algebra of variables of classical mechanical system defined, as usually, by functions over the phase space. In this way, the semiclassical limit of kinematical part of quantum mechanics is established through the generalized operator framework.