Posts Tagged planck length

Recent Postings from planck length

Fermions and gravitational gyrotropy [Cross-Listing]

In conventional general relativity without torsion, high-frequency gravitational waves couple to the chiral number density of spin one-half quanta: the polarization of the waves is rotated by $2\pi N_5 {\ell _{\rm Pl}^2}$, where $N_5$ is the chiral column density and $\ell _{\rm Pl}$ is the Planck length. This means that if a primordial distribution of gravitational waves with E-E or B-B correlations passed through a chiral density of fermions in the very early Universe, an E-B correlation in the waves, and one in the cosmic microwave background, would be generated. Less obviously but more primitively, the condition Albrecht called cosmic coherence’ would be violated, changing the restrictions on the class of admissible cosmological gravitational waves.

Fermions and gravitational gyrotropy

In conventional general relativity without torsion, high-frequency gravitational waves couple to the chiral number density of spin one-half quanta: the polarization of the waves is rotated by $2\pi N_5 {\ell _{\rm Pl}^2}$, where $N_5$ is the chiral column density and $\ell _{\rm Pl}$ is the Planck length. This means that if a primordial distribution of gravitational waves with E-E or B-B correlations passed through a chiral density of fermions in the very early Universe, an E-B correlation in the waves, and one in the cosmic microwave background, would be generated. Less obviously but more primitively, the condition Albrecht called cosmic coherence’ would be violated, changing the restrictions on the class of admissible cosmological gravitational waves.

The Minimal Length and the Quantum Partition Functions

We study the thermodynamics of various physical systems in the framework of the Generalized Uncertainty Principle that implies a minimal length uncertainty proportional to the Planck length. We present a general scheme to analytically calculate the quantum partition function of the physical systems to first order of the deformation parameter based on the behavior of the modified energy spectrum and compare our results with the classical approach. Also, we find the modified internal energy and heat capacity of the systems for the anti-Snyder framework.

Emergent gravity by tuning the effective Planck length in Bose-Einstein Condensate

We show that at lowest energy nonlocal interactions, the tuning of s-wave scattering length can enable a systematic control over the quantum pressure term in a Bose-Einstein condensate (BEC). We derive the equation for the massless free excitations in an analogue curved space-time by controlling the effective Planck length. Our controlled derivation indicates a breakdown of this dynamics at length scales comparable to effective Planck length. We also specify the correction that one has to take into account at a larger length scale in a flat space-time due to the emergent gravity at intermediate length scales.

Spacetime-symmetry violations: motivations, phenomenology, and tests

An important open question in fundamental physics concerns the nature of spacetime at distance scales associated with the Planck length. The widespread belief that probing such distances necessitates Planck-energy particles has impeded phenomenological and experimental research in this context. However, it has been realized that various theoretical approaches to underlying physics can accommodate Planck-scale violations of spacetime symmetries. This talk surveys the motivations for spacetime-symmetry research, the SME test framework, and experimental efforts in this field.

Cosmological Constant from the Emergent Gravity Perspective [Cross-Listing]

Observations indicate that our universe is characterized by a late-time accelerating phase, possibly driven by a cosmological constant $\Lambda$, with the dimensionless parameter $\Lambda L_P^2 \simeq 10^{-122}$, where $L_P = (G \hbar /c^3)^{1/2}$ is the Planck length. In this review, we describe how the emergent gravity paradigm provides a new insight and a possible solution to the cosmological constant problem. After reviewing the necessary background material, we identify the necessary and sufficient conditions for solving the cosmological constant problem. We show that these conditions are naturally satisfied in the emergent gravity paradigm in which (i) the field equations of gravity are invariant under the addition of a constant to the matter Lagrangian and (ii) the cosmological constant appears as an integration constant in the solution. The numerical value of this integration constant can be related to another dimensionless number (called CosMIn) that counts the number of modes inside a Hubble volume that cross the Hubble radius during the radiation and the matter dominated epochs of the universe. The emergent gravity paradigm suggests that CosMIn has the numerical value $4 \pi$, which, in turn, leads to the correct, observed value of the cosmological constant. Further, the emergent gravity paradigm provides an alternative perspective on cosmology and interprets the expansion of the universe itself as a quest towards holographic equipartition. We discuss the implications of this novel and alternate description of cosmology.

Cosmological Constant from the Emergent Gravity Perspective [Cross-Listing]

Observations indicate that our universe is characterized by a late-time accelerating phase, possibly driven by a cosmological constant $\Lambda$, with the dimensionless parameter $\Lambda L_P^2 \simeq 10^{-122}$, where $L_P = (G \hbar /c^3)^{1/2}$ is the Planck length. In this review, we describe how the emergent gravity paradigm provides a new insight and a possible solution to the cosmological constant problem. After reviewing the necessary background material, we identify the necessary and sufficient conditions for solving the cosmological constant problem. We show that these conditions are naturally satisfied in the emergent gravity paradigm in which (i) the field equations of gravity are invariant under the addition of a constant to the matter Lagrangian and (ii) the cosmological constant appears as an integration constant in the solution. The numerical value of this integration constant can be related to another dimensionless number (called CosMIn) that counts the number of modes inside a Hubble volume that cross the Hubble radius during the radiation and the matter dominated epochs of the universe. The emergent gravity paradigm suggests that CosMIn has the numerical value $4 \pi$, which, in turn, leads to the correct, observed value of the cosmological constant. Further, the emergent gravity paradigm provides an alternative perspective on cosmology and interprets the expansion of the universe itself as a quest towards holographic equipartition. We discuss the implications of this novel and alternate description of cosmology.

Cosmological Constant from the Emergent Gravity Perspective

Observations indicate that our universe is characterized by a late-time accelerating phase, possibly driven by a cosmological constant $\Lambda$, with the dimensionless parameter $\Lambda L_P^2 \simeq 10^{-122}$, where $L_P = (G \hbar /c^3)^{1/2}$ is the Planck length. In this review, we describe how the emergent gravity paradigm provides a new insight and a possible solution to the cosmological constant problem. After reviewing the necessary background material, we identify the necessary and sufficient conditions for solving the cosmological constant problem. We show that these conditions are naturally satisfied in the emergent gravity paradigm in which (i) the field equations of gravity are invariant under the addition of a constant to the matter Lagrangian and (ii) the cosmological constant appears as an integration constant in the solution. The numerical value of this integration constant can be related to another dimensionless number (called CosMIn) that counts the number of modes inside a Hubble volume that cross the Hubble radius during the radiation and the matter dominated epochs of the universe. The emergent gravity paradigm suggests that CosMIn has the numerical value $4 \pi$, which, in turn, leads to the correct, observed value of the cosmological constant. Further, the emergent gravity paradigm provides an alternative perspective on cosmology and interprets the expansion of the universe itself as a quest towards holographic equipartition. We discuss the implications of this novel and alternate description of cosmology.

Towards a Cosmology with Minimal Length and Maximal Energy [Replacement]

The Friedmann-Robertson-Walker (FRW) universe and Bianchi I,II universes are investigated in the framework of the generalized uncertainty principle (GUP) with a linear and a quadratic term in Planck length and momentum, which predicts minimum measurable length as well as maximum measurable momentum. We get a dynamic cosmological bounce for the FRW universe. With Bianchi universe, we found that the universe may be still isotropic by implementing GUP. Moreover, the wall velocity appears to be stationary with respect to the universe velocity which means that when the momentum of the Universe evolves into a maximum measurable energy, the bounce is enhanced against the wall which means no maximum limit angle is manifested anymore.

Towards a Cosmology with Minimal Length and Maximal Energy [Replacement]

The Friedmann-Robertson-Walker (FRW) universe and Bianchi I,II universes are investigated in the framework of the generalized uncertainty principle (GUP) with a linear and a quadratic term in Planck length and momentum, which predicts minimum measurable length as well as maximum measurable momentum. We get a dynamic cosmological bounce for the FRW universe. With Bianchi universe, we found that the universe may be still isotropic by implementing GUP. Moreover, the wall velocity appears to be stationary with respect to the universe velocity which means that when the momentum of the Universe evolves into a maximum measurable energy, the bounce is enhanced against the wall which means no maximum limit angle is manifested anymore.

$\lambda\phi^{4}$ Kink and sine-Gordon Soliton in the GUP Framework

We consider $\lambda\phi^{4}$ kink and sine-Gordon soliton in the presence of a minimal length uncertainty proportional to the Planck length. The modified Hamiltonian contains an extra term proportional to $p^4$ and the generalized Schr\"odinger equation is expressed as a forth-order differential equation in quasiposition space. We obtain the modified energy spectrum for the discrete states and compare our results with 1-loop resummed and Hartree approximations for the quantum fluctuations. We finally find some lower bounds for the deformations parameter so that the effects of the minimal length have the dominant role.

$\lambda\phi^{4}$ Kink and sine-Gordon Soliton in the GUP Framework [Replacement]

We consider $\lambda\phi^{4}$ kink and sine-Gordon soliton in the presence of a minimal length uncertainty proportional to the Planck length. The modified Hamiltonian contains an extra term proportional to $p^4$ and the generalized Schr\"odinger equation is expressed as a forth-order differential equation in quasiposition space. We obtain the modified energy spectrum for the discrete states and compare our results with 1-loop resummed and Hartree approximations for the quantum fluctuations. We finally find some lower bounds for the deformations parameter so that the effects of the minimal length have the dominant role.

Directional Entanglement of Quantum Fields with Quantum Geometry [Replacement]

It is conjectured that the spatial structure of quantum field states is influenced by a new kind of directional indeterminacy of quantum geometry set by the Planck length, $l_P$, that does not occur in the usual classical background geometry. Entanglement of field and geometry states is described in the small angle approximation, using paraxial wave solutions instead of the usual plane waves. It is shown to have almost no effect on local measurements, microscopic particle interactions, or measurements of propagating states that depend only on longitudinal coordinates, but it significantly alter properties of field states at wavelength $\lambda$ that depend on transverse coordinates or direction, in systems larger than $\approx \lambda^2/l_P$. The reduced information content of fields in large systems is consistent with holographic bounds from gravitation theory, significantly reduces the energy density of field vacua, and may appear as measurable quantum-geometrical noise in interferometers.

Directional Entanglement of Quantum Fields with Quantum Geometry [Replacement]

It is conjectured that the spatial structure of quantum field states is influenced by a new kind of directional indeterminacy of quantum geometry set by the Planck length, $l_P$, that does not occur in the usual classical background geometry. Entanglement of field and geometry states is described in the small angle approximation, using paraxial wave solutions instead of the usual plane waves. It is shown to have almost no effect on local measurements, microscopic particle interactions, or measurements of propagating states that depend only on longitudinal coordinates, but it significantly alter properties of field states at wavelength $\lambda$ that depend on transverse coordinates or direction, in systems larger than $\approx \lambda^2/l_P$. The reduced information content of fields in large systems is consistent with holographic bounds from gravitation theory, significantly reduces the energy density of field vacua, and may appear as measurable quantum-geometrical noise in interferometers.

Why the length of a quantum string cannot be Lorentz contracted [Cross-Listing]

We propose a quantum gravity-extended form of the classical length contraction law obtained in Special Relativity. More specifically, the framework of our discussion is the UV self-complete theory of quantum gravity. Against this background, we show how our results are consistent with, i) the generalised form of the Uncertainty Principle (GUP), ii) the so called hoop-conjecture which we interpret, presently, as the saturation of a Lorentz boost by the formation of a black hole in a two-body scattering, and iii) the intriguing notion of "classicalization" of trans-Planckian physics. Pushing these ideas to their logical conclusion, we argue that there is a physical limit to the Lorentz contraction rule in the form of some minimal universal length determined by quantum gravity, say the Planck Length, or any of its current embodiments such as the string length, or the TeV quantum gravity length scale. In the latter case, we determine the \emph{critical boost} that separates the ordinary "particle phase," characterized by the Compton wavelength, from the "black hole phase", characterized by the effective Schwarzschild radius of the colliding system. Finally, with the "classicalization" of quantum gravity in mind, we comment on the remarkable identity, to our knowledge never noticed before, between three seemingly independent universal quantities, namely, a) the "string tension", b) the "linear energy density," or \emph{tension} that exists at the core of all Schwarzschild black holes, and c) the "superforce" i.e., the Planckian limit of the static electro-gravitational force and, presumably, the unification point of all fundamental forces.

Planck's uncertainty principle and the saturation of Lorentz boosts by Planckian black holes

A basic inconsistency arises when the Theory of Special Relativity meets with quantum phenomena at the Planck scale. Specifically, the Planck length is Lorentz invariant and should not be affected by a Lorentz boost. We argue that Planckian relativity must necessarily involve the effect of black hole formation. Recent proposals for resolving the noted inconsistency seem unsatisfactory in that they ignore the crucial role of gravity in the saturation of Lorentz boosts. Furthermore, an invariant length at he Planck scale amounts to a universal quantum of resolution in the fabric of spacetime. We argue, therefore, that the universal Planck length requires an extension of the Uncertainty Principle as well. Thus, the noted inconsistency lies at the core of Quantum Gravity. In this essay we reflect on a possible resolution of these outstanding problems.

Distribution of Entropy of Bardeen Regular Black Hole with Corrected State Density

We consider corrections to all orders in the Planck length on the quantum state density, and calculate the statistical entropy of the scalar field on the background of the Bardeen regular black hole numerically. We obtain the distribution of entropy which is inside the horizon of black hole and the contribution of the vicinity of horizon takes a great part of the whole entropy.

Notes on several phenomenological laws of quantum gravity [Cross-Listing]

Phenomenological approaches to quantum gravity try to infer model-independent laws by analyzing thought experiments and combining both quantum, relativistic, and gravitational ingredients. We first review these ingredients -three basic inequalities- and discuss their relationships with the nature of fundamental constants. In particular, we argue for a covariant mass bound conjecture: in a spacetime free of horizon, the mass inside a surface $A$ cannot exceed $16 \pi G^2 m^2< A$, while the reverse holds in a spacetime with horizons. This is given a precise definition using the formalism of light-sheets. We show that $\hbar/c$ may be also given a geometrical interpretation, namely $4 \pi \hbar^2/m^2< A$. We then combine these inequalities and find/review the following: (1) Any system must have a size greater than the Planck length, in the sense that there exists a minimal area (2) We comment on the Minimal Length Scenarios and the fate of Lorentz symmetry near the Planck scale (3) Quanta with transplanckian frequencies are allowed in a large enough boxes (4) There exists a mass-dependent maximal acceleration given by $m c^3/\hbar$ if $m<m_p$ and by $c^4/G m$ if $m>m_p$ (5) There exists a mass dependent maximal force and power (6) There exists a maximal energy density and pressure (7) Physical systems must obey the Holographic Principle (8) Holographic bounds can only be saturated by systems with $m>m_p$; systems lying on the “Compton line” $l \sim 1/m$ are fundamental objects without substructures (9) We speculate on a new bound from above for the action. In passing, we note that the maximal acceleration is of the order of Milgrom’s acceleration $a_0$ for ultra-light particles ($m\sim H_0)$ that could be associated to the Dark Energy fluid. This suggests designing toy-models in which modified gravity in galaxies is driven by the DE field, via the maximal acceleration principle.

Building non commutative spacetimes at the Planck length for Friedmann flat cosmologies [Replacement]

We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lema\^{i}tre cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we costruct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on some Hilbert space.

Building non commutative spacetimes at the Planck length for Friedmann flat cosmologies [Replacement]

We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lema\^{i}tre cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we costruct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on a Hilbert space.

Building non commutative spacetimes at the Planck length for Friedmann flat cosmologies [Replacement]

We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lema\^{i}tre cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we costruct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on some Hilbert space.

Building non commutative spacetimes at the Planck length for Friedmann flat cosmologies [Replacement]

We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lema\^{i}tre cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we costruct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on a Hilbert space.

Building non commutative spacetimes at the Planck length for Friedmann flat cosmologies [Replacement]

We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lema\^{i}tre cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we costruct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on a Hilbert space.

Building non commutative spacetimes at the Planck length for Friedmann flat cosmologies [Replacement]

We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lema\^{i}tre cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we construct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on some Hilbert space.

Building non commutative spacetimes at the Planck length for Friedmann flat cosmologies [Replacement]

We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lema\^{i}tre cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we costruct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on some Hilbert space.

Building non commutative spacetimes at the Planck length for Friedmann flat cosmologies [Replacement]

We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lema\^{i}tre cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we construct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on some Hilbert space.

Quantum astrometric observables II: time delay in linearized quantum gravity [Replacement]

A clock synchronization thought experiment is modeled by a diffeomorphism invariant "time delay" observable. In a sense, this observable probes the causal structure of the ambient Lorentzian spacetime. Thus, upon quantization, it is sensitive to the long expected smearing of the light cone by vacuum fluctuations in quantum gravity. After perturbative linearization, its mean and variance are computed in the Minkowski Fock vacuum of linearized gravity. The na\"ive divergence of the variance is meaningfully regularized by a length scale $\mu$, the physical detector resolution. This is the first time vacuum fluctuations have been fully taken into account in a similar calculation. Despite some drawbacks this calculation provides a useful template for the study of a large class of similar observables in quantum gravity. Due to their large volume, intermediate calculations were performed using computer algebra software. The resulting variance scales like $(s \ell_p/\mu)^2$, where $\ell_p$ is the Planck length and $s$ is the distance scale separating the ("lab" and "probe") clocks. Additionally, the variance depends on the relative velocity of the lab and the probe, diverging for low velocities. This puzzling behavior may be due to an oversimplified detector resolution model or a neglected second order term in the time delay.

Bimetric Gravity, Variable Speed of Light Cosmology and Planck2013 [Cross-Listing]

A bimetric gravity model with a variable speed of light is shown to be in agreement with the results reported from the Planck satellite in 2013. The predicted scalar mode spectral index is $n_s\approx 0.96$ and its running is $\alpha_s\approx 8\times 10^{-4}$ when the fundamental length scale $\ell_0$ in the model is fixed to be $\ell_0\approx 10^5\ell_P$, where $\ell_P$ is the Planck length $\ell_P=1.62\times 10^{-33}\,{\rm cm}$, giving the observed CMB fluctuations: $\delta_H\approx 10^{-5}$. The enlarged lightcone ensures that horizon and flatness problems are solved. The model is free from many of the fine-tuning problems of the inflationary models and the fluctuations that form the seeds of structure formation do not lead to a chaotic inhomogeneous universe and the need for a multiverse.

Wave function of the Universe, preferred reference frame effects and metric signature transition [Replacement]

Non-minimally coupled Brans Dicke (BD) gravity with dynamical unit time-like four vector field is used to study flat Robertson Walker (RW) cosmology in the presence of variable cosmological parameter described in terms of the BD field as $~\phi^n.$ Aim of the paper is to seek cosmological models exhibiting metric signature transition. The problem is studied in both classical and quantum cosmological approach. Solutions of classical dynamical equations lead to nonsingular inflationary scale factor of space time as $R(t)=l_p\cosh(t/l_p)$ where $l_p$ denotes to Planck length. Corresponding Euclidean signature scale factor is obtained directly by changing $t\to it$ which describes re-collapsing universe. Dynamical vector field together with the BD scalar field treats as fluid with time dependent barotropic index $\gamma(t)$. At large scales of the space time we obtain $\gamma(t)\to -1$ corresponding to dark matter dominant of the fluid. Positive values of this parameter is obtained only at the Euclidean regime of the space time and whose values are changed from $-\infty$ to $+\infty$ on the metric signature transition hypersurface $t=0$ where metric is degenerated. Dust and radiation domains of the fluid stands on the Euclidean regime of the space time. Euclidean regime is also contained $\gamma(t)<0$ corresponding dark matter dominate for short times. In the quantum cosmological approach we solve corresponding Weeler De Witt (WD) wave equation with large values of BD parameter. Assuming a discreet non-zero ADM mass $M_j=2(2j+1)/l_p$ with $j=0,1,2,\cdots$, WD wave solution is described in terms of simple harmonic quantum Oscillator eigne functionals. WD wave solutions of the Lorentzian and Euclidean signature of the flat RW space time have same nonzero values on the metric signature transition hypersurface and whose maximum value is obtained at ground state $j=0$.

Challenge to Macroscopic Probes of Quantum Spacetime Based on Noncommutative Geometry [Replacement]

Over the last decade a growing number of quantum-gravity researchers has been looking for opportunities for the first ever experimental evidence of a Planck-length quantum property of spacetime. These studies are usually based on the analysis of some candidate indirect implications of spacetime quantization, such as a possible curvature of momentum space. Some recent proposals have raised hope that we might also gain direct experimental access to quantum properties of spacetime, by finding evidence of limitations to the measurability of the center-of-mass coordinates of some macroscopic bodies. However I here observe that the arguments that originally lead to speculating about spacetime quantization do not apply to the localization of the center of mass of a macroscopic body. And I also analyze some popular formalizations of the notion of quantum spacetime, finding that when the quantization of spacetime is Planckian for the constituent particles then for the composite macroscopic body the quantization of spacetime is much weaker than Planckian. These results show that finding evidence of spacetime quantization with studies of macroscopic bodies is extremely unlikely. And they also raise some conceptual challenges for theories of mechanics in quantum spacetime, in which for example free protons and free atoms should feel the effects of spacetime quantization differently.

Solution to the cosmological constant problem

The current, accelerated, phase of expansion of our universe can be modeled in terms of a cosmological constant. A key issue in theoretical physics is to explain the extremely small value of the dimensionless parameter \Lambda L_P^2 ~ 3.4 x 10^{-122}, where L_P is the Planck length. We show that this value can be understood in terms of a new dimensionless parameter N, which counts the number of modes inside a Hubble volume crossing the Hubble radius, from the end of inflation until the beginning of the accelerating phase. Theoretical considerations suggest that N = 4\pi. On the other hand, N is related to ln (\Lambda L_P^2) and two other parameters which will be determined by high energy particle physics: (a) the ratio between the number densities of photons and matter and (b) the energy scale of inflation. For realistic values of (n_\gamma / n_m) ~ 4.3 x 10^{10} and E_{inf} ~ 10^{15} GeV, our postulate N =4\pi leads to the observed value of the cosmological constant. This provides a unified picture of cosmic evolution relating the early inflationary phase to the late accelerating phase.

Can quantum gravity be exposed in the laboratory?: A tabletop experiment to reveal the quantum foam [Replacement]

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.

Can quantum gravity be exposed in the laboratory?: A tabletop experiment to reveal the quantum foam [Replacement]

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.

Can quantum gravity be exposed in the laboratory?: A tabletop experiment to reveal the quantum foam [Replacement]

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.

Can quantum gravity be exposed in the laboratory?: A tabletop experiment to reveal the quantum foam [Cross-Listing]

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.

Minimum-length deformed QM/QFT, issues and problems [Replacement]

Using a particular Hilbert space representation of minimum-length deformed quantum mechanics, we show that the resolution of the wave-function singularities for strongly attractive potentials, as well as cosmological singularity in the framework of a minisuperspace approximation, is uniquely tied to the fact that this sort of quantum mechanics implies the reduced Hilbert space of state-vectors consisting of the functions nonlocalizable beneath the Planck length. (Corrections to the Hamiltonian do not provide such an universal mechanism for avoiding singularities.) Following this discussion, as a next step we take a critical view of the meaning of wave-function in such a quantum theory. For this reason we focus on the construction of current vector and the subsequent continuity equation. Some issues gained in the framework of this discussion are then considered in the context of field theory. Finally, we discuss the classical limit of the minimum-length deformed quantum mechanics and its dramatic consequences.

Minimum-length deformed QM/QFT, issues and problems [Replacement]

Using a particular Hilbert space representation of minimum-length deformed quantum mechanics, we show that the resolution of the wave-function singularities for strongly attractive potentials, as well as cosmological singularity in the framework of a minisuperspace approximation, is uniquely tied to the fact that this sort of quantum mechanics implies the reduced Hilbert space of state-vectors consisting of the functions nonlocalizable beneath the Planck length. (Corrections to the Hamiltonian do not provide such an universal mechanism for avoiding singularities.) Following this discussion, as a next step we take a critical view of the meaning of wave-function in such a quantum theory. For this reason we focus on the construction of current vector and the subsequent continuity equation. Some issues gained in the framework of this discussion are then considered in the context of field theory. Finally, we discuss the classical limit of the minimum-length deformed quantum mechanics and its dramatic consequences.

Trans-Planckian Issues for Inflationary Cosmology

The accelerated expansion of space during the period of cosmological inflation leads to trans-Planckian issues which need to be addressed. Most importantly, the physical wavelength of fluctuations which are studied at the present time by means of cosmological observations may well originate with a wavelength smaller than the Planck length at the beginning of the inflationary phase. Thus, questions arise as to whether the usual predictions of inflationary cosmology are robust considering our ignorance of physics on trans-Planckian scales, and whether the imprints of Planck-scale physics are at the present time observable. These and other related questions are reviewed in this article.

Is a tabletop search for Planck scale signals feasible? [Replacement]

Quantum gravity theory is untested experimentally. Could it be tested with tabletop experiments? While the common feeling is pessimistic, a detailed inquiry shows it possible to sidestep the onerous requirement of localization of a probe on Planck length scale. I suggest a tabletop experiment which, given state of the art ultrahigh vacuum and cryogenic technology, could already be sensitive enough to detect Planck scale signals. The experiment combines a single photon’s degree of freedom with one of a macroscopic probe to test Wheeler’s conception of "quantum foam", the assertion that on length scales of the order Planck’s, spacetime is no longer a smooth manifold. The scheme makes few assumptions beyond energy and momentum conservations, and is not based on a specific quantum gravity scheme.

Is a tabletop search for Planck scale signals feasible [Cross-Listing]

Quantum gravity theory is untested experimentally. Could it be tested with tabletop experiments? While the common feeling is pessimistic, a detailed inquiry shows it possible to sidestep the onerous requirement of localization of a probe on Planck length scale. I suggest a tabletop experiment which, given state of the art ultrahigh vacuum and cryogenic technology, could already be sensitive enough to detect Planck scale signals. The experiment combines a single photon’s degree of freedom with one of a macroscopic probe to test Wheeler’s conception of "spacetime foam", the assertion that on length scales of the order Planck’s, spacetime is no longer a smooth manifold. The scheme makes few assumptions beyond energy and momentum conservations, and is not based on a specific quantum gravity scheme.

The Physical Principle that determines the Value of the Cosmological Constant [Cross-Listing]

Observations indicate that the evolution of our universe can be divided into three epochs consisting of early time inflation, radiation (and matter) domination and the late time acceleration. One can associate with each of these epochs a number N which is the phase space volume of the modes which cross the Hubble radius during the corresponding epoch. This number turns out to be (approximately) the same for the cosmologically relevant ranges of the three epochs. When the initial de Sitter space is characterized by the Planck length, the natural value for N is 4\pi. This allows us to determine the cosmological constant which drives the late time acceleration, to be \Lambda L_P^2 = 3 \exp(-24\pi^2 \mu) where \mu\ is a number of order unity. This expression leads to the observed value of cosmological constant for \mu ~ 1.19. The implications are discussed.

A simple model of universe with a polytropic equation of state

We construct a simple model of universe with a generalized equation of state $p=(\alpha +k\rho^{1/n})\rho c^2$ having a linear component $p=\alpha\rho c^2$ and a polytropic component $p=k\rho^{1+1/n}c^2$. For $\alpha=1/3$, $n=1$ and $k=-4/(3\rho_P)$, where $\rho_P=5.16 10^{99} {\rm g/m}^3$ is the Planck density, this equation of state provides a model of the early universe without singularity describing the transition between the pre-radiation era and the radiation era. The universe starts from $t=-\infty$ but, when $t<0$, its size is less than the Planck length $l_P=1.62 10^{-35} {\rm m}$. The universe undergoes an inflationary expansion that brings it to a size $a_1=2.61 10^{-6} {\rm m}$ on a timescale of a few Planck times $t_P=5.39 10^{-44} {\rm s}$. When $t \gg t_P$, the universe decelerates and enters in the radiation era. For $\alpha=0$, $n=-1$ and $k=-\rho_{\Lambda}$, where $\rho_{\Lambda}=7.02 10^{-24} {\rm g/m}^3$ is the cosmological density, this equation of state describes the transition from a decelerating universe dominated by baryonic and dark matter to an accelerating universe dominated by dark energy (second inflation). The transition takes place at a size $a_2=8.95 10^{25} {\rm m}$ corresponding to a time of the order of the cosmological time $t_{\Lambda}=1.46 \times 10^{18} {\rm s}$. This polytropic model reveals a nice "symmetry" between the early and late evolution of the universe, the cosmological constant $\Lambda$ in the late universe playing a role similar to the Planck constant $\hbar$ in the early universe. We interpret the cosmological constant as a fundamental constant of nature describing the "cosmophysics" just like the Planck constant describes the microphysics. The Planck density and the cosmological density represent fundamental upper and lower bounds differing by ${122}$ orders of magnitude. The cosmological constant "problem" may be a false problem.

Models of universe with a polytropic equation of state: I. The early universe

We construct models of universe with a generalized equation of state $p=(\alpha \rho+k\rho^{1+1/n})c^2$ having a linear component and a polytropic component. In this paper, we consider positive indices $n>0$. In that case, the polytropic component dominates in the early universe where the density is high. For $\alpha=1/3$, $n=1$ and $k=-4/(3\rho_P)$, we obtain a model of early universe describing the transition from a pre-radiation era to the radiation era. The universe exists at any time in the past and there is no singularity. However, for $t<0$, its size is less than the Planck length $l_P=1.62 10^{-35} {\rm m}$. In this model, the universe undergoes an inflationary expansion with the Planck density $\rho_P=5.16 10^{99} {\rm g/m}^3$ that brings it to a size $a_1=2.61 10^{-6} {\rm m}$ at $t_1=1.25 10^{-42} {\rm s}$ (about 20 Planck times $t_P$). For $\alpha=1/3$, $n=1$ and $k=4/(3\rho_P)$, we obtain a model of early universe with a new form of primordial singularity: The universe starts at t=0 with an infinite density and a finite radius $a=a_1$. Actually, this universe becomes physical at a time $t_i=8.32 10^{-45} {\rm s}$ from which the velocity of sound is less than the speed of light. When $a\gg a_1$, the universe evolves like in the standard model. We describe the transition from the pre-radiation era to the radiation era by analogy with a second order phase transition where the Planck constant $\hbar$ plays the role of finite size effects (the standard Big Bang theory is recovered for $\hbar=0$).

A Model of Macroscopic Geometrical Uncertainty [Replacement]

A model quantum system is proposed to describe position states of a massive body in flat space on large scales, excluding all standard quantum and gravitational degrees of freedom. The model is based on standard quantum spin commutators, with operators interpreted as positions instead of spin, and a Planck-scale length $\ell_P$ in place of Planck’s constant $\hbar$. The algebra is used to derive a new quantum geometrical uncertainty in direction, with variance given by $\langle \Delta \theta^2\rangle = \ell_P/L$ at separation $L$, that dominates over standard quantum position uncertainty for bodies greater than the Planck mass. The system is discrete and holographic, and agrees with gravitational entropy if $\ell_P= l_P/\sqrt{4\pi}$, where $l_P\equiv \sqrt{\hbar G/c^3}$ denotes the standard Planck length. A physical interpretation is proposed that connects the operators with properties of classical position in the macroscopic limit: to approximate locality and causality in macroscopic systems, position states of multiple bodies must be entangled by proximity. This interpretation predicts coherent directional fluctuations with variance $\langle \Delta \theta^2\rangle$ on timescale $\tau \approx L/c$ that lead to correlated signals between adjacent interferometers. It is argued that such a signal could provide compelling evidence of Planck scale quantum geometry, even in the absence of a complete dynamical or fundamental theory.

A Model of Macroscopic Geometrical Uncertainty [Replacement]

A model quantum system is proposed to describe position states of a massive body in flat space on large scales, excluding all standard quantum and gravitational degrees of freedom. The model is based on standard quantum spin commutators, with operators interpreted as positions instead of spin, and a Planck-scale length $\ell_P$ in place of Planck’s constant $\hbar$. The algebra is used to derive a new quantum geometrical uncertainty in direction, with variance given by $\langle \Delta \theta^2\rangle = \ell_P/L$ at separation $L$, that dominates over standard quantum position uncertainty for bodies greater than the Planck mass. The system is discrete and holographic, and agrees with gravitational entropy if $\ell_P= l_P/\sqrt{4\pi}$, where $l_P\equiv \sqrt{\hbar G/c^3}$ denotes the standard Planck length. A physical interpretation is proposed that connects the operators with properties of classical position in the macroscopic limit: to approximate locality and causality in macroscopic systems, position states of multiple bodies must be entangled by proximity. This interpretation predicts coherent directional fluctuations with variance $\langle \Delta \theta^2\rangle$ on timescale $\tau \approx L/c$ that lead to correlated signals between adjacent interferometers. It is argued that such a signal could provide compelling evidence of Planck scale quantum geometry, even in the absence of a complete dynamical or fundamental theory.

A Model of Macroscopic Quantum Geometry [Replacement]

A model quantum system is proposed to describe states of flat space on large scales, excluding all standard quantum and gravitational degrees of freedom. The model is based on standard quantum spin commutators, with operators interpreted as positions instead of spin, and a Planck-scale length $\ell_P$ in place of Planck’s constant $\hbar$. The algebra is used to derive a new quantum geometrical uncertainty in direction, with variance given by $\langle \Delta \theta^2\rangle = \ell_P/L$ at separation $L$, that dominates over standard quantum position uncertainty for bodies greater than the Planck mass. The system is discrete and holographic, and agrees with gravitational entropy if $\ell_P= l_P/\sqrt{4\pi}$, where $l_P\equiv \sqrt{\hbar G/c^3}$ denotes the standard Planck length. A physical interpretation is proposed that accounts for properties of classical space-time in the macroscopic limit; to approximate locality and causality in macroscopic systems, position states of multiple bodies must be entangled by proximity. The model predicts coherent directional fluctuations with variance $\langle \Delta \theta^2\rangle$ on timescale $\tau \approx L/c$ that lead to correlated signals between adjacent interferometers. It is argued that such a signal could provide compelling evidence of Planck scale quantum geometry, even in the absence of a complete dynamical or fundamental theory.

A Model of Macroscopic Quantum Geometry [Replacement]

A model quantum system is proposed to describe states of flat space on large scales, excluding all standard quantum and gravitational degrees of freedom. The model is based on standard quantum spin commutators, with operators interpreted as positions instead of spin, and a Planck-scale length $\ell_P$ in place of Planck’s constant $\hbar$. The algebra is used to derive a new quantum geometrical uncertainty in direction, with variance given by $\langle \Delta \theta^2\rangle = \ell_P/L$ at separation $L$, that dominates over standard quantum position uncertainty for bodies greater than the Planck mass. The system is discrete and holographic, and agrees with gravitational entropy if $\ell_P= l_P/\sqrt{4\pi}$, where $l_P\equiv \sqrt{\hbar G/c^3}$ denotes the standard Planck length. A physical interpretation is proposed that accounts for properties of classical space-time in the macroscopic limit; to approximate locality and causality in macroscopic systems, position states of multiple bodies must be entangled by proximity. The model predicts coherent directional fluctuations with variance $\langle \Delta \theta^2\rangle$ on timescale $\tau \approx L/c$ that lead to correlated signals between adjacent interferometers. It is argued that such a signal could provide compelling evidence of Planck scale quantum geometry, even in the absence of a complete dynamical or fundamental theory.

A Model of Macroscopic Quantum Geometry [Replacement]

A model quantum system is proposed to describe states of flat space on large scales, excluding all standard quantum and gravitational degrees of freedom. It is based on standard quantum spin commutators, with operators interpreted as positions instead of spin, and a Planck-scale length $\ell_P$ in place of Planck’s constant $\hbar$. The algebra is used to derive a new quantum geometrical uncertainty in direction, with variance given by $\langle \Delta \theta^2\rangle = \ell_P/L$ at separation $L$, that dominates over standard quantum position uncertainty for bodies greater than the Planck mass. The system is discrete and holographic, and agrees with gravitational entropy if $\ell_P= l_P/\sqrt{4\pi}$, where $l_P\equiv \sqrt{\hbar G/c^3}$ denotes the standard Planck length. A physical interpretation is proposed that accounts for properties of classical space-time in the macroscopic limit; to approximate locality and causality in macroscopic systems, position states of multiple bodies must be entangled by proximity. The model predicts directional fluctuations on timescale $\tau \approx L/c$ that lead to correlated signals between adjacent interferometers.

A Model of Macroscopic Quantum Geometry [Replacement]

A model quantum system is proposed to describe states of flat space on large scales, excluding all standard quantum and gravitational degrees of freedom. It is based on standard quantum spin commutators, with operators interpreted as positions instead of spin, and a Planck-scale length $\ell_P$ in place of Planck’s constant $\hbar$. The algebra is used to derive a new quantum geometrical uncertainty in direction, with variance given by $\langle \Delta \theta^2\rangle = \ell_P/L$ at separation $L$, that dominates over standard quantum position uncertainty for bodies greater than the Planck mass. The system is discrete and holographic, and agrees with gravitational entropy if $\ell_P= l_P/\sqrt{4\pi}$, where $l_P\equiv \sqrt{\hbar G/c^3}$ denotes the standard Planck length. A physical interpretation is proposed that accounts for properties of classical space-time in the macroscopic limit; to approximate locality and causality in macroscopic systems, position states of multiple bodies must be entangled by proximity. The model predicts directional fluctuations on timescale $\tau \approx L/c$ that lead to correlated signals between adjacent interferometers.

A Model of Macroscopic Quantum Geometry [Replacement]

A model quantum system is proposed to describe quantum geometrical states of a flat, emergent space-time on large scales. It excludes all standard quantum degrees of freedom as well as gravity, but describes new quantum properties of position states of a distant massive body in the emergent geometry. The proposed algebra of position operators is manifestly covariant in the classical limit. In the non relativistic limit, it is identical to the standard quantum algebra of angular momentum, with a Planck-scale length $\ell_P$ in place of Planck’s constant $\hbar$. The system is discrete and holographic, and agrees with thermodynamic derivations of gravity if $\ell_P= l_P/\sqrt{4\pi}$, where $l_P\equiv \sqrt{\hbar G/c^3}$ denotes the standard Planck length. The model displays quantum geometrical uncertainty in direction with variance given by $\langle \Delta \theta^2\rangle = l_P/\sqrt{4\pi}L$ at separation $L$, and directional fluctuations with this magnitude on timescale $\tau \approx L/c$. To approximate locality in the macroscopic limit, position states of multiple bodies must be entangled, and fluctuations of neighboring bodies must be correlated, simply by proximity. The model and its physical interpretation can be tested by correlating signals between appropriately configured interferometers.