scholarly journals Geodesic distance: A descriptor of geometry and correlator of pregeometric density of spacetime events

2020 ◽  
Vol 35 (12) ◽  
pp. 2030008
Author(s):  
T. Padmanabhan
Keyword(s):  
Quantum Theory ◽  
Geodesic Distance ◽  
Zero Point ◽  
Special Role ◽  
Quantum Structure ◽  
Metric Tensor ◽  
Variable Formula ◽  
Classical Geometry ◽  
Tensor Formula ◽  
Null Surfaces

Classical geometry can be described either in terms of a metric tensor [Formula: see text] or in terms of the geodesic distance [Formula: see text]. Recent work, however, has shown that the geodesic distance is better suited to describe the quantum structure of spacetime. This is because one can incorporate some of the key quantum effects by replacing [Formula: see text] by another function [Formula: see text] such that [Formula: see text] is nonzero. This allows one to introduce a zero-point-length in the spacetime. I show that the geodesic distance can be an emergent construct, arising in the form of a correlator [Formula: see text], of a pregeometric variable [Formula: see text], which can be interpreted as the quantum density of spacetime events. This approach also shows why null surfaces play a special role in the interface of quantum theory and gravity. I describe several technical and conceptual aspects of this construction and discuss some of its implications.

scholarly journals The atoms of space, gravity and the cosmological constant

2016 ◽  
Vol 25 (07) ◽  
pp. 1630020 ◽  
Author(s):  
T. Padmanabhan
Keyword(s):  
Cosmological Constant ◽  
Density Of States ◽  
Zero Point ◽  
Integration Constant ◽  
Quantum Structure ◽  
Field Equations ◽  
Classical Gravity ◽  
Matter Sector ◽  
Null Surfaces

I describe an approach which connects classical gravity with the quantum microstructure of spacetime. The field equations arise from maximizing the density of states of matter plus geometry. The former is identified using the thermodynamics of null surfaces while the latter arises due to the existence of a zero-point length in the spacetime. The resulting field equations remain invariant when a constant is added to the matter Lagrangian, which is a symmetry of the matter sector. Therefore, the cosmological constant arises as an integration constant. A nonzero value [Formula: see text] of the cosmological constant renders the amount of cosmic information [Formula: see text] accessible to an eternal observer finite and hence is directly related to it. This relation allows us to determine the numerical value of [Formula: see text] from the quantum structure of spacetime.

Black hole in balance with dark matter

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040050
Author(s):  
Boris E. Meierovich
Keyword(s):  
Black Hole ◽  
Dark Matter ◽  
Phase Equilibrium ◽  
Vector Field ◽  
Scalar Field ◽  
Total Mass ◽  
Metric Tensor ◽  
Static Solutions ◽  
Tensor Formula ◽  
Galaxy Rotation Curves

Equilibrium of a gravitating scalar field inside a black hole compressed to the state of a boson matter, in balance with a longitudinal vector field (dark matter) from outside is considered. Analytical consideration, confirmed numerically, shows that there exist static solutions of Einstein’s equations with arbitrary high total mass of a black hole, where the component of the metric tensor [Formula: see text] changes its sign twice. The balance of the energy-momentum tensors of the scalar field and the longitudinal vector field at the interface ensures the equilibrium of these phases. Considering a gravitating scalar field as an example, the internal structure of a black hole is revealed. Its phase equilibrium with the longitudinal vector field, describing dark matter on the periphery of a galaxy, determines the dependence of the velocity on the plateau of galaxy rotation curves on the mass of a black hole, located in the center of a galaxy.

scholarly journals Bounds on the power of proofs and advice in general physical theories

2016 ◽  
Vol 472 (2190) ◽  
pp. 20160076 ◽  
Author(s):  
Ciarán M. Lee ◽  
Matty J. Hoban
Keyword(s):  
Quantum Theory ◽  
Quantum Structure ◽  
Interactive Proof ◽  
Interactive Proof Systems ◽  
Proof Systems ◽  
Local Measurements ◽  
General Physical ◽  
Adjoint Operators ◽  
Physical Features ◽  
Physical Principles

Quantum theory presents us with the tools for computational and communication advantages over classical theory. One approach to uncovering the source of these advantages is to determine how computation and communication power vary as quantum theory is replaced by other operationally defined theories from a broad framework of such theories. Such investigations may reveal some of the key physical features required for powerful computation and communication. In this paper, we investigate how simple physical principles bound the power of two different computational paradigms which combine computation and communication in a non-trivial fashion: computation with advice and interactive proof systems. We show that the existence of non-trivial dynamics in a theory implies a bound on the power of computation with advice. Moreover, we provide an explicit example of a theory with no non-trivial dynamics in which the power of computation with advice is unbounded. Finally, we show that the power of simple interactive proof systems in theories where local measurements suffice for tomography is non-trivially bounded. This result provides a proof that Q M A is contained in P P , which does not make use of any uniquely quantum structure—such as the fact that observables correspond to self-adjoint operators—and thus may be of independent interest.

Small-scale structure of spacetime and its implications

2019 ◽  
Vol 28 (06) ◽  
pp. 1950079
Author(s):  
Dawood Kothawala
Keyword(s):  
Lower Bound ◽  
Perturbative Expansion ◽  
Scale Structure ◽  
Small Scale ◽  
Metric Tensor ◽  
Small Scale Structure ◽  
Van Vleck ◽  
Tensor Formula ◽  
Effective Description ◽  
World Function

If there exists a lower bound [Formula: see text] to spacetime intervals which is Lorentz-invariant, then the effective description of spacetime that incorporates such a lower bound must necessarily be nonlocal. Such a nonlocal description can be derived using standard tools of differential geometry, but using as basic variables certain bi-tensors instead of the conventional metric tensor [Formula: see text]. This allows one to construct a qmetric [Formula: see text], using the Synge’s world function [Formula: see text] and the van Vleck determinant [Formula: see text], that incorporates the lower bound on spacetime intervals. The same nonanalytic structure of the reconstructed spacetime which renders a perturbative expansion in [Formula: see text] meaningless, will then also generically leave a non-trivial “relic” in the limit [Formula: see text]. We present specific results derived from [Formula: see text] where such a relic term manifests, and discuss several implications of the same. Specifically, we will discuss how these results: (i) suggest a description of gravitational dynamics different from the conventional one based on the Einstein–Hilbert Lagrangian, (ii) imply a dimensional reduction to [Formula: see text] at small scales and (iii) can be significant for the idea that the cosmological constant itself might be related to some nonlocal vestige of the small-scale structure of spacetime. We will conclude by discussing the ramifications of these ideas in the context of quantum gravity.

scholarly journals Dispersive property of the quantum vacuum and the speed of light

2019 ◽  
Vol 34 (04) ◽  
pp. 1950035 ◽  
Author(s):  
H. Razmi ◽  
N. Baramzadeh ◽  
H. Baramzadeh
Keyword(s):  
Quantum Theory ◽  
Light Propagation ◽  
Vacuum Energy ◽  
Nonlinear Effects ◽  
Zero Point ◽  
Quantum Vacuum ◽  
Electric Permittivity ◽  
Speed Of Light ◽  
Standard Linear ◽  
Linear Quantum

We want to study the influence of the quantum vacuum on light propagation. At first, by working in the standard linear quantum theory of the electromagnetic fields, it is shown that the electric permittivity and the magnetic permeability of the vacuum medium are changed; but, the resulting speed of light is not modified. Then, taking into account nonlinear effects by considering the Euler–Heisenberg Lagrangian, the corresponding zero point (vacuum) energy and the resulting modification of the speed of light are found up to the first nonvanishing correction.

scholarly journals Gravity and quantum theory: Domains of conflict and contact

2019 ◽  
Vol 29 (01) ◽  
pp. 2030001
Author(s):  
T. Padmanabhan
Keyword(s):  
Thermal Properties ◽  
Cosmological Constant ◽  
First Principles ◽  
Degrees Of Freedom ◽  
Dynamical Variable ◽  
Quantum Structure ◽  
Cosmological Constant Problem ◽  
Metric Tensor ◽  
Long Wavelength ◽  
Thermodynamic Interpretation

There are two strong clues about the quantum structure of spacetime and the gravitational dynamics, which are almost universally ignored in the conventional approaches to quantize gravity. The first clue is that null surfaces exhibit (observer-dependent) thermal properties and possess a heat density. This suggests that spacetime, like matter, has microscopic degrees of freedom and its long wavelength limit should be described in thermodynamic language and not in a geometric language. Second clue is related to the existence of the cosmological constant. Its understanding from first-principles will require the dynamical principles of the theory to be invariant under the shift [Formula: see text]. This puts strong constraints on the nature of gravitational dynamics and excludes metric tensor as a fundamental dynamical variable. In fact, these two clues are closely related to each other. When the dynamical principles are recast, respecting the symmetry [Formula: see text], they automatically acquire a thermodynamic interpretation related to the first clue. The first part of this review provides a pedagogical introduction to thermal properties of the horizons, including some novel derivations. The second part describes some aspects of cosmological constant problem and the last part provides a perspective on gravity which takes into account these principles.

On the Evaluation of Scalarproducts of Nonlinear Spinorfield State Functionals

1981 ◽  
Vol 36 (10) ◽  
pp. 1024-1031
Author(s):  
H. Stumpf
Keyword(s):  
Quantum Theory ◽  
State Space ◽  
Quark Model ◽  
A Priori ◽  
Preceding Paper ◽  
Functional Space ◽  
Nonlinear Field ◽  
Metrical Structure ◽  
Metric Tensor ◽  
Linear State

The metrical structure of the linear state space of a quantized nonlinear field cannot be given a priori. Rather it is determined by the dynamics of the field itself. For the evaluation of state norms and scalarproducts this metric must be known. In functional quantum theory the metrical structure is expressed by the metric tensor G (j) in functional space. Equivalent to the knowledge of G (j) is the knowledge of the set of dual state functionals {|S(j, a)〉} together with the corre-sponding original state functionals {|F(j, a)〉} . In preceding papers attempts were made to calculate G (j). In this paper an approach is made to determine the dual state functionals directly. Equations are derived which have to be satisfied by the dual functionals. The method works in those state sectors which are characterized by real (monopole) particles or monopole ghosts, while it does not work for multipole ghost states. Norm calculations are performed for local monopole fermion states and local monopole boson states of the lepton-quark model derived in a preceding paper.

scholarly journals A Theoretical Calculation of the Cosmological Constant Based on a Mechanical Model of Vacuum

2021 ◽  
Author(s):  
Xiao-Song Wang
Keyword(s):  
Cosmological Constant ◽  
Mass Density ◽  
Zero Point ◽  
Momentum Tensor ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Cosmological Constant Problem ◽  
Metric Tensor ◽  
Point Energy ◽  
Einstein's Equations

We suppose that vacuum is filled with a kind of continuously distributed matter, which may be called the $\Omega(1)$ substratum, or the electromagnetic aether. Lord Kelvin believes that the electromagnetic aether must also generate gravity. We also suppose that vacuum is filled with another kind of continuously distributed substance, which may be called the $\Omega(2)$ substratum. Based on a theorem of V. Fock on the mass tensor of a fluid, the contravariant energy-momentum tensors of the $\Omega(1)$ and $\Omega(2)$ substratums are established. Quasi-static solutions of the gravitational field equations in vacuum are obtained. Based on an assumption, relationships between the contravariant energy-momentum tensor of the $\Omega(1)$ and $\Omega(2)$ substratums and the contravariant metric tensor are obtained. Thus, the cosmological constant is calculated theoretically. The $\Omega(1)$ and $\Omega(2)$ substratums may be a possible candidate of the dark energy. The zero-point energy of electromagnetic fields will not appear as a source term in the Einstein's equations. The cosmological constant problem is one of the puzzles in physics. Some people believed that all kinds of energies should appear as source terms in the Einstein's equations. It may be this belief that leads to the cosmological constant problem. The mass density of the $\Omega(1)$ and $\Omega(2)$ substratums is equivalent to that $31.33195$ protons contained in a box with a volume of $1.0 {m}^{3}$.

scholarly journals The kinetic theory of the mesoscopic spacetime

2018 ◽  
Vol 27 (14) ◽  
pp. 1846004
Author(s):  
T. Padmanabhan
Keyword(s):  
Equilibrium State ◽  
Density Of States ◽  
Heat Dissipation ◽  
Zero Point ◽  
Internal Degree ◽  
Total Density ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Classical Geometry ◽  
Internal Degree Of Freedom

At the mesoscopic scales — which interpolate between the macroscopic, classical, geometry and the microscopic, quantum, structure of spacetime — one can identify the density of states of the geometry, which arises from the existence of a zero-point length in the spacetime. This spacetime discreteness also associates an internal degree of freedom with each event, in the form of a fluctuating vector of constant norm. The equilibrium state, corresponding to the extremum of the total density of states of geometry plus matter, leads precisely to Einstein’s equations. In fact, the field equation can now be reinterpreted as a zero-heat-dissipation principle. The analysis of fluctuations around the equilibrium state (which is described by Einstein’s equations), will provide new insights about the quantum gravity.

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