scholarly journals The Spinor-Tensor Gravity of the Classical Dirac Field

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1124 ◽  
Author(s):  
Piero Chiarelli
Keyword(s):  
General Relativity ◽  
Cosmological Constant ◽  
Space Time ◽  
Action Principle ◽  
Quantum Decoherence ◽  
Dirac Field ◽  
Perturbative Approach ◽  
Stable Quantum ◽  
Quantum Hydrodynamic ◽  
Relativity Equation

In this work, with the help of the quantum hydrodynamic formalism, the gravitational equation associated with the classical Dirac field is derived. The hydrodynamic representation of the Dirac equation described by the evolution of four mass densities, subject to the theory-defined quantum potential, has been generalized to the curved space-time in the covariant form. Thence, the metric of space-time has been defined by imposing the minimum action principle. The derived gravity shows the spontaneous emergence of the “cosmological” gravity tensor (CGT), a generalization of the classical cosmological constant (CC), as a part of the energy-impulse tensor density (EITD). Even if the classical cosmological constant is set to zero, the CGT is non-zero, allowing a stable quantum vacuum (out of the collapsed branched polymer phase). The theory shows that in the classical macroscopic limit, the general relativity equation is recovered. In the perturbative approach, the CGT leads to a second-order correction to Newtonian gravity that takes contribution from the space where the mass is localized (and the space-time is curvilinear), while it tends to zero as the space-time approaches the flat vacuum, leading, as a means, to an overall cosmological constant that may possibly be compatible with the astronomical observations. The Dirac field gravity shows analogies with the modified Brans–Dicke gravity, where each spinor term brings an effective gravity constant G divided by its field squared. The work shows that in order to obtain the classical minimum action principle and the general relativity limit of the macroscopic classical scale, quantum decoherence is necessary.

scholarly journals ON THE TOPOLOGICAL NATURE OF THE COSMOLOGICAL CONSTANT

2012 ◽  
Vol 18 ◽  
pp. 109-114
Author(s):  
M. D. MAIA
Keyword(s):  
General Relativity ◽  
Cosmological Constant ◽  
Cosmic Radiation ◽  
Cosmic Time ◽  
Space Time ◽  
Time Flow ◽  
Acceleration Of The Universe ◽  
Expansion Of The Universe ◽  
The Universe ◽  
Topological Changes

It is shown that topological changes in space-time are necessary to make General Relativity compatible with the Newtonian limit and to solve the hierarchy of the fundamental interactions. We detail how topology and topological changes appear in General Relativity and how it leaves an observable footprint in space-time. In cosmology we show that such topological observable is the cosmic radiation produced by the acceleration of the universe. The cosmological constant is a very particular case which occurs when the expansion of the universe into the vacuum occurs only in the direction of the cosmic time flow.

The Cosmic Fragment: Härte des Logischen Zwangs und Unendliche Möglichkeit

2015 ◽  
Vol 6 (1) ◽  
Author(s):  
Susan Edwards-McKie
Keyword(s):  
General Relativity ◽  
Cosmological Constant ◽  
Infinite System ◽  
Philosophy Of Mathematics ◽  
Space Time ◽  
Systemic Approach ◽  
Language Games ◽  
Final Version ◽  
Alternative Approaches ◽  
Scholarly Discussion

AbstractWittgenstein’s unrelenting criticism of Cantor, Euler, and Gödel falls within a larger strategy to disarm a philosophy of mathematics which relies on completed infinite sets. Because transfinite numbers are seen to resolve the Zeno paradoxes, creating “a paradise from which we shall not be driven”, according to Hilbert, Wittgenstein’s mathematics began to be seen as backwardlooking, particularly in the period of Turing’s work on the Entscheidungsproblem. It is argued that Wittgenstein offered consistent criticism and alternative approaches to paradoxes of the infinitely large and small through a consistent systemic approach to space, time, and generality. The centrality of proof is looked at carefully, with implications for conceptions of time and generality.Fragment MS 178e which I here, recalling Heraclitus, term the Cosmic Fragment, combined with the correction of a von Wright error, is used to explore these arguments, from both mathematical and Philosophische Untersuchungen (PU) Nachlass exegesis perspectives. The dating of the Fragment impacts on the wider scholarly discussion of the completion of MS 142 and TS 220, and the Fragment’s clustering of concepts is reflected in the significant re-ordering of remarks in the Zwischenfassung, which are carried through to the final version of PU. Affinities between Wittgensteinian mathematics and language games emerge within the textual network of the Cosmic Fragment and the new connections between MS 117 and TS 213.It is suggested that a proof-theoretic, potentially infinite system such as Wittgenstein’s, as contrasted with a set-theoretic, actual infinite such as Cantor’s and Gödel’s, in certain respects aligns Wittgenstein’s remarks on space, time and generality with Einsteinian general relativity as originally postulated with the cosmological constant. However, Wittgenstein’s conception of time is neither fully Parmenidean nor fully Heraclitean.

LIMIT TO SPACE-TIME MEASUREMENT

1994 ◽  
Vol 09 (04) ◽  
pp. 335-340 ◽  
Author(s):  
Y. JACK NG ◽  
H. VAN DAM
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Time Measurement ◽  
Space Time ◽  
Quantum Measurements ◽  
Quantum Decoherence ◽  
Planck Mass ◽  
The One

Applying simultaneously the principles of quantum mechanics and general relativity we find an intrinsic limitation to quantum measurements of space-time distances. The intrinsic uncertainty of a length is shown to be proportional to the one third power of the length itself. This uncertainty in space-time measurements implies an intrinsic uncertainty of the space-time metric and yields quantum decoherence for particles heavier than the Planck mass.

scholarly journals WEYL GEOMETRY AS CHARACTERIZATION OF SPACE-TIME

2011 ◽  
Vol 03 ◽  
pp. 87-97 ◽  
Author(s):  
F. P. POULIS ◽  
J. M. SALIM
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Riemannian Geometry ◽  
Axiomatic Approach ◽  
Space Time ◽  
Weyl Geometry ◽  
Test Particles ◽  
Variational Formalism ◽  
Physical Fields

Motivated by an axiomatic approach to characterize space-time it is investigated a reformulation of Einstein's gravity where the pseudo-riemannian geometry is substituted by a Weyl one. It is presented the main properties of the Weyl geometry and it is shown that it gives extra contributions to the trajectories of test particles, serving as one more motivation to study general relativity in Weyl geometry. It is introduced its variational formalism and it is established the coupling with other physical fields in such a way that the theory acquires a gauge symmetry for the geometrical fields. It is shown that this symmetry is still present for the red-shift and it is concluded that for cosmological models it opens the possibility that observations can be fully described by the new geometrical scalar field. It is concluded then that this reformulation, although representing a theoretical advance, still needs a complete description of their objects.

ON THE COSMOLOGICAL CONSTANT AS A CONSTANT OF INTEGRATION

1991 ◽  
Vol 06 (23) ◽  
pp. 2107-2111 ◽  
Author(s):  
A. N. PETROV
Keyword(s):  
General Relativity ◽  
Cosmological Constant

The possibilities to construct a modification of General Relativity (MGR), where the cosmological constant appears as a constant of integration are considered. A class of new constraints on the metric is found, such that their inclusion in the Hilbert–Einstein action before its variation leads to MGR.

scholarly journals Space time geometry in the atomic hydrogenoid system. Approach to a dust relativistic model from causal quantum mechanics

2018 ◽  
Vol 64 (1) ◽  
pp. 18
Author(s):  
G. Gómez ◽  
I. Kotsireas ◽  
I. Gkigkitzis ◽  
I. Haranas ◽  
M.J. Fullana
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
General Equation ◽  
System Approach ◽  
Space Time ◽  
Relativistic Model ◽  
Time Deformation ◽  
Non Local ◽  
De Broglie Bohm

Weintend to use the description oftheelectron orbital trajectory in the de Broglie-Bohm (dBB) theory to assimilate to a geodesiccorresponding to the General Relativity (GR) and get from itphysicalconclusions. ThedBBapproachindicatesustheexistenceof a non-local quantumfield (correspondingwiththequantumpotential), anelectromagneticfield and a comparativelyveryweakgravitatoryfield, togetherwith a translationkineticenergyofelectron. Ifweadmitthatthosefields and kineticenergy can deformthespace time, according to Einstein'sfield equations (and to avoidtheviolationoftheequivalenceprinciple as well), we can madethehypothesisthatthegeodesicsof this space-time deformation coincide withtheorbitsbelonging to thedBBapproach (hypothesisthat is coherentwiththestabilityofmatter). Fromit, we deduce a general equation that relates thecomponentsofthemetric tensor. Thenwe find anappropriatemetric for it, bymodificationofanexactsolutionofEinstein'sfield equations, whichcorresponds to dust in cylindricalsymmetry. Thefoundmodelproofs to be in agreementwiththebasicphysicalfeaturesofthehydrogenquantum system, particularlywiththeindependenceoftheelectronkineticmomentum in relationwiththeorbit radius. Moreover, themodel can be done Minkowski-like for a macroscopicshortdistancewith a convenientelectionof a constant. According to this approach, theguiding function ofthewaveontheparticlecould be identifiedwiththedeformationsofthespace-time and thestabilityofmatterwould be easilyjustifiedbythe null accelerationcorresponding to a geodesicorbit.

scholarly journals Stress Energy Tensor Study in Fluid Mechanics

2019 ◽  
Author(s):  
Roman Baudrimont
Keyword(s):  
General Relativity ◽  
Fluid Mechanics ◽  
Space Time ◽  
Newtonian Fluids ◽  
Third Party ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Perfect Fluids ◽  
Stress Energy

This paper is to summarize the involvement of the stress energy tensor in the study of fluid mechanics. In the first part we will see the implication that carries the stress energy tensor in the framework of general relativity. In the second part, we will study the stress energy tensor under the mechanics of perfect fluids, allowing us to lead third party in the case of Newtonian fluids, and in the last part we will see that it is possible to define space-time as a no-Newtonian fluids.

scholarly journals STEPHEN HAWKING: SPACE, TIME AND QUANTA

2020 ◽  
Author(s):  
Mauro Carfora
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Space Time ◽  
Stephen Hawking

A brief introduction to the scientic work of Stephen Hawking and to his contributions to our understanding of the interplay between general relativity and quantum theory.

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