Is spacetime absolutely or just most probably Lorentzian?

Davidson, Aharon; Yellin, Ben

doi:10.1088/0264-9381/33/16/165009

Cited by 2 publications

(3 citation statements)

References 37 publications

(29 reference statements)

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“…[27] and references mentioned therein). Different approaches exist to the change of metric; some are classical [28], while others are quantum [29,30]. Here we will not concern ourselves with the mechanism of metric change (however, the interested reader can refer to Ref.…”

Section: Introductionmentioning

confidence: 99%

The Primordial Particle Accelerator of the Cosmos

Yahalom

2022

Universe

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In a previous paper we have shown that superluminal particles are allowed by the general relativistic theory of gravity provided that the metric is locally Euclidean. Here we calculate the probability density function of a canonical ensemble of superluminal particles as function of temperature. This is done for both space-times invariant under the Lorentz symmetry group, and for space times invariant under an Euclidean symmetry group. Although only the Lorentzian metric is stable for normal matter density, an Euclidian metric can be created under special gravitational circumstances and persist in a limited region of space-time consisting of the very early universe, which is characterized by extremely high densities and temperatures. Superluminal particles also allow attaining thermodynamic equilibrium at a shorter duration and suggest a rapid expansion of the matter density.

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Section: Introductionmentioning

confidence: 99%

The Primordial Particle Accelerator of the Cosmos

Yahalom

2022

Universe

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“…where a is the dynamical variable and a(t) is an arbitrary (but fixed) positive function obeyingȧ(t) > 0 (see [22] for an alternative approach). In fact, this gauge breaks down whenȧ = 0, but if one assumesȧ > 0 then for any a one can apply the gauge symmetry (7) with a suitable k 0 to transform a to the given a(t), which shows that (9) is a proper gauge choice.…”

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confidence: 99%

“…where U (a 2 , a 1 ), which is given in (22), can be calculated without any issues at a 1 = 0. The initial energy can be considered to vanish for any ψ(0) since the Hamiltonian degenerates to zero, which provides a concrete realization of the zero energy universe hypothesis [23].…”

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confidence: 99%

Initial wave function of the universe is arbitrary

Kaya

2019

Mod. Phys. Lett. A

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We consider quantization of the gravity-scalar field system in the minisuperspace approximation. It turns out that in the gauge fixed deparametrized theory where the scale factor plays the role of time, the Hamiltonian can be uniquely defined without any ordering ambiguity as the square root of a self-adjoint operator. Moreover, the Hamiltonian degenerates to zero and the Schrödinger equation becomes well behaved as the scale factor vanishes. Therefore, there is no technical or physical obstruction for the initial wave-function of the universe to be an arbitrary vector in the Hilbert space, which demonstrates the severeness of the initial condition problem in quantum cosmology.Although quantum mechanics has a lot of intriguing features, the evolution dictated by the Schrödinger equation is fully deterministic, which is no more different than classical wave propagation. The wave-function is uniquely determined in time once the initial state is somehow specified at the beginning. In principle, the initial state can be arbitrarily chosen by the external agent preparing the system inasmuch as the freedom of choosing initial conditions in classical mechanics.The situation seems to be different in an approach to quantum cosmology based on the Wheeler-DeWitt (WDW) equation due to its timeless characteristic. Some would argue that timelessness is a fundamental property of quantum gravity. One then hopes to impose certain (mathematically and physically motivated) boundary conditions for the WDW equation in quantum cosmology that are supposed to fix the wave-function of the universe uniquely. This, however, is not easily achievable and there are different viable suggestions like the no boundary [1] or the tunneling [2] proposals (see also [3,4] for other alternatives and [5] for an attempt to determine the initial state by referring to the special dynamics of the loop quantum cosmology).More recently, a Lorentzian path integral method based on the Picard-Lefschetz theory has been put forward as the basis of quantum cosmology and it has been claimed that both the no boundary and the tunneling proposals yield unsuppressed perturbations, thus they are problematic in the Lorentzian framework [6][7][8][9]. This has raised a debate in the literature, see [10][11][12][13][14][15][16][17]. The wave-function obtained by the Lorentzian path integral solves the WDW equation, at least in the minisuperspace model when the proper-time gauge is employed [18], and the recent discussion is again centered around the WDW approach.General relativity has many peculiarities that clearly distinguish it from a standard gauge theory of internal symmetries. To begin with the spacetime itself becomes dynamical rather than being a fixed background. Somehow relatedly, the "structure constants" of the gauge algebra of coordinate transformations turn out to be field dependent. Moreover, the Hamiltonian of general relativity vanishes and it becomes a constraint of the theory.Nevertheless, all these properties do not imply a perfect timelessness and indee...

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Is spacetime absolutely or just most probably Lorentzian?

Cited by 2 publications

References 37 publications

The Primordial Particle Accelerator of the Cosmos

The Primordial Particle Accelerator of the Cosmos

Initial wave function of the universe is arbitrary

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