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Quantum General Relativity 1 An extended zero-energy hypothesis predicting negative GF potential energy. ZEUT explains that, during the the existence of negative-energy gravitons and inflation phase of our universe, energy flows from the (negative energy) GF to the (positive energy) inflation field possibly explaining the accelerated expansion of (IF) so that the total (negative) GF-energy decreases our universe (becoming more negative) and the total (positive) IF-energy increases (becoming more positive): however, the respective * [1] GF/IF energy densities remain constant and opposite since Andrei-Lucian Drăgoi , Independent researcher the region is inflating; consequently, IF explains the (Bucharest, Romania) cancellation between matter (including radiation) and GF DOI: 10.13140/RG.2.2.36245.99044 energies on cosmological scales, which is consistent with * astronomical observations (concordant with the observable Abstract universe being flat) [2]. The negative energy GF and the positive energy matter (and radiation) may exactly cancel out only if our universe is completely flat: such a zero-energy flat This paper proposes an extended (e) zero-energy universe can theoretically last forever. Tryon acknowledged hypothesis (eZEH) starting from the “classical” speculative zero-energy universe hypothesis (ZEUH) (first proposed by that his ZEUT was inspired by the general relativist Peter physicist Pascual Jordan), which mainly states that the total Bergmann, who showed (before Tryon) how a universe could amount of energy in our universe is exactly zero: its amount come from nothing without contradicting ECP (with the 1st of positive energy (in the form of matter and radiation) is law of thermodynamics being also an ECP version). The first exactly canceled out by its negative energy (in the form of documented mention of ZEUH (1934) (in the context of gravity). eZEH “pushes” ZEUH “to its quantum limits” and some possible oscillating models of our universe) belongs to generates some new predictions: (1) the existence of multiple Richard C. Tolman from the California Institute of types of negative-energy gravitons; (2) a strong quantum gravitational field acting at very small subatomic length Technology [3]. The well-known physicists Stephen scales (which is measured by a quantum strong gravitational Hawking, Alexei V. Filippenko and Jay M. Pasachoff also constant and which is predicted to make Hawking radiation appear to agree with ZEUH, at least in part. Cite no. 1 from very improbable to form at the first place); (3) a Stephen Hawking: “The total energy of the universe is (macrocosmic) black hole Casimir effect which may explain exactly zero. The matter in the universe is made out of the accelerated expansion of our universe etc. positive energy. However, the matter is all attracting itself by Keywords: the zero-energy universe hypothesis (ZEUH); an extended zero-energy hypothesis (eZEH); quantum gravity. Two pieces of matter that are close to each other vacuum; negative-energy graviton; quantum strong have less energy than the same two pieces a long way apart, gravitational constant; Hawking radiation; black hole Casimir because you have to expend energy to separate them against effect; accelerated expansion of our universe. the gravitational force that is pulling them together. Thus, in a sense, the gravitational field has negative energy. In the *** case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly I. Introduction cancels the positive energy represented by the matter. So the total energy of the universe is zero.” [4]. Cite no. 2 from The zero-energy universe theory. The zero-energy Stephen Hawking: “We might decide that there wasn't any universe hypothesis (ZEUH) states that the total amount of singularity. The point is that the raw material doesn't really energy in our universe is exactly zero: its amount of positive have to come from anywhere. When you have strong energy (in the form of matter and radiation) is exactly gravitational fields, they can create matter [in form of canceled out by its negative energy (in the form of gravity). particle-antiparticle pairs: my note]. It may be that there ZEUH was first proposed by the mathematical physicist aren't really any quantities which are constant in time in the Ernst Pascual Jordan who argued that, in principle, since the universe. The quantity of matter is not constant, because positive energy of a star's mass and its (negative energy) matter can be created or destroyed. But we might say that the gravitational field (GF) together may have zero total energy, energy of the universe would be constant, because when you the energy conservation principle (ECP) wouldn’t prevent a create matter, you need to use energy. And in a sense the star being created by starting from a quantum transition of energy of the universe is constant; it is a constant whose the (quantum) vacuum state [1]. value is zero. The positive energy of the matter is exactly ZEU theory (ZEUT) was independently proposed by balanced by the negative energy of the gravitational field. So Edward Tryon in 1973 (in the “Nature” journal) who the universe can start off with zero energy and still create speculated that our universe may have emerged from a large- matter. Obviously, the universe starts off at a certain time. scale quantum fluctuation of the vacuum energy, resulting in Now you can ask: what sets the universe off. There doesn't its positive mass-energy being exactly balanced by its really have to be any beginning to the universe. It might be that space and time together are like the surface of the Earth, but with two more dimensions, with degrees of latitude [1] Email: [email protected]; Research Gate page: playing the role of time.” [5]. Cite from Alexei V. www.researchgate.net/profile/Andrei_Lucian_Dragoi2 2 Filippenko and Jay M. Pasachoff: "In the inflationary EEEE theory, matter, antimatter, and photons were produced by the tot PAp EM G (Eq.1) energy of the false vacuum, which was released following the 2m c2 k q22 G m / r 0 phase transition. All of these particles consist of positive EP ex() EPx EP x energy. This energy, however, is exactly balanced by the negative gravitational energy of everything pulling on Based on eZEH and Eq.1, a general function measuring everything else. In other words, the total energy of the the reciprocal distance r between any two paired (virtual) universe is zero!" [6]. x The concept of negative energy is not only used to EPs (in the exact moment of their “birth” as a PAP) can be describe GF, but also other attractive quantum fields (like the defined as: electromagnetic field between opposite sign charges). The concept of negative energy density also explains 22 kex() qEP Gx m EP (Eq.2) Casimir effect: when two flat plates are placed very close to rxx kex(),,, qEP G m EP 2 each other (at a distance dm 1 ), they restrict the number 2mcEP of virtual photons (vPHs) (allowing only vPHs with wavelengths d ) and particle-antiparticle pairs (PAPs) eZEH statement no. 2. eZEH additionally states that which can exist between them; this results in a negative NOT ONLY fermionic PAPs (with non-zero rest masses) energy density, which causes an attractive force between the obey eZEH, but also the other bosonic EPs with theoretical plates, that has been demonstrated and measured. zero rest masses (and possessing only relativistic masses) like the photon (PH), the gluon and the hypothetical graviton: more specifically, eZEH states that (virtual) PHs also pop up *** (or can be “extracted” from) the vacuum ONLY in pairs composed from a (spin-1) positive-energy PH EhPH II. The extended zero-energy hypothesis (eZEH) and a spin-1 negative-energy PH (nePH) Eh() (with negative linear/angular frequency eZEH statement no. 1. The extended zero-energy nePH hypothesis (eZEH) (proposed in this paper) states that, when , with nePH travelling backwards in time) so that the total an particle-antiparticle pair (PAP) pops out from the energy of the two-PHs system conserves and remains zero: (quantum) vacuum, NOT ONLY the total electromagnetic (EM) charge is conserved (and equals zero in that PAP), EEEtot() PHs PH nePH 0 (Eq.3) BUT also the total energy of that PAP E is also tot conserved and equals zero. Notes. nePHs are the negative energy solutions of Etot 0 at non-relativistic speeds (and considering Maxwell's equations for propagating PH energy. nePHs were that the inverse square law is preserved or offers a reasonable first proposed by physicist Paul Dirac in his notorious “Dirac approximation/prediction in both EM field and GF acting on sea” theoretical model (in which vacuum was stated to be a point-like elementary particles (EPs) even at very small “sea” containing an infinite number of virtual EPs with length scales, comparable to Planck scale) is defined as the negative rest energies, including nePHs). Virtual negative sum between these three energy quantities: (1) the rest energy EPs (including nePHs) can exist for a short time 2 interval: this phenomenon is a part of the mechanism energy of a PAP EPAP 2 mEP c ; (2) the EM attraction involved in Hawking radiation (HR) (by which black holes (negative) energy between EP and its antiparticle evaporate and which HR also implies the existence of 2 conjugated PHs and nePHs. nePHs are currently under EEM kex() q EP / rx (with: rx being the distance research [7]. between the EPs of that PAP in the exact moment of its eZEH statement no. 3. The rx distance between PH and “birth”, kex() being the Coulomb constant at those rx length its paired nePH (in the exact moment of their “co-birth”) is scales and qEP being the zero/non-zero EM charge of each stated by eZEH to have any random finite/infinite value, EP from that PAP); (3) the (negative) gravitational energy because the total energy of that PH-nePH pair Etot() PHs between EPs of that PAP E G m2 / r (with: G xxEP remains zero, no matter the value.
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