The Big Bang Ex Nihilo

Rev Dr Adam Hincks considers the relationship between the scientific and theological understandings of the beginning of the universe and creation. He explores the question 'Do we need God to explain why there is something rather than nothing?'
Rev Dr Adam Hincks is a Jesuit priest and an Assistant Professor at the University of Toronto, where he holds the Sutton Family Chair in Science, Christianity and Cultures. Within the university he has a joint appointment to the Department of Astronomy of Astrophysics and to St. Michael’s College. His research is focussed on physical cosmology.

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28:02 Pauli, RT, paragraph 22, Geometry of the Real World, "So far we have assumed that the form ds^2 is a definite form. In the real space-time world, this does not take place, since ds^2 in normal form has three positive and one negative term." On the Protouniverse: 0.in RT the main invariant is the 4-interval (a mathematical description of the constant c), however, it could offer another invariant value based on another physical constant. 1.Comparing with Einstein's equations of 1915, we find a=-c^3/16πG. Strictly speaking, in order to determine the constant a, it was necessary to make a transition to the Poisson equation. Thus, a rigorous derivation of Einstein's equations can be given. The transition to the non-relativistic limit allows us to determine a constant factor for the integral of the gravitational field according to: R[(0)^0]=(4πG/c^2)p; Δφ=-pc^3/4a=4πGр. And a=(1/16π)m(pl)w(pl). 2.From Kepler's third law follows: M/t=v^3/G, where M/t=I(G)=[gram•sec^-1] is the gravitational current. By the way, in SR: I(G)=inv; this follows from the Lorentz transformations: m=m(0)/√(1-v^2/c^2) and ∆t=∆t(0)/√(1-v^2/c^2). Hence, obviously, we have I(G)=m/t=m(0)/t(0)=inv. 3.Therefore, the Poisson equation can be written as: ∆g(00)=8πGT(00)/c^4, where g(00) is the time component of the metric tensor (for a weakly curved metric the time component of the energy-momentum tensor: T(00)~=pc^2). This equation is true only in the non-relativistic case, but it is applicable to the case of a homogeneous and isotropic Universe, when Einstein's equations have only solutions with a time-varying space-time metric. Then the energy density of the gravitational field: g^2/8πG=T(00)=pc^2 [~=(ħ/8πc^3)w(relic)^4= =1600 quanta/cm^3, which is in order of magnitude consistent with the observational-measured data (~500 quanta/cm^3)], where the critical density value determining the nature of the model is: p=(3/8π)H^2/G. Hence it follows: g~πcH. 4.Expansion is a special kind of motion, and it seems that the Universe is a non-inertial frame of reference that performs variably accelerated motion along a phase trajectory, and thereby creates a phase space. And according to the strong equivalence principle: g=|a*|=πcH [=r(pl)w(relic)^2], and w(relic)^2=πw(pl)H. Thus H=1,72*10^-20sec^-1. {By the way, at t(universe)= πт(pl), w(“relic”) was =w(pl); at 1/”H”= t(universe)=380000 years, w(“relic”)/2π was =3.5*10^14 Hz} 5.Intra-metagalactic gravitational potential: |ф0|=πGmpl/λ(relic)=[Gm(pl)/2c]w(relic), where the constant Gm(pl)/2c is a quantum of the inertial flow Ф(i) = (½)S(pl)w(pl) = h/4πm(pl) (magnetic flux is quantized: = h/2e, Josephson’s const; and the mechanical and magnetic moments are proportional).Thus, the phenomenon can be interpreted as gravity/inertial induction. 5(a).The basic formula QG of the quantum expression of the Newtonian gravitational potential is: ф(G)=-Ф(i)w, where w is the frequency of the quanta of the gravitational (~ vibrational) field. (b).“Giving the interval ds the size of time, we will denote it by dт: in this case, the constant k will have the dimension length divided by mass and in CGS units will be equal to 1,87*10^-27", Friedmann, (On the curvature of space, 1922). [The ds, which is assumed to have the dimension of time, we denote by dт; then the constant k has the dimension Length Mass and in CGS-units is equal to 1, 87.10^ ± 27. See Laue, Die Relativitatstheorie, Bd. II, S. 185. Braunschweig 1921.] (c.)Apparently, the following expression takes place: μ(0)ε(0)Gi=1, which means that Gi=с^2 where i is inertial constant, i=1,346*10^28[g/cm]; or k°=1/i=7,429*10^-29[cm/g]: (d.)k(Friedmann)/k°=8π; where k°=r(pl)/m(pl)=r(G)/2m(0); i=m(pl)/r(pl)=(1/c)m(pl)w(pl), (e.)w=[r(G)/r]w(pl). That is ф(G)=-[Gm(pl)/2c]w=-(½)[w/w(pl)]c^2=-(½)(√Għ/c)w=-Ф(i)w.* 6. And а*=-2πcа/M(universe), what is F=M(universe)а*=-2πса=-с^4/8G=-(⅛)F(pl). I(G)=M(universe)H=m(pl)w(pl)/8π=c^3/8πG=-2a (~ the "dark" const~inv), where M(universe)=E/c^2 is the full mass of the Universe, and the total energy E is spent on creating a phase-quantized space-time: m(pl)w(pl)=8πM(Universe)H { w(relic)^2=πw(pl)H. 7.That is: Δφ=-pc^3/4a= рс^3/2M(universe)H^2. And Δφ=4π[с^3/Gm(pl)w(pl)]H^2= 4πH^2; which is evidence of a phenomenon: spontaneous Lorentz transformations. 8.Thus; Δφ(0)/Δφ=w(pl)^2/H^2~10^126, where Δφ(0)=4πw(pl)^2; the best prediction. ---------------- *) - So, ф(G)=-[w/w(pl)]c^2/2, where ф(G) - is Newtonian gravitational potential, r(n')=nλ/π=(n+n')2r(pl)l , the corresponding orbital radius, w - the frequency of the quanta of the gravitational field (space-time); - obviously, the quanta of the field are themselves quantized: λ=(1+n'/n)λ(pl) = 2πc/w, where n'/n=M/2∆m: system gravity unpacking ratio, n'- the orbit number (n'=0,1,2,3…). 1.Obviously, on the horizon {r=r[r(G)]}, n'=0] the "door" is closed, however, the quanta [λ=λ(pl)] can go out singly and form the first and all subsequent half-orbits (n'=1,2, 3 ...) during the time t(0)=r/c=2nт, where т=1/w, т=((1+n'/n)т(pl), spending part of their energy on it each time. And it is this mechanism that provides the step-by-step formation of a variable gravitational field: variably accelerated expansion of spacetime as a phase space: |a|=g=πc^2/L, where L[=πr^2/r(G)] is the length of the phase trajectory (of course, the quanta coming through the "window" are also rhythmically restored: from the source- protouniverse). 2.Moreover, the parameter r(0)=r(G)-r(pl)=(2n-1)r(pl), defining the interval of the formation of the system, at n=0, when r=r(G)=0 (for example, the state of the "universe" before the Big Bang) turns out to be a quite definite quantity: r(0)=-r(pl). In the area [(-rpl) - 0 - (+rpl)] there is an implementation of external forces, "distance": (-rpl)+(+rpl)=0 (≠2rpl). 3.The phase velocity of evolution v'/π= r(pl)w/π; m(0)=(c/2G)rv', where v'=v^2/c. The angular momentum: L(p)=|pr|=n^2ћ [const for all orbits of the system; at n=1: L(p)=ћ] and moment of power: M(F)=dL(p)/dt(0)=nћw/2=-E(G)=E*, where t(0)=r/c, E*- energy of self-action. 4.The gravitational field is characterized by a spontaneous flow: J*=(v'/π )(1/4π) g^2/G, where v'/π- phase velocity of field evolution. 5.Entropy (here: a measure of diversity/variety, not ugliness/disorder) of the system: S=πε(pl)r(t)=(n+n')k, where k is the Boltzmann constant. Obviously, on the horizon entropy=min and with fundamental irreversibility, information is preserved (+ evolves, accumulates). 6.Accordingly, m=m(pl)/(1+n'/n), where m=ħw/c^2, is the quantum of the full mass: M=n'm [