From the Planck Universe to Einstein, Schwarzschild and the Universe now – A. Zichichi – PAS, October 2014
Evolving Concepts of Nature
PAS Plenary Session 25 – 28 October 2014
From the Planck Universe to Einstein, Schwarzschild
and the Universe now
Antonino Zichichi
INFN and University of Bologna, Italy
CERN, Geneva, Switzerland
Enrico Fermi Centre, Rome, Italy
Pontifical Academy of Sciences, Vatican City
World Federation of Scientists, Beijing, Geneva, Moscow, New York
The President of our Academy, Professor Arber, asked me when the Third Big Bang happened. During our open Discussion Sessions and private interactions many interesting questions concerning the correlation between the Subnuclear Universe and the Universe which consists of Stars and Galaxies have been posed.
On many occasions, during the activities of the International School of Cosmology and Gravitation, I have been discussing with friends and colleagues (including John Wheeler [1], Nathan Rosen [2] and Peter Bergmann [3]) how it happens that no one has been able so far to derive two basic values of our Universe:
j the number of protons, neutrons and electrons, N(p n e), which our Universe is made of, i.e.
j N(p n e) ≃ 1080 ;
and k the volume of our Universe, V(U), which is empty, i.e.
k VU≃ 98% .
Despite the enormous work devoted to understand the physics of Black–Holes [4] including the study of Quantum Gravity [5] and the Relativistic Quantum String Theory (RQST) [6] with the interesting discovery of the “Landscape”[7], no one has been able to get the values of the two quantities (1) and (2). The values of these two quantities can be obtained using the Schwarzschild solution [8] of Einstein equation in the Planck Universe [9]. The result is that the world we are coming from is the Planck Black–Hole and the knowledge of our world today gives the correct values for N(p n e) and the Universe vacuum [10].
The origin of this intellectual venture is very interesting.
In his universal outlook of the world – independent of our restricted environment – Planck in 1899 wanted that the fundamental units of Mass, Length and Time should be derived [9] from the values of the Fundamental Constants ofNature: c (the speed of light), h (the Planck Constant) and GN (the Newton Gravitational coupling).
These quantities had a special meaning for Planck [9]: «These quantities retain their natural significance as long as the Law of Gravitation and that of the propagation of light in a vacuum and the two principles of thermodynamics remain valid; they therefore must be found always to be the same, when measured by the most widely differing intelligence according to the most widely differing methods». It is remarkable the way Planck considered these quantities: «In the new system of measurement each of the four preceding constants of Nature (G, h, c, k) has the value one». Planck included the Boltzmann’s constant k which converts the units of Energy into units of Temperature. This allowed Planck to have a fundamental value also for the Temperature, 3.5 ´ 1032 Kelvin. This is the meaning of measuring Lengths, Times, Masses and Temperatures in Planck’s units, given in Table 1.
For all quantities we use the order of magnitudes since we do not need high precision for our qualitative approach to try giving an answer [10] to this very difficult problem.
The Planck Universe units are
for Lenght ≅ 10-33 cm
for Mass ≅ 10-5 gr
for Time ≅ 10-44 sec
The World
we come from is
the Planck Black–Hole (PBH)
the PBH Density is
1093 × gr/cm3
Table 1
When Planck was expressing his ideas on the meaning of his fundamental natural units there was neither the Big–Bang nor the Einstein equation which describes the correlation between Mass-Energy and the curvature of Space–Time in the Universe. And no one knew that the Einstein equation had a solution, discovered by Schwarzschild [8], which describes the gravitational field of a massive point particle. John Wheeler in 1967 gave to this solution the name of “Black–Hole”, the reason being that it corresponds to such a density of matter that even the light cannot escape the gravitational attraction. Schwarzschild formula establishes the correlation between the Radius of a Black–Hole, RBH, and its Mass, MBH:
RBH= 2G MBHc2 ≅1.5 ∙10-28∙cm ∙ gr-1∙ MBH . (1)
The Black–Hole Radius increases with its Mass, as shown in Figure 7. The Schwarzschild formula remains as it is despite all developments [4] in the physics of Black–Holes including what has been discovered by RQST.
The remarkable fact is however that if we look at the point where the Radius is that of theworld where we leave (about 1029 cm) the Mass turns out to be
mU ≃ 1056 grams,
which is the Mass of our Universe.
Let us now assume that MBH, is not concentrated in a point, as in the Schwarzschild solution of the Einstein equation, but distributed inside the volume defined by the sphere of the Black–Hole-Horizon [11].
We assume that the Black–Hole-Horizon [11] is the surface of a sphere where MBH is distributed.
Since the density is given by the Mass over the volume
ρBH= MBHVBH ,
the result – following the Schwarzschild equation (1) – is that the Black–Hole density decreases with the square of the Black–Hole Mass
with
K = 2Gc2 ≅ 1.5 ∙ 10-28 ∙ cm ∙ gr-1 .
Figure 7
We neglect details like [(4/3) p] in front of RBH to have the Black–Hole volume. In Figure 8 the density of our Universe, ρU, and the Planck density, ρPlanck , are given as function of the Radius of all possible horizons produced by all possible Masses allowed by the Schwarzschild solution of the Einstein equation.
It is interesting to see (Figure 8) the different values of densities which can go from the minimum, ρUniverse , to the maximum, ρPlanck.
The density which has attracted the interest of John Michell in 1783 and independently of Pierre-Simon de Laplace in 1796 is the “atomic” density (Figure 8). It was necessary more than a century for the “nuclear” density to come in the game and attract in 1939 the interest of Robert Oppenheimer, George Volkoff, Hartland Snyder and Fritz Zwicky (Figure 8).
We have shown that it is possible to provide an answer to the question why N(p n e) ≃ 1080 and VU≃ 98% based on the three Fundamental Constants of Nature [9] and the Schwarzschild solution [8] of the Einstein equation. This means that our Universe has its quantitative basis in the Planck Universe [9] and its evolution must follow the conditions dictated by the Schwarzschild equation.
Let us go back to the Subnuclear Physics Universe. Here we could find the reason for the existence of two types of Black–Holes. Figure 9 shows the problem – mentioned in the Opening Lecture – called the GAP, between the Energy level EGUT where the three couplings (α3 α2 α1) of the three gauge Forces converge
EGUT ≃ 1016 GeV
and the Planck Energy level,
EPlanck ≃ 1019 GeV.
The String Unification Energy, ESU , is the energy where the RQST (Relativistic Quantum String Theory) puts the origin of all Forces.
Figure 8: The Figure shows the relation which exists between the value of the Black–Hole Radius (RBH) and the corresponding density (rBH), from the Planck scale to the Universe scale now.
Figure 9
This Energy GAP could tell us that, during this time interval, the Universe was governed only by the Gravitational Forces. The Masses produced are Primordial Black–Holes which act as seeds for the formation of Galaxies. At present all Galaxies have at their center a Black–Hole whose Mass is never higher than a fraction of percent of the total Galaxy Mass.
At the Planck Instant (Δt ≃ 10-44 sec) all started with the Planck Mass given in the previous Table 1, i.e.
MPlanck ≃ 10-5 gr ;
the correspondent Radius of the Planck Black–Hole being
RBHPlanck ≅ 10-33 cm.
Following the Schwarzschild equation, the Planck Black–Hole Radius increases with its Mass value, as shown in Figure 7.
The remarkable fact is that the Radius of the world we leave in is (1029 cm) and its density (Figure 8) satisfies the same relation of the world we come from, whose Radius was 10-33 cm and its density
ρPlanck ≅ 1093 gr × cm-3.
It turns out that the Planck Black–Hole density and Radius satisfy the conditions exactly as the present day density of the Universe and its Radius satisfy the Black–Hole conditions: our Universe has the characteristic as if we come from a Black–Hole and we are still in a Black–Hole [10].
It cannot be a casual coincidence the fact that in the Planck Universe theSchwarzschild equation (1) gives the correct value for the Mass (Figure 7) (N(p n e)≃ 1080) and the density of the Universe (Figure 8) when its Radius increases by 62 powers of ten. The structure of our Universe has the Galaxies concentrated along lines and planes immersed in very large amount of empty spaces. The first of these empty spaces was discovered in 1981 in the Boöte Constellation. It is estimated that about 98% of the Universe volume is empty. The reason why these empty spaces must exist at the 98% level is in the Schwarzschild equation (1) which establishes that the density of the Universe must decrease with the square of its Mass.
The Universe where we are seems to be the proof that a Black–Hole can expand its Radius by something like 62 orders of magnitudes going from 10-33 cm up to 1029 cm. The basic quantity in this expansion being the density, which seems to follow the conditions dictated by the Schwarzschild solution [8] of the Einstein equation.
What is needed is an equation which describes the evolution of the Radius and the evolution of Mass of the Universe as a function of Time. This equation we have not been able to find, so far.
All we know is that the evolution of the Universe must obey the Schwarzschild equation as shown in Figures 7 and 8.
Now the problem arises: are Black–Holes phenomena scale-invariant? If Black–Hole properties are scale invariant, and, if it is correct that inside a Small Black–Hole the laws of physics we know should lose their validity, Small and Big Black–Holes should be such that in their inner structure the law of physics known to us should no longer be valid.
But, in our Black–Hole we study all laws of physics which go from the Standard Model to the extrapolation called Beyond Standard Model (BSM).
The laws of Physics we know remain valid well inside a Black–Hole, provided that this Black–Hole is as large as our Universe.
This finding could be related with the properties theoretically mentioned by Gerardus 't Hooft [5]. He says on page 77: «If the original amount of material was big enough, the contraction will proceed, and, in the limit of zero pressure and purely radial, spherically symmetric motion, the equations can easily be solved exactly. We obtain flat Space-Time inside, and a pure Schwarzschild metric outside. As the ball contracts, a moment will arrive when the Schwarzschild Horizon appears. From that moment on, an outside observer will no-longer detect any radiation from the shell, but a Black–Hole instead». All we need is to apply Time-reversal invariance to the't Hooft Black–Hole [5]. Our Universe seems to be like a Black–Hole which, only asymptotically, could reach the Schwarzschild Horizon.
Suppose we were able to find – from basic principles – the function which describes the Universe, ψUniverse , having as basic quantities the Radius R and the MassM. This function must evolve in Time
∂ψU (R, M)∂t
in such a way that the correlation between Radius and Mass of the Universe obeys the Schwarzschild equation (1) already quoted:
RUt≅1.5 × 10-28 ∙cm ∙ gr-1 ∙MU(t) .
The evolution of ψUniverse must describe the change of density of the Universe, from
ρUniverse t=0 ≅ 1093 ∙gr ∙ cm-3
down to
ρUniverse now ≅ 5 × 10-30 ∙gr ∙ cm-3
i.e. along a change of density by 123 powers of ten as illustrated in Figure 8.
It should be pointed out that the Einstein equation establishes a correlation between Mass-Energy and the curvature of Space-Time: high curvature corresponds to high values for the Mass-Energy. Since high curvature corresponds to small Radius, the Mass-Energy goes like 1/R. On the other handin the Schwarzschild equation (1) the Mass MBH increases with the RadiusRBH.
The equation (1) is only one line (R º M) in the plain defined by Einstein equation which gives the Mass-Energy versus the Radius.
What is needed is the function
ψUniverse
which evolves with Time along the line (R = M) given by the Schwarzschild condition (1).
The Einstein equation and the Schwarzschild solution ignore the existence of the Fundamental Forces SU(3) × SU(2) × U(1) which came from our discovery of the Subnuclear Universe. The convergence of the three couplings α3 α2 α1 at EGUT is at least two orders of magnitudes below ESU. In this Energy GAP the primordial Black–Holes are produced, which are the seeds of allGalaxies. The other Black–Holes, produced in the Universe long time afterthe first Big Bang, have in their inner structure protons, neutrons and electrons.
If we could see the inner structure of these Black–Holes we would find that, the matter they are made with, is the one familiar to us, i.e. the matter made with (p, n, e). The primordial Black–Holes, as said before, are made with matter whose charge is only the gravitational charge.
Conclusion.
All we could at present say on the correlation between the Subnuclear Universe and the one with Stars and Galaxies is therefore to explain why: N(p n e)≃1080 and VU≃98% ; and to predict the existence of two types of Black–Holes: Primordial Black–Holes where matter has only thegravitational charge and Standard Black–Holes where matter is made withp, n, e.
Appendix 1
Time, Energy and Phase Transition
t(sec) E(GeV) Phase Transition
10-44 1018 Planck epoch º Quantum Gravity º Supergravity Superstring
10-35 1516 GUT
10-10 102 Weak Symmetry Breaking º Fermi epoch
10-5 10-1 Confinement Transition
1-102 10-3-10-2 Nucleo-Synthesis
1012 10-9 Recombination/Galaxy Formation
1017 10-13 Today
1