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Large Numbers:

Particles in the Universe

and

Pions in the Planck Mass


                     0 Tao, Simplex Physics
    1 bit
                   2 superposition qbit
          4 spacetime
                     16 fermions Ilm-al-Raml
          256 Cl(8) IFA
            65,536 Torah Genes
           2^32 ~ 4 x 10^9 Genome Base Pairs
                2^64 ~ 16 x 10^18 Brain Electrons Planck
                       2^128 ~ 256 x 10^36 Brain GraviPhotons Uncertainty
              2^256 ~ 65,536 x 10^72 Particles in Universe

Uncertainty and Quantum Fluctuations

What is hbar ?

How Many Particles are in our Universe?

At the end of inflation:

Each qubit at the end of inflation corresponds to a Planck Mass Black Hole, which in the D4-D5-E6-E7 physics model undergoes decoherence and,

in a process corresponding to Reheating in the Standard Inflationary Model,

each qubit transforms into 2^64 = 10^19 elementary first-generation fermion particle-antiparticle pairs.  

The resulting 2^64 x 2^64 = 2^128 = 10^19 x 10^19 = 10^38 fermion pairs populating the Universe Immediately After Inflation constitutes a Zizzi Quantum Register of order n_reh = 10^38 = 2^128.

Since, as Paola Zizzi says in gr-qc/0007006, ( with some editing by me denoted by [ ] ): "... the quantum register grows with time. ... At time Tn = (n+1) Tplanck the quantum gravity register will consist of (n+1)^2 qubits. [ Let N = (n+1)^2 ] ...", we have the number of qubits at Reheating:

Nreh = ( n_reh )^2 = ( 2^128 )^2 = 2^256 = 10^77

Since each qubit at Reheating should correspond, not to Planck Mass Black Holes, but to fermion particle-antiparticle pairs that average about 0.66 GeV, we have the result that

the number of particles in our Universe at Reheating is about 10^77 nucleons.

After Reheating, our Universe enters the Radiation-Dominated Era, and, since there is no continuous creation, particle production stops, so

the 10^77 nucleon Baryonic Mass of our Universe has been mostly constant since Reheating,

and will continue to be mostly constant until Proton Decay.

 

The present scale of our Universe is about R(tnow) = 10^28 cm, so that its volume is now about 10^84 cm^3, and its baryon density is now about 10^77 protons / 10^84 cm^3 = 10^(-7) protons/cm^3 = 10^(-7-19-5) gm / cm^3 = 10^(-31) gm / cm^3 = roughly the baryonic mass density of our Universe.

Since the critical density of our Universe is about 10^(-29) gm / cm^3, it is likely that the excess of the critical mass of our Universe over its baryonic mass is due to a cosmological constant.

 

Uncertainty and Quantum Fluctuations:

According to section 4.3 of The Anthropic Cosmological Principle by Barrow and Tipler (Oxford 1988), Eddington (and others including Haas, Hayakawa, Tanaka, Hokkyo) related R / sqrt(N) to the quantum uncertainty of position of the particles of which the Universe is composed.

Eddington is quoted as saying "Since most of the particles in the Universe interact very infrequently they may be represented by plane waves with a uniform probability distribution. If their positions are random, each with positional uncertainty R then, by the law of large numbers, the controid of this distribution also possesses a postional uncertainty delta_x, where
delta_x = R / sqrt(N).

Barrow and Tipler go on to say: If we enploy the Uncertainty Principle of Heisenber, a mass scale m0 can be associated with this uncertainty,

m0 = h sqrt(N) / R c.

 

For various ages t of the Universe:

 

 

 

 

 

 

 

As the characteristic uncertainty mass Muncertainty(t) decreases, and the Universe expands and becomes more dilute, it becomes more likely that a Quantum Fluctuation will become a New Universe.

 

 

Physically, what is hbar?

Mplanck = (hbar c / G )^(1/2)

tplanck = (hbar G / c^5)^(1/2) = Mplanck G / c^3

hbar is the uncertainty product of the Planck Energy and the Planck Time:

hbar = Mplanck^2 G / c = c^2 Mplanck^2 G / c^3 =

= ( c^2 Mplanck ) ( Mplanck^2 G / c^3 ) =

= Eplanck tplanck

hbar is the uncertainty probability for Gravitons to create a new bit of SpaceTime

or, from the point of view of

hbar = Mplanck^2 G / c

the Geometric part of the Gravitational Force Strength

since

the Gravitational Force Strength G is suppressed by 1 Mplanck^2

and

1 / c is a conversion factor to represent Time of SpaceTime as time units when converted from spatial units of the Space of SpaceTime (the new bit of SpaceTime having all 4 dimensions of SpaceTime in spatial units - for example the new bit of SpaceTime being initially in cm^4, the 1/c converts to cm^3sec).

 

 

 

References:

Gravitation, by Misner, Thorne, andWheeler (Freeman 1973).

John Gribbin, in his book In Search of the Big Bang (Bantam 1986, page 374), says that Einstein was almost run down by several cars when he stopped in his tracks while crossing a street in Princeton, because George Gamow had just told Einstein about the idea of ceating the Universe from Nothing, which had been just then (in the 1940s) been thought of by Pascual Jordan. See the autobiography My World Line of George Gamow.

 

 

 

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