and

## Pions in the PlanckMass

`                     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`

## How Many Particles are in our Universe?

• the time Tdecoh = 10^(-34 sec)
• the number of qubits is Ndecoh = 10^19 = 2^64

Each qubit at the end of inflation corresponds to a PlanckMass Black Hole, which in theD4-D5-E6-E7 physics model undergoes decoherence and,

in a process corresponding to Reheating in the StandardInflationary Model,

The resulting 2^64 x 2^64 = 2^128 = 10^19 x 10^19 = 10^38 fermionpairs populating the Universe Immediately After Inflation constitutesa 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 quantumregister grows with time. ... Attime Tn = (n+1) Tplanck the quantum gravity register will consist of(n+1)^2 qubits. [ Let N = (n+1)^2 ] ...", we have the numberof qubits at Reheating:

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

Since each qubit at Reheating should correspond, not to PlanckMass Black Holes, but to fermionparticle-antiparticle pairs that average about 0.66 GeV, we havethe result that

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

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

the 10^77 nucleon BaryonicMass of our Universe has been mostly constant sinceReheating,

and will continue to be mostly constant until ProtonDecay.

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

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

### Uncertainty and Quantum Fluctuations:

According to section 4.3 of The Anthropic Cosmological Principleby Barrow and Tipler (Oxford 1988), Eddington (andothers including Haas, Hayakawa, Tanaka, Hokkyo) related R /sqrt(N) to the quantum uncertainty of position of the particles ofwhich 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:

• hbar = 10^(-27)gm cm^2 / sec
• c = 3 x 10^10 cm / sec

• tplanck = 5 x 10^(-44) sec (big bang)
• R(tplanck) = 10^(-33) cm
• Nplanckons(tplanck) = 1
• sqrt(Nplanckons(tplanck)) = 1
• R(tplanck) / sqrt(Nplanck)) = 10^(-33) cm = Planck length,
• Muncertainty(tnow) = (1/3) x 10^(-27-10+33) = 10^(-5) gm = Mplanck

• t = 10^13 sec = 3 x 10^5 years (recombination forming hydrogen atoms)
• R(t) = 3 x 10^23 cm
• Nproton = 10^77
• sqrt(Nproton) =3x10^38
• R(t) / sqrt(N(t)) = 10^(-15) cm
• Muncertainty(t) = (1/3) x 10^(-27-10+15) = 10^(-23) gm = 10 GeV

• t = 3 x 10^15 sec = 10^8 years (just before galaxies form)
• R(t) = 10^26 cm
• Nproton = 10^77
• sqrt(Nproton) = 3x10^38
• R(tproton) / sqrt(Nproton(tproton)) = 10^(-13) cm
• Muncertainty(tproton) = (1/3) x 10^(-27-10+13) = (1/3) x 10^(-24) gm = (1/3) x 10^(-19) Mplanck = (1/3) GeV = Mquark = (1/3) Mproton

• tnow = 3 x 10^17 sec = 10^10 years (present)
• R(tnow) = 10^28 cm
• Nproton = 10^77
• sqrt(Nproton) = 3x10^38
• R(tnow) / sqrt(Nproton) = (1/3) x 10^(-10) cm
• Muncertainty(tnow) = 10^(-27-10+10) = 10^(-27) gm = 10^(-22) Mplanck = 10^(-3) GeV = 1 MeV = Melectron/positron

• t = 3 x 10^21 sec = 10^14 years (last red dwarf stars die)
• R(t) = 10^32 cm
• Nproton = 10^77
• sqrt(Nproton) = 3x10^38
• R(t) / sqrt(Nproton)) = (1/3) x 10^(-6) cm
• Muncertainty(telectron) = 10^(-27-10+6) = 10^(-31) gm =10^(-26) Mplanck = 100 eV

• t = 3 x 10^27 sec = 10^20 years (stars have left galaxies)
• R(t) = 10^38 cm
• Nproton = 10^77
• sqrt(Nproton) = 3x10^38
• R(t) / sqrt(Nproton) = (1/3) x 10 cm
• Muncertainty(t) = 10^(-27-10-1) = 10^(-38) gm = 10^(-33) Mplanck = 10^(-14) GeV = 10^(-5) eV

As the characteristic uncertainty mass Muncertainty(t)decreases, and the Universe expands and becomes more dilute, itbecomes more likely that a QuantumFluctuation 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 andthe 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 Gravitonsto create a new bit of SpaceTime

or, from the point of view of

hbar = Mplanck^2 G / c

### the Geometric part ofthe Gravitational Force Strength

since

the Gravitational Force StrengthG is suppressed by 1 Mplanck^2

and

1 / c is a conversionfactor to represent Time of SpaceTime as time units whenconverted from spatial units of the Space of SpaceTime (the new bitof SpaceTime having all 4 dimensions of SpaceTime in spatial units -for example the new bit of SpaceTime being initially in cm^4, the 1/cconverts 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 carswhen he stopped in his tracks while crossing a street in Princeton,because George Gamow had just told Einstein about the idea ofceating the Universe from Nothing, which hadbeen just then (in the 1940s) been thought of by Pascual Jordan. Seethe autobiography My World Line of George Gamow.