A Conditional Baryon-Clock Closure for the 15.4/13.8 Gyr Readout

Reference: 10.5281/zenodo.17527179

Standard cosmology tells us the Universe is about 13.8 billion years old. In Quantum Traction Theory (QTT), there is a deeper absolute time, and in that clock the age comes out closer to 15.4 billion years.

This note evaluates a conditional closure: observed expansion and baryon inputs are passed through the stated QTT clock and creation-ledger relations, and the resulting 15.4/13.8 Gyr readout is audited. Because those cosmological quantities are upstream observations, the exercise is an anchored inverse/consistency calculation rather than a source-only prediction of the Universe's age.

1. The Observed Baryon Density Today

We begin with two pieces of observational input:

1. The present-day Hubble rate (from e.g. Planck CMB data).
2. The present baryon density parameter .

1.1. Critical density and baryon fraction

The critical density today is

Equation

ρ_c,0 = (3H_0²)/(8π G).

Take (Planck-like values for definiteness):

• ,
• (about 4.9% of the critical density).

Convert to SI units. One megaparsec is , so

Equation

H_0 = 67.4 (km)/(s Mpc) = 67.4 (10³ m)/(s) · (1)/(3.0857× 10²² m) ≈ 2.19× 10⁻¹⁸ s⁻¹.

Now square it:

Equation

H_0² ≈ (2.19× 10⁻¹⁸)² ≈ 4.80× 10⁻³⁶ s⁻².

Newton’s constant is . Compute :

Equation

8π ≈ 25.133, 8π G ≈ 25.133× 6.6743× 10⁻¹¹ ≈ 1.678× 10⁻⁹ m³kg⁻¹s⁻².

Then

Equation

ρ_c,0 = (3H_0²)/(8π G) ≈ (1.44× 10⁻³⁵)/(1.678× 10⁻⁹) ≈ 8.6× 10⁻²⁷ kg m⁻³.

This is the familiar critical density. Now the baryon density is simply

Equation

ρ_b,0 = Ω_b ρ_c,0 ≈ 0.049× 8.6× 10⁻²⁷ ≈ 4.2× 10⁻²⁸ kg m⁻³.

Cross-check: this corresponds to roughly 0.25 protons per cubic metre (since and ). Good.

We will now take

as our single observational input about “how many baryons per cubic metre” the Universe has today.

2. The QTT White Void Ledger: How Baryons Create Space

Quantum Traction Theory adds a microscopic law of creation: each Planck bundle of baryons seeds a fixed number of White Voids, and each White Void mints a fixed quantum of space per Planck tick.

2.1. From Planck bundles to White Voids

In the QTT ledger:

• Each Planck mass of baryons seeds exactly 24 White Voids over cosmic history.
• Each White Void (WV), once born, produces one space quantum every Planck tick .
• Each space quantum has volume , with the Planck length.

If the domain has baryon mass , then the number of Planck bundles is

Equation

N_bundles = (M_b)/(m_P),

and as QTT counts through all the WV births and SQ ticks, one finds that the total 3-volume minted by baryons by absolute time T is

Equation

V_WV^(b)(T) ≃ 48π G M_b T².

This is a QTT result: the comes from counting ticks, and the coefficient comes from identifying the creation units with Planck geometry and using .

2.2. Baryon density as a function of absolute time

From that volume, the baryon density at absolute age T is simply mass over volume:

Equation

ρ_b(T) = (M_b)/(V_WV^(b)(T)) = (M_b)/(48π G M_b T²) = (1)/(48π G T²).

QTT baryon density law:

Notice something crucial: the baryon mass cancels out. Once you accept the WV ledger, the relation between baryon density and absolute age is completely independent of how big a chunk of the Universe you choose. It’s a pure law of the form with a fixed prefactor.

3. Equating QTT and Observations: Solve for the Absolute Age

We now impose that the QTT baryon density at “today” equals the observed baryon density:

Equation

ρ_b(T_0) = ρ_b,0.

Using the QTT law,

Equation

(1)/(48π G T_0²) = ρ_b,0.

Solve this for the absolute age :

Equation

T_0² = (1)/(48π Gρ_b,0), T_0 = 1/√(48π Gρ_b,0).

3.1. Plug in the numbers

We already have:

• ,
• ,
• 

First compute :

Equation

Gρ_b,0 ≈ (6.6743× 10⁻¹¹)×(4.2× 10⁻²⁸) = 6.6743× 4.2× 10⁻³⁹.

Multiply the mantissas:

• 6.6743× 4 ≈ 26.6972,
• 0.2× 6.6743 ≈ 1.3349,
• sum ≈ 28.032.

So

Equation

Gρ_b,0 ≈ 2.803× 10⁻³⁸ s⁻².

Now multiply by :

Equation

48π Gρ_b,0 ≈ 150.80× 2.803× 10⁻³⁸.

Compute the mantissa:

• 150.8× 2.8 ≈ 422.2,
• 150.8× 0.003 ≈ 0.45,
• total ≈ 422.7.

Thus

Equation

48π Gρ_b,0 ≈ 4.23× 10²× 10⁻³⁸ = 4.23× 10⁻³⁶ s⁻².

Therefore

Equation

T_0² ≈ (1)/(4.23× 10⁻³⁶) s² = (1)/(4.23)× 10³⁶ s².

Since ,

Equation

T_0² ≈ 2.364× 10³⁵ s².

Take the square root:

• (because and ),
• √(10³⁵) = 10¹⁷.5 = 10¹⁷sqrt(10) ≈ 3.1623× 10¹⁷.

So

Equation

T_0 ≈ 1.538× 3.1623× 10¹⁷ s ≈ 4.86× 10¹⁷ s.

3.2. Convert seconds to billions of years

Convert to years using :

Equation

T_0 (yr) ≈ (4.86× 10¹⁷)/(3.15576× 10⁷) ≈ 1.54× 10¹⁰ yr.

Divide by to get gigayears:

We have just derived an absolute age of about 15.4 billion years directly from

• the observed baryon density ,
• Newton’s constant G,
• and the QTT WV microcreation law .

No dark energy term, no arbitrary cosmological constant, and no free “time drift” parameter entered this derivation.

4. Coasting Gauge Check: The Absolute Hubble Rate

QTT’s coasting gauge says the absolute Hubble rate is simply

Equation

H_tau(T) = (1)/(T).

So at ,

Equation

H_tau 0 = (1)/(T_0) ≈ 2.06× 10⁻¹⁸ s⁻¹.

Convert this to the usual km s Mpc:

• 1 Mpc ,
• and 1 km = 1000 m.

Thus

Equation

H_tau 0 ≈ 2.06× 10⁻¹⁸ s⁻¹ × 3.0857× 10²² (m)/(Mpc) × (1 km)/(10³ m).

Combine the powers of ten:

Equation

2.06× 3.0857 ≈ 6.36, 10⁻¹⁸× 10²²× 10⁻³ = 10¹.

So

H_tau 0 ≈ 6.36× 10¹ km s⁻¹Mpc⁻¹ ≈ 63.6 km s⁻¹Mpc⁻¹.

This matches the QTT “ledger values”:

• ,
• .

5. Where Does the 13.8 Gyr Lab Age Enter?

The derivation above never used the familiar 13.8 Gyr. That number appears when we project absolute time onto our tilted laboratory time axis.

QTT says our lab time axis is not aligned with absolute time. There is:

• a fixed Time Tilt from an eightfold symmetry in the time plane, , giving a baseline factor I_clk = cos((π)/(8)) ≈ 0.92388, (1)/(I_clk) ≈ 1.0824 i.e. roughly an 8.2 % age boost;
• and a small extra Time Drift from creation that adds a few degrees more tilt.

If is the age you infer assuming a single lab clock with no tilt/drift, while is the QTT absolute age, then

Equation

tau_0 = (t_0)/(cos(θ_star + δ_rm eff)).

We already saw that:

• tilt alone (no drift) would give tau_0^(star) = (t_0)/(cos((π)/(8))) ≈ 1.0824 t_0;
• with the drift we just implicitly used, you need (tau_0)/(tau_0^(star)) = (cosθ_star)/(cos(θ_star+δ_rm eff)) ≈ 1.03 to go from Gyr to Gyr.

That extra 3 % corresponds to a small drift angle rad (about ) in the time plane.

What we have shown here is the hard part: starting from the observed baryon density alone, the QTT White Void law fixes the absolute age at about 15.4 Gyr and, via coasting, the absolute Hubble scale. The 13.8 Gyr then appears as a projection effect of that absolute history onto our slightly tilted and drifted lab clocks.

6. Summary: Baryons, WVs, and a 15.4-Gyr Universe

• Observed baryon density today: .
• QTT White Void creation law: .
• Equating them and solving for T gives: .
• In coasting gauge, .
• The familiar 13.8 Gyr lab age is a tilted, slightly drifted projection of this 15.4 Gyr absolute history onto our local clocks.

In other words, the Universe tells you how old it is in absolute time just by how many baryons it has per cubic metre – once you include the QTT White Void creation ledger.