In modern physics, there exists a famous paradox often referred to as "the worst prediction in the history of science." It is known as the "Cosmological Constant Problem."
When calculating the vacuum energy density using quantum mechanics (Quantum Field Theory), the result is \(10^{122}\) times larger (a 1 followed by 122 zeros) than the actual observed value of the universe. This astronomical, utterly hopeless discrepancy in calculation has plagued the world's greatest physicists for decades.
However, the Intergeometric Theory has proven that this problem is not due to missing physical laws, but is simply "a forgotten calculation of geometric spatial dilution (a scale illusion)."
Let's look at the conclusion first. Below is a comparison between the equation of conventional physics and the equation derived by this theory.
[ Prediction of Conventional Physics (Quantum Field Theory) ]
Calculation based on the Planck mass (\(M_P\)) and Planck length (\(l_P\)):
\[\rho_P\sim\frac{M_P}{l_P^3}\sim10^{96}\text{ kg/m}^3\]
(Off by 122 orders of magnitude from the actual observation)
[ Prediction of the Intergeometric Theory ]
Calculation based on the Higgs mass (\(M_H\)) and Higgs length (\(l_H\)), accounting for spatial hierarchization—length expansion (\(Wl_H\)) and degrees of freedom (81):
\[\rho_{\Lambda s}=\left(\frac{2}{81}\right)\frac{M_H}{\frac{4\pi}{3}\left(Wl_H^3\right)}=5.73\times10^{-27}\text{ kg/m}^3\]
(Perfectly matches the latest Cosmic Microwave Background observations within the margin of error)
Why does the equation of this theory hit the observational facts with such terrifying precision?
The secret lies in reconsidering the "true standard scale" of the universe, the number 81 included in the equation, and an unknown parameter W (the Hierarchy Constant).
1. We Had the "True Standard Size" of the Universe Wrong
he first reason conventional physics was wrong by 122 orders of magnitude lies in a misunderstanding of the "fundamental unit of the universe."
Physicists used the "Planck scale"—the ultimate microscopic scale involving gravity—as the baseline for their calculations. The Planck mass (\(M_P\)) is about \(10^{19}\) GeV, and the Planck length (\(l_P\)) is an unimaginably small \(10^{-35}\) m.
However, the true natural unit of the universe, derived from the first principles of this theory, is the "Higgs scale," which gives mass to elementary particles. The Higgs mass (\(M_H\)) is about 125 GeV, and the Higgs length (\(l_H\)) is about \(10^{-18}\) m.
Look at the logarithmic ruler below.
The Planck scale was nothing more than a "shadow of a higher-order hierarchy," far removed from the true baseline of this universe (the Higgs scale).
2. Space Differentiates into "81" Blocks
So, what exactly is the 81 in the equation?
It is the "number of information (geometric states)" created when space self-replicated during inflation (the rapid expansion of the universe).
Imagine the process of space hierarchizing (inflating). When a reference block of space replicates itself, to maintain symmetry, it must add copies equally to "both sides," not just one. As this "addition to both sides" repeats, the division ratio of space approaches not the Golden Ratio, but the Silver Ratio, which possesses more perfect symmetry. (We will explain why the universe chose the Silver Ratio over the Golden Ratio and its geometric beauty in [another article].)
As a result, one dimension (e.g., the X-axis) inevitably differentiates into three independent geometric states (blocks): "the original self" and "the additions on both sides."
Our universe is a 4-dimensional spacetime consisting of 3 spatial dimensions (X, Y, Z) and 1 time dimension (T).
Since each dimension differentiates into 3, the maximum capacity of information (degrees of freedom) N that the entire space can hold is determined as follows:
\[N=3\times 3\times 3\times 3=3^4=81\]
The enormous energy present in the pre-inflationary universe was evenly distributed (diluted) into these 81 degrees of freedom as space expanded.
(By the way, the "2" in the numerator comes from the geometric reason that dark energy occupies the "two orthogonal spatial directions (X, Y)" of the total energy, which will also be explained in [another article].)
3. The "Magic Number W" and the Completion of the 122-Order Puzzle
When we calculate how many states a space with N=81 degrees of freedom can hold as thermodynamic information (entropy), a massive constant is derived:
\[\ln W=\frac{81}{2}\implies W=e^{81/2}\approx10^{17.5}\]
This W (Hierarchy Constant) is precisely the "scale conversion multiplier" that bridges the microscopic Higgs scale and the macroscopic universe scale.
In fact, a beautiful law involving this W exists between the Planck scale, which conventional physics relied on, and the true baseline, the Higgs scale:
- Mass Relationship: The Planck mass is roughly W times the Higgs mass. (\(M_P\approx WM_H\))
- Length Relationship: The Higgs length is roughly W times the Planck length. (\(l_H\approx Wl_P\))
Now, the dimension of density is "Mass \(\div\) Volume (Length cubed)." Let's calculate the discrepancy between the conventional Planck density (\(\rho_P\sim m_P/l_P^3\)) and the density in this theory (\(\rho\sim M_H/(Wl_H)^3\)).
\[\text{Density Discrepancy}\sim\frac{M_P}{M_H}\times\left(\frac{Wl_H}{l_P}\right)^3\]
First, the mass discrepancy (\(M_P/M_H\)) is exactly one W, based on the relationship above.
Next is the length discrepancy. Due to inflation, the reference length expanded from \(l_H\) to \(Wl_H\). Since \(l_H\approx Wl_P\), the length after inflation becomes \(W^2\) times the Planck length (\(Wl_H\approx W^2 l_P\)). That is, the length discrepancy is \(W^2\).
Since volume is length cubed, \((W^2)^3=W^6\). Thus, the volume discrepancy is six Ws.
What happens when we multiply these together?
\[W\times W^6=W^7\]
Since \(W\approx 10^{17.5}\), what happens if we raise it to the 7th power?
\[(10^{17.5})^7\approx 10^{122}\]
Do you see it now?
The "122-order discrepancy" that tormented modern physics did not arise because we were missing unknown particles or dark fluids.
Physicists had simply forgotten to account for the total \(W^7\) geometric dilution of information—the mass illusion (\(W^1\)) and volume dilution (\((W^2)^3\))—that accompanied the hierarchization of cosmic space through inflation.
The universe was not as complicated as humans thought.
Once you understand the beautiful geometric rules of spatial directionality and the resulting distribution of information (81 and W), the universe's greatest paradox turns into a simple arithmetic puzzle you can solve on a calculator.
(Further truths of the universe revealed by the Intergeometric Theory are proven in detail in [Paper Part II (Cosmology)].)
