The 31th of May : toward a unified NTU interpretation of c, H₀, G and the Higgs mechanism

The No-Time Universe framework suggests that the fundamental constants of physics are not independent quantities but different projections of the same underlying process: the cosmological rigidification of the pre-link substrate.

The primordial closure front generated during the Big Bang progressively transforms an initially pre-causal substrate into the causal Universe we observe today.

Within this picture, three major constants acquire a new interpretation.

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The new interpretation of c

Along the quantum axis, the closure front is observed through the local propagation of pre-link closures.

The speed of light becomes:$$\boxed{ c=\langle v_{\rm close}\rangle }$$

where:$$\langle v_{\rm close}\rangle$$

is the average velocity of pre-link closure propagation.

The speed of light is therefore no longer a fundamental postulate but the asymptotic propagation velocity of the closure dynamics.

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The new interpretation of H₀

Along the gravitational axis, the same process is observed through the growth of the already causalized region.

The Hubble constant becomes:$$\boxed{ H_0=\langle \Gamma_{\rm exp}\rangle }$$H0​=⟨Γexp​⟩​

where:$$\Gamma_{\rm exp}$$Γexp​

is the average expansion coefficient generated by the closure front.

The Hubble parameter is therefore the large-scale projection of the same dynamics that produces the speed of light locally.

In NTU:$$c \longleftrightarrow \text{local closure dynamics}$$$$H_0 \longleftrightarrow \text{global closure dynamics}$$

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The new interpretation of G

The gravitational constant should then characterize not a force, but the resistance of the substrate to geometric deformation.

Matter corresponds to highly rigidified regions of the pre-link network.

Curvature appears when closure densities vary spatially.

The gravitational constant becomes:$$\boxed{ G = \text{rigidity coefficient of the NTU substrate} }$$G=rigidity coefficient of the NTU substrate​

or formally:$$G \propto \frac{\ell_P^2} {\Gamma_\Sigma^2}$$

where:$$\Gamma_\Sigma$$

represents the local density of stabilized pre-link closures.

The stronger the closure density, the stronger the geometric rigidity.

Gravity therefore becomes an emergent elasticity of the substrate.

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Reinterpreting the Higgs field

Within the Standard Model, the Higgs field is introduced as a universal field filling spacetime and giving mass to elementary particles through spontaneous symmetry breaking.

Within NTU, a different interpretation becomes possible.

Mass does not arise because particles interact with an independent Higgs medium.

Instead, mass measures the degree of local rigidification of the pre-link network.

One may define a local rigidity field:$$R(x)$$

such that:$$m(x) \propto R(x)$$

The Higgs field then becomes the effective quantum description of the underlying rigidification process.

In this interpretation:$$\boxed{ \text{Higgs field} = \text{effective description of NTU rigidification} }$$Higgs field=effective description of NTU rigidification​

The Higgs boson remains real and observable, but it is no longer fundamental.

It becomes the quantum excitation of the rigidification field.

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Unified NTU structure

The complete picture becomes:$$\ell_P \rightarrow \text{pre-link network} \rightarrow \text{closure front} \rightarrow \text{rigidification}$$

From this single process emerge:$$\boxed{ c = \text{average closure velocity} }$$$$\boxed{ H_0 = \text{average expansion coefficient} }$$$$\boxed{ G = \text{substrate rigidity coefficient} }$$$$\boxed{ m = \text{local rigidification density} }$$

and therefore:$$\boxed{ \text{Higgs field} = \text{effective field of rigidification} }$$

Within this framework, the speed of light, the Hubble constant, gravitation, and mass are no longer independent ingredients of nature. They become complementary manifestations of a single geometric process: the fractal rigidification of the cosmological pre-link closure front propagating through the No-Time Universe substrate.

The 26th of May’26 : a new conceptual bridge may have emerged inside the NTU framework (episode 2)

Several mathematical structures historically introduced as technical constructions in modern physics now appear to share a common geometric pattern. One particularly striking example concerns Stephen Hawking’s use of imaginary time.

In Hawking’s approach, the transformation:

t → iτ

combined with Wick rotation, allowed the spacetime metric to transition from Lorentzian geometry:

(-,+,+,+)

to Euclidean geometry:

(+,+,+,+)

thereby removing the initial singularity and restoring a globally regular geometry near the Big Bang. However, as Hawking himself acknowledged in discussions with Roger Penrose, the physical meaning of this procedure remained unclear:

“his Euclideanization procedure based on the introduction of imaginary time remains obscure. It remains a pure computational procedure without physical interpretation.”

Within the NTU framework, this structure may receive a direct physical interpretation. The pre-causal NTU regime is fundamentally atemporal and globally rigid. In this regime, ordinary causal time has not yet emerged, and the geometry is naturally closer to a Euclidean structure.

The emergence of time then appears through cosmological symmetry breaking and causal rigidification transitions.

This perspective becomes particularly interesting when compared with Louis de Broglie’s phase harmony theorem.

De Broglie originally noted that the Lorentz factor appears simultaneously and symmetrically in the two complementary descriptions of a particle’s energy — one expressed through frequency and wave propagation, the other through relativistic mass and inertia:

E = hν = γmc²

with:

γ = 1 / √(1 − v²/c²)

At the same time:

ν_wave = γν₀

while:

ν_internal = ν₀ / γ

The Lorentz factor therefore appears:

• at the numerator in the wave description,
• and at the denominator in the internal frequency transformation.

Within NTU, this inverse transformation structure appears naturally through the pantographic principle:
the quantum and gravitational branches transform inversely while remaining globally coherent.

In this interpretation:

• Hawking’s imaginary time,
• de Broglie’s phase harmony,
• Lorentz dual transformations,
• and emergent spacetime

may all correspond to partial manifestations of a deeper pantographic geometry of the underlying NTU substrate. Historically, many essential ingredients already existed separately:

• Einstein’s relation between geometry and rigid bodies,
• de Broglie’s wave-particle duality,
• Dirac and Vigier’s deeper physical substrate,
• Hawking’s non-fundamental time,
• and Smolin’s critique of fixed background physics.

The NTU framework attempts to reconnect these ideas into a single emergent structure.

This is also fully consistent with the second principle and the third rule of Lee Smolin : the NTU framework attempts to position itself within this perspective by proposing an emergent ontology reconnecting quantum mechanics, relativity, causal structure, cosmology and the emergence of time itself within a single coherent substrate dynamics.

The 26th of May’26 : a new conceptual bridge may have emerged inside the NTU framework

The de Broglie phase harmony theorem — one of the original foundations of wave mechanics — already appears to contain the core structure of the NTU pantographic principle with both axes. Louis de Broglie originally noted that the Lorentz factor appears simultaneously and symmetrically in the two complementary descriptions of a particle’s energy — one expressed through frequency and wave propagation, the other through relativistic mass and inertia:

Wave frequency:
E = hν

Relativistic mass:
E = γmc²

with the Lorentz transformation factor:

γ = 1 / √(1 − v²/c²)

At the same time, de Broglie showed that the associated wave frequency transforms as ν_wave = γν₀ while the internal clock frequency transforms inversely ν_internal = ν₀ / γ.

The remarkable point is that the Lorentz factor γ appears:

• at the numerator in the wave description,
• and at the denominator in the internal frequency transformation.

This inverse transformation structure is remarkably similar to the NTU pantographic transformation law, where:

• the quantum axis is associated with frequency and wave propagation,
• while the gravitational axis is associated with mass and inertia.

The 21th of May’26 : CMB test of NTU refined

The NTU experimental approach does not require a fundamentally new type of measurement.

The relevant experiments already perform the most difficult part of the work: separating the true cosmological signal from instrumental noise, atmospheric contamination and astrophysical foregrounds.

The key difference is therefore not technical, but interpretational.

Current CMB spectral distortion programs primarily search for:

• deviations from a perfect blackbody spectrum,
• global mu-distortions,
• y-distortions,
• free-free emission,
• unresolved radio foregrounds,
• or instrumental systematics.

In the NTU framework, the hypothesis is that some residual structures currently treated as foreground uncertainties, diffuse radio excesses or calibration artifacts could instead correspond to fossil signatures of cosmological rigidification transitions.

The NTU prediction is not the existence of narrow spectral lines, but rather broad multi-frequency coherence regimes (“spectral bumps”) generated by the NTU transformation law.

The starting point is the NTU transformation law which is not Lorentz transformation, but:

$$\Delta k_{NTU} = \frac{\Delta p}{\hbar}$$

or equivalently:$$\Delta\left(\frac{1}{\lambda}\right)=\frac{\Delta p}{h}$$

For relic coherent modes dominated by their rest-energy scale:$$\Delta p \sim \frac{E}{c}$$

which leads to:$$\Delta\left(\frac{1}{\lambda}\right)\simeq\frac{E}{hc}$$

Using the photon relation:$$\nu=\frac{c}{\lambda}$$

one obtains the NTU coherence frequency:$$\nu_{NTU}\simeq\frac{E}{h}$$

The observed frequency today must then be cosmologically redshifted:$$\nu_{obs}=\frac{1}{1+z_*}\frac{m_i c^2}{h}$$

with:$$1+z_* \simeq 1090$$

This produces the approximate NTU fossil coherence bands:

nu_1 ≈ 0.2 GHz

nu_2 ≈ 2 GHz

nu_3 ≈ 10–11 GHz

Additional rigidification transitions associated with electroweak and QCD phases may generate broader structures around:

40–80 GHz

The proposed observational test therefore consists of:

1. Measuring the absolute sky spectrum:
   T_obs(nu)
2. Modeling the conventional foregrounds:

T_model(nu) =
T_CMB

• T_syn(nu)
• T_ff(nu)
• T_dust(nu)
• T_sources(nu)

with synchrotron emission approximated by:

T_syn(nu) = A_syn × (nu / nu_0)^(-beta)

where:

beta ≈ 2.6–2.8

3. Computing the residual spectrum:

R(nu) = T_obs(nu) − T_model(nu)

4. Searching for broad residual structures centered around the NTU-predicted frequency bands.

The NTU residual contribution is modeled as:

T_NTU(nu) =
SUM_i A_i exp[ −(ln(nu) − ln(nu_i))² / (2 sigma_i²) ]

where:

• A_i is the amplitude,
• nu_i is the central frequency,
• sigma_i is the coherence width.

The crucial point is that the NTU does not predict a simple global radio excess, but a coherent multi-band residual structure associated with successive cosmological rigidification transitions.

In practice, some of these structures may already have been partially absorbed into foreground modeling or interpreted as diffuse residual noise during the construction of the “pure” CMB spectrum.

The NTU hypothesis therefore becomes directly falsifiable:

if no statistically significant residual curvature remains after robust foreground subtraction, the model is disfavored;

if coherent broad residual structures persist near the predicted bands across independent datasets, the NTU framework gains strong experimental support.

The 18th of May’26 : first test feedback

Small but important milestone for the NTU program. We recently exchanged with South Pole / White Mountain and ARCADE 2 program/project leaders regarding the possible search for broad residual spectral structures in CMB low-frequency data. One very important clarification emerged from this discussion: the right experimental framework for NTU is probably not differential CMB mapping (Planck LFI / WMAP), but absolute spectral distortion measurements.

This is fully consistent with the current NTU direction:

• broad coherence regimes rather than narrow spectral lines;
• low-frequency residual structures;
• fossil signatures linked to cosmological phase transitions / rigidification transitions.

The South Pole / White Mountain measurements and ARCADE 2 results are compatible but absolutely not sufficient at this stage to claim any confirmation of the NTU framework. The main challenge remains:

• foreground subtraction,
• synchrotron modeling,
• and absolute sensitivity.

The next step is therefore becoming clearer:
refining the predicted frequency bands and comparing them against absolute spectral distortion datasets and future projects such as COSMO, BISOU or FOSSIL.