0-point energy,
Planck force and gravity
MAY 8, 2025
Table of contents
In the previous article, we familiarized ourselves with the vacuum density 𝜌vac and the key notion of screening. As we saw, a first screening of 𝜌vac results in the very high mass of the proton black hole (around 1014 g). Then a second screening, on a larger scale, gives the particle’s rest mass, a much lower mass (around 10-24 g), used in standard theory. And where there’s mass… there’s gravity! In this article, we explore the quantum gravitational model proposed by Nassim Haramein, Oliver Alirol and Cyprien Guermonprez [1]. May the force be with us ^^
According to general relativity, mass curves spacetime, a curvature we perceive as gravity. The smaller the mass, the weaker the gravity, and vice versa. So, depending on whether we consider the rest mass of the proton or that of the black hole proton, our understanding of gravity is different.This is why, according to the standard model, gravity is extremely weak at the particle scale, far behind the strong force or the electromagnetic interaction. But for Nassim Haramein and his co-authors, the situation is quite different.
Their work proposes a unification of gravity with the fundamental forces, based on the organization of fluctuations in the quantum vacuum; in particular when they are coherent and produce a mass equivalent to that of the proton black hole, implying a very intense gravitational force. Planck force is the keystone of their model. It leads to a reconsideration of gravity, which turns out to be a strong interaction on the quantum scale, particularly in the context of the proton’s internal structure.
The Planck force, source of gravity gravity
A maximum expression of coherent vacuum energy energy
At the crossroads of general relativity and quantum mechanics, the Planck force 𝐹𝑝 is defined as the force of maximum intensity that exists in the universe. It is equal to 1044 N [2].
In the standard model, it represents a threshold of instability: beyond this intensity, the structure of spacetime becomes distorted, matter collapses gravitationally and a black hole appears.
In Nassim Haramein’s model, by contrast, the Planck force is the maximum local expression of the vacuum’s gravitational coherence. It manifests itself as a point of dynamic equilibrium at the heart of the proton, which is continuously fed by the energy of the coherent vacuum, thus maintaining its stability. The PSU [3], which geometrically structures the proton, establishes a direct link between Planck’s force and the 0-point energy. Indeed, quantum fluctuations generate extremely intense local forces; when structured into PSU, they give rise to a gravitational force equivalent to the Planck force. In other words, this is the Planck force that acts between two perfectly organized PSU when the 0-point energy is 100% coherent (equal to 𝜌vac). It can be expressed by the following relation:
Where V is the volume of a PSU, and 𝑘 a proportionality factor that depends on the coherence of the vacuum energy.
Thus, the Planck force is a direct and maximal manifestation of coherent vacuum energy. It is the starting point for the emergence of the other fundamental forces, via a screening mechanism.
Screening and fine structure constant
A geometric coupling constant…
Each screening step from the Planck force is associated with a change in the energy configuration of the vacuum. This modification is expressed by a transformation of the geometric boundaries – the surfaces η (Eta) – that surround the volumes in which the coherent vacuum fluctuations are stably organized. The intensity of the interaction of vacuum fluctuations with these surfaces can be quantified by a coupling constant.
In the standard model, there are several coupling constants. For example, the gravitational coupling constant is used to compare the intensity of gravity with that of the other fundamental forces. For a proton, this constant is of the order of 10−38, which illustrates, in this model, the weak intensity of gravity on the quantum scale.
Nassim Haramein’s model reveals a geometric coupling constant, the square of which defines the ratio between two successive screening surfaces:
Where ηλ is the area related to the first screening, on the scale of the reduced Compton wavelength; and ηp is the area related to the second screening, on the scale of the charge radius [4].
This constant thus represents the attenuation of coherent vacuum energy across these surfaces; it is analogous to a classical coupling constant. The authors identify it with the fine structure constant (α ≈ 1/137) – which characterizes the intensity of the electromagnetic interaction between charged particles in the standard model – i.e. :
...for two screenings
At the scale of the reduced Compton wavelength, one PSU is projected holographically onto the surface ηλ [5] (see section on entropy below); at the scale of the proton’s charge radius, there are the equivalent of 512 PSU on the surface ηp. The model thus relates the surface ratio α² (using the factor 1/512) to the fraction of coherent vacuum energy encapsulated in the proton:
With ρproton the effective energy density contained in the proton, and ρvac the maximum energy density of the coherent vacuum.
After the two screenings, the energy density at the proton surface remains very close to ρvac. In contrast, the average density in the volume is much lower, representing only a small fraction of ρvac after the second screening. It then corresponds to the energy that forms the rest mass of the standard proton.
PSU forming the surface η surrounding the proton volume
Strong force = quantum gravity
The energy density contained in the proton black hole is such that it implies a very high internal pressure P. In Nassim Haramein’s model, this pressure is obtained from the local gravitational force Fg – about 10⁴ N – generated by the first screening of the Planck force. It is expressed by :
Where A is the surface area of the proton [6].
The result gives a pressure of the order of 10³⁴ Pa [7]. This is where Nassim Haramein’s approach joins the empirical results of standard theory. The latter gives the same estimate of internal pressure, but based on analysis of the energy and pressure distributions of quarks and gluons [8] inside the proton [9]. The two models lead to the same order of magnitude, but with different approaches.
Note that this pressure is comparable to that found at the heart of extremely dense objects such as neutron stars or black holes, which logically leads Nassim Haramein (but not standard theory…) to consider the proton as a stable micro-black hole.
By inverting the previous formula, the authors investigate which gravitational force would correspond to this pressure within the framework of the standard model:
The result (88.668 N) is very close, in terms of order of magnitude, to 104 N [10]. This not only validates numerically the Kernel-64-based screening model; but also allows the strong force of the Standard Model to be interpreted as a form of intense quantum gravity.
In this model, it is the intensity of fluctuations still coherent at the proton scale that contains the energy and quarks in a finite volume. Finally, what QCD describes as a confining force [11], the authors explain it as local quantum gravity arising from the coherent organization of the vacuum.
Gravity crosses scales
In the Sstandard model, gravity is neither unified with the other forces, nor considered significant on the quantum scale. It seems extremely weak compared to the other fundamental interactions [12], because it acts on tiny masses at subatomic distances. But if, as Nassim Haramein proposes, the proton has a mass equivalent to that of a black hole, it’s logical that the local gravity associated with it is extremely intense ^^.
The first screening of the Planck force gives rise to a gravitational force intense enough (10⁴ N) to contain the energy of the black-hole proton. The second screening, on a larger scale, produces a much weaker force (10⁻³⁴ N). In this model, the latter corresponds to the gravitational force between two PSU in fluctuating Planck plasma [13].
It so happens that this value (10⁻³⁴ N) also has a particular significance in the standard model (second point of convergence, after the proton’s internal pressure ^^); it corresponds in fact to the Newtonian gravitational force between two protons; a force that is negligible on this scale because the mass of these particles is minuscule. But if we consider billions of billions of protons (which make up planets or stars…), their gravitational effects add up. So, even if the intensity of the gravitational force is the same on a macroscopic scale, gravity becomes dominant.
For Nassim Haramein, this is the result of a drastic reduction, through successive screenings, of a much greater force, the Planck force. Thus, the gravity we perceive at our scale is a residual manifestation of coherent quantum gravity.
Gravity and entropy: two interrelated geometric manifestations
A Schwarzschild solution at every scale
The first exact solution to Einstein’s field equations was found by the German physicist Karl Schwarzschild in 1916. The Schwarzschild solution describes the geometry of spacetime around a massive spherical object, and predicts the existence of a critical radius, called the Schwarzschild radius, given by :
With M the mass, G the gravitational constant, and c the speed of light in the vacuum.
This radius defines the event horizon, beyond which nothing, not even light, can escape. The object becomes a black hole.
In Nassim Haramein’s model, the proton — considered as a concentration of energy in the coherent vacuum — satisfies this condition. It can therefore be interpreted as a microscopic, stable black hole [14]. We can look at it this way: if we multiply the volume of the proton by ρvac, we obtain an effective mass that generates a Schwarzschild solution with radius rs. But this reasoning doesn’t just apply to the proton: if we apply it to any physical volume (stars, galaxies and even the universe), we get a Schwarzschild solution. At every scale, there is a stable gravitational structure, encoded in the very geometry of the vacuum.
This principle follows on from the work of Nassim Haramein, who established back in 2012 that the universe is made up entirely of black holes at different scales. Far from being isolated singularities, they are simply natural states of matter. This structuring gives rise to a fractal organization of gravity — a form of geometric order — where each level of screening generates a stable, self-similar structure.
And we’ll see that in this model, and against the trend of standard theory, entropy also structures the universe…
In the standard model, entropy is disorder and loss of information
In thermodynamics and statistical mechanics, entropy measures the disorder of a system. The second law of thermodynamics states that entropy can only increase in an isolated system [15].
According to Jacob Bekenstein and Stephen Hawking, the entropy of a black hole is proportional to the surface area of its event horizon, not its volume. This reflects the idea that information, or energy, in a gravitational system is primarily related to the geometry of the spacetime surrounding the object. From their work comes the holographic principle: all the information contained in a volume of space can be encoded on its surface. In this model, the entropy of black holes is linked to a thermal temperature (Hawking temperature), and to an apparent loss of information through radiation [16].
In Nassim Haramein's model, entropy is structuring information
Nassim Haramein’s model uses the holographic principle, integrating it with the dynamics of a structured quantum vacuum. Here, entropy measures the amount of information (from vacuum fluctuations) geometrically encoded on the surface of a stable structure (such as a proton black hole).
More precisely, the decoherence of fluctuations due to screening represents a form of informational disorder, and therefore an increase in entropy. However, this loss of information is not dissipated: it is reconfigured on the surface η of the emerging mass. Entropy thus becomes the result of a loss of local order (decoherence), but also the trace of a reconstructed order in the holographic geometry.
The authors thus link entropy to the geometry of spacetime around massive black holes, taking into account not only classical energy but also the quantum organization of vacuum fluctuations [17]. They extend this idea to smaller black holes such as protons, and suggest that geometric entropy is a key element in understanding the emergence of mass and the relationship between gravity, thermodynamics and quantum mechanics. This leads to a new perspective where entropy measures the geometric organization of quantum energy in spacetime.
This geometric entropy depends on the way PSU interact and organize themselves around gravitational structures. It is directly related to real, measurable quantum fluctuations: it is no longer a statistical abstraction, but a physical property of the vacuum itself.
Unlike Hawking’s thermal temperature, the effective temperature defined by the authors is not linked to radiation, but reflects the internal dynamic activity of a gravitational structure arising from the coherent vacuum. Precisely, it reflects the level of pressure and internal gravitational coherence, which is equivalent to around 10³⁴ Pa for the proton.
Entropy and gravity are two sides of the same phenomenon
… ... in Nassim Haramein's model...
As we have seen, entropy reflects a loss of coherence compensated by the emergence of a geometric order stabilized by gravity, and encoded on the surface η. More precisely, this holographic entropy measures the degree of geometric organization and encoding required to stabilize, in a globally decoherent vacuum, the information that remains locally coherent.
Coherent energy remains available thanks to the local curvature of spacetime, which forms a stable structure — such as a proton — and produces gravity. Gravity is therefore a geometric response to the loss of surrounding coherence, or the increase of holographic entropy.
The more a system is affected by vacuum decoherence, the more gravity it needs to maintain coherence: there is therefore a direct link between entropy, structure and gravitational mass. Gravity can thus be seen as a consequence of increasing entropy.
This model is closely related to the physics of dissipative structures, to which physicist Ilya Prigogine made a major contribution. The idea is that open systems, far from thermodynamic equilibrium, can generate order from disorder by dissipating energy. This dynamic corresponds closely to that described in Nassim Haramein’s model, where order emerges from decoherence via a geometric structuring of the vacuum.
... but not in the standard model
Knowing the Schwarzschild radius, we can calculate the spherical surface of the corresponding event horizon:
The area of a black hole’s horizon is therefore proportional to the square of its mass:
Knowing that the entropy of a black hole is proportional to the area of its horizon :
We deduce that entropy is itself proportional to the square of the black hole’s mass, i.e. :
However, the standard model does not see the link between entropy increase and the gravitational rearrangement (mass increase, increased curvature of spacetime, etc.) that goes with it, because it does not consider the universe as a black hole made up of black holes linked by a fractal scale.
In Nassim Haramein’s model, entropy cannot increase independently of gravity [18]. Thus, the decoherence of the vacuum can be interpreted as a dissipative process in which entropy increases at the same time as gravity manifests itself. These two quantities, far from evolving independently, remain deeply coupled in the gravitational holographic model.
In this vision, any increase in entropy must be manifested by gravity – curvature, mass, structure. Entropy and gravity thus become the two complementary expressions of the dynamic organization of the quantum vacuum.
In conclusion
Nassim Haramein and his co-authors revisit the standard model, reconciling gravity, quantum mechanics, thermodynamics and the structure of spacetime through a unifying principle: the dynamic organization of the vacuum.
In this framework, entropy is no longer a simple measure of disorder, but an indicator of the organization of vacuum information on stable gravitational structures. Gravity then becomes the geometric response to this organization, structuring spacetime on all scales — from the proton-black hole to the entire universe — to maintain a dynamic equilibrium between coherence and decoherence.
This approach traces the path to a unified, geometric and holographic physics, where information, energy and structure appear to depend on each other.
Key points
The Planck force (1044 N) is the force from which gravity emerges, via a screening mechanism.
The geometric coupling constant α² represents the attenuation of coherent vacuum energy across two successive η-screening surfaces.
Gravity is a universal force that crosses scales via vacuum energy organization mechanisms, losing intensity from PSU to the cosmos.
Entropy reflects a loss of coherence compensated by the emergence of a geometric order stabilized by gravity, and encoded on the η surface.
Notes & references
[1] According to their paper The Origin of Mass and the Nature of Gravity
[2] For further information on Planck units, see the Planck scale infographic.
[3] PSU (Planck Spherical Units) are elementary harmonic oscillators made up of quantum fluctuations. They become detectable when they form a structure called Kernel-64. See also the previous article for more details on the internal dynamics of the proton.
Geometric coupling constant
[4] The reduced Compton wavelength (approx. 0.21 fm, or 2.1×10−14 m) represents the limit at which a particle must be treated with relativistic quantum mechanical tools. The proton charge radius rp (approx. 0.84 fm, or 8.4×10−14 m) indicates the extent of the zone in which the proton’s electric charge is concentrated.
[5] This does not mean that the inner volume is that of a single PSU; but that the coherent gravitational information perceived at this scale is equivalent to that of a single PSU.
Strong force = quantum gravity
[6] Here, we consider the gravitational force resulting from the 1st screening (reduced Compton wavelength), but the proton surface on the scale of the charge radius (2nd screening); the authors thus link the confining force of standard theory to the final observable structure of the proton.
[7] This pressure is linked to the Planck plasma; see also the internal dynamics of the proton for more details.
[8] Gluons are particles that mediate the strong interaction between quarks (the constituents of observable matter that form protons for example).
[9] The internal pressure of the proton is mainly calculated theoretically within the framework of Quantum Chromodynamics (QCD), but it is also deduced from experimental measurements by indirect methods.
[10] The order of magnitude of a value is commonly expressed as a power of 10. The base-10 logarithm can be used to reduce any value to a decimal exponent that directly shows its order of magnitude. For example, log10(88,668) ≈ 4.95, which means that 88.668 N is worth around 104.95 N, a value very close to 104 in terms of order of magnitude.
[11] The strong force is responsible for keeping quarks inside protons and neutrons. The confinement force is an aspect of the strong force, which specifically describes how quarks are bound together.
Gravity crosses scales
[12] Gravity, for example, is about 1024 times weaker than the confining force.
[13] The Planck force only applies in a state of maximum coherence. This is a theoretical value representing a force that would apply between two perfectly coherent PSU, superposed, and without any screening. The gravitational force between two PSU in a fluctuating plasma is partially screened, of the order of 10−34 N.
Gravity and entropy: two interrelated geometric manifestations
[14] There is, however, a significant difference between the classical Schwarzschild solution, in which “the vacuum is empty”, and Nassim Haramein’s model, in which the energy of the vacuum structures the black hole itself.
[15] See also the article Irreversibility, memory and entropy for more details.
[16] See also the article Gravity, entropy and self-organization for more details.
[17] Classical energy refers to energy as considered in general relativity or classical mechanics — that is, energy associated with mass via the curvature of spacetime. In Nassim Haramein’s model, entropy is therefore linked not only to visible mass, but also to the coherence of the underlying quantum fluctuations.
[18] This is the path I explored (” with the hands ” as Nassim would say ;)) in the article Gravity, entropy and self-organization.
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