Zero-point energy,
space and mass
MARCH, 2 2025
Table des matières
Third part of the series on zero-point energy: I’ll start with a brief summary of the previous episodes, so that you have the essential concepts in mind! After that, we’ll take a look at the concept of mass. How it evolved, from Newton to Einstein, without ever really having been defined, nor related to the quantum scale; and how, at this scale, the concept of screening linked to bare mass was not necessarily understood in the right way… until the arrival of Nassim Haramein ^^.
Mass being closely linked to space – since mass curves space-time – we’ll take a look at Einstein’s field equations, which describe this curvature. Finally, we’ll see that they naturally contain zero-point energy; and that, from both cosmological and quantum points of view, space can be considered as a fluid. This will lay a good foundation for the next article, which will detail how mass-energy and gravity are, ultimately, emergent properties of spacetime at the quantum level.
Zero-point energy
Origin and importance of zero-point energy
“Based on early explorations of thermodynamics and the characterization of black body radiation, Max Planck predicted the existence of an unexpected non-zero value for the electromagnetic energy density of the quantum vacuum, or zero-point energy (…). ) Although a common approach is [to make] all ground-state modes cancel out, by artificially setting the zero-point energy to zero [1], this is essential for the mathematical consistency of quantum mechanics, as it maintains the non-commutativity of the creation and annihilation operators, leading to Heisenberg’s uncertainty principle. ” [2]
Planck’s law, derived from these explorations, describes the electromagnetic energy radiated by a black body at a given temperature, as a function of wavelength. To arrive at this description, Planck had to assume that light – and electromagnetic radiation in general – is absorbed and emitted discretely, a phenomenon that Einstein explained in 1905 with the photoelectric effect [3]. These discoveries marked the birth of quantum mechanics.
“Even if Planck thought that zero-point energy would not be observed in experiments, today a long list of experimental works can only be explained by taking this energy into account, for example (…) the Casimir effect (…)” [4].
Can this energy be calculated, and if so, what is its value?
Maximum vacuum density value
ρvac = 8.90 x 10113 J/m3
Or ρvac = 9,89 x 1093 g/m3 in units of mass [7]
This is very close to Planck’s energy density of 5,16 x 1093 g/m3. The paper on the origin of mass explains how this energy is screened; first, to give the mass of the black hole proton (of the order of 1014 g); then, a second time, to give the rest mass of the prooton (of the order of 10-24 g). Before going into more detail in the next article, let’s take a closer look at the Planck scale, and the concepts of mass and space.Planck scale
The Planck scale marks a limit below which our current understanding of physics, based on general relativity and quantum mechanics, is no longer applicable.
The Planck scale represents values that are totally unfamiliar to us. I’ve attempted a few comparisons in the infographic below, which I hope will enable you to speak Planck’s language more fluently… !
*For more on Planck’s constant and the reduced Planck’s constant (Dirac’s constant), see the article on the black body and the ultraviolet catastrophy.
Zero-point energy is linked to quantum field fluctuations at all scales, but it is at the Planck scale that these fluctuations reach their maximum. At this point, they become so intense that their energy may not only be comparable to the Planck energy itself, but may also play a central role in shaping the structure of spacetime, thus necessitating a quantum description of gravity.
And gravity means mass…
Mass
What is mass ?
Einstein’s famous equation E = mc² showed that mass is a form of energy [8]. Although this equation is extremely useful in physics, it is limited in explaining the nature of mass. Where does the invariant mass [9] of elementary particles come from? How is it created? Why do particles have this property of mass?
“The general idea that mass is some kind of immutable value independent of forces and energies was dispelled at the beginning of the 20th century by the advent of special and general relativity, when it was realized that there is a fundamental equivalence between the concept of mass, energy and the geometry of space.
General relativity clearly demonstrates a relationship between mass-energy and the structure of space-time, which has real physical effects we call gravity, where massive objects made up of elementary particles producing the mass of these objects, curve space-time, resulting in a gravitational force.
However, applying the same principles at particle level produces gravitational forces so infinitesimally small that they are considered insignificant. Yet, at the proton scale, we find extremely large confining forces that would require extremely high energy levels (or masses) to be produced in the context of general relativity.
In fact, these very high energy levels were predicted by early Quantum Field Theories (QFT) [10], which led to the so-called “bare mass” of particles, but have been renormalized by modern Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD), which use quantum vacuum fluctuations as a screening mechanism.” [11]
Bare mass, renormalization and rest mass
Bare mass is a theoretical value introduced into the QFT equations. It is a free parameter, arbitrarily adjusted according to experiments. It represents the mass of a real particle that would be totally isolated from any interaction, notably with the fluctuations of the quantum vacuum.
Such a situation does not exist in physical reality, because in practice, a real particle is in constant interaction with virtual particles present in the vacuum. QFT then describes these virtual particles as a screen, acting as a screening mechanism on the real particle. Thus, virtual particles contribute to the real particle’s rest mass by screening its bare mass, so that the effective (observed) mass-energy matches the experimental values.
These contributions can sometimes lead to infinities in the equations, which physicists seek to eliminate in order to perform their calculations. To do this, they use the mathematical process of renormalization, which allows them to take infinities into account by absorbing them into theoretical parameters such as bare mass, and to obtain a finite, measurable value for the real particle’s rest mass. Without renormalization, this mass would be infinite and would have no real meaning. The renormalized mass is then reintroduced into the QCT equations to predict other particle properties and interactions.
Renormalization is therefore an essential mathematical procedure for making final calculations consistent, without the direct influence of infinities; and a method with a physical interpretation, which takes into account the effects of vacuum fluctuations and particle interactions. However, it has been, and still is today, questioned by some renowned physicists, including Paul Dirac and Richard Feynman [12] and Stephen Hawking.
Mass and energy scales
The mass considered – bare mass or rest mass – depends on the distance (or energy scale) at which the particle is observed. To understand this, we need the uncertainty principle. We have seen that this applies to pairs of conjugate quantities, such as energy and time, or position and momentum. Since energy depends on motion, energy and momentum are linked; if we combine this with the relativistic concept of space-time, we can draw an implicit parallel between energy and distance. This is equivalent to saying that quantum fluctuations occur on very short space-time scales, or at very high energies. This gives rise to two scenarios and, in this case, two masses:
1. At low energies: measuring rest mass
An observer at a distance from the proton (i.e. at low energy) does not “see” the proton’s bare mass, but a reduced mass due to the virtual particles that modify its bare mass. In other words, at low energies, the proton appears to have a lower mass than its bare mass, because the latter is partially “masked” by the cloud of virtual particles.
2. At high energies: closer to bare mass
When we study the proton at higher energies, we scan smaller distances. At these smaller distances, vacuum fluctuations (the virtual particles surrounding the proton) become less important. We could say that we “penetrate” through the cloud of virtual particles that screen the mass, and begin to “see” the bare mass of the proton.
A brief summary in pictures:
The origin of mass
For Nassim Haramein, Olivier Alirol and Cyprien Guermonprez, the notion of screening, as defined and used in standard theory, does not lead to a correct understanding of mass. In their view, the screening should be based on zero-point energy, ρvac, not bare mass.
They introduce the concept of PSU (Planck Spherical Units), which are units based on Planck length, mass and density. These quantum oscillators are the smallest that can exist; they are bound to the foam of spacetime and fill the universe. When PSU are in their ground state, their energy is less than the energy quantum (E0 < ħꞷ), making them undetectable. But when they become coherent and adopt a collective motion, they begin to create an energy flow called mass. We identify this energy flow with a Planck plasma.
Now let’s take a look at what’s happening in space.
Space
From space to spacetime
At the end of the 17th century, Newton conceived of space as a fixed, unchanging frame, in which objects had absolute positions and velocities. Time was also absolute, universal and uniformly measurable; it did not depend on the observer or his movement.
This idea of space and time dominated physics for over two centuries, before being called into question, mainly by Einstein’s 1905 theory of special relativity. Einstein presented a dynamic and flexible conception of space and time, which became relative to the observer and intrinsically linked by the concept of spacetime. The latter is seen as a fixed canvas where moving objects follow straight trajectories at constant speed.
Einstein evolved this concept in his theory of general relativity, published in 1915. Spacetime is now curved, “[a] curvature [that] results [however] from an indefinite source of energy called mass, emerging from quantum entities that we call particles” [13].
Even if, at the time, the cosmological and quantum worlds seemed very far apart, it is very interesting to note that the field equations published with general relativity make zero-point energy emerge…
Einstein field equations
These tensor equations form a system of 10 equations that must be solved simultaneously to determine the shape of spacetime. In 1917, Einstein added the cosmological constant Ʌ – whose role is to counterbalance gravitational attraction – to account for a universe thought to be static at the time. But by observing galaxies moving away from each other, Edwin Hubble discovered in 1929 that the universe was expanding. This forced Einstein to remove the cosmological constant from his equations in 1930, considering its addition in 1917 to have been his “biggest mistake”.
The cosmological constant was finally reintroduced in 1998, following the discovery that the expansion of the universe was accelerating. In cosmological terms, it corresponds to a constant energy density everywhere in the universe, which could be explained by zero-point energy. This remains conditional in standard theory, which cannot explain the difference in value between the energy density of the vacuum at the quantum level (ρvac = 1093 g/cm3) and the cosmological constant (Ʌ = 10-29 g/cm3).
Still, Einstein’s equations naturally contain ρvac (on the side of space curvature); so do Planck units, in the sense that we can express these equations in normalized Planck units in order to simplify them.
From spacetime to quantum space... there's only one fluid
Einstein described the curvature of spacetime as smooth and continuous. However, in some formulations of general relativity, spacetime is sometimes modeled as a fluid. This is because it reacts dynamically to the presence of matter and energy, curving around massive objects just as a fluid does when interacting with a body. Moreover, just as a fluid can carry waves or disturbances, spacetime carries gravitational waves traveling at the speed of light.
At the Planck scale, space is a vast sea of oscillating energy – similar to a fluid – quantified in PSU, according to Nassim Haramein and his co-authors. Fluctuations in the curvature of spacetime, due to vacuum fluctuations, give rise to the creation and annihilation of virtual vortices, with a charge approximately equal to the Planck charge, and a mass approximately equal to the Planck mass, as well as an energy associated with ρvac. This is the famous Planck plasma which, like any plasma, can be modeled as a continuous fluid [14], despite the discrete nature of the particles that make it up.
In this plasma, tiny PSU oscillators constitute not only the fluid medium of space, but also matter [15]. Thus, mass-energy is an emergent property of spacetime at the quantum level.
A brief summary, and even more, in an infographic…
*For more details on holographic mass and the resolution of the vacuum catastrophy, see the article on the Schwarzschild proton and quantum gravity.
Now it’s time to take a closer look at how mass and forces emerge from the vacuum’s energy density… Coming soon in the next article!
Key points
- When the vacuum is 100% coherent, the value of the vacuum energy density is maximal, and very close to the Planck density.
- Mass depends on the distance (or energy scale) at which the particle is observed. At low energies, we measure rest mass; at high energies, we approach bare mass.
- When they adopt a coherent collective motion, PSU begin to create a flow of energy called mass. They then constitute the fluid medium of space, which also includes matter.
- Einstein’s field equations naturally contain Planck units and the energy density of the vacuum.
- Mass-energy is an emergent property of spacetime at the quantum level.
Notes & references
Zero-point energy
[1] On this subject, see the article From renormalization to fractals.
[2] Source : The origin of mass and the nature of gravity, p.1
[3] Zero-point energy plays a crucial role in the photoelectric effect, as it determines the minimum frequency of light needed to extract an electron from a metal when exposed to light of sufficiently high frequency.
[4] See The origin of mass and the nature of gravity, op.cit, p.10, for an exhaustive list of these works.
[5] In terms of waves, coherence refers to the property of these waves to remain in phase and synchronized over a given period of time or across a given spacetime. An example of a coherent system is a laser.
[6] The concept of a “100% coherent” vacuum is more of a theoretical abstraction than an accessible physical reality, since a 100% coherent vacuum would presuppose a level of perfect order and no random fluctuations. But even in coherent vacuum states, certain fluctuations and uncertainties remain. This concept therefore serves primarily as a framework for modeling states close to coherence under certain conditions.
[7] The equivalence between mass and energy is given by the equation E = mc²
Mass
[8] This energy-impulse relation allows energy to be converted into mass by the speed of light c. This brought a breakthrough in the classical concept of mass, since massless particles could be assembled to create massive particles; for example, in standard theory, 99% of the mass of the proton is generated by the interactions of quarks with massless gluons.
[9] For a single particle, the invariant mass corresponds to the rest mass. For a system of particles, the invariant mass corresponds to a global property that can be calculated from the total energy and momentum of the system; it may differ from the sum of the rest masses of the individual particles.
[10] Quantum field theory, of which Paul Dirac is one of the main architects, is a theoretical framework unifying quantum mechanics and special relativity. It describes particles and their interactions in terms of quantum fields. Particles are no longer seen as independent point-like objects, but rather as energy quanta (or quantum particles) associated with the oscillations of a field. Since QCT incorporates special relativity, quantum fields are defined not only in terms of space, but also in terms of time, forming an entity called a relativistic quantum field.
[11] The origin of mass and the nature of gravity, op.cit, p.2
[12] Voir The origin of mass and the nature of gravity, op.cit, p.9 for their views.
Space
[13] The origin of mass and the nature of gravity, op.cit, p.2
[14] The behavior of a plasma is often described by equations similar to those describing fluids, such as the Navier-Stokes equations, but with additional terms that take electromagnetic forces into account. A plasma is in fact a very special fluid, characterized by the presence of charged particles that interact strongly with electromagnetic fields.
[15] Nassim Haramein tells us that “if we could see light on the Planck scale (…) then we would see space directly as a fluid, and our view would relay an integrally interconnected world of a single substance; objects would not appear as separate and distinct or even fundamentally different from the substance that makes up the overall space. Rather, “material” objects would appear as vortices of the fluid that is the very substance of space.”
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