There is nothing in the world except empty curved space.  Matter, charge, electromagnetism, and other fields are only manifestations of the curvature of space.  Physics is geometry.”

~ Charles Misner & John Wheeler

Following the progression of scientific theory regarding the ontological nature of the physical world — inevitably leading to theory unified by a ‘connected world-view’ perspective— we get to perhaps one of the greatest factors connecting all things together: space. Because space is the one thing connecting all things, it forms the foundation from which a unification of physics theory can be realized. Space is an interesting component to use as the foundation of a unified science, since classically space is empty, devoid of substance—it is a term we conventionally use to refer to a “body” of nothing. This nothingness is what separates objects, giving material bodies a definitive location in space, thus allowing them to exist as distinct objects. So, shouldn’t physics be focused on the objects instead of their background arena of space, which is fundamentally a vacuum and therefore nothing? 

Well, as 20th century science has advanced it has become an indubitable fact that a true vacuum cannot exist, that even seemingly empty space is full of oscillating fields, phantom particles, and geometrical structure. From an ontological perspective, this should have been obvious from the beginning, because nothing—by definition—does not exist. Space exists, so it can’t be nothing (a vacuum). 

Indeed, space is quite the opposite of empty. When physicists were first formulating quantum field theory (QFT) they ran calculations for how much energy should be present in the quantum fields devoid of any observable excitation, what should be a vacuum. This vacuum state is the zero-point field, however summing all of the allowable energy modes resulted in an infinite density for the energy expectation value of the vacuum, supposedly empty space. How could empty space have an infinite energy expectation value? The answer, again, is due to the fact that seemingly empty space is not a vacuum, it is the base of all mass-energy, a quantum vacuum. As physicist Nassim Haramein describes it: “objects do not define space, space defines objects”. Haramein has demonstrated the validity of this statement by showing how mass and the physical properties of particles emerge from the structure of space. 

The original QFT calculations predicted an infinite energy density in part because of the Heisenberg uncertainty principle—a key postulate of the Bohr-Heisenberg model of quantum mechanics, also known as the Copenhagen Interpretation—which due to its innate indeterminacy required that there must be ever-present energetic fluctuations of the quantized fields, such as the electromagnetic and mass fields, even when there were no apparent source charges, matter, or energetic radiation present. In terms of quantum field theory, this is known as the ground state, or as previously stated the zero-point field, so named because at the ground, or vacuum state there should be zero energy, yet quantum theory stipulates that is not the case. Even at the ground state there will be quantum oscillations, or vacuum fluctuations, also known as zero-point energy.

It is a consequence of the Heisenberg uncertainty limit that QFT predicted a non-zero energy value at the ground state of any quantum field, because the famous Heisenberg inequalities restrict the precision with which any two complementary variables of a field or particle’s state can be known. If one tries to describe the dynamical state of a quantum particle by methods of classical mechanics, then precision of such description is limited in principle. The classical state of the particle turns out to be badly defined. It is kind of akin to saying that “well, at time intervals that are shorter than we are able to measure, the energy value can be whatever it wants”. The more common example of this is the inverse precision with which either position or momentum of a particle can be simultaneously known—a high precision in the determination of one of the variables results in a resolution of the other. Now, quantum mechanics does not view the Heisenberg uncertainty limit as a consequence of our technological capabilities to measure the ultra-small, and ultra-fast; but instead, it is viewed as an inherent property of the universe—that there is intrinsic indeterminacy at the foundation of reality. 

While conventional quantum theory requires there to be a non-zero energy value at the ground state because of the Heisenberg uncertainty limit, unified physics demonstrates that the quantum vacuum energy is not due to uncertainty and indeterminacy, but due to the intrinsic high curvature of micro-degrees of spacetime (the micro-scale in this context refers to sizes around the Planck length 1.6 x 10-35 m), an immanent infinite energy density.

Vacuum Energy Expectation Value & Heisenberg Uncertainty Principle

According to this formulation, energetic fluctuations of virtually any size can occur if they only exist for an exceedingly short period of time. This has important and observable effects, for instance the Standard Model predicts an infinite charge density for the electron point particle, the self-energy of which (the energy contribution of electrostatic force to the mass) produces an infinite mass for the electron. This value is renormalized by calculating the quantum vacuum fluctuations surrounding the electron—fluctuations that are twice the mass-energy of the electron itself, producing electron-positron pairs, that “smear” out the charge density so that it does not contribute an infinite mass to the electron.

With several billion of these particle-antiparticle electron-positron pairs fluctuating around the electron proper, the infinite charge is effectively shielded, resulting in a finite value (-1.602 x 10-19 coulombs).While the uncertainty principle is taken to be an intrinsic property of quantum systems, instead of just a statement about the current state of our technological capabilities to observe such quantum systems with determinism exceeding the Heisenberg limit, recent experiments have appeared to exceed the limit stipulated by this principle (1,2).

Infinite Curvature & Spacetime Geometry at the Micro-scale

So then, how do we account for the energy expectation value of the quantum vacuum if it is not due to energetic fluctuations that are allowed to occur because they are within the bounds of intrinsic uncertainty? The solution to this quandary is that space (the vacuum) does not have an intrinsic zero-energy value, if it were not for quantum fluctuations. But instead, space is infinitely curved, particularly when we consider the micro-scale (sizes around the Planck length 1.6 x 10-35 m).

Now, this is obviously a point of contention, because although quantum field theory calculates a nearly infinite energy density for the vacuum, most physicists regard this as a non-real result, and point to astronomical observations and measurements (relating to the determination of the value of the cosmological constant) that suggest that the vacuum energy density is around 10−9 joules (10−2 ergs) per cubic meter, versus the value of 10113 joules per cubic meter predicted by quantum field theory (the vacuum catastrophe3).

As such, although the large energy expectation value of the vacuum is used frequently (to renormalize the infinite charge density of the electron, to account for 98% of the mass-energy of the proton that does not come from the Higg’s interaction, etc…) many physicists will still regard it as foolish to use the large energy density value predicted by QFT for serious calculations. Although there are exceptions, such as the preeminent physicist Dr. Unruh, who using the QFT value of the vacuum energy density was able to correctly calculate the cosmological constant and showed that the huge gravitational force of all that vacuum mass-energy is what is driving the expansion of the universe—i.e. it is the source of dark energy4. 

So, the value of 10−9 joules per cubic meter, which implies space has a flat geometry, is only an apparent value. Space is, most probably, infinitely positively and infinitely negatively curved. For the most part, the two cancel each other out, except in places where there is a large gradient, such as with matter (resulting in a positive curvature proportional to the amount of gradient that is present). At the cosmological scale, however, the two do not completely mask each other—because infinities can have different sizes5. It may be the case that the infinite negative curvature of space is slightly larger than the infinite positive curvature of space, and therefore, there is an accelerating expansion of space (dark energy).

3. The Vacuum Catastrophe and the Holographic Mass. Accessible on Resonance.is Publications.

4. Investigation of the gravitational property of the quantum vacuum may explain the accelerating expansion of the universe. Accessible on Resonance.is News.

5. Strange but True: Infinity Comes in Different Sizes. Scientific American. July 19, 2007. 

So, although from unified physics we see that it is the high curvature of the micro-scale of spacetime that results in the non-zero energy potential of quantum fields, it is useful to consider the situation from the canonical perspective, where spacetime is flat and smooth, to see how in fact spacetime geometry (gravity) and the fundamental forces, like electromagnetism, are in fact unified. This is most evident at the Planck scale where the quantum energetic oscillations increase in energy so much that the vacuum fluctuations of the quantized electromagnetic field are of the Planck energy E ∼ MP ≃ 1019 GeV, where Mp ∼ 2.2 X 10-5 g (by comparison, ∼1019 GeV is released when one gram of deuterium is converted into helium during thermonuclear fusion, the equivalent of about 145 tons of TNT).

This means that photons, or vacuum fluctuations, of Planck frequencies and wavelengths have so much energy that they result in infinitely curved spacetime geometry at the micro-scale—a quantum black hole. Of course, this is occurring on inconceivably fast time scales and infinitesimally small volumes (hence it is at the micro, or unobservable scale), and is occurring with such great frequency that it results in an ever fluctuating multiply-connected spacetime geometry, a micro-wormhole network of spacetime at the Planck scale.

It is this quantum structure of space that offers the path to unification of the two disparate fields of physics, relativity and quantum mechanics. Because at high-energy scales, like that around the event horizon of a black hole or at the Planck vacuum level, quantum mechanics becomes necessary to explain the behavior of spacetime. And conversely, the geometry of spacetime is influencing quantum behaviors. 

This unification was first realized by Wheeler in his formulation of quantum geometrodynamics and has led to impactful theories like Hawking-Unruh radiation. Most recently, the multiply-connected geometry of spacetime at the Planck scale has been postulated to engender nonlocal phenomena like quantum entanglement. Quantum entanglement seems to be irreconcilable with the theory of general relativity, because it suggests some form of faster-than-light signaling, or retrocausal signaling. However, there is an object in general relativity that permits such activity, and that is the Einstein-Rosen bridge, also known as wormholes. As such, the quantum entanglement of particle-pairs may be the result of their spacetime connection via micro-wormholes; they are Wheeler wormhole particle-pairs. 

Furthermore, understanding that the gravitational force—a manifestation of the underlying spacetime geometry and information (entropic) structure—is already present, as well as the “dark energy” that has an anti-gravitational effect, but that the two are balanced unless there is a gradient in the spacetime structure, we can begin to postulate mechanisms by which we might modulated, or engineer this vacuum structure to produce gravitationally-based energy and propulsion technologies.

In fact, it has already been shown that the ability to produce a gravitational dipole in the geometry of space can enable superluminal travel, without any violation of the “speed of light limit” set in general relativity. This is known as the Alcubierre warp-drive, something that may be possible in the near future following this new understanding of the fundamental nature of space and how to engineer the vacuum to utilize the nearly infinite energy potential of the zero-point field. 

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