# Overview of quantum space theory

Quantum space theory is a pilot-wave theory [1] (similar to de Broglie’s double solution theory, [2] the de Broglie-Bohm theory, [3] and Vigier’s stochastic approach [4]) that mathematically reproduces the predictions of canonical quantum mechanics while maintaining a completely lucid and intuitively accessible ontology. The theory takes the vacuum to be a physical fluid with low viscosity (a superfluid), and captures the attributes of quantum mechanics and general relativity from the flow parameters of that fluid. This approach objectively demystifies wave-particle duality, eliminates state vector reduction, reveals the physical nature of the wave function, and exposes the geometric roots of Heisenberg uncertainty, quantum tunneling, non-locality, gravity, dark matter, and dark energy—making it a candidate theory of quantum gravity and a possible GUT.

**Evolution of the idea**

**Quantum mechanics from pilot wave theory**

- The wave evolves according to the Schrödinger equation,
- The probability distribution of an ensemble of particles described by the wave function , is , and
- Particles are carried by their local “fluid” flow. In other words, the change of particle’s position with respect to time is equal to the local stream velocity , where , and the “velocity potential” is related to the phase of by .

*Physical Review*.

**85**(2): 166–179 (1952).

*Nature*(London) 169, 702 (1952).

*Phys. Rev.*

**109**(5): 1492–1505 (1958); Roati, Giacomo; et al., “Anderson localization of a non-interacting Bose-Einstein condensate”.

*Nature*.

**453**(7197): 895–898 (2008).

*Ann. Phys. (Leipzig)*

**17**, 132. “Concerning an Heuristic Point of View Toward the Emission and Transformation of Light”(1905).

*Ann. Phys. (Paris)*

**3**, 22 (1925).

*Phys. Rev*.

**85**, 166, 180 (1952).

*Physik*

**40**, 332 (1926). See also: Madelung equations.

*Phys. Rev.*

**96**, 208 (1954).

*Une tentative d’interprétation causale et non-linéaire de la Mécanique Ondulatorie*(Gauthier-Villars, Paris), (1956).

**Where do we go from here?**

#### The axioms of qst are:

- The hierarchical structure of the superfluid vacuum is self-similar and, therefore, conforms to a perfect fractal. In short, the familiar medium of
*x, y, z*space is composed of a large number of “space atoms” called quanta that dynamically mix and interact. Those quanta are composed of a large number of sub-quanta and the sub-quanta are composed of sub-sub-quanta and so on, ad infinitum. Vacuum superfluidity constrains the possible states of the vacuum in accordance with energy conservation, de Broglie relations, and linearity. More generally it constrains the vacuum as an acoustic metric. - Time is uniquely defined at each location in space and evolves discretely (for each quantum) as the number of whole resonations each quantum undergoes. As a result, the acoustic metric inherits a Newtonian time parameter and therefore exhibits the important property of stable causality.
- Energy (total geometric distortion) is conserved. Energy conservation means that all metric distortions (phonons, quantum vortices, etc.) are interchangeable from one kind to another, including the transference of metric distortions from one hierarchical level to another, like the quantum level to the sub-quantum level.

#### Some of the theorems/consequences that follow from those axioms are:

- The wave equation (the non-linear Schrödinger equation, also known as the Gross-Pitaevskii equation) can be derived from first principles (see here, or here), from the assumption that the vacuum is a BEC whose state can be described by the wavefunction of the condensate.
- Modeling the superfluid vacuum as an acoustic metric reproduces an analogue for general relativity’s curved spacetime within low momenta regimes.
- Mass generation is a consequence of the symmetry breaking that occurs when quantum vortices form in the vacuum condensate.
- The total number of spacetime dimensions in or spatiotemporal map depends on the resolution we desire. (Are we only quantizing the fabric of
*x, y, z*? Or are we also keeping track of the subquanta that those quanta are composed of? and so on.) For any arbitrary resolution, the number of dimensions is equal to 3^{n}+*n*. A second order perspective (*n*= 2) quantizes the fabric of space one time, and a third order perspective quantizes the volumes of that fabric, and so on, ad infinitum. - Quantization restricts the range of spacetime curvature: the minimum state of curvature (zero curvature) can be represented by the ratio of a circle’s circumference to its diameter in flat space (π), and the maximum state of curvature can be represented by the value of that ratio in maximally curved spacetime, a number that we will represent with the letter ж (“zhe”).
- The constants of Nature are derivatives of the geometry of spacetime: they are simple composites of π, ж, and the five Planck numbers.
- When the quanta of space are maximally packed they do not experience time because they cannot independently or uniquely resonate.
- Black holes are collections of quanta that are maximally packed—regions of maximum spatial density.
- When two objects occupy regions of different quantum density, the object in the region of greater density will experience less time.
- Because the quanta are ultimately composed of subquanta, all propagations through space necessarily transfer some energy from the quantum level (motion of the quanta) to the subquantum level (to the internal geometric arrangements and motions of the subquanta). Although this transference of energy is proportionally very small (being approximately equal to the energy multiplied by the ratio of the subquantum scale to the quantum scale) it is additive. Therefore, it can become significant over large scales—leading to what we now call red-shift.

#### Some of the testable hypotheses, or predictions, of this theory are:

- Although the superfluid vacuum is non-relativistic, small fluctuations in the superfluid background obey Lorentz symmetry. This means that for low momenta conditions the theory captures the expectations of general relativity, but at high energy and high momenta conditions the theory projects Newtonian expectations over relativistic ones. Therefore, the theory predicts that when massive objects are accelerated to near the speed of light they will exhibit effects that will contradict general relativity in favor of Newtonian projections.
- When we place a circle of any (macroscopic) size in a region where the gradient of spacetime curvature is at a minimum (where there is zero change in curvature throughout the region) the ratio of its circumference to its diameter gives us a value of 3.141592653589… (π). Qst predicts that this ratio will decrease if the circle occupies a region with a nonzero gradient of spacetime curvature. Furthermore, it predicts that in regions where the gradient of spacetime curvature is at a maximum there will be a minimum possible value for this circumference to diameter ratio. More specifically, for all possible circles centered around a black hole (or approaching the quantum scale) the minimum circumference to diameter ratio will be equal to a minimum value of 0.0854245431(31) (ж). This means that, instead of being randomly ascribed, the constants of Nature are immediate consequences of the geometric character of spacetime. A quantized picture of spacetime requires a natural minimum unit of distance (the Planck length), a natural minimum unit of time (the Planck time), and maximum amounts of mass, charge, and temperature in reference to the minimum units of space and time (Planck mass, Planck charge, and Planck temperature). Furthermore, quantization dictates minimum and maximum limits for the gradient of spacetime curvature (π and ж). According to qst, the constants of Nature are composites of these seven numbers. It turns out that this claim holds when ж is equal to 0.0854245431(31).
- The theory predicts that temperature dependent phase changes exist in space—regions where the average geometric connectivity of the quanta of space transition from one state to another. Furthermore, the theory predicts that because the background temperature of the universe is cooling (the average wavelength of the Cosmic Microwave Background Radiation is increasing), the fraction of space characterized by the denser geometric phase should become more prevalent with time.
- The theory predicts that the average radii of dark matter haloes should decrease as the energy output of the host galaxy decreases. It predicts that by comparing contemporary haloes we should find that the average radii of these haloes should depend on the energy output of the host galaxy and that the further the background temperature of space drops below the temperature of the critical phase transition the smaller the average radii of dark matter haloes should be. It follows from this that the radii of local dark matter haloes should decrease in the future (with a dependence on its host galaxy’s output).
- The theory predicts that quantum tunneling should be less frequent in regions of greater curvature (regions with a greater density of space quanta).
- The theory predicts that supersymmetric geometries are available only in axiomatic frameworks with a total number of dimensions equal to 3
^{n}+*n*, where n is an integer. - The theory leads us to expect that when the highest-energy gamma rays reach us from extremely distant supernova, they should be less red-shifted in proportion to the difference in time between the arrival of the gamma rays and the remaining wavelengths divided by the travel time of the longer wavelengths.

#### Impact

*straight through space*) by inventing “forces” that we have held responsible (in the non-explanatory sense) for those effects. This process has restricted our ontological access.

#### Why it is needed

*Einstein’s Intuition*, we need to return to a place akin to where the young Einstein found himself, a place where the senses are allowed a deep connection to Nature, facilitating Einstein’s envisionment of the properties of light and time. Thad goes on, “this … highlights a fundamental problem in the approach taken by modern physics. For the past several decades, theorists and mathematicians have been working on constructing a framework of Nature that is capable of mathematically combining the descriptions of general relativity and quantum mechanics under the same rubric. … But their efforts have been focused on organizing Nature’s data into a self-consistent assembly—like the ones and zeros of a digital picture. The problem is that this inductive approach does not encourage, let alone require, the discovery of a conceptual portal.”

*x, y, z*and

*t*dimensions we experience every day. Qst further elaborates a hierarchical structure to these extra dimensions that allows us to comprehend, and even visualize, the super and intra dimensions.

- The constants of Nature—as a consequence of vacuum geometry
- Force phenomena—in terms of allowed geometric distortions in the vacuum
- The wave equation—as a descriptor of how distortions translate though the vacuum
- Heisenberg uncertainty—as a manifestation of vacuum quantization and mixing
- Wave-particle duality—as a manifestation of the vacuum’s fluid nature
- Dark matter—as a phase change in the vacuum
- Dark energy—as a transference of energy from the quanta to the sub-quanta
- The State Vector—as a blurred (ensemble) representation of the vacuum’s possible state (given our ignorance of its exact state at any moment), and more.