Overview of qst


quantum space theory: the short version


As a specific form of Superfluid Vacuum theory (SVT), quantum space theory (qst) is an approach within theoretical physics and quantum mechanics that stands as a candidate for the theory of quantum gravity. The theory assumes a superfluid vacuum whose geometric structure can be proximately described as an acoustic metric and ultimately described as a hierarchal fractal. Specifically it assumes that the superfluid vacuum is constructed from quanta that are in turn constructed (via self-similarity and scale invariance) from subquanta, and so on ad infinitum.


This geometric picture realigns our expectations of Nature. In as much as those expectations reproduce the mysteries of physics, they give us intuitive access to (and geometric explanations of) their origins. For example, the assumption that the vacuum is a superfluid (or a BEC) automatically enables us to derive Schrödinger’s non-linear wave equation, also known as the Gross-Pitaevskii equation, from first principles. This offers us unprecedented ontological access to what the wave equation means and why it is written into Nature. Furthermore, by treating the vacuum as an acoustic metric, we automatically end up with an analogue for general relativity’s curved spacetime within regimes of low momenta. This picture also dissolves the mystery of mass generation, the question of how the fundamental particles get their mass, because it portrays mass generation similar to the gap generation mechanism in superconductors or superfluids. In other words, mass becomes a consequence of symmetry breaking quantum vortices forming in the vacuum condensate.


How many other mysteries can we ontologically penetrate with this model? To answer that question Thad Roberts, and a team of others, are currently pursuing the full set of implications of this geometry and developing its complete mathematical formulation. Whether or not this new model turns out to completely map Nature, it, at minimum, offers a unique and creative perspective. The theory paints a multi-dimensional realm, a vacuum with more texture than previously assumed, and all of the dynamics in that medium are controlled by the laws of cause and effect. This offers us the chance to get beneath the modern formalism of quantum mechanics by positing that the effects of quantum mechanics and general relativity are emergent phenomena that supervene on spacetime’s superfluid structure. Consequently, this approach explicitly reveals a Universe that is, on every level, deterministic.


Those working on this project are motivated by the potential this return to determinism has to put us in better touch with reality and heighten our humanity. The more we understand Nature’s infinitely cascading structure and its dynamics, the more we can come to grips with our ‘magnificent insignificance.’ In the spirit of that investigation, we invite you to critically explore this new perspective and thank you for participating in the adventure of discovering Nature’s truths for yourself.


Please note that we are acutely aware that this new theory might not turn out to accurately map Nature. So far, several testable predictions have fallen out of the theory, and any one of them could falsify it. This is part of the process of scientific investigation. Our desire to complete Einstein’s task moves us to explore theories that are capable of making epistemic contributions. In general, such efforts should be focused (in response to the constraints we are under) toward those theories with the greatest ontological potential. As the candidate for the theory of quantum gravity that offers the most intuitive accessibility, quantum space theory is our pick for the theory with the greatest ontological potential.


All professional and constructive reviews of this work are welcome. A book on this topic, written for a general audience (of science enthusiasts) can be found here. (If cost is a barrier please send us a message.) Contact us with questions, comments, or to join the research effort at ei at EinsteinsIntuition dot com.




Quantum space theory posits itself as a possible coherent axiomatic explanation for the mysterious effects described in quantum mechanics and general relativity. This picture of spacetime can be codified by a simple set of postulates, a set of axioms about the structure of spacetime’s superfluid fabric (defining it to be a geometric fractal that on any one level behaves as an acoustic metric). The theory depends upon those axioms in a deductive-nomological fashion.


To date, effects like curved spacetime, black holes, quantum tunneling, wave-particle duality, dark energy, dark matter, nonlocality, Heisenberg uncertainty, etc., have remained logically unintelligible when filtered through Euclidean assumptions (treating space as though it were infinitely smooth, continuous, and made up of only three dimensions). Qst is driven by the goal of obtaining a complete and intuitive understanding of those effects by starting over with the assumption that the vacuum is a superfluid.


The axioms of qst are:

  1. 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.
  2. 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.
  3. 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:

  1. 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.
  2. Modeling the superfluid vacuum as an acoustic metric reproduces an analogue for general relativity’s curved spacetime within low momenta regimes.
  3. Mass generation is a consequence of the symmetry breaking that occurs when quantum vortices form in the vacuum condensate.
  4. 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 3n + 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.
  5. 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”).
  6. The constants of Nature are derivatives of the geometry of spacetime: they are simple composites of π, ж, and the five Planck numbers.
  7. When the quanta of space are maximally packed they do not experience time because they cannot independently or uniquely resonate.
  8. Black holes are collections of quanta that are maximally packed — regions of maximum spatial density.
  9. When two objects occupy regions of different quantum density, the object in the region of greater density will experience less time.
  10. 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:

  1. 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.
  2. 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).
  3. 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.
  4. 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).
  5. The theory predicts that quantum tunneling should be less frequent in regions of greater curvature (regions with a greater density of space quanta).
  6. The theory predicts that supersymmetric geometries are available only in axiomatic frameworks with a total number of dimensions equal to 3n + n, where n is an integer.
  7. 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.



Up until now, our intuitions about the world have, for the most part, been imprisoned by the confines of four dimensions (three dimensions of space plus one dimension of time). Our investigations of the mysteries effects we have observed in Nature have all started from this reference. As a consequence, we have tried to explain unexpected effects (like the Moon orbiting the Earth instead of just going 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.


When we hold onto these traditional assumptions about space and time it becomes necessary to awkwardly superimpose equations for four forces on top of our preconceived axiomatic construction in order to retain predictability. The problem is that this method of regaining predictability robs us of the ability to explain those effects. Einstein interrupted this process by constructing a geometry that included the effects of gravity within his metric. Qst extends this approach by introducing an intuitive eleven-dimensional vacuum geometry (nine space dimensions and two time dimensions). So far this geometry appears to have the ability to contain Nature’s strange characteristics (the effects traditionally assigned to the four forces). To more rigorously determine whether or not those geometric characteristics fully account for the effects we have observed, we are working to complete a full mathematical formalism of the axiomatic structure.


This picture gives us intuitive access to Nature’s mysteries by transforming the arcana of general relativity and quantum mechanics into necessary conditions of Nature’s geometric structure. Just how precisely qst maps all of Nature’s characteristics is a matter of scientific investigation. Before that question is resolved we can be assured that, as an intuitively accessible deductive construction, the model has significant scientific value. (Note that we have known for quite some time that Nature does not actually map to Euclidean geometry, nevertheless, the deductive, axiomatic framework known as Euclidean geometry continues to be a very useful and practical tool).


The mere possibility that quantum space theory maps something new in the spectrum of Nature’s colorful character makes it worth investigating. But the fact that it enables us to visualize eleven dimensions simultaneously, something that has never been done before,  is what most directly speaks to its contributory value to science. From this we gain the potential to expand our intuitive horizon beyond our inbuilt senses and begin to penetrate the geometric origins of Nature’s mysteries: Heisenberg uncertainty, wave-particle duality, what the insides of black holes are like, the cause of the Big Bang, why the constants of Nature are what they are, dark matter, dark energy, etc.


With an intuitively accessible model big science is no longer only for the professional physicist. Whether or not the model of quantum space theory is eventually shown to map Nature with precision, it provides us value because once we are equipped with the eleven-dimensional geometry of a superfluid vacuum, the biggest questions in physics gain elegant and simple analogies that anyone can understand.


For more information check out this 54 minute introduction video, or pick up your copy of  ‘Einstein’s Intuition‘ by Thad Roberts.


why it is needed

As Thad states in chapter one of his book, 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.”


“Even if physicists were one day to conclude that their assembly was mathematically correct, it would not actually increase our ability to truly comprehend Nature unless it was translated into some sort of picture. Therefore, since it is really the picture that we are after, maybe it is time for us to consider whether or not our efforts will bear more fruit under a different approach. Specifically, to maximize our chances of completing our goal of intuitively grasping Nature’s complete form, maybe we should follow the lead of young Einstein and return to a deductive conceptual approach. Perhaps it is time for us to place our focus on constructing a richer map of physical reality.”


But, how do we actually do this? We are told, over and over, by the professional physicist that it is impossible to visualize more than three spatial dimensions. Yet, today’s leading theories routinely suggest, or even require, more than three spatial dimensions. Many people find the notion of additional dimensions absurd. They suggest that when other dimensions pop up in our equations they are just artifacts of our intricate mathematics of theoretical physics. They claim that those equations should not be taken as an indication of the “actual” existence of these extra dimensions. It is in response to this reaction that Thad comes in loud and clear.


following an idea

qst proposes that these extra dimensions are real, as real as the 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.


A rather significant and often overlooked (under-visualized) remnant of modern physics is that space appears to be quantized, that is, made of tiny, indivisible pieces (quanta). This flies in the face of our common-sense experience of Nature (of the continuous three dimensions of space that we usually try to assign to Nature), but quantum mechanics seems to point to this fact (if it can be said to point to anything). In the act of embracing the quantized nature of spacetime and coupling that realization with the requirement of extra dimensions, a simple, elegant picture of reality emerges. Qst is that picture.


qst proposes that space is literally quantized into discrete pieces (quanta), and then shows how an eleven-dimensional structure follows from that claim. 


problems solved?

The notion that the vacuum is a superfluid (whose geometric structure is hierarchically  quantized) gives us the ability to explain:


  • 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


Instead of resting on a set of impenetrable dialogue filled with complex and distracting jargon, the solutions proposed by quantum space theory are all intelligible. What excites supporters of qst most is that, by examining the idea that the vacuum is a superfluid they have gained intuitive, simultaneous access to more than four spacetime dimensions and come to intuitively absorb details of Nature that allow them to intimately understand the mysteries of physics.


We invite you to participate in the task of steering science back towards its goal of obtaining  ontological clarity, of acquiring intuitive pictures, deductive solutions, and accessible explanations for Nature’s baffling effects. We invite you to read the opening chapters of the upcoming book and to learn how to visualize eleven dimensions, or pick up your copy of the book. Open yourself to a change in perspective and escape the conceptual limitations of three dimensions of space and one dimension of time.


Contact us with questions, comments, or to join the research effort at ei at EinsteinsIntuition dot com.