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.