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, or a BEC, 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 Higgs boson gets its mass, because it por­trays mass gen­er­a­tion sim­ilar to the gap gen­er­a­tion mech­a­nism in super­con­duc­tors or super­fluids. In other words, mass become 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, with more tex­ture than we pre­vi­ously assumed, which is con­trolled by the laws of cause and effect. It gets beneath the modern for­malism of quantum mechanics and posits that quantum mechan­ical and gen­eral rel­a­tivistic effects are emer­gent phe­nomena that super­vene on spacetime’s super­fluid struc­ture. Consequently, it explic­itly reveals a Universe that is, on every level, deterministic.

Those working on this project believe that this return to deter­minism has the ability to heighten our humanity by putting us in better touch with reality. It does this by helping us under­stand Nature’s struc­ture and char­acter, helping us intel­lec­tu­ally pen­e­trate the infi­nite cas­cade of our actions, and by giving us clarity of our ‘mag­nif­i­cent insignif­i­cance.’ We invite you to crit­i­cally explore this new per­spec­tive and hope that you will par­tic­i­pate 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 a 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 only can­di­date for the theory of quantum gravity that is intu­itively acces­sible, quantum space theory is our pick for the theory with the greatest onto­log­ical potential.

All pro­fes­sional and con­struc­tive reviews of this work are wel­come. Contact us with ques­tions, com­ments, to get a free pdf copy of the book, or to join the research effort at qst@​EinsteinsIntuition.​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 (or BEC vacuum) mimics a per­fect fractal: the familiar medium of x, y, z space is com­posed of a large number of “space atoms” called quanta that inter­ac­tively mix about; those quanta are com­posed of a large number of sub-quanta and so on, ad infinitum. This claim of 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 (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) in its com­plete form, 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 should obey Lorentz sym­metry. This means that for low momenta con­di­tions the theory expects to cap­ture 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 the min­imum cir­cum­fer­ence to diam­eter ratio will be equal to a min­imum value, which at this point we believe is 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 decreasing), the frac­tion of space char­ac­ter­ized by the denser geom­etry 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” for those effects (in the non-explanatory sense). In this process we have restricted our own 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, a full math­e­mat­ical for­malism of the axiomatic struc­ture will have to be com­pleted — a project that is underway.

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 the entire spec­trum of Nature’s col­orful char­acter makes it worthy of inves­ti­ga­tion. The fact that the model enables us to visu­alize eleven dimen­sions simul­ta­ne­ously — some­thing that has never been done before — speaks to its con­trib­u­tory value to sci­ence and the goal of expanding the reach of human intu­itions beyond our inbuilt senses. It offers us the pos­si­bility of onto­log­ical clarity.

To start grasping this higher-dimensional intu­itive pic­ture check out the book excerpts in the book excerpts sec­tion. If you are more ana­lyt­i­cally inclined you may desire to skip ahead to the con­stants of Nature sec­tion where you will dis­cover how 27 con­stants are pre­cisely and non-arbitrarily deter­mined by the eleven-dimensional geom­etry of qst. Or visit the pre­dic­tions sec­tion where sev­eral of the con­se­quences of this new geom­etry are laid out. Then examine the for­malism sec­tion where the foun­da­tional math­e­matics of vacuum super­flu­idity is explained.

A 54 minute intro­duc­tion to this eleven dimen­sional geom­etry is avail­able via the “Conversations” video posted on this site. The full geo­metric expla­na­tion, laid out in the forth­coming book titled ‘Einstein’s Intuition’ by Thad Roberts, is also avail­able by spe­cial request.

In short, qst is a spe­cific ver­sion of super­fluid vacuum theory. It is a deduc­tive theory that the­o­ret­i­cally welds the effects of gen­eral rel­a­tivity and quantum mechanics together into one intu­itively acces­sible eleven-dimensional geom­etry. In his book, Thad Roberts lays out a intu­itive con­cep­tual bridge into the mys­teries of modern physics, and then he invites us all to use that bridge to become a part of the sci­en­tific inves­ti­ga­tion that Einstein ded­i­cated his life to. Some of the mys­teries this process allows us to pen­e­trate are: 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, and dark energy.

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, once we are equipped with the eleven-dimensional geom­etry that Thad describes in his book, all of the biggest ques­tions in physics become reducible to mat­ters that are ele­gant and simple for anyone to under­stand. Through this new geom­etry we all become capable of reaching beyond the limits of human senses and par­tic­i­pating in the mys­teries that extend beyond our his­tor­ical horizon.


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 geo­metric ori­gins of the con­stants of Nature
  • The geo­metric ori­gins of force phenomena
  • Why the wave equa­tion is a descriptor of Nature (which also explains Heisenberg uncer­tainty & wave-particle duality)
  • Red-shift/dark energy in geo­metric terms
  • The geo­metric ori­gins of dark matter
  • and, what caused the Big Bang

This claim does not rest on a set of impen­e­trable dia­logue filled with com­plex and dis­tracting jargon. The solu­tions offered by quantum space theory are all intel­li­gible. Thad presents these solu­tions in great detail in the third part of his book. This is what most excites the sup­porters of quantum space theory. By exam­ining this new geo­metric struc­ture for space­time they have gained intu­itive, simul­ta­neous access to more than four space­time dimen­sions and gazed upon details of Nature that had pre­vi­ously gone unimagined.

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 send a request for the entire book). We invite you to open your­self to a change in per­cep­tion and to dis­cover how to escape the con­cep­tual lim­i­ta­tions of three dimen­sions of space and one dimen­sion of time.