Questions and answers:

I’d like to ded­i­cate this page to ques­tions that anyone out there might have regarding the axioms, ten­ants, con­clu­sions, or insights of quantum space theory. Please send me your ques­tions and I will do my best to respond via video. My hope is that this forum will be a useful resource for those that have unan­swered ques­tions about quantum space theory.


Question 1: From Fred Goode

I’m inter­ested in better under­standing the 11 dimen­sions of the QST.

I under­stand that a dimen­sion is an axis along which some­thing can move without requiring any move­ment in another axis or dimension.
x, y, and z are obvious exam­ples of (3) dimen­sions. I would say time is a 4th as you can move through time without moving in x, y, or z. I see time as being a dimen­sion because there is direc­tion. Past – present – future.
I also under­stand the tiny size of the planck. It’s really REALLY small. You describe in Conversations One that this is the smallest we can divide space into. Like the AU (gold) atom, if you divide it again, it’s no longer AU. But for a planck length, I don’t get this.
Is there no such thing as a 1/2 of a planck?  I look at the planck as a scale like a ruler. A ruler is 12 ” long, and has 12 single inch seg­ments on it, with each inch being sep­a­rated into some frac­tion of an inch. It is up to the man­u­fac­turer as to what frac­tional amount he wants to dis­play.  1″, 1/2″, 1/4″, 1/8″, and very com­monly, 1/16″ or even 1/64th inch. Why do we never see rulers with 1/128th inch incre­ments? Because it’s too small to “eye ball”.  That does not mean the dimen­sions smaller than 1/64″ don’t exist. We mea­sure them with other tools.  Just not with a ruler. How is the Planck scale dif­ferent from what I describe?
Ok, ques­tion part 2. If the planck is a scale and quanta exists within this scale, you seem to be saying that because it’s sub-planck size, it can no longer adhere to the x, y, z dimen­sions to pin­point it’s phys­ical loca­tion. I think the problem for me is that I don’t yet get how dis­tance (1 planck length) cannot be fur­ther divided. I under­stand this with the AU atom, but it’s not apples and apples. At least I don’t yet see it.
The other stuff falls into place for me fine as long as I accept this geom­etry as fact. I see what a black hole is, how time slows down approaching the black hole, why red shift occurs, what dark matter is, why quantum tun­neling occurs, why the chicken crossed the road, and every­thing else. I just need help with describing this to other people in the area of “you cannot divide a planck’s length into a 1/2 planck”. WHY NOT??!!??!!   :)
Thanks for your time
Fred Goode


Click on the video below to view my response to ques­tion 1:


Comments (71)

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  1. Thad, a sum­mary of my mus­ings yes­terday on your model in terms of wave dynamics. What do you think?

    Space may reg­ister to us only as the tips of standing three dimen­sional quantum-bit wave struc­tures always only as a single quantum of one Planck length only above a cer­tain threshold ampli­tude in rep­re­sen­ta­tion of space, and indi­vid­u­ally vibrating as the smallest gran­u­larity of space-time and col­lec­tively vibrating as what we per­ceive as space and time. There is a super­space at higher res­o­lu­tion in which the full super­volume of these standing cen­ters move around and through each other (but col­li­sions happen at that super space-time scale at a far lower fre­quency than the fre­quency of vibra­tions of each spher­ical standing wave). Each of these spheres is a uni­verse in itself with exactly the same char­ac­ter­is­tics rel­a­tive to its res­o­lu­tion as ours, only at the next fractal res­o­lu­tion up. Similarly con­cerning our uni­verse, the absolute direc­tion into entropy may be simply a col­lapse to and through zero (if seen as sinu­soidal wave). Another uni­verse could move through us and screw every­thing up, but it hap­pens far less fre­quently than the 100 bil­lion odd years it could take to fall into com­plete entropy.

  2. Joe Fill says:

    Hello Thad –

    First off, let me say thanks for sending me your book. After watching your TEDx Boulder talk, I couldn’t wait to delve deeper into your theory, and I wasn’t disappointed.

    My formal sci­en­tific studies began and ended with my high school physics class in 1971, and I’ve never devel­oped a feel for math beyond Euclidian geom­etry. However, I’ve tried to edu­cate (or at least famil­iarize) myself in a variety of sub­jects, from quantum mechanics to cos­mology to rel­a­tivity. Your book went a long way to helping me under­stand the con­cepts from the Boulder talk, but I still have a few ques­tions you might clarify.

    1) You talk about time as being defined by the res­o­nance of the quanta. Does every­thing in the uni­verse res­onate, and if not, why do the quanta res­onate? What exactly does it mean to have res­onating quanta? Do the quanta change size or shape during this resonation?

    2) As the space quanta move around in super­space, do they main­tain the the same X,Y,Z rela­tion­ship to other quanta (although not the same dis­tance)? Or are their X,Y,Z posi­tions only defined on an average or macro scale?

    3) Possibly related to and answered by 2) above, if each quanta iden­ti­fies (or is iden­ti­fied by) a unique X,Y,Z coor­di­nate, and even the smallest bit of matter is many orders of mag­ni­tude larger than a single quanta, how is matter’s loca­tion spec­i­fied? Am I cor­rect that even a single elec­tron would occupy bil­lions of quanta of space?

    One con­cept that always both­ered me, and which you address in your book, is the idea that move­ment through a con­tin­uous space­time is log­i­cally impos­sible. In order to go from point A to point B, you’d have to leave point A, and before arriving at point B, you’d have to get to a point 1/2 way. But to get to the 1/2 way point, you’d have to get to a point 1/2 way to there, or 1/4 of the way to point B. For each point you’d have to get to, you’d always have to get to a point 1/2 way to that point, and you’d never to point B. Quantized spce solves this little problem.

    Thanks in advance for any insight you can give me on this, and I look for­ward to seeing the illus­tra­tions for Einstein’s Intuition.

    – Joe Fill
    Indianapolis, IN

    • Thad Roberts says:


      I recently fin­ished going through the entire book for another round of edits, improving the flow quite a bit, cor­recting some errors, and adding many fig­ures. If you are inter­ested in the updated ver­sion send me an email and I’ll pass it along.

      As for your questions:

      1 – In this model all things in the uni­verse are thought of as being made up of space quanta, but not all space quanta freely res­onate. Quanta that are stuck together, touching, are, by def­i­n­i­tion, not able to freely res­onate until they are sep­a­rated again. Some quanta are only in this sit­u­a­tion for a short dura­tion while others might take it on for a long dura­tion (dura­tion here ref­er­ences the average number of free res­ig­na­tions that the average back­ground quanta in empty space undergo while these quanta are stuck together). Also, in this model, each quanta is, to first approx­i­ma­tion, an elastic sphere. Their elastic prop­erty, added to the fact that they are moving around and bumping into each other, is the reason that they are res­onating. Resonation means a geo­metric con­tor­tion of the elastic sphere. If the uni­verse were close to absolute zero, if the average super­spa­tial velocity of each quanta was next to zero, then the expec­ta­tion would be that the quanta would freely vibrate unto them­selves, with less and less ampli­tude, until they ran out of energy (i.e. all the energy (geo­metric con­tor­tion) of res­onation trans­ferred inter­nally). This would slowly change the sig­na­ture of time in the universe.

      2 – As the quanta move around in super­space, they mix the x, y, z grid. So, no – they do not main­tain the same x, y, z rela­tion­ship to the other quanta. However, since all the quanta are iden­tical, most effects from this mixing wash out as we approach macro­scopic scales. Exact x, y, z posi­tions are defined only for exact moments – snap­shots of the entire grid at that point. Because the quanta are mixing about, spe­cific points flicker around in posi­tion from the x, y, z per­spec­tive. This flick­ering, how­ever, even washes out (it is gen­er­ally con­fined to a rel­a­tively small region) as we zoom out.

      3 – There are two pos­sible answers to this ques­tion. In the first pos­si­bility, the most fun­da­mental mass par­ti­cles may be as simple as being two (or three or four and so on) quanta stuck together (for any dura­tion). This inter­esting thing about this pos­si­bility is that while the quanta are stuck together they act as the same unique loca­tion in the x, y, z metric. They no longer rep­re­sent unique loca­tions, so they, in effect take on the char­ac­ter­is­tics of being one loca­tion. Still, other quanta inter­acting with them will rebound in a dif­ferent way then they would with quanta that are not stuck together, so the map around them warps – the average geo­metric con­nec­tivity warps. In this case, the loca­tion of this matter par­ticle would be spec­i­fied in ref­er­ence to the col­lec­tion of all the other quanta around it – just as it would if it were a single quanta. In the second pos­si­bility, matter may make ref­er­ence to geo­metric eddies. If the metric of space is a per­fect super­fluid many forms of extremely stable eddies are allowed. These eddies might even be infi­nitely stable so long as they are not inter­rupted. If these swirling eddies in the metric ref­er­ence mass par­ti­cles, then mass par­ti­cles only have posi­tions in the more fuzzy sense – gaining res­o­lu­tion on larger scales. Still, one could imagine that in a stable eddy there is a center, and this center posi­tion could fill in as the meaning of the loca­tion of the particle.

      These are spec­tac­ular ques­tions Joe. As you can tell, I’m still working out the ram­i­fi­ca­tions of the last ques­tion. Excited to see where it takes us. :-)

    • Joe Fill, re. Q&A(3) above, matter as clumps of quanta or alter­na­tively eddies in a super fluid. Geoffrey Haselhurst’s model con­sists of standing 3D point waves in an infi­nite medium, and matter as stable 3D lat­tice struc­tures. http://​www​.space​and​mo​tion​.com/

      • Thad Roberts says:

        The main­te­nance of 3D standing waves requires con­stant inputs that are per­fectly tuned from every direc­tion. An eddy in the super­fluid, how­ever, main­tains itself because of the non-rotationality of the super­fluid – its ten­dency to form quan­tized eddies. In a way what Geoffrey and I are moving towards is sim­ilar, but sta­bility in the idea of a standing wave requires a very large coin­ci­dence for each par­ticle. This leads to a problem when trying to explain how all elec­trons appear iden­tical. If, instead, these lat­tice struc­tures are explained as quan­tized eddies in the super­fluid vacuum, this ques­tion is nat­u­rally accounted for.

  3. Aaron says:

    Hi Thad,

    I just dis­cov­ered your TED talk yes­terday evening and it blew my mind! After piecing it back together (my mind, that is), I decided to check out your web­site. I ended up spending sev­eral hours reading through the site (including your blogs) and watching the videos. Fascinating stuff! A few ques­tions have popped into my mind, but I think many of them are prob­ably answered in your book. In fact, after reading the syn­opsis of your book, I know that the answers to many of my ques­tions are addressed there.

    I’d like to get a better handle on the work that’s already been done before asking any ques­tions. Are you still emailing copies of your book? If so, I’d love to read through it. I’m not sure how close you are to print (it’s been a while since your last blog post), but if the book is already out, I’ll hap­pily pur­chase a copy :)

    Anyway, thanks for sharing qst. I’ve come across a handful of TOEs over the years, and none of them have suc­cess­fully been able to explain and account for all of the odd­i­ties that exist in the stan­dard model — let alone pro­vide an intu­itive frame­work. I agree that all phys­ical the­o­ries, their math­e­mat­ical expres­sions apart, ought to lend them­selves to so simple a descrip­tion that, in the words of Einstein, “even a child could under­stand them.”


    • Thad Roberts says:

      I’ve emailed you a link to the pdf. Much progress has been made recently, inspiring some revi­sions in chap­ters 19-21 and improving the overall clarity. When you reach chapter 21 I rec­om­mend re-downloading the pdf to make sure you have the most updated ver­sion. If you feel any­thing in the book could be made more clear please let me know :-). I look for­ward to your feed­back.

      • Aaron says:

        Hello again,

        Thanks for the link. I down­loaded the pdf and just fin­ished chapter 4. I’m really impressed by the sequence in which you’ve laid every­thing out. The hard work that you’ve put into this is plainly evi­dent. So far, I’ve been able to follow every­thing easily, and I have prior knowl­edge of each of the con­cepts that you’ve dis­cussed (with the excep­tion of qua­sicrys­tals, which I did a little internet research on).

        Just for the record, I’m not a trained sci­en­tist in any area, and my knowl­edge of cos­mology, astro­physics, quantum mechanics, etc. comes from the few books that I’ve read and doc­u­men­taries that I’ve watched. I have hopes of ulti­mately under­standing the con­cepts, his­tory, and math on a level equal to that of a researcher in the field, but I have a VERY long way to go. That being said, the fact that I can under­stand your book clearly up to this point gives me encour­age­ment that I’m making progress on this goal.

        If I have any editing related sug­ges­tions, I’ll men­tion them through email.

        Thanks again. This is awesome!


  4. Laz says:

    Hi Thad,

    I have been always inter­ested in our mys­te­rious Universe. I enjoy reading ur web­site, watching ur videos. However, i did not notice that u men­tioned the string or M theory before. What is ur view about it? Everything made up of vibrating strings which are 11 dimen­sional? What about 1 piece of space quanta which is 1 plank length (1.6 × 10 to the power of -35 metres), is it made up of 1 single string? According to some sci­en­tists, the size of a string can be some­where between 10 to the power of -34 or -35. So maybe a piece of string as the same as a space quanta?

    Thank u for ur help :)
    and…It would be amazing if u could send me ur book as well.


    • Thad Roberts says:

      Thank you for your ques­tions :-). I will email you a link to a copy of the book today. In response to your ques­tions, I enjoy the efforts made by the devel­opers of string theory to onto­log­i­cally access a causal story behind the mys­teries of quantum mechanics. However, I don’t think that such a story has been suc­cess­fully achieved as of yet by that theory. Nevertheless, string theory, now extended into super­string theory and M-theory, does have some inter­esting and notable par­al­lels that are high­lighted by the assump­tion that the vacuum is a super­fluid (quan­tized). Some of these are men­tioned in ‘Einstein’s Intuition.’ I look for­ward to your feed­back as you read.

  5. Laz says:

    Thanks a mil­lion Thad, i really appre­ciate ur reply and the great book!!!

    I will let u know if some­thing is not clear for me for sure :)

    All the best,

  6. Chris says:

    Hi Thad,
    I just came across your TED talk video the other day. I’m just an ama­teur when it comes to physics and cos­mology, but I love to listen to all these new, inspiring ideas. I’m very impressed with how much your theory was able to explain (espe­cially that phys­ical con­stants depend on the geom­etry of space itself, which I once spec­u­lated on… although ‘fan­ta­sized about’ would be prob­ably a better choice of words). Anyway, I’m just writing to say: Thanks! and: Keep it up! :)

    Also, my mind just hap­pened upon this ques­tion: is super­space also quantum in nature, or do you assume it’s infi­nitely smooth?

    • Thad Roberts says:

      Thanks for your ques­tion. In response to your ques­tion, the model we are working with assumes a per­fect fractal struc­ture, so yes it assumes that super­space is quan­tized, and that those quanta are com­posite enti­ties of much smaller sub-quanta, and so on. If you are inter­ested I can send you the book on this. Chapter 11 specif­i­cally covers this issue.

      • Chris says:

        Yes, thank you! I’d very much like to read more on this topic. I’ve watched the Conversations videos in the last few days, but some things are still not entirely, intu­itively clear to me (blame my brain). It’s only fair if I first learn more about it, before I take any more of your time. One thing I’d like to ask ahead though is how the quanta of space transfer energy, if they’re not actu­ally touching? Do they do it in our three spa­tial dimen­sions (where they’re pre­sum­ably always in con­tact) as long as they’re not touching in super­space? (Sorry, if I mixed up something).

        Actually, I have also some other comments/questions about things I think I under­stood a little bit better:
        1. Gravitational lensing was explained by dark matter. You explained it by a phase change of space caused by dif­fer­ences of tem­per­a­ture in space. Would the lensing effect always be in a form of a circle? Even in galaxy clus­ters, like here?: http://​upload​.wiki​media​.org/​w​i​k​i​p​e​d​i​a​/​c​o​m​m​o​n​s​/​0​/​0​b​/​G​r​a​v​i​t​a​t​i​o​n​e​l​l​-​l​i​n​s​-​4​.​jpg

        Ok, I’m not really sure it’s a per­fect circle on that pic­ture, but anyway, I imag­ined that if it all comes down to dif­fer­ences of tem­per­a­ture, then the lensing effect of the whole cluster should be prob­ably much more… dis­torted, irreg­ular? (Then again, it’s just my intu­ition which I learned not to trust fully 😉 ).

        2. You explained that the red shift of galaxies’ light is caused by loss of its energy due to kind of internal fric­tion of space-quanta (hope I got that right) …anyway it’s lost to the space itself. You also talked about the uni­verse from the time of the Big Bang till now. But wasn’t the red shift our only hint at the Big Bang from sin­gu­larity (or some­thing close to it) and infla­tion in the first place? If the energy of pho­tons is ‘lost’ in space, then maybe there is no infla­tion at all, and the uni­verse is basi­cally static in size. Only there is more and more of that ‘fric­tion’ in the space (or some parts of it) and so far we wrongly inter­preted data as accel­er­ating inflation?

        That would be all, for now anyway.
        Thanks again, Thad!

        • Thad Roberts says:

          Thank you for your ques­tions. First, in this model the quanta do touch. They elas­ti­cally interact in the super­spa­tial dimen­sions, col­liding and bouncing off of each other. I’ll try to even­tu­ally get a video of this up to make it more clear. Second, as for your ques­tion about grav­i­ta­tional lensing, there is no shape dif­fer­ence between the pro­jec­tions this theory makes and the tra­di­tional claims about dark matter. The dark matter haloes, or regions of phase tran­si­tion, around even cigar shaped galaxies is spher­ical. Therefore, we do expect the lensing effect to be cir­cular. There can be excep­tions from that cir­cular pro­jected image. For example if there are other objects between the source and observer fur­ther dis­torting the image. The spher­ical shape found in Nature is not fully explained in the tra­di­tional expla­na­tion of dark matter. But if it is a phase chance then we expect this spher­ical shape because of how ther­mo­dy­namic prop­er­ties are com­mu­ni­cated out­ward from their sources. You are right to sus­pect that ulti­mately there can in prin­ciple be a non spher­ical shape, but this will occur only as a grouping of other spher­ical shapes. So you might find some­thing that approx­i­mates a 3D Mickey Mouse out there, but this would require a very spe­cific place­ment of very spe­cific galaxies, all at just the right tem­per­a­tures and sizes and spac­ings. In gen­eral we just expect spher­ical mea­sure­ments for the halo region. Your second ques­tion is awe­some by the way. As it turns out, red­shift is not our ONLY hint that the uni­verse had a “first” moment. I use first here only in ref­er­ence to an inter­nally trace­able chain of cause and effect – not a claim that it was an ulti­mate cut off on cause and effect. The most solid way to get to the claim that the uni­verse must have had a begin­ning (in the sense we are taking about – a Big Bang) is to secure the second law of ther­mo­dy­namics and to rec­og­nize that all of physics is time-reverse sym­metric (some might sug­gest that the wave func­tion col­lapse might escape this, but it can be shown that this claim is unnec­es­sary – see Bohm’s inter­pre­ta­tion of quantum mechanics). With these two con­di­tions on board we fully expect that when­ever there appears some mea­sure of order in the uni­verse it is extremely likely that both before and after the emer­gence of that order it was less. Imaging a pool table with no fric­tion and no pockets. The balls have been moving around col­liding for a long time before you looked at it. Note that you can take snap­shots of the posi­tions of the balls, but most of these pic­tures will show you just random ori­en­ta­tions. This system has max­imum entropy – min­imum order. However, even­tu­ally all the balls will happen to col­lide all at once, packed into one corner. Clearly if we took a snap­shot of that moment it would be obvious that the system had some order. Now the expec­ta­tion. If we had access to pic­tures from before and after that point of order, what would we expect to see? We would expect to see the order decay in both direc­tions in time. This is what it means to say that Nature is time-reverse sym­metric. The second law of ther­mo­dy­namics tells us that Nature behaves this way. The time-reverse sym­metry encoded in our physics equa­tions also sup­ports this. But when we look into the world we also see many occur­rences that seem to have time direc­tion­ality to them. Events unfold one way far more than they do in the other way. Why? Well if the second law of ther­mo­dy­namics holds, if time-reverse sym­metry accu­rately describes the physics (these two claims are syn­ony­mous by the way) then there is only one con­clu­sion. Our uni­verse has not yet reached a max­imum state of entropy. This means that the uni­verse had a begin­ning. It was charged with extremely low entropy at some point, and that low entropy has not fully decayed yet.
          I explain this in detail in my book. If you’d like to read it just send me your email and request it. I’ll for­ward you a pdf. I also explain infla­tion in that chapter, and the accel­er­ated recent phase of red­shift. All of these effects are nat­ural expec­ta­tions of this model. That, of course, does not auto­mat­i­cally make the model right, but it does make it inter­esting. The value here is that we may now have a model that explains our obser­va­tions wholly, and in a way that is intu­itively accessible. :-)

  7. Iiro says:


    Great work indeed!!!
    I have been watching most of your videos during last two days and I really like the sim­plicity and ele­gance of your approach. It will take some more time and reading for me to arrive in deeper under­standing but there is one problem all­ready that I am not able to solve by my self and it is this:

    In your theory there is no need for grav­i­ta­tional force. Direct line is defined so that there is same amount of quanta passing by in all sides of a moving object. This leeds to a curved path (euclidean sence) when ther is more quanta (object with mass) in on side of an moving object. Now we run to a problem (it is most propably my monkey mind missing some simple thing because of late hours :-) because in this sce­nario the path that the object takes does not depend on its velocity. So if we douple the velocity, we should still have the same path which we no is not true.

    So please show me what I am missing so that I can move on!!!

    Thanks for bringing the common sense back to the basic science!!!

    • Thad Roberts says:

      Great ques­tion! You may be pleased to dis­cover that this model does say that the path an object will follow depends on its velocity. With a den­sity gra­dient of space in place, the straight path, the path an object will take, depends on its velocity. To see why, imagine an object that moves through flat space at a slow rate – let’s say 20 quanta per unit of time. When that object moves into a region with a den­sity gra­dient it will take the path in which both sides still expe­ri­ence the same amount of space per unit of time. Let’s say that the gra­dient makes a dif­fer­ence in den­sity such that a super­spa­tial straight path would lead to 20 more quanta on one side than the other. This object will then follow a highly curved path (from the Euclidean per­spec­tive). However, if the same object entered the region moving at 1000 quanta per unit of time, then the 1020 vs. 1000 side to side would not create a path with strong cur­va­ture. I hope this addresses your ques­tion. Please elab­o­rate if you have fur­ther ques­tions :-).

  8. Martin says:

    Hi Thad, I’ve got a couple of ques­tions:
    1. Can you help me envisage why a mass (like an apple) falls toward the Earth? In the absence of a force called gravity I’m guessing this must be hap­pening because the apple has velocity (that of the Earth through space) in a den­sity gra­dient… But I can’t quite pic­ture it.
    2. What is it that is within a planck bubble that has co-ordinates described by the intra-spatial x,y,z?
    3. Sub-atomic par­ti­cles are huge com­pared to the planck length so how do you pic­ture a quark occu­pying space? Does it ‘occupy’ bil­lions of planck bub­bles? What does that ‘look’ like?
    4. What is the mech­a­nism by which mass affects the den­sity of planck bub­bles? How does mass cause them to coa­lesce? I think what I’m trying to get at here is that, having done away with gravity, with what do I replace my con­cep­tion of matter clumping together (to make planets etc…)
    5. I think you said a black hole had a size of 1 planck. Surely if you make planck bub­bles coa­lesce as in a black hole, its ‘size’ is how­ever many planck bub­bles it has inside it. From your expla­na­tion, I imagine them densely packed (and not ‘res­onating’)… and if more matter is sucked in, with more planck bub­bles, I imagine the event horizon expands to acco­mo­date more planck bub­bles at some sort of max­imum den­sity.
    6. I never came across your expla­na­tion of how QST explains wave par­ticle duality. I’d love to hear it.
    I’m enjoying how you convey the con­cept of QST as some­thing I can actu­ally imagine. Thanks.

    • Thad Roberts says:

      1. Of course. ☺ First let me say that the dif­fi­culty would be to explain how a force called gravity causes an apple to fall toward the Earth. Forces are used in lieu of expla­na­tions. Therefore, when we rely on “forces” our under­standing of the world is empty. When it came to gravity, Einstein over­came this stum­bling block by reducing the effects of gravity to con­se­quences of a geo­metric prop­erty (that nobody had pre­vi­ously imag­ined). According to Einstein, the metric of space­time curves in con­junc­tion with the pres­ence of mass. As a result, objects like the Moon orbit the Earth because this orbit is the straight path through space­time (despite our naïve Euclidean expec­ta­tions). Once we com­pre­hend space­time in its full geo­metric splendor the mys­tery of forces dis­solve. Since the Moon is going straight, there is no deep mystery.

      We can use our qst model to fully under­stand the geo­metric prop­erty of space­time cur­va­ture. In our model, cur­va­ture is rep­re­sented by the radial den­sity gra­di­ents that extend from mas­sive objects. Once we have these radial den­sity gra­di­ents our solu­tion falls into place by con­sid­ering what it means to call a path “straight” in space. An object that is moving straight expe­ri­ences equal amounts of space. In other words, its left side moves through the same amount of space as its right side (and all other sides). Imagine extending your hands as you drift in space. If your left hand trans­verses the same amount of space as your right hand during some interval of time, then you are moving straight. Now imaging an object entering a region of space that sup­ports radial den­sity gra­dient. In order for the object to con­tinue going straight it must con­tinue to follow the path that has it inter­acting with the same amount of space on its left side and its right side. The radial den­sity gra­dient per­turbs this path from Euclidean pro­jec­tions. Can you imagine it now?

      2. If we assume that space (the x, y, z we are familiar with) is actu­ally a super­fluid made up of many quanta of space, then the indi­vidual quanta of space become the smallest con­tri­bu­tions to the metric that por­trays the rel­a­tive arrange­ments of those quanta. The quanta them­selves are made up of a volume, but that volume cannot coher­ently par­tic­i­pate or con­tribute to the metric of x, y, z. Therefore, their metric is uniquely sep­a­rate. As an analogy, let’s imagine that you were asking what is within the mol­e­cules of water in a lake. A col­lec­tion of these mol­e­cules defines water, and they can allow waves to prop­a­gate through the medium, but inside the mol­e­cules them­selves the notion of “water” is nowhere to be found. The ref­er­ence has entirely changed, even though the mol­e­cules of H2O make up water. Does that help?

      3. Great ques­tion. Particles of mass in this model turn out to be little vor­tices in the super­fluid vacuum. In this sense they are stable metric dis­tor­tions that pos­sess the ability to be locally defined (at least on scales larger than the vortex in question).

      4. Mass/energy exists any time there is a metric dis­tor­tion. This means that when­ever the quanta are not per­fectly arranged into an evenly spaced lat­tice, matter/energy is present. On the quantum scales this is always the case, but as you zoom out the average den­sity evens out (so long are there is not a radial den­sity gra­dient present), giving rise to the appear­ance of empti­ness (leaving only zero point energy, the spon­ta­neous cre­ation and anni­hi­la­tion of par­ti­cles in pairs, which are described on the smallest scales only). What you appear to be get­ting would be best elu­ci­dated by a rich under­standing of super­fluids. In super­fluids stable quantum vor­tices can form and remain without dis­si­pa­tion. This for­ma­tion is the cre­ation of ‘matter par­ti­cles’ and the metric swirls that extend from them give rise to the effects of the elec­tric force etc. I expand on this in my book, in the Forces chapter.

      5. When we are talking about x, y, z size, yes all black holes have an effec­tive size of one Planck length. That is because they rep­re­sent only one unique loca­tion in the x, y, z metric. However, super­spa­tially black holes are much more than this. A black hole’s super­spa­tial size is a func­tion of how many quanta make it up. The rest of what you said sounds accu­rate to me.

      6. Please go to http://​www​.EinsteinsIntuition​.com and select the pull down menu titled ‘What is qst?’ and select the for­malism page. This should give you a great overview of how wave/particle duality is required by the assump­tion that the vacuum is a super­fluid. Also, chap­ters 12 and 13 in my book intro­duce these con­cepts with less math.

      • matt says:

        I don’t think you answered Martin’s #1 ques­tion fully. In the apple, the left and right ‘hands’ will ‘expe­ri­ences equal amounts of space.’ I came to Q&A looking for an expla­na­tion of the apple falling from the tree, not orbiting the earth! As to how the (familiar) poten­tial energy changes to kinetic energy (the moment the stem breaks) , I guess we’d con­sider the den­sity gra­dient front-to-back but i can’t think of what makes the apple want to fall…

        • Thad Roberts says:


          Please excuse the delay in reply, I’ve been exploring Central America. I believe my response to your reworded ques­tion below addresses your ques­tion. If it does not please let me know.


  9. matt says:

    After some reck­oning I sim­pli­fied the ques­tion thus: What causes accel­er­a­tion in an orbiting object? Because an apple breaking from a tree is the same as a satel­lite at the apex of a flat-elliptical path.

    Objects in an ellip­tical orbit expe­ri­ence a reversal of accel­er­a­tion when its path is per­pen­dic­ular to a radial line of the den­sity gra­dient. All other moments it will expe­ri­ence (de/a)cceleration because of the gra­dient from ‘front’ to ‘back’. Is this because the ‘front’ expe­ri­ences less time res­onations than the ‘back’ which pushes it forward?

    Does that mean (familiar) inertia is an illusion?

    Is the inertia in super­space an illu­sion better explained by goings-on in supersuperspace?

    • Thad Roberts says:

      Thanks for the clar­i­fi­ca­tion Matt. In response let me begin by pointing out that an orbiting body is only “accel­er­ating” from an Euclidean per­spec­tive. For any per­spec­tive that reveals the cur­va­ture of space­time there is no accel­er­a­tion involved at any time (no force either). In short, by switching to a frame that includes space­time cur­va­ture we dis­solve the “force” of gravity. So yes, in part, familiar inertia is an illu­sion. Because it is a func­tion of mass and velocity, an Euclidean painting of velocity intro­duces the illu­sory part. From a per­spec­tive that includes space­time cur­va­ture the inertia of an orbiting body does not change. It remains trav­eling straight through space­time. This illu­sion, along with the illu­sions of the other “forces” is elu­ci­dated best, to my knowl­edge, by the “goings-on in super­space”. Chapter 20 in my book covers this topic in greater detail. If you would like a pdf copy let me know.

  10. Nick Grover says:

    I have a sim­ilar ques­tion as other people on this forum, I searched a bit and couldn’t find the answer so here goes.

    If the moon were (hypo­thet­i­cally) stopped in it’s orbital path, why would it fall towards the Earth?

    • Thad Roberts says:

      Great ques­tion. I assume that it makes sense to you why an orbit fol­lows from a den­sity gra­dient in space – why the moon orbits instead of flying right by. To tie the rest of the pic­ture together we need to remember that ele­men­tary par­ti­cles in this model are quantum vor­tices in the super­fluid vacuum. Particles com­bine to form atoms and larger groups via the rules of com­bining quantum vor­tices. So we can imagine the Moon as a large col­lec­tion of these swirling vor­tices. When it is in the pres­ence of a den­sity gra­dient (like the one that sur­rounds the Earth) the straight path for each vortex depends on that gra­dient. And, since the vor­tices are held in com­bi­na­tion, by bal­ancing fluid dynamic inter­ac­tions, the fate of the col­lec­tion is for the most part shared. Therefore, if the moon were stopped in its orbital path it would follow the only straight path avail­able. Each vortex that makes it up would swirl about such that the dis­tor­tion parts of its swirling action (the phonons that make it up) share iden­tical expe­ri­ences of space. The com­bined effect of this expo­sure to the Earth’s spa­tial den­sity gra­dient (space­time cur­va­ture), and the sta­bi­liza­tion between the vor­tices making up the matter of the Moon, brings the whole thing straight towards the earth.

      Please let me know if I can attempt to make this more clear.


      • matt says:

        that explains the apple falling (not that i fully under­stand)… I would appre­ciate a link to your book.

        • Thad Roberts says:

          I’ve sent you the link. Please let me know if you have any prob­lems opening it. I look for­ward to your feedback.

  11. Ron says:


    I’ve been waiting for the apple to fall! Thanks for that response. May I get a copy of your book also?

    I had won­dered if the reason the apple would fall is because of the time dif­fer­ences in the gra­dient. It seems that mol­e­cules vibrating “up and down” in the gra­dient would move slightly slower rel­a­tive to the mol­e­cules directly above them, tending to pull the ones above them down. But the time gra­dient prob­ably isn’t steep enough to pro­duce the effect that we think of as weight. And I haven’t heard of super cold mate­rials having less weight than the same mate­rial at room tem­per­a­ture. So your answer is very sat­is­fying. Would the mol­e­c­ular vibra­tion in the time gra­dient have any effect at all on the motion of the apple, even very slightly?

    Great videos, great site. Can’t wait to read the book.

  12. Viktor says:

    Hi Thad!

    I watched your talk on TEDx – Boulder and I was very inspired. I would like to get a copy of your book in order to dig deeper in to the idea. I have a few ques­tions con­cerning the 11-dimensions you talk about.

    1. Is 11 dimen­sion a sim­pli­fied pic­ture? Have I under­stood it cor­rectly if you believe that we live in an infi­nitely dimen­sional world? Does more dimen­sions pop up as we look closer?

    2. Is the super space including super time a E^4 space, and if so, what reason do we have to believe that?

    3. What forces are changing the path and shape of the space quanta, or is that just a geo­metric effect of even deeper lying dimensions?

    Thanks in advance!

    • Thad Roberts says:

      1. Yes, the 11-dimensional pic­ture is a sim­pli­fied pic­ture. The com­plete pic­ture relies on spa­tial struc­ture that mimics a per­fect fractal, each level resolving more internal parts that interact with the same set of rules.
      2. Superspace is only approx­i­mately an E^4 space in this model. This is a self-consistent neces­sity within the model because of the dif­fer­ence in size of the sub quanta to the quanta. The scale dif­fer­ence forces the expec­ta­tion of a near E^4 struc­ture.
      3. In this model there are no “forces” because all effects come with a com­plete causal story, negating any need to pull in a mag­ical entity respon­sible for strange occur­rences. I just emailed you a link to the book. To get a more com­plete answer to this ques­tion, read the super­fluid chapter.

  13. matt says:

    i’m almost through the book; i’ll email it back to you with cor­rec­tions (typos, for­mat­ting, few comments)

    I was dis­ap­pointed at the way you have the qst recur­sively over­lap­ping — sub­space in frame B is super­space in frame C…

    did you even try to make it overlap so that familiar space in frame B is super­space in frame C?

    maybe I just like to imagine receiving jounce from a higher dimension.

    • Thad Roberts says:

      Technically the struc­ture of the map is reflexive, meaning the order is mir­rored. Look through Chapter 11 again, and if this isn’t clear please let me know.

  14. trollthetrolls says:

    hi thad i have a ques­tion about red shift,im won­dering the system or star that they say is accel­er­ating does it auto­mat­icly mean the hole uni­verse is accel­er­ating or per­haps just that por­tion .How many obser­vances of this phe­nomena have they observed . Is it pos­sible there is an enor­mous mass in front of this system that is pulling it faster,maybe a black hole .are the dis­tant sys­tems that are heading towards us ??? curious .

    • Thad Roberts says:

      These are good ques­tions. For a more in depth answer than I will be pro­viding here, please see my Chapter on Dark Energy in Einstein’s Intuition. If you do not have the book send me a request by email. The short answers are… When we observe red­shift there are many pos­sible (valid) expla­na­tions for this effect. The most pop­ular expla­na­tion, is called the Doppler effect, which char­ac­ter­izes a change in observed wave­length due to motion of the emit­ting object. If from within the ref­er­ence frame of the emit­ting object it is putting out a yellow light, but is moving away from you very rapidly, then from your ref­er­ence frame you will see a color that is shifted towards the red end of the light spec­trum. The amount of shifting depends on the speed. If it is moving towards you then the light will be blue-shifted. This effect is undoubt­edly real. When we look at sys­tems far away that are spin­ning rapidly, the edge moving towards us exhibits blue shift, while the edge of the system moving away from us exhibits red shift. The ques­tion is, does the gen­eral red shift we observe for all dis­tant sys­tems imply reces­sion veloc­i­ties? The answer is that it does not nec­es­sarily imply this. There are other options. I explore one par­tic­u­larly beau­tiful and simple option in that chapter if you’d like to under­stand another option. How many obser­va­tions of red shift are there? Many. In fact, at large dis­tance every system is red­shifted. I sup­pose tech­ni­cally it is pos­sible that they all have enor­mous masses behind them pulling them faster away from us, causing the doppler effect, but the odds of this would be extremely low for two rea­sons. The first reason is that all of those objects would have to be strate­gi­cally placed such that they were exactly oppo­site of the object from our loca­tion, which doesn’t seem to have any moti­va­tion or expla­na­tion, seems con­trived and sta­tis­ti­cally com­pletely unex­pected, and the second is that there is no reason to expect that all dis­tant objects would be paired in this way.

  15. miles says:

    Only a new­comer to this theory, having only seen the “visu­al­izing 11 dimen­sion” ted talk and reading some of the con­tent on the site. What intrigues me the most is an extrap­o­la­tion from the accep­tance that space­time is a super­fluid; the idea of vor­tices appearing on a quan­tized level (i.e rather than all the water in the bucket spin­ning around a cen­tral axis, quan­tised vor­tices appearing within the super­fluid). Could the quanta them­selves be defined as vor­tices in 11 dimen­sions, and could this fur­ther imply that it is the motion of the super­fluid space­time as a whole that causes these vor­tices to occur? Just as in the super­fluid in the bucket, within which the system as a whole is moving causing these quan­tised vor­tices to appear. That is to say, that the space­time that makes up the entire uni­verse has some fun­da­mental motion as a whole which in turn gives rise to these vor­tices which we expe­ri­ence as par­ticels and charge.

    • Thad Roberts says:

      This is a beau­tiful insight. Yes, this model leads to the expec­ta­tion that the quan­tized vor­tices internal to the system are man­i­fes­ta­tions of some external motion (left over from the big bang). But the vor­tices are not the quanta them­selves, instead the vor­tices are made of of the super­fluid that the quanta con­struct. The quan­tized vor­tices instead become, as you sug­gest in your last sen­tence, the fun­da­mental par­ti­cles of mass. If you’d like to read more on this, I rec­om­mend my Chapter 21 – Superfluidity and Chapter 22 – Quantized Vortices.

  16. Peter says:

    You men­tion that mass gen­er­a­tion can be described as a sym­metry breaking event, but the pri­mary lit­er­a­ture is pretty dense. Is there an easier way to con­cep­tu­alize “mass” in qst, and from that, better under­stand how mass might alter the den­sity of ‘space-bubbles’ and hence, gravity? The pop­u­lar­ized notion of gravity as a “charge” of mass–which results from par­ticle inter­ac­tion with the higgs field–doesn’t seem to mesh well with qst. help!

    • Thad Roberts says:

      Dear Peter,
      Yes, this model does offer an easier way to con­cep­tu­alize “mass.” Here’s an excerpt that should help make the con­nec­tion (if you’d like to see this dis­cus­sion with its ref­er­ences, fig­ures, and equa­tions, send me a request for the book via email):

      The word mass ref­er­ences the pres­ence of a geo­metric dis­tor­tion in the metric – specif­i­cally the pres­ence of a local­ized dis­tor­tion in the vacuum of increased den­sity. Distortions that are not local­ized, dis­tor­tions that require trans­verse prop­a­ga­tion in order to be sus­tained, are referred to as light, or more gen­er­ally as energy. Distortions with a decrease in den­sity are referred to as neg­a­tive energy.

      In a fluid metric, the total geo­metric mag­ni­tude of each dis­tor­tion will vary depending upon speed. When a mass par­ticle (a local­ized vacuum dis­tor­tion) is not moving, the mag­ni­tude of that dis­tor­tion chac­ter­izes the particle’s rest mass, also known as its intrinsic mass. When the par­ticle moves, a wave­front builds up in front of it, adding to the total dis­tor­tion of the vacuum’s geom­etry. The faster it moves the greater the dis­tor­tion. The addi­tional dis­tor­tion char­ac­ter­izes the particle’s kinetic mass. As it approaches the prop­a­ga­tion speed of the medium, the total metric dis­tor­tion approaches an infi­nite value. This is why it takes an infi­nite amount of energy to accel­erate a par­ticle with non-zero rest mass to the speed of light.

      Once we assume that the vacuum is quan­tized (like air), the notion of rel­a­tivistic mass, whose value depends on velocity, auto­mat­i­cally fol­lows. Once we have par­ti­cles with rest mass, it is trivial (given vacuum quan­ti­za­tion) to explain kinetic mass (also known as rel­a­tivistic mass). But how do we explain the emer­gence of rest mass? How do those local­ized regions of increased den­sity form? Why do they only come in cer­tain sizes – specif­i­cally pre­scribing the ele­men­tary par­ti­cles we find in Nature? What makes these quan­ti­ties of mass so special?

      In ref­er­ence to these ques­tions, Frank Wilczek, a physics Nobel Laureate, noted that William Thomson (also known as Lord Kelvin) pos­tu­lated one of the most beau­tiful ‘failed’ ideas in the his­tory of sci­ence when he sug­gested that atoms might be vor­tices in an aether that per­vades space. Believing in aether, an invis­ible medium in space­time that sus­tained elec­tro­mag­netic waves, Thomson became intrigued by the work of Hermann Helmholtz, who demon­strated that “vor­tices exert forces on one another, and those forces take a form rem­i­nis­cent of the mag­netic forces between wires car­rying elec­tric cur­rents.” As he explored this con­nec­tion he rec­og­nized that vor­ticity was the key to obtaining a model that could explain how a few types of atoms, each existing in very large num­bers of iden­tical copies, could arise in Nature.

      To get his theory of vortex atoms off the ground, Thomson assumed that the aether was endowed with the ability to sup­port stable vor­tices. Following Helmholtz’ the­o­rems, he then noted that dis­tinct types, or “species,” of vor­tices would per­sist in the medium, and that these fun­da­mental vor­tices could aggre­gate into a variety of quasi-stable “mol­e­cules.”
      Thomson’s idea is quite appealing – the idea that stable quantum vor­tices, whose topo­log­i­cally dis­tinct forms and sizes are nat­u­rally and repro­ducibly authored by the prop­er­ties of the medium itself, are the building blocks of the mate­rial world. Sadly the idea has faded into obscu­rity, clod­dishly dis­missed and rejected, because the aether, the back­ground fluid that these vor­tic­i­ties were thought to crit­i­cally depend on, has been aban­doned. Scientists assumed that if the aether is out, then Kelvin’s quan­tized vor­tic­i­ties are also out. They mis­tak­enly threw the baby out with the bath water.

      Providentially, the ele­gance of Thomson’s quan­tized vor­tic­i­ties is res­ur­rected when we trade the aether assump­tion, that there is a medium in the vacuum that sup­ports elec­tro­mag­netic waves, for the assump­tion that the vacuum itself is a super­fluid medium with a metric that is macro­scop­i­cally describ­able by the wave func­tion. The assump­tion that the vacuum is a super­fluid, also called a quantum fluid, instinc­tively estab­lishes vortex sta­bility. It also leads to the expec­ta­tion that the struc­ture of the mate­rial world is written into the sub­strate of the vacuum itself, that as quan­tized vor­tices form in the vacuum, super­sym­metry is broken and sub­atomic par­ti­cles emerge with very spe­cific properties.

      We are just begin­ning to explore some of the promising new pos­si­bil­i­ties offered by quantum fluids. Current research is focused on, among other things, the­o­ret­i­cally under­standing the for­ma­tion of quantum vor­tices in Bose-Einstein con­den­sates (and how they com­bine to form stable unions), linking those quantum vor­tices to a con­cept of matter ori­gins, and using BEC’s to model black holes and their related phe­nomena in the lab.

      If vor­tices in the vacuum cor­re­spond to par­ti­cles then “con­cen­trated energy in empty space can trans­form vir­tual par­ti­cles into real ones.” If this is what is going on then the mech­a­nism behind this trans­for­ma­tion (the Higgs mech­a­nism) needs to be explained. We need to explore how mass­less par­ti­cles with two phys­ical polar­iza­tions acquire a third stable polar­iza­tion in the lon­gi­tu­dinal direc­tion. We need to figure out how the prop­erty of mass (locally main­tained geo­metric dis­tor­tions, or quan­tized vor­tices) spring into existence.

      To push us towards an answer, we note that if we spin a beaker con­taining a super­fluid we end up with an array of vor­tices scat­tered about in that fluid. (The number of vor­tices intro­duced is pro­por­tional to ħ/m.) Interestingly, super­flu­idity breaks down within each of these vor­tices, while every­where else the fluid retains its super­fluid char­ac­ter­i­za­tion, and remains still (in the macro­scopic sense). Therefore, the rota­tional energy of the external rota­tion becomes con­tained within these quan­tized vor­tices. The dif­fer­ences in response to rota­tion can be more pre­cisely quan­ti­fied by noting that the tan­gen­tial velocity of the quan­tized vor­tices has a mod­ulus that decreases with r:
      (Equations did not fully copy – see Chapter 22 – Quantum Vortices for equa­tions and figures.)

      whereas the tan­gen­tial velocity of a rigid rotator has a mod­ulus that increases with r: v = Ω × r.

      This is what allows us to claim that the vor­tices are local­ized. This, com­bined with the fact that vor­tices are defined as cer­tain geo­metric dis­tor­tions in the vacuum that spon­ta­neously break or hide the under­lying higher sym­metric state, makes them per­fect can­di­dates for par­ti­cles that inherit their rest mass via the Higgs field. Vacuum super­flu­idity, there­fore, gives teeth to the Higgs field hypothesis.

      The Higgs field (also called the Higgs boson, or the God par­ticle) is used to codify the mys­te­rious fact that par­ti­cles pos­sess rest mass. It is held respon­sible for causing cer­tain geo­metric dis­tor­tions in the vacuum and thereby spon­ta­neously breaking or hiding the under­lying higher sym­metric state of space­time. How this field spon­ta­neously breaks the sym­metry asso­ci­ated with the weak force and gives ele­men­tary par­ti­cles their mass, how it lowers the total energy state of the uni­verse, or how vis­cosity is intro­duced into the system, is not yet clear.

      The Higgs boson was intro­duced into the elec­troweak theory as an ad hoc way of giving mass to the weak boson. Even with this inser­tion the elec­troweak theory fails to solve the mass gen­er­a­tion problem because it does not explain the origin of mass in the Higgs boson. Instead, the theory intro­duces this mass as a free para­meter via the Higgs poten­tial, making the value of the Higgs mass ulti­mately just another free para­meter in quantum mechanics.

      Matters are fur­ther com­pli­cated by the fact that the value of this Higgs para­meter has only been indi­rectly esti­mated. Many dif­ferent esti­mates for the value of the Higgs have been posited by the stan­dard model (and its exten­sions). But even if the­o­rists knew how to pick among these values, even if the mass of the Higgs boson were the­o­ret­i­cally fixed, we would not have a fun­da­mental solu­tion of the mass gen­er­a­tion problem. The Higgs pos­tu­la­tion only refor­mu­lates the problem of mass gen­er­a­tion, pushing the ques­tion back to ‘How does the Higgs boson get its mass?’

      This is where vacuum super­flu­idity comes to the rescue. Vacuum super­flu­idity nat­u­rally pos­tu­lates a fun­da­mental mech­a­nism for mass gen­er­a­tion, without explic­itly for­bid­ding the exis­tence of an elec­troweak Higgs par­ticle. In short, it has been shown that ele­men­tary par­ti­cles can acquire their mass due to an inter­ac­tion with the vacuum con­den­sate – much like the gap gen­er­a­tion mech­a­nism in super­con­duc­tors or super­fluids. Therefore, if the Higgs boson exists, then vacuum super­flu­idity explains the origin of its mass by pro­viding a mech­a­nism that can gen­erate its mass. If the Higgs boson does not exist, then the weak bosons acquire their mass via direct inter­ac­tion with the vacuum con­den­sate. Either way the mass of the weak boson is a by- product of the fun­da­mental mass gen­er­a­tion mech­a­nism encoded by vacuum super­flu­idity, not a cause of it.

      This idea is not entirely novel to a super­fluid vacuum theory. Nevertheless, this topo­log­ical expla­na­tion for mass gen­er­a­tion ele­vates this theory to a con­struc­tion that is at least onto­log­i­cally on par with braid theory or loop quantum gravity. The assump­tion that the vacuum is a super­fluid makes it pos­sible to describe the symmetry-breaking rel­a­tivistic scalar field (which is respon­sible for mass gen­er­a­tion) in terms of small fluc­tu­a­tions in the back­ground super­fluid. Under cer­tain con­di­tions these fluc­tu­a­tions come together to take on the prop­er­ties of ele­men­tary particles.

      As vacuum fluc­tu­a­tions come together to create stable metric ‘braids,’ as twisting vor­tices form and sta­bi­lize, they become capable of taking on mass par­ticle char­ac­ter­is­tics – a third polar­iza­tion state and the prop­erty of being local­ized. (Not all fluc­tu­a­tions will com­bine into sta­bi­lized vor­tices.) This opens up the pos­si­bility of topo­log­i­cally inter­preting elec­tric charge as twists that are car­ried on the indi­vidual rib­bons of a braid. Likewise, color charge can be inter­preted topo­log­i­cally as the avail­able twisting modes.

      All of this sug­gests that matter gen­er­a­tion is explic­itly related to quantum vortex for­ma­tion in the super­fluid vacuum (or the gen­er­a­tion of dark soli­tons in one-dimensional BEC’s). Superfluid vor­tices are allowed for by the non-linear  term in the Gross-Pitaevskii equa­tion.
      These plaits of quan­tized angular momentum are most nat­u­rally rep­re­sented by a wave­func­tion of the form  , where ρ, z, and θ are rep­re­sen­ta­tions of the cylin­drical coor­di­nate system and l is the angular number. In an axi­ally sym­metric (har­monic) con­fining poten­tial this
      is the form that is gen­er­ally expected. To gen­er­alize this notion we deter­mine  by min­i­mizing the energy of  according to the con­straint  . In a uni­form medium this becomes:
      where: n2 is den­sity far from the vortex, x = ρ / l ξ, and ξ is healing length of the con­den­sate. For a singly charged vortex (l = 1) in the ground state, has an energy  given by:
      where b is the far­thest dis­tance from the vortex con­sid­ered. (A well-defined energy neces­si­tates this boundary b.)
      For mul­tiply charged vor­tices (l > 1) the energy is approx­i­mated by: .
      Such vor­tices tend to be unstable because they have greater energy than that of singly charged vor­tices. There may, how­ever, be metastable states, that have rel­a­tively long life­times, and it may be pos­sible for vor­tices to come together and create sta­bi­lized unions.

      Dark soli­tons are topo­log­ical fea­tures in one-dimensional BEC’s that pos­sess a phase gra­dient across their nodal plane. This phase gra­dient sta­bi­lizes their shape even during prop­a­ga­tion and inter­ac­tion. Because these soli­tons carry no charge they are prone to decay. Nevertheless, “rel­a­tively long-lived dark soli­tons have been pro­duced and studied extensively.”

      When it comes to the mass gen­er­a­tion problem vacuum super­flu­idity has become a thriving con­tender among a swarm of com­peting the­o­ries. Because it explains mass and energy strictly in terms of geom­etry it has posi­tioned itself as the con­tender with the most onto­log­ical potential.

      – I hope that helps.


  17. Carnoy Aurelien says:

    hello dear Thad

    I am not sure this is the right place to post my com­ment,
    so feel free to move it if you need too. ty

    i hear you say all elec­trons look alike
    would it help you to hypoth­esis that they are all the same one?
    what i mean by this is: an elec­tron is a place in space time
    that phe­nom­enon is the same one ,
    we just observe it from dif­ferent points of view

    I’m not saying it is reality
    it is just a tool
    to nicely illus­trate
    how one can con­sider realty

    an other example of that tool would be
    the sim­i­larity between black/white whole and the big bag theory
    though many dif­ferent point of vue on what we are talking about
    can lead people to disagree 😛

    This is why i used the elec­tron example
    as it seemed sim­pler
    (i hope my English convey my meaning
    as i an French)

    i hope to hear from you
    take care

    • Thad Roberts says:

      Dear Carnoy,
      The idea that there is only one elec­tron in the Universe man­i­festing itself in many places (with many com­plex sto­ries for how it gets to all of those places) has already been pro­posed. What people are trying to achieve in this pro­posal is an expla­na­tion for the uni­for­mity between all elec­trons. Personally I find the sim­plest story to be most likely, and most expla­na­tions I’ve heard for how one elec­tron man­i­fests itself in mul­tiple places in space and time have been very com­plex. The sim­plest expla­na­tion I know of so far is that there is a prop­erty in the vacuum itself that inscribes the prop­er­ties of the ele­men­tary par­ti­cles (including the elec­tron). If the vacuum is a super­fluid, then the quantum eddies that form due to super­flu­idity, which only come in very spe­cific states (eddie 1, 2, 3… but no eddies with prop­er­ties between those), are nat­ural expec­ta­tions. If those eddies are the ele­men­tary par­ti­cles, than that would be the most simple expla­na­tion pos­sible. This is not to say that I am dis­cour­aging the idea you are sug­gesting. All ideas have value in sci­ence, and sci­ence needs people that are willing to use their cre­ative imag­i­na­tions to come up with new ways of seeing things.

  18. eric says:

    i have listen to your tedx talk with a lot of interest.i have a few ques­tion that i cant realy grasp with this con­sept. if the space is made of `some­thing` you still endup with some­thing empty between those little space, what is empty made of? if all the space touch at some point and allow thing to move from a space to another space whitout having to pass into some­thing that dont exist/empty it would ease my mind but dont allow for 3 dimen­tion you talk about. at what level of the atom do the space interact to create gravity? how can we manip­u­late space from the atomic point of view to test that theory?
    thank you

    • eric says:

      i forgot to ask how energy intereact with space?
      thank you

    • Thad Roberts says:

      Thank you for your ques­tions. The TED talk did not go into much depth. Let me pro­vide a little more here. The full struc­ture of this model assumes a fractal geom­etry, meaning that it assumes that the vacuum is made of parts, and that those parts (and the medium that sep­a­rates them) are made of smaller parts, and so on. Due to this hier­ar­chical struc­ture, the exact model we are dis­cussing depends upon the res­o­lu­tion we choose to focus on. If we stick to 11 dimen­sions, then the vacuum is made of quanta, each of which con­tain inter­spa­tial volume, the vacuum quanta are sep­a­rated by super­spa­tial volume, and the entire col­lec­tion fills out the familiar spa­tial volume. Your first ques­tion asks what the super­spa­tial volume is, or per­haps what it is made of. The model ulti­mately assumes that super­space is, in a self-similiar way, made of sub-quanta, and there­fore has fluid prop­er­ties of its own. The sub-quanta are not resolved in our 11 dimen­sional res­o­lu­tion, but if we want to resolve them we simply jump to the next level of res­o­lu­tion, which is a 30 dimen­sional map (27 spa­tial dimen­sions, and 3 tem­poral dimen­sions). Also, in the model the vacuum com­prises all the “fur­ni­ture of the world” or every­thing that man­i­fests in space. Quantum vor­tices in the super­fluid vacuum are the fun­da­mental matter par­ti­cles, and the den­sity gra­di­ents that sur­round them are the gravity fields. All forms of energy are marked by metric dis­tor­tions, dif­fer­ences in the dis­tri­b­u­tions of the quanta that make up the vacuum. These dis­tor­tions can be prop­a­gating waves, or phonons, like sound waves through air, or they can be quantum eddies, gaining what physi­cists call a third polar­iza­tion – making it pos­sible for the dis­tor­tion to be main­tained without nec­es­sarily having to move through the metric. The vacuum is more fun­da­mental than atoms of matter. Many vacuum of quanta chore­o­graph together to make quantum vor­tices, which form the fun­da­mental par­ti­cles, like quarks, which com­bine to make pro­tons and neu­trons, and even­tu­ally atoms. As for testing the theory, there are sev­eral ways to test this theory, as it makes clear depar­tures from tra­di­tional pro­jec­tions in cos­mology, gen­eral rel­a­tivity, and quantum mechanics. First off, it posits that Lorentz sym­metry is not an exact sym­metry of Nature but instead a sym­metry that man­i­fests in the low momentum regime. The pre­dic­tion, then, is that with enough energy and momentum we should be able to detect Lorentz-breaking cor­rec­tions. To do this we need ener­gies and momenta that extend beyond the exci­ta­tion threshold of the super­fluid vacuum. Also, it offers an expla­na­tion for red-shifted light in cos­mology, which, of course, leads to com­pletely dif­ferent claims about dark energy. Also, its quantum mechan­ical pre­dic­tions insert a non­linear term in its wave equa­tion, whereas the stan­dard inter­pre­ta­tion of quantum mechanics sticks with the linear term only (which is why it remains restricted from wrestling with the phe­nomena of gen­eral rel­a­tivity). If you’d like to look into this in greater depth, feel free to send me a request for a free copy of the book.

  19. eric says:

    sure, thank you

  20. Stolrael Dowell says:

    You touched on it. But I really want an elab­o­ra­tion on how matter moves from one quantum of space to the next. You said quanta can touch super­spa­tially, but do they have to be?

    • Thad Roberts says:

      Matter par­ti­cles are quantum vor­tices in this model, which means that even fun­da­mental quarks are made up of many quanta of space. For matter par­ti­cles to move through space the col­lec­tion of vor­tices that make it up, or at min­imum the vortex that makes it up, moves through the medium in a way very sim­ilar to how a whirlpool moves through water. To begin exploring the basics of this kind of motion I sug­gest looking up phonons, oth­er­wise known as qua­si­par­ti­cles, which can be defined as col­lec­tive exci­ta­tions in the peri­odic, elastic arrange­ments of atoms or mol­e­cules of a medium (in this case the quanta of the super­fluid vacuum). These phonons can take on dif­ferent forms, but they all rep­re­sent excited states in the medium. When these excited states become quantum vor­tices, they rep­re­sent matter, instead of energy in the form of light, but the motion of these vor­tices is still deter­mined by the para­me­ters of the elastic medium.

  21. Nathan Duke says:

    Dear Mr. Roberts,

    1. Are Quanta phys­i­cally real, mate­rial objects (as in sub­stan­tive com­po­nents of a super­fluid)? Or are they rather, like a Euclidian coor­di­nate plane, a con­cep­tual rep­re­sen­ta­tion of space (with the addi­tional prop­erty of rep­re­senting the con­flu­ence of the five con­stants of nature within any given unit of space) to be super­im­posed upon it, for the pur­pose of stan­dard­izing a base unit of mea­sure so that we can more clearly per­ceive it’s prop­er­ties and more com­pletely & accu­rately ana­lyze & explain it’s behavior?

    2. If so, do Quanta have mass?
    3. Is the “space” between Quanta quantiz(ed/able)?
    4. If quanta are indi­vis­ible, how then are they com­prised of “sub-quanta and so on, ad infinitum”?

    As R.B. Fuller once said, “All truths are omni­in­ter­op­er­able.” Please help me rec­on­cile these seem­ingly non-interoperable asser­tions of truth on the part of your the­o­ret­ical frame­work. I am a lay person with only the most rudi­men­tary grasp of this mate­rial. But since you state that QST offers an intel­li­gible view of these nor­mally inscrutable con­cepts, I write to you in the spirit of under­standing (or at least aspiring thereto!).

    Thank you.

    P.S. Your alter­nate expla­na­tion of red-shift gave me the first glimmer of hope for the future of the cosmos since Edwin Hubble’s entropic prophecy seem­ingly sealed it’s doom. I still have some ques­tions about that, but I’ll leave those for later…

    Best regards,
    Nathan Duke
    Lead Designer
    949-468-5688 cell
    619-567-0000 office
    619-916-3630 fax

    • Thad Roberts says:

      Hi Nathan,

      Thanks for your ques­tions. I’ll attempt a con­cise set of answers here and point you towards my book for a richer expla­na­tion. (I’ve just emailed a pdf copy of it to you.)

      You asked, “Are we to under­stand that Quanta are lit­er­ally real mate­rial objects? Or, like a Euclidian coor­di­nate plane, are they simply a con­cep­tual rep­re­sen­ta­tion of space (with the addi­tional prop­erty of rep­re­senting the con­flu­ence of the five con­stants of nature within any given unit of space) to be super­im­posed upon it for the pur­pose of stan­dard­izing a base unit of mea­sure so that we can more clearly per­ceive it’s prop­er­ties and more com­pletely and accu­rately explain it’s behavior?”

      I am aiming at the former of these options, as the super­fluid vacuum model of quantum space theoy is meant to pro­vide a com­plete ontology. However, I would not object to someone fleshing out an inter­pre­ta­tion based on the latter, but I sus­pect it would not carry as much explana­tory import.

      In response to your other questions:

      1. Do Quanta have mass?

      No, quanta do not have mass. Mass is a dis­tor­tion in the geo­metric arrange­ments of the quanta. It is a col­lec­tive prop­erty and there­fore cannot be attrib­uted to a single ele­ment of the col­lec­tion – just as one mol­e­cule of air cannot have pressure.

      2. Is the space between Quanta quantiz(ed/able)?

      Yes it is, but on a com­pletely dif­ferent scale – the same scale on which the quanta them­selves are quan­tized. Chapter 11 should help with these concerns/questions. If it doesn’t resolve them please let me know.

      3. If quanta are indi­vis­ible, how then are they com­prised of “sub-quanta and so on, ad infinitum”?

      Quanta are not indi­vis­ible. They are merely the smallest units if space. The same applies to gold. It can be divided down to one atom if gold and still be gold. We cannot divide one atom of gold and still have gold, but this doesn’t ulti­mately or log­i­cally stop us from dividing it. The divi­sion is pos­sible, but it requires moving beyond the prop­er­ties and def­i­n­i­tion of the medium (gold). The claim here is that the same applies to space as a medium.

      I hope that helped. While you read the book please keep a list of your ques­tions and com­ments and send me any unre­solved ques­tions or con­struc­tive com­ments. If you find any par­tic­ular sec­tion unclear I would like to know. Your crit­ical analysis is valu­able to me as the aim of my book is to make these topics acces­sible to everyone with a sharp mind regard­less of their level of training in physics.

      Thank you.


      P.S. Questions related to your post­script com­ment are cov­ered in Chapter 28 of my book. Enjoy.

  22. Thad,

    Watched your TEDx Youtube video last night and was blown away. I spent this morning reading your web site and would now like to see the tech­nical details of your QST book.

    My back­ground is BSc Physics, MM Mathematics. I spent my working life in com­puting and am now retired.

    I left grad school (UMd, College Park ) in quantum physics because of a deep dis­sat­is­fac­tion with QM: I under­stood the math – but had grave doubts about the epis­te­mology. I have tried to keep cur­rent over the past 50 years ( my God, has it been that long? ) reading as much as pos­sible on cur­rent theories.

    Your ideas – if I under­stand them cor­rectly – are utterly won­derful. I have believed for some time that what­ever reality is – it is emer­gent with infi­nite com­plexity deriv­able from simple recur­sive rules.

    I spent some time a few decades ago exploring the world of frac­tals ( see https://​www​.flickr​.com/​p​h​o​t​o​s​/​h​o​r​t​o​n​h​e​a​r​d​a​w​h​o​/​4​4​8​2​2​2​6​0​23/ for a sample of my Mandelbrot set ani­ma­tions ) and am par­tic­u­larly excited that you rec­og­nize the deeper fractal nature of reality.

    I also happen to have many of the same per­sonal interest as you ( PADI Divemaster, Space enthu­siast, Fossil hunter, ama­teur geologists. )

    Looking for­ward to an exciting read and hope I can pro­vide you with some useful feedback.


    • Jeff Chapple says:

      Thad is abroad at the moment, so I’m not sure how long it will take him to respond.

    • Thad Roberts says:

      Hi Marvin,

      I apol­o­gize for taking this long to respond. I’ve been abroad for sev­eral months, trav­eling with a quantum physi­cist and then a philoso­pher of physics. It seems that you and I do have much in common, and I look for­ward to exploring that with you. Throughout the book my main goal remains to return us to an inves­ti­ga­tion that does not turn its back on epis­te­mo­log­ical con­cerns, so I would very much appre­ciate it if one of the lenses you eval­u­ated my book through was the epis­te­mo­log­ical lens. Let me know if it holds up a sat­is­fac­tory epis­te­mo­log­ical argu­ment. Of course, there is no require­ment that you end up believing that Nature per­fectly con­forms to the model, as keeping our doubt around in healthy doses is impor­tant, but it is impor­tant that what­ever route we explore does not turn it back on ontology and epis­te­mology. If you have any thoughts as you read, or think any par­tic­ular parts could be improved, please let me know. I’m sending you a copy of the book to your email. I very much look for­ward to your feed­back and starting a dia­logue with you.


  23. Dr. Morozov says:

    Hello Mr. Roberts,

    I have only one ques­tion without a good answer to which it would be impos­sible for me to accept that space is quantized.

    The problem is that any quan­tized struc­ture auto­mat­i­cally makes space anisotrop­ical. In other words some direc­tions in space become “favorable”.

    I sup­pose in the case of no dis­tor­tion the “space” quan­tums you intro­duce would form a 3d grid, packed in nice rows along the 3 mains axis. As long as you move along an axis ever­thing is fine – the dis­tance trav­eled is equal to the number of space “quan­tums” passsed.

    But sup­pose you were to go in a right angle tri­angle with its sides along the axises along the hypotenuse. If you are hoping over “quan­tums” you will have to do this in a stepped-like manner, gath­ering the same number of steps as the sum along the sides. Obviously according to the Pythagorean the­orem this can not be true.

    • Thad Roberts says:

      Dr. Morozov,

      As you might recall isotropy is defined macro­scop­i­cally, like pres­sure. In this sense there is no inherent anisotropy inscribed by quan­ti­za­tion. For example, if we have a con­tainer of gas, which we believe to be made of quan­tized parts (atoms or mol­e­cules) and we are in space with no mea­sur­able grav­i­ta­tional field, then the gas will dis­play uni­for­mity in all direc­tions, having no pre­ferred arrange­ment one way versus another and having equal den­sity throughout. In other words, it will be isotropic. Isotropy could be intro­duced into this system of gas, how­ever, if we put a cold sink in the middle. Then we would find that the gas was denser near the cold sink and radi­ally less dense as dis­tance from the cold sink increased. This would create anisotropy in the system. The same is an option for quan­tized space, and such anisotropic regions rep­re­sent grav­i­ta­tional fields, or Einstein’s curved space.

      To your second point, you are right to rec­og­nize that the Pythagorean the­orem is chal­lenged by quan­ti­za­tion, at least in its the­o­ret­ical limit. And as it turns out, it is already well estab­lished that the Pythagorean the­orem does not ubiq­ui­tously hold in Nature. Wherever space is curved the Pythagorean the­orem no longer holds, the greater the cur­va­ture the more it fails to rep­re­sent the system. Also, on micro­scopic scales it may not hold unless we take time aver­ages with sig­nif­i­cant spans.

      Your points are quite insightful. I address them to much greater lengths in my book. If you’d like a copy please let me know.


  24. Ben says:

    Thank you so much for sharing your ideas. I would love a link to your book

  25. Vivek says:

    Hello Mr. Roberts,

    I recently watched your TED talk and am fas­ci­nated by the idea. The expla­na­tion of gravity was very ele­gant! However, I still have a few questions:

    1. I didn’t quite under­stand the expla­na­tion of red­shift. Could you please elaborate?

    2. Does the theory pre­dict an expanding uni­verse? The big bang?

    3. What is the fate of the uni­verse if this theory is correct?

    4. Does it have any con­nec­tion to string theory?

    5. Why 11 dimensions?

    Also, could you please email me a copy of your book?

    Thanks much.

    • Thad Roberts says:

      Hi Vivek,
      I’m sending you the book. Let me pro­vide short answers here and direct you to the sec­tions of the book that answer your ques­tions in more depth.
      1,2 – I agree, the TED talk was very rushed and short – there is much to elab­o­rate on. Redshift in this model is accounted for in two ways. The doppler effect (a func­tion of rel­a­tive motion between source and observer) causes light to become red (or blue) shifted, as the rel­a­tive motion lengthens or shortens the received wave­length. Redshift also occurs for waves in a medium if the pres­sure of that medium decreases as those waves travel through it. Therefore, if the vacuum is a fluid medium, then plane wave phonons (light) that travel long dis­tances through it will become red­shifted as the pres­sure of the vacuum looses pres­sure. This decrease in pres­sure is explained by the fractal struc­ture of the vacuum. Because the vacuum is made up of quanta, which are in turn made up of sub-quanta, and so on. Collisions between two quanta rearrange the internal sub-quanta, and this geo­metric dis­tor­tion draws some energy from the motion of the quanta. The dif­fer­ence in size between levels (between the quanta and the sub­quanta) is very large, so the amount of energy lost to the internal degrees of freedom is very small, but over many col­li­sions the energy loss becomes note­worthy. The model pre­dicts a Big Bang, and infla­tion, but because it accounts for red­shift geo­met­ri­cally it does not follow that obser­va­tions of red­shift sug­gest that the uni­verse is expanding. See Chapter 28.
      3 – The fate of the uni­verse is to even­tu­ally suffer another external col­li­sion, causing the uni­verse to reset in low entropy and high energy. The internal laws and con­stants of nature will remain the same, but the starting state may be dif­ferent, directing its evo­lu­tion until the next col­li­sion. See Chapter 27.
      4 – Yes there is some overlap with this theory and the ideas held by string theory, but its con­cep­tual foun­da­tions differ sig­nif­i­cantly. Nevertheless, the branes of string theory might be con­sid­ered to be what is mod­eled by the sur­face areas of the vacuum quanta. (See pages 33, 35-36, 53, 186-187, & 318-319.)
      5 – 11 dimen­sions is a geo­metric con­se­quence of vacuum quan­ti­za­tion. This is cov­ered in Chapter 11.
      Please let me know if your ques­tions are sat­is­fied when you read the book, and if more ques­tions come up, please share. The book has greatly improved in response to ques­tions shared by others.

  26. Vivek says:

    I had a few more ques­tions I forgot to ask:

    Does the theory have any prob­a­bilistic aspects at all?

    Does it get rid of quantum theory entirely?

    What does it say about vir­tual par­ti­cles? quantum tunneling?

    What exactly do you mean when you talk about the fractal struc­ture of the theory?


    • Thad Roberts says:

      The theory repro­duces quantum mechanics is a deter­min­istic way (just as Bohmian mechanics does). Probability is cap­tured as a reflec­tion of our igno­rance of the actual state of space at any given moment. Specifying a spe­cific exact state leads to a deter­min­istic evo­lu­tion to another exact state at a dif­ferent time, but in prac­tice we cannot access the exact state of space, so prob­a­bilistic pro­jec­tions come from deter­min­istic physics. (See pages: 32, 79, 113-116, 204-214, 226-229, 243-245, 289-299, 382-391.) Virtual par­ti­cles is briefly men­tioned on page 362, quantum tun­neling is cov­ered in Chapter 14, an the fractal struc­ture of the theory is fully explained in Chapter 11.

  27. P.Dingen says:

    Dear Thad,

    Thank you for sharing your ideas with our world. Could you send me a link to your book, would love to read more about your theory. Thanks in advance!

  28. Cosmin says:


    I’m a Physics pas­sionate and I’d very much like to know more about your model and it’s con­se­quences. Are there PDF copies of your book still available ?

    Thank you.

    • Thad Roberts says:

      I just pub­lished it yes­terday, but since you asked before that, sending you a pdf now 😉

      • Cosmin says:

        Thank you, I’ll come back with com­ments and questions.

        What I can say for now is that my next point of interest is to under­stand what con­se­quences has the mobility of quanta, as opposed to a static grid arrange­ment, on the move­ment of matter/energy.

        If I under­stand cor­rectly from what I’ve read so far on your site, the (super)fluidity allows for stable vor­tices that cor­re­spond to “mate­rial” par­ti­cles. But what I try to under­stand is the impact said mobility of quanta has on the move­ment (as in trans­la­tion) of those “particles”.

        Does the vortex move like a prop­a­gating wave (at each moment the vortex is made up of dif­ferent quanta), or do the quanta actu­ally trans­late with respect to the rest of the “sea” of other quanta. This is prob­ably a simple ques­tion of (super)fluid dynamics, but nev­er­the­less I try to under­stand what the con­se­quences of this model are.

        Thanks again and keep up the good work. :)

        • Thad Roberts says:

          It sounds like you’ll really enjoy the Superfluidity Chapter in my book.
          It was just pub­lished, avail­able through Lulu​.com in hard­cover full color inte­rior.
          Softcover full color will be avail­able soon through Amazon, and the iBook and audio­book will follow.

          In short, the vor­tices move like prop­a­gating waves, at each moment made up of dif­ferent quanta. Nevertheless, even in regions of the vacuum that have no vor­tices, the vacuum itself has a dynamic equa­tion. This is also very sim­ilar to Bohmian mechanics, so you may enjoy reading Chapter 24 in the book also.

    • Thad Roberts says:

      I think that an inves­ti­ga­tion sounds rea­son­able. They aren’t denying that Americans went to the moon, but they want some account­ability as to what hap­pened to the moon rocks. From per­sonal expe­ri­ence I can say that the American gov­ern­ment can take this quite seri­ously, so they might as well be con­sis­tent and be con­cerned about this account­ability issue also.

  29. Dan D says:

    There have been sev­eral arti­cles recently about a working elec­tro­mag­netic propul­sion drive and how it shouldn’t work based on the law of con­ser­va­tion of momentum. In my mind, I keep thinking of your theory of quan­tized space and am won­dering whether space quanta is what is being pro­pelled by the engine to gain velocity. Do you have any thoughts?

    • Thad Roberts says:

      I’ve read these papers and don’t think the effect can be teased apart from the noise yet. There is more work to be done, but I worry that the the­o­ret­ical expla­na­tion at hand so far doesn’t have much weight to it. It is impor­tant to keep an open mind, but part of this means reading the mate­rial our­selves instead of just fol­lowing the public hype. The jury is still out.

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