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Vacuum Superfluidity

Thad Roberts and Marcus Tofanelli explore the assumption that the vacuum is a superfluid. They reveal that vacuum superfluidity imports a mechanism for mass generation, explains wave-particle duality, inscribes the constants of nature, and carves out room for geometric authorship of the four forces.

Comments (91)

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  1. Srdjan Petrovic says:

    ok, I have one question:
    If the number of Pi is obtained by expressing the ratio of the number of quanta of the circle and diameter, we can conclude that the number Pi has a finite number of decimal places …. probably when their number reaches the area of ​​the Planck scale. “Circle” in Planck size then would not really was a circle but a polygon hence the ratio of the circumference and diameter of was an integer. If you transfer that to the macro scale, we have a deal with the polygon a very close to the circle but still a polygon. As in the example with the gold, if we reduce the circumference of a circle more and more, at some point we will realize that it is not a circle … So, the number Pi has a finite number of decimal places (or not), but in any case it is not transcendental number .
    I apologize to my English which is not satisfactory.

    • Thad Roberts says:

      Good insight. To make things as clear as possible I should say that pi, as a theoretical transcendental number, embedded within the Euclidean projection, does exist. But, as you have noticed, if the vacuum is quantized then pi is only approximated in Nature. The theoretical value of pi depends upon Euclidean form, and since Nature only approximates the Euclidean form macroscopically, the value of pi is also only be approximated in Nature.

      • Jason says:

        Curious to read more on this topic. Can I get a copy of that PDF?

        • Thad Roberts says:

          Jason,
          The book is now out (hardcover, softcover and iBook – the audiobook will be out soon). If you’re on a budget I recommend the iBook, however, as always, if that is a problem for any reason just let me know and I’ll send you a promo code or a pre-published version of the pdf.

      • Dougal says:

        Can that logic/model be extended to include a Planck length quanta as a solution for the centre of a black hole instead of a singularity ?

        • Thad Roberts says:

          Kind of a bridge between the two ideas. A quantum has a unique history in as much as it evolves independently, which means that it is separated from other quanta. When quanta are together they evolve with identical histories and therefore represent only one unique location in the vacuum. The singularity of a black hole is simply a large composite of these quanta, a single unique location that shares the same evolution and experiences no time.

  2. Bruce Penney says:

    I am pleased to see someone is thinking along the same lines as myself about the nature of space and gravity.
    I believe there is just quantum space, all else evolves from that. My website should be interesting to you. The math is simple but you may be surprised by my insights. I have been working on this idea since 2006.
    I do not understand why the scientific community has not deduced that space must be quantisized, and that this makes the basis for relativity and quantum physics so simple to derive.
    Please take a look at my website. Don’t be put off by the long list of postulates and implications at the beginning, please.
    Thanks
    BW Penney
    Canada

  3. Adrian du Plessis says:

    I just what request a copy of Einsteins Intuition,
    I am only an undergrad student, so I imagine most of it might go over my head. Though I am very interested in anything that would keep me questioning other teachings, so as to keep my mind from becoming a stagnant vessel of ancient teachings.

    Thank you in advance,
    Adrian du Plessis

  4. Brian Dubbert says:

    Hi I would also like to request a copy of Einstein’s Intuition.

    I am only a high school student but I am very interested in this sort of subject matter and the idea of vacuum super-fluidity gels with me a lot more than many other things I’ve read

    Thanks a lot!

    • Thad Roberts says:

      Hi Brian,
      If you’re already reading about such things in high school then I very much look forward to the insights you’ll make throughout your life. I’m sending the book to your email. Please send your feedback.

      Thad

  5. Tim James says:

    Please send me the PDF copy of Einstein’s Intuition.

  6. Bobby Viera says:

    Hi Thad, great work–it really makes an understanding of how things really work much more accessible in a non-grueling way (thanks for that). I would love a pdf copy of Einstein’s Intuition, and please post some more of the Conversations videos soon if possible. Love the site!

    • Thad Roberts says:

      Hi Bobby,
      Thank you. There is still much work to be done and you are right, at minimum this approach does offer appealing ontological access. So far its leading us to some very interesting insights. Those of us working on it are quite excited about its potential. I’m sending you the book via email. I plan to make more videos, but I’ve just come off of a two year around the world adventure, including CERN, a Physics and Philosophy of Time conference in the Black Forest, sailing across two oceans in a 55′ sloop (including through a tropical storm) and a total of 57 boarder crossings, and am now working as a theoretical physicist for a think tank. Life is a whirlwind! 😉
      – Thad

      • Bobby Viera says:

        Wow, that sounds like quite an adventure indeed! If you ever decided to venture into Hemingway-style fiction-writing, I’m sure you would have a ton of experiential knowledge to draw upon. Haha, on a similar note, I dabble in sci-fi/fantasy writing, and I can’t tell you how exponentially much more interesting my story outline has become after just a few days of pondering some of fictional applications of the insights your work brings to the table. :)

        • Thad Roberts says:

          I’m happy to hear that. And yes, I’m planning on doing some other kind of writing eventually. At the moment one of my projects is writing a book about the crazy experience of prison. I’m up to 40,000 words. Let me know where your newly inspired thoughts go. 😉

  7. Does Thad’s theory of superfluidity complement the mathematics of superstring theory?

    • Thad Roberts says:

      Hi Betsy,
      Your question is a bit difficult to answer, as the mathematics of string theory to date is so complicated that no one even knows what the exact equations are. Instead physicists work with approximations to these equations. These approximations are so complicated that they have only been partially solved. But if your concern is about whether or not qst complements the claims of superstring theory, then we should compare them based on their ontological claims. Superstring theory posits that there are fundamental strings that make up everything. The different vibrational modes of these strings account for the furniture of the world. Qst posits that the vacuum is made up of fundamental quanta (think of little elastic spheres composing a medium, like atoms in a gas) and the different waves supported by that medium (sonons) account for the furniture of the world. For example, quantized plane wave phonons in the vacuum behave as photons (light), and nonlinear sonons (like smoke rings) behave as fundamental matter particles. The “forces” of Nature are then simple derivatives of the fluid properties of the medium: spinning vortices are drawn together or drawn apart by fluid dynamic interactions, radial density gradients become the curvature fields of general relativity, and so on. How much these two approaches compliment each other is debatable I suppose, but I would put the basic goal of each on par with each other as they are post attempting to provide an ontologically sound explanation of the world we see.

      • David Heggli says:

        Hey Thad!

        I think you’re really onto sth big here! So far with every other theory: the most simple explanation possible (answering all questions), is the right one.

        => QST vs String theory: 1 : 0 :-))

        I’ve got two questions for you:

        1. What do you think of Garrett Lisi’s E8 Geometric Theory of everything? Could it be, that your theory provides actually the missing link he needs to finish it? On the first look, it seems to be much more compatible with your approach than the string theory…

        2. Would it be save to assume, that you wouldn’t have come up with this great theory without having served some time in a very confined space?
        BTW: I can totally feel with you on what happened there and where you were coming from. Being in love isn’t accidentally described as being very similar to a state of mental illness 😉
        And luckily my father was a judge for adolescents – I think only thanks to his huge experience with strong willed kids I didn’t end up in prison myself ;-D

        Alright – while waiting for your book about your experiences in prison, I’d happily read your eBook about Einsteins Intuition :-)

        • Thad Roberts says:

          Hi David,
          I think that Garrett Lisi’s E8 approach, like all insights that shed light on gauge invariance, are very useful and interesting. I cannot answer your question about how connected the two theories are, but I am actively developing the formalism of gauge invariance captured by qst. I leave the comparison to you after I post the report. As for the notion that my time in confined space, yes, I think it is safe to say that the intense and focused period of introspection and intellectual exploration definitely had a marked impact. I’ll send you a copy of the book now. The prison book is almost half done, but it will be another 6 months at least.

  8. Chris Poapst says:

    Hi Thad,

    I don’t have any scientific background, although i do have a very strong passion for learning about the universe. I would really appreciate a PDF copy of Einstein’s Intuition.

    Thank you!

  9. Marc Geddes says:

    Thad,

    The idea of space-time as a superfluid is very intriguing! What got me interested was an article in Wired describing strong analogies between fluid mechanics and quantum mechanics – this article has been getting a lot of attention this year, I highly recommend you read it if you haven’t already done so. I would be interested in hearing your opinion on this:

    “The experiments began a decade ago, when Yves Couder and colleagues at Paris Diderot University discovered that vibrating a silicon oil bath up and down at a particular frequency can induce a droplet to bounce along the surface. The droplet’s path, they found, was guided by the slanted contours of the liquid’s surface generated from the droplet’s own bounces — a mutual particle-wave interaction analogous to de Broglie’s pilot-wave concept.”

    and

    “If space and time behave like a superfluid, or a fluid that experiences no dissipation at all, then path memory could conceivably give rise to the strange quantum phenomenon of entanglement — what Einstein referred to as “spooky action at a distance.” When two particles become entangled, a measurement of the state of one instantly affects that of the other. The entanglement holds even if the two particles are light-years apart.”

    Link:
    http://www.wired.com/2014/06/the-new-quantum-reality/

    I agree the Bohm interpretation of QM seems to follow naturally from the idea of space-time as a fluid.

  10. Eric says:

    Hi Thad,

    I am also an undergraduate student studying engineering with interests in theoretical physics. I would like to read a copy of your work, Einstein’s Intuition.

    Thank you!

  11. Rodrigo Esteves says:

    Hi Thad, onto­log­i­cally it’s really make at first sight a sound and clear explanation of our perceivable and measurable reality – great insights! I’m a mechanical engineer, very passionate about physics (mainly quantum mechanics, QFTs and cosmology) and I would really appreciate a PDF copy of Einstein’s Intuition.
    Thanks,
    Rodrigo

    • Thad Roberts says:

      Hi Rodrigo,
      You’ll find a link to the book in your email ;-).
      As this is part of your passion, I look forward to hearing what you think of it.

  12. Maurizio says:

    Dear Thad,
    I just saw the TED video. I’m a theoretical physicist, but after my PhD I stopped work on String theory and its evolution mainly because I didn’t “believe” in the theory anymore. With my fellows we discussed of why physics was going in a dark tunnel, without admit any error and start to try another way. In the end, more than 30 years of String theory succeed in just one actual result: the black hole entropy derived by Bekenstein and Hawking!
    I would appre­ciate a pdf copy of Einstein’s Intuition.
    Thank you

  13. Jonatanson says:

    I have seen your TED presentation what brought me here.
    I would gladly read about this theory in your book.

    Thanks,
    Jonatanson

  14. David says:

    I came here to your site after viewing your short introduction on TED. I found your interpretation compelling. I am interested in your PDF document. I most curious to play with the calculations of the constants of nature. I am also interested in your maximum curvature. Have you considered how you might go about proving your hypothesis with experimentation? Do you have any thoughts on how to falsify it? Thank you for sharing and please continue to innovate.

    • Thad Roberts says:

      Hi David,
      Sending you the book now. Chapter 16 covers the constants. And yes, I have considered a few ways to test this. First off, it implies a specific cut off for the infinity gravity well for black holes, which has theoretical implications and direct physical implications. This cut off also implies that quantum tunneling rates will vary as spacetime curvature varies. Near super massive objects, where the curvature is high, the rates of tunneling should decrease. To turn this into a full prediction we need to calculate the exact expectation for that change, and then test against it. If, while reading the book, you come up with more ways to test this limit of maximum curvature, an independent way of deriving its value, or any additional falsifiable tests for the model, we welcome them.

  15. Al Rees says:

    Hello Thad,
    I find your information very interesting and see that you are a person of insight.
    I am just a humble construction worker who does research when I have time.I have to re read items to get the real understanding from time to time but your illustrations have really helped.Could you kindly send me a PDF of “Einstein’s Intuition”
    Thank you
    AL

    • Thad Roberts says:

      Hi Al,
      Yes of course. I’m sending it now. Please let me know if you have any suggestion for how it can be improved.

  16. Snehan Kekre says:

    I love that you, Sir, are infused with the spirit of adventure. You seem to enjoy life and beauty, as well as make sense of it at the fundamental level. I’m a first year undergraduate student(BSc in Physics and Math) wanting to understand the idea of quantized space. I had written to Prof.Julian Barbour two years ago about his amazing theory of the Universe being a string of snapshots following a linear time dependency. He replied and hoped that many more would work along those lines. I’m really inspired by your work.
    Year before last, in 12th grade, I re-created the oil-drop experiment at home using baby oil, a styrofoam plate, my loud speaker and a tone generator. Using my camera and a bit of Java programming, I plotted the drop’s motion over time and concluded that the trajectory could be plotted as a statistical density fuction. With this in mind, I sent my findings to MIT as my application essay also adding that I had conducted the interference experiment and that this was proof enough that the system behaved quantum mechanically. Sadly, my grades did not reflect my keen passion and yearning to understand the beauty of Nature. I was rejected. Notwithstanding, I’ve spent this year learning the fundamentals from various books(mostly pdfs) and free journals such arXiv.
    Most days I revel in awe when I try to comprehend my own existence and my part in the Cosmic drama. To be honest, I cry at times because I fail to grasp this elusive but all pervasive thing that transcends comprehension. I sincerely hope that you will be able to guide me on my journey as a student of Physics and Life.
    I would be excited if you could email a copy of your book to my ID. Thank you,kindly.
    Your virtual student,
    Snehan. (@ssnehan)

    • Thad Roberts says:

      Hi Snehan,
      That’s quite impressive. I didn’t reproduce Millikan’s oil drop experiment until college. Your curiosity is going to take you very far in life. There are so many things to discover, and so many unsolved mysteries waiting for your contribution. Don’t get discouraged by the immensity of all there is to learn, for it is what provides us with the great adventure. If my book can assist you on your journey I’m happy to share. I have made a great effort to make all of the ideas in my book very accessible and clear. Should you encounter anything that is unclear to you, please let me know. I’m sending you the book now. I look forward to your feedback.

    • Thad Roberts says:

      Hi Snehan,
      That’s quite impres­sive. I didn’t repro­duce Millikan’s oil drop exper­i­ment until col­lege. Your curiosity is going to take you very far in life. There are so many things to dis­cover, and so many unsolved mys­teries waiting for your con­tri­bu­tion. Don’t get dis­cour­aged by the immen­sity of all there is to learn, for it is what pro­vides us with the great adven­ture. If my book can assist you on your journey I’m happy to share. I have made a great effort to make all of the ideas in my book very acces­sible and clear. Should you encounter any­thing that is unclear to you, please let me know. I’m sending you the book now. I look for­ward to your feedback.

  17. Snehan Kekre says:

    Thank you for your reply, Sir. I’ve just received your pdf and will begin reading it tonight. I can’t wait to start!

    The oil-drop experiment that I mentioned was the Yves Couder silicon drop experiment.

  18. Andy H. says:

    Hi,
    I’ve been thinking along similar (though less refined) lines with regard to the fact(?) that photos and electrons behave as a distortion of the spacetime superfluid (I didn’t surmise the superfluid part). Anyway, I hate the double slit experiment. It’s like a trick you play to get the result you want. So…it occurred to me just now that if you take any number of “double slits” and enclose the region where the photon or electron “fly” the distortion wave should propagate through all of these slits (picture a box with slits on all sides but the opening through which the quantum particle goes). This would be very similar to a shock wave propagating off of an object moving above Mach 1. Has this experiment ever been done?
    Best Regards,
    Andy

    • Thad Roberts says:

      I haven’t heard of that experiment being performed. Let me know how it goes. I’m curious what your take might be on my treatment of the double slit experiment, and its philosophical implications, in my book. Sending it to you now. The most relevant sections are Chapters 12 and 13.

  19. Allen Azar says:

    I like it. It’s intuitive.

    Questions:
    1. If there’s density in space quanta, there is potentially emptiness between the quanta. What are you calling that, does it have any properties, predictions, etc.

    2. How do you prove this out experimentally?

    3. Does qst have its own force interactions? Can we push/pull qs?

    4. Is evenly distributed qs the end game entropy.

    5. How might pair production (energy to matter) function in qst, if youre creating matter from photons which would require position in space. How would the qs be called for newly created matter?

    6. does qs have alignment thru the universe , do they spin?

    7. how might this help explain electron orbital transitions.

    8. does qst predict a graviton or a different force mediator.

    9. How much smaller is a qs than say an electron?

    10. Might qs be a particle that imbues 3 dimensions?

    Please send me the pdf.

    • Thad Roberts says:

      Hi Allen,

      These are great questions. I’ll respond here and send you the book, which should answer these questions more richly.

      1. The dimensions that separate the quanta of space are called superspatial dimensions, and they allow us to model the states of space (how the quanta are arranged relative to each other) and define how that state evolves.

      2. There are several ways to prove the model wrong, but as with all scientific theories it cannot be proven correct. It makes predictions for supersymmetric dimensional sets (11, 30, 85, 248 dimensions and so on). If any supersymmetric dimensional sets are found outside of that series, it will count as an observation against the model. Also, there are several predictions made in the realm of astrophysics. For example, the model predicts that quantum tunneling will be less likely in regions of higher curvature, and less likely when the temperature of space was higher. There are falsifiable measurements to be made in that vein. It also predicts a correlation between the average radius of dark matter haloes around host galaxies, and their temperature – positing that colder galactic cores will have smaller dark matter haloes. We are also trying to model the sonons allowed by the wave equation of this superfluid, and to match those sonons with the fundamental particles of matter. This process might end up making specific predictions for particles unobserved.

      3. The four forces (gravity, electromagnetism, the weak and strong nuclear forces) are all translated as geometric deformations in the superfluid vacuum. Gravity is a density gradient in that vacuum, the electric field references divergent flow, the magnetic field references curl, the weak force references the quantization (versus a smoothly connected) of the fluid, and the strong force references the formation and stabilization of sonons (smoke rings), or vortices, in the fluid. All of these geometric distortions reference ways that the vacuum differ from an Euclidean expectation. Therefore, there are no forces, or fields in the vacuum, but you could consider a force description in the elastic collisions of the quanta themselves – as least until you resolve the higher order perspective.

      4. Yes. At that point the entire universe would have no matter, no energy or light, or anything. There would be complete symmetry in space.

      5.Energy, like light, is a plane wave phonon in the vacuum. If phonons of the right energy intersect the right way they can create a sonon (think smoke ring). In superfluids these sonons are stable and do not dissipate. This transformation results in the third polarization state – granting the distortion the properties of a matter particle.

      6. No they are not all aligned. They move and twist about in response to their collisions.

      7. Electron orbits are quantized because the electrons themselves are quantized solutions to the wave equation, representing very discrete amounts of energy in the vacuum in a wave form. Cotangling waves means capturing those interactions wholly – leading to quantum jumps.

      8. No. It specifically dissolves particle force mediators. Instead it reveals “forces” as expressions of the ways in which the vacuum’s geometry differs from Euclidean geometry. Someone might want to claim that the quanta themselves could be thought of as force mediators, but given that the distortions that reference forces are flow descriptors, or general geometry descriptors, a geometry that refers to the vacuum geometry, not the geometry of its quanta, I feel the most accurate answer to your question is that there are no force mediating particles.

      9. Just a few orders of magnitude. See this paper for some details:
      http://arxiv.org/pdf/1301.7351v1.pdf

      10. The quanta of space do collectively give rise the the familiar three dimensions.

      Sending you the book via email.

  20. Tony says:

    Please send me the PDF copy of Einstein’s Intuition.
    Very interested to read more on your ideas.
    Thanks in advance.

  21. Ed Slattery says:

    I enjoyed the interesting video, and requested the PDF on Einstein’s intuitions last night.

    I did have a question related to the generation of repulsive gravity by the concentration of the space quanta through the rotation of adjacent vortices. My physics is very limited, but I had the impression that the shifting of fluids (air, water, etc.) by meteorological systems results much less from their concentration through horizontal flows than from precipitation or evaporation through vertical flows. In your cosmological view, do the other 9 dimensions serve that function?

    Because I’m trying to get through Bojowald’s popularization (the book called “Once Before Time”) of Loop Quantum Cosmology, I’d also like to know whether you feel your views on cosmology to be similar to LQC.

    Thank you for your attention to this long-winded note.

    • Thad Roberts says:

      There are some similarities, for example both models offer mechanisms for the Big Bang, interpreting it in terms of a quantum bounce, but they do so if slightly different ways. Also both models resolve black hole singularities, but again in different ways.
      As for your fluid dynamic question / additional dimension question, the other 9 dimensions primarily serve the function of resolving the quantized nature of the vacuum. In doing this, they also resolve degrees of freedom that allow us to talk about the vacuum in terms of flow, divergence, curl, and changes in density. Basically this opens the door to hydrodynamically framing the universe, or hydrodynamically explaining the four forces.

  22. Micah Buckley says:

    Hey Mr. Thad,

    I would like to request a copy of Einstein’s Intuition, if I may. Your work looks amazing! Keep it up! :)

  23. Miguel Bernadin says:

    Hi Thad,

    I saw your TEDx talk and I was pleasently surprised how you were able to discover the speed of light by using simple quantum constants. My intuition tells me that you are on the right track and are asking great questions. I come from a computer engineering background so I wonder what changes can come from this from a practical quantum space theory perspective.

    Looking forward to diving deeper with a copy of your PDF wen you get a chance.

    • Thad Roberts says:

      Hi Miguel,
      Instead of explaining how I see the quantum space theory perspective impacting your world, I’ll send you the book and then look forward to seeing how you answer that question. 😉 Emailing it to you now.

  24. Tamaat says:

    Hey Thad,
    I had come to the same basic realization of quantized space when I happened to stumble upon your Ted Talk. I was delighted to see the idea refined as elegantly as you have done. To make the circumstances even better you had calculated and defined the mystery number whose necessity I have only recently realized. Zhe was the final key to understanding the universe and dimensionality. I’m writing to request Einstein’s Intuition, but more importantly I’m writing to correct a mistake. There are not 11 dimensions in your diagram there are 12. If you would like to discuss this 12th dimension with me I would be delighted to get an email from you. Thank you for your work. With love, Conor “Tamaat” Sullivan.

    • Thad Roberts says:

      Hi Tamaat,
      The total number of dimensions depends on resolution. In Chapter 11 I explain the dimensional hierarchical equation, which states that the number of dimensions in the map is equal to 3^n + n, where n is the order of perspective. From a first order perspective there are (3+1) dimensions, from a second order perspective there are (9+2) dimensions and so on. Most of the book focuses on a second order perspective, which resolves 9 spatial dimensions and two temporal dimensions. You may be thinking that since there are 3 kinds of volume resolved, there should also be three kinds of time resolved, but that would be an overstep as there are no evolutions tracked in a second order perspective that do not map to time or supertime. I look forward to hearing what you have to say after reading through the book. Sending it to you now.

  25. vijay says:

    I would really appre­ciate a PDF copy of Einstein’s Intuition. I would like to add the importance of consciousness n sleeps.

  26. Garry J. Flynn says:

    Most impressive work Thad.
    The theories presented seem to be well calculated indeed. In fact the model I was able to make in my head of this has revolutionized all thought of the physical world. Frankly I have never quite seen anything of the sort presented as a possibility. I would be most excited to own a copy of the book and if the depth of the arguments meet my curiosity with sound prediction, I will be sure enough to present the knowledge to all open ears.

    • Thad Roberts says:

      Hi Garry,
      The book officially comes out next month. In the mean time I’m sending you the current version via pdf. I look forward to your thoughts as you read.

  27. László Csontos says:

    Hi Thad! I met your very exciting approach on youtube, watching TEDx, and I want to learn more about it. I’m a biotechnologist, but I’m interested in physics too. Could you be so kind and send me a copy of your book? I would appreciate it!
    Thank you very much, best wishes :)
    Laca

  28. Alex Georgopoulos says:

    Hi,
    The universe has always baffled me. I’ve always been interested in the stars/space. Always looking up. Since i heard of the “curvature” of the universe I became so intrigued that I often tried to visualize it myself, and the best approximation I could produce is that it is like a double cone-like structure. These cones are opposed in direction and we are located in the tip of both (approximately like an hour glass). How wide is the tip or junction is a most difficult question to answer. One opening of the cone-like points to above, or up, and the other opening points to below, or down, because infinite is at the end of any direction (what you gain in terms of having less distance to travel you loose in terms of bigger number of possibilities…)
    So many things have been running through my head that its difficult to remember them all, but one that is a thorn for me is the dumbing of our intellectual capacities caused by Geometry. Specifically the Sphere, because the Sphere, since it is like a representation of “all possible directions” is the Nemesis of the understanding of more than three spacial dimensions.
    Also, I see Time as more than one dimension and I can’t explain why but I can give an example. Suppose Time is actually two arrows. One is the chronological time, the one measured with precision, with machines etc. This one goes in a straight line from past to future. The other is the psychological time. This one goes spiraling around the chronological time, also from past to future but with variable speed, meaning that it can make many laps around the linear time when things are “accelerated” or less laps when things are “quiet”.
    More recently the existence of Transparency is what has been occupying my mind. Transparency is difficult to accept (and on the other hand non-transparency is even more difficult, since most of the universe IS transparent – or invisible – to us like dark matter and dark energy…)
    Most recently it came to my mind that our thoughts are like soft/intangible/transparent probes of the universe, with which we can probe not only the existing things but also ideas that exist only in our or other minds. But again, in order to understand an object, for instance, our mind “surrounds” this object with transparency, insulating it from whatever we are not concerned with at the moment…
    Well, that’s a lot already. The point is that I’d like to receive a copy of your book, if it is still possible, because I’m sure it will be great, as was your presentation.
    Thanks in advance,
    alex.

  29. David Faren says:

    Hello,

    someone just shared your tedx talk with me and I would love to read your book Einstein’s Intuition. Could I please have copy?

    David

    • Thad Roberts says:

      Yes of course. The official version is coming out at the end of this month, until then, I’ll email you the current version 😉

      • David says:

        Hi Thad,
        I purchased your book on th ibook store and I’m halfway through. It’s fascinating and love the visuals. I have a PhD in pharmacology, but love anything physics.

        1. How has been the reception of your theory by the scientific community?
        2. I see a lot of similarities between Brian Greene’s description of new dimension at the smallest level and the quanta concept, are you considering collaboration with other physicists such as Greene, it seems like a collaborative effort could accelerate the development of concrete equations to your theory (and a nobel prize 😉
        3. The dimension that is between the quanta, is it made up of anything or is it pure empty space?

        Great work Thad! Love new radical ideas!

        • Thad Roberts says:

          Hi David,

          I’m happy to hear you are enjoying the book and the visuals. Send me another note when you finish, I’d like to hear if you have any more feedback. To answer your questions (1) the scientific community at large has never heard of Bohmian Mechanics, or Superfluid Vacuum Theory. Quantum Space Theory is a specific version of SVT, which comes with a particularly compelling and intuitively accessible model, but it still falls within the umbrella of SVT – so it still is relatively unknown. (2) I am collaborating and always open to more, but new theories usually have to swim rather vigorously upstream for a generation or two before they are seen by the public. Surviving that swim will make for a great story in itself ;-). Anyway, the tenants of Bohmian mechanics and SVT are taken very seriously among scientists and philosophers, despite the fact that mainstream physics has not taken notice. Check out the wiki pages on both to get an idea. Also, check out my Quora answer for a richer story of this kind of development: https://www.quora.com/Why-dont-more-physicists-subscribe-to-pilot-wave-theory/answer/Thad-Roberts
          (3) The dimensions between quanta (superspatial dimensions) are not space, that is they do not have the substance that adds to the medium of space. When more closely examined, at higher resolution, however, they too are quantized and have their own fluid character. Hope that helps.

  30. Joe Bliss says:

    Thad,
    Your ideas on space being a fluid is something I always thought had to be the case. The ‘Ether’ is what I believe it was referred to as. The statement I’ve heard, that light travels through a vacuum, just doesn’t set right with me, as well as the idea of a singularity (though I suspect at a certain density there might be no discernible difference), and I also have a suspicion about red-shifting of light over great distances. As I’ve been reading more and more, I get a sense that time and space (or rather the density of space, as it changes near a massive object) are proportionately constant, though as space compresses near a massive object, time seems to slow for that object compared to space that is less compressed (inverse). And so traveling at high speeds, and increasing your mass, (and perhaps altering the density of the traveling objects space?!?) alters time for the traveling object even though it’s in relatively low-density space. Just musing there, but I’ve read the laymans’ version of this and it just tells what happens, not why. I’m an electrician slowly putting some higher ed together for an engineering degree, and though my math is seriously lacking, the concepts seem easy to grasp. I’d love to read what you have, so please send me the pdf.
    It does seem like contemporary science is getting too narrow, but I’m hopeful. Also, when I’m thinking about your graphics, it occurs to me that the space between the spheres might be the solid material (where instead of distance you would have energy, also inverse), and the sphere’s would be more like bubbles, but with no definitive demarcation between the two, only a gradual change in energy. Exchanges of energy position in this substrate would relate to rotation, but not in the conventional sense. And in a system, say subatomic particles, harmonized rotation would be the definition of matter, where structures are stabilized by the harmonic which would stabilize itself by propagation if there is a maximum amount of energy that can occupy the same space (hence the inverse proportion between distance and energy); and a cross-sectional view would look like what I imagine String Theory as. More musing. Thoughts?
    Good luck with your proofs, I have a good feeling about your model, as I understand it.
    Joe Bliss
    P.S. One more thought. The greater the compression of space, the greater the stability of the energy in a system. This stability would inhibit energy transfer in a system, lengthening time as described as the speed of light. This, however would require an even smaller medium to describe the energy, with larger numbers of particles in a given space and a constant for the time for interaction between these particles of energy to describe slower transfer at denser spaces. At maximum density, near singularity. But it would not be infinite. Counter intuitive, though. No play on words intended.

    • Joe Bliss says:

      Thad,
      I just watched the ‘Conversation’ video. I’m kinda stoked that I wasn’t very far off on most of the things you said, considering my education level. I also noticed you are already releasing your book. My loss. I still haven’t gotten to an explanation of superposition, or the attraction of matter to denser space. But I’m still a fan, and will keep an eye out for more developments.
      Thanks for sharing this. Joe Bliss.

      • Thad Roberts says:

        Just sent it to you, sorry I was very behind on communications, while wrapping up the book.

        • Joe Bliss says:

          Thad,
          I really appreciate it. Finished watching ‘Conversations’ I and II. Very cool. Keep up the work and good luck. Joe Bliss.

    • Thad Roberts says:

      Whew, that was a lot. Sorry I’ve been busy. Just published the book. But since you requested before it came out I’ll send you the pdf and look forward to seeing how your thoughts evolve or strengthen from reading it.

  31. Dawid Czaja says:

    This theory looks so elegant…. I’m very impressed

    Please send me the PDF copy of Einstein’s Intuition.

    • Thad Roberts says:

      The book is now available via Lulu.com (hardcover full color), Amazon.com (softcover full color), or through iTunes (iBook). You’ll find links to each here.

      http://www.einsteinsintuition.com

      If you’d like a signed copy please let me know. If you cannot afford the $14.99 at this time (for the iBook) send me another message and let me know.

  32. Sidney Jones says:

    Hi Thad:

    This superfluidity is a very interesting idea. Please send a copy of Einstein’s Intuition. Thanks in advance. Sid

    • Thad Roberts says:

      Hi Sidney,

      The book is now available via Lulu.com (hardcover full color), Amazon.com (softcover full color), or through iTunes (iBook). You’ll find links to each here.

      http://www.einsteinsintuition.com

      If you’d like a signed copy please let me know. If you cannot afford the $14.99 at this time (for the iBook) send me another message and let me know.

  33. Kyle Brooks says:

    Thad,

    I am a Audio Engineer and have always been intrigued by space, matter and the science that works to understand it. I am an avid watcher of TED talks and happened upon this site after watching your amazing talk at TEDxBoulder. If you are still giving out Einsteins Intuition in PDF I would love to have a copy.

    Kyle Brooks

    • Thad Roberts says:

      Hi Kyle,

      The book is now available via Lulu.com (hardcover full color), Amazon.com (softcover full color), or through iTunes (iBook). You’ll find links to each here.

      http://www.einsteinsintuition.com

      If you’d like a signed copy please let me know. If you cannot afford the $14.99 at this time (for the iBook) send me another message and let me know.

  34. Andrew says:

    Hello Thad,

    interesting claims that you made, and the fascinating about it that it’s based on simplicity.
    I have been seeking in kinds of simplicity, so it was just a matter of time, btw in my capability of imagining the highest term in the universe – so therefore curious about your thought about stasis of time in densest states of quants, to get to your perceptions.
    Unfortunately I couldn’t face simplicity in my first, not succeeded college studies of technical physics.
    I would like to know how you think about and how you link Einsteins & Plancks theories, hopefully in your iBooks version for threatening our existence students…

    • Thad Roberts says:

      Hi Andrew,
      I’m confident that reading the iBook will give you a full take on my view of Einstein’s and Planck’s insights. They are both integral to the superfluid vacuum theory perspective. Keep track of your questions as you read.

  35. Lynn Nicholson says:

    Hi Thad,

    Congratulations on the publication of the book! I think I’ve got a long way to go before I think I’ll be able to draw new conclusions about electromagnetism using qst as the framework, or even be able to explain every phenomenon in detail, but I’m looking forward. I was the epitome of the Why-child and for something so important as electricity, magnetism, light, etc., I’ve always felt let down by the explanations available even as an adult. “Here are some equations that explain how it work.” Well, that just never has been enough.

    I have a few questions that I’d love your thoughts on:

    (1) How do the simplest particles of matter interact with the quanta? – I’m sort of lost in a sea of possibilities when I try to visualize what exactly is going on (or can go on) within a superspatial volume and its constituent quanta. For example, can these quanta bounce around freely or do they inherently want to sit still and equalize the pressure within the superspatial volume?

    (2) Can there be the analog of wind – quanta flowing away from high pressure areas into lower pressure zones? This doesn’t seem to be the case – or if it is possible, there’s a counteracting force that prevents densely-packed quanta from doing so when those quanta are the space occupied by a black hole or star, etc.

    (3) I’ve also wondered why the superspatial volume should be a nothingness when nothingness is exactly what is done away with by having quanta (in other words, is superspace itself a Euclidian expanse, not really made of anything?) Perhaps there’s nothing additional we’d be able to explain if superspatial volume itself had an underlying quantized fabric.

    (4) Do you have any thoughts on what the boundary of a quanta “is” or why such a boundary is necessary other than to firmly define dimensional boundaries?

    (5) I’ve been watching the videos and reading the comments available on your site. One of your responses was about speed of light depending on density (with more nuance than this of course).

    I took some time just now to rethink things a bit. Initially, my question/interest centered upon the density of quanta within a volume of the vacuum of space (yes, our x, y, z space)…as if that concept made any sense (I think it actually doesn’t because as far as our 3 dimensions of space are concerned, they’re made of quanta rather than contain them). What I was thinking fundamentally boils down to the idea that the speed of light in a vacuum, as we see it, would depend on the density of the quanta within superspace.

    I now believe that to be the wrong way of looking at things because a cubic meter of our x, y, z space, for example, must always consist of the same exact number of quanta – a meter’s worth of planck lengths cubed – because length is a measurement of n quanta and therefore, so is volume by extrapolation. My key insight I think I had, which fixes the misunderstanding I think I was under, is the density of the quanta – how packed or loose they are within superspace – doesn’t affect our perception of a cubic meter being a cubic meter.

    Where I was going in my mind was the idea of using what we know from already-performed experiments regarding the speed of light in various materials to reverse-engineer some information about the required density of quanta in order to produce those speeds. That idea still may be worthwhile, but I now see that the density of quanta has to look at superspatial volumes to make any sense at all.

    Am I in the ballpark here? Or am I still missing something fundamental with this?

    (6) What kind of self-study syllabus would recommend in order to become fluent in the fields of math and physics required to deeply understand qst – say for a person who has taken differential calculus and a year of undergrad physics? Like, right now I can Google, “what do I need to study in order to understand superfluids?” But when you try to backtrack through layers of dependent fields of knowledge you’ve never studied, back to a good point of entry it’s easy to get lost.

    Thanks!

    Lynn

    • Thad Roberts says:

      Hi Lynn,

      I’m delighted to hear that you were the epitome of the why-child, and more importantly that you stayed in touch with this quality. The world needs far more people to carry their childlike curiosity into adulthood. You are right to note that modern day “explanations” of electricity, magnetism, light, etc. are unsatisfactory. In fact, the modern treatment of these topics is in terms of fields, without any direct conversation about what the fields themselves are. We cannot claim understanding until we bridge this gap. Forces, or fields, are just placeholders of our ignorance. They may give us powerful mathematical predictions, but as long as they remain fundamentally mysterious they cannot satisfy our philosophical hunger to scientifically know the universe.

      To answer your questions…

      (1) How do the simplest particles of matter interact with the quanta – I’m sort of lost in a sea of possibilities when I try to visualize what exactly is going on (or can go on) within a superspatial volume and its constituent quanta. For example, can these quanta bounce around freely or do they inherently want to sit still and equalize the pressure within the superspatial volume?

      – The key insight here is that the quanta make up the vacuum (spacetime). Uniformly spaced quanta would define a vacuum without any interesting things in it (zero curvature, zero electromagnetism, zero mass, zero wormholes…). All of the things we think of as being in the vacuum are emergent properties, collective consequences of many quanta interactions. Vacuum curvature is a density gradient in the quanta, going from more densely arranged in superspace to less densely arranged. Waves that propagate through the vacuum (we call them acoustic waves because they are made up of the metric of the medium itself and simply represents undulations that move through it) make up light (electric fields represent divergence in vacuum flow, and magnetic fields represent curl, therefore a passing packet or impulse wave introduces both fields). In order for these waves of energy to be converted into “mass” they must gain locality. That is, they must be able to stand still yet still be waving. This is accomplished by forming a vortex (more accurately a sonon, which resembles a smoke ring). Now to your questions. The simplest vortices, like the one that composes the electron are made up of swirling collections of quanta. The combined interactions of the vacuum fluid (made up of the quanta) is controlled by Euler’s equation for compressible inviscid fluids. For more on this topic see (http://arxiv.org/abs/1301.7351 and http://arxiv.org/abs/1301.7540).

      (2) Can there be the analog of wind – quanta flowing away from high pressure areas into lower pressure zones? This doesn’t seem to be the case – or if it is possible, there’s a counteracting force that prevents densely-packed quanta from doing so when those quanta are the space occupied by a black hole or star, etc.

      – Yes, absolutely. Euler’s fluid dynamics fully apply, but they apply as they would for an inviscid fluid (one without viscosity). So remember that vortices are what we call irrotational. Perhaps this will help. Imagine that near a black hole’s center all of the quanta are moving around in one big vortex. Now note that because the quanta are circling around together they are not colliding into each other in random directions. The density is higher here because the quanta are aligned in their motions. As you move away from the center the alignment of motion of the quanta becomes less and less aligned until they are entirely random, and following this change we go from denser (more curved) vacuum to less dense (zero curvature) space. Does that help?

      (3) I’ve also wondered why the superspatial volume should be a nothingness when nothingness is exactly what is done away with by having quanta. Perhaps there’s nothing additional we’d be able to explain if superspatial volume itself had an underlying quantized fabric.

      – Great question. This is an oversimplification. In a closer examination this model actually projects a fractal construction of the vacuum. That is, it breaks up the vacuum into a medium of quanta separated throughout superspace, but when we look closer it also makes the claim that the quanta themselves are composed of smaller quantized ingredients separated through another volume, and so on. Chapter 11 discussed this in detail. If it doesn’t address all of your concerns please let me know.

      (4) Do you have any thoughts on what the boundary of a quanta “is” or why such a boundary is necessary other than to firmly define dimensional boundaries?

      – Excellent question again, and in good succession. Following the previous answer, this model leads us to believe that the boundary of the quanta themselves is actually more detailed than a thin wall. In fact, it posits that the quanta are quantum vortices within the superspace. Therefore, the boundaries have a faded edge just like a vortex does. For most of my book I don’t model the universe in anything past 11D, which means I’m ignoring this level of detail, but the modeling of that complexity will mimic the modeling of vacuum vortices and how they interact.

      (5) I’ve been watching the videos and reading the comments available on your site. One of your responses was about speed of light depending on density (with more nuance than this of course).

      There was a ten minute gap between paragraphs here while I rethought things a bit. Initially, my question/interest centered upon the density of quanta within a volume of the vacuum of space (yes, our x, y, z space)…as if that concept made any sense (I think it actually doesn’t thanks to the ten minute gap). What I was thinking fundamentally boils down to the idea that the speed of light in a vacuum, as we see it, would depend on the density of the quanta within superspace.

      I now believe that to be the wrong way of looking at things because a cubic meter of our x, y, z space, for example, must always contain the same exact number of quanta – because length is a measurement of n quanta and therefore, so is volume by extrapolation. My key insight I think I had, which fixes the misunderstanding I think I was under, is the density of the quanta – how packed or loose they are within superspace – doesn’t affect our perception of a cubic meter being a cubic meter.

      Am I in the ballpark here? Or am I still missing something fundamental with this?

      – You are dead on with this insight! Congratulations ;-). The thing to keep in mind when exploring the model of the universe we are employing is that it interjects a coherent picture from an outsider perspective. That is, it explains what observers “inside” the vacuum will observe, but only offers a fully locally deterministic explanation of those effects from a perspective that is “outside” of the vacuum. Inside of the vacuum the speed of light is always constant, because we cannot distinguish different densities of space from within space, but outside of the vacuum we can talk about different densities and varying light speeds.

      (6) What kind of self-study syl­labus would rec­om­mend in order to become fluent in the fields of math and physics required to deeply under­stand qst – say for a person who has taken dif­fer­en­tial cal­culus and a year of under­grad physics? Like, right now I can Google, “what do I need to study in order to under­stand super­fluids?” But when you try to back­track through layers of depen­dent fields of knowl­edge you’ve never studied, back to a good point of entry it’s easy to get lost.

      – First I recommend fully absorbing my book (which I hear takes about 3 reads). This will allow you to have the full picture in your head, and to understand exactly what qst is claiming. Once you have that full picture, you can reinforce your math and physics knowledge in many ways. Here’s a short list of papers/publications to get you started. Reading these will definitely give you a sense of where to go next. If you feel intimidated by any of these, that’s fine, don’t let it discourage you. Just read through and absorb the parts you can, and then keep a list of topics that you need a richer background on. Then send me the topics and I’ll forward some books that will help.

      http://arxiv.org/abs/1301.7540
      http://arxiv.org/abs/1502.05926
      http://arxiv.org/abs/1401.4356
      http://arxiv.org/abs/1305.6822
      http://arxiv.org/abs/1301.7351
      http://arxiv.org/abs/1507.03013
      http://arxiv.org/abs/1508.05619
      http://arxiv.org/abs/1507.01019
      http://arxiv.org/abs/1506.07877
      http://arxiv.org/abs/1506.00882
      http://arxiv.org/abs/1505.03879
      http://arxiv.org/abs/hep-th/9602081
      http://arxiv.org/abs/1204.6157
      http://arxiv.org/abs/gr-qc/0111111
      http://arxiv.org/abs/gr-qc/9712010
      http://relativity.livingreviews.org/Articles/lrr-2011-3/fulltext.html
      http://iopscience.iop.org/article/10.1088/0264-9381/18/6/312/meta;jsessionid=4939D2C2F84083D0C0777572632E463B.ip-10-40-2-121
      http://arxiv.org/abs/1004.0597

      Meanwhile, I’ll be working to eventually put out some videos with great graphics to make the superfluid vacuum even more accessible to a wider range of people.

      Thanks again for your questions. I look forward to seeing your discovery process blossom ;-).

      Thad

      • Lynn Nicholson says:

        Hi Thad,

        Thanks for all the great information in your answers. I read the pre-published version of Einstein’s Intuition you sent me all the way back in July, 2014 and am making my way through the first reading of the published edition and things are definitely clearer for having read the earlier version.

        You mentioned sonons which triggered my recollection of something recently in the news: http://news.sciencemag.org/physics/2015/10/researchers-create-sonic-tractor-beam

        If this can be done acoustically, I can only imagine what will be possible when the acoustic metric of the vacuum superfluid is put to full use.

        On my question #3, I’m still not sure if we’re on the same page. Looking at the model, we have intraspatial volumes, spatial volumes (our x, y, z) and superspatial volumes. Of these three types of volume, the first two are composed of subquanta and quanta respectively. Superspace, on the other hand appears to be a void of nothingness (the regions, at least, not occupied at any given time by quanta).

        That seemed interesting to me because many people view the vacuum of spacetime to be a void of nothingness while qst says it is actually quantized and is made of this substrate of quanta. And yet, here we are with superspace – the space in between the quanta – which I currently understand to be just like the nothingness I was taught earlier on in life to be the vacuum of outer space.

        So it appears that the nothingness of the vacuum has been eliminated but now shows up in the unoccupied volume of superspace. Any nuances I’m missing about superspace?

        And a question about quantum vortices. Does a quantum vortex behave as a wave when it comes to have a wave can travel through vast quantities (and distances) of quanta without the quanta traveling all the way with them? In other words, in a moving quantum vortex does the set of quanta within the vortex maintain the same members? Or do quantum vortices share a property of waves in that the wave can propagate across significant distance without any of the quanta that were temporarily a part of it moving very far from where they were?

        Thanks again for all your answers!

        Lynn

        • Thad Roberts says:

          Lynn,

          Yes, there is more nuance to this structure than the 11D resolution shows. From 11D the picture you have in your head is accurate, but it incomplete. It may help to think of the vacuum quanta as vortices in the background subquanta fluid (superspace). If we only resolve 11 dimensions about the vacuum’s structure, then we ignore the structure of that superspace fluid and think of it much like you thought of empty space until now.

          As for your question about quantum vortices, no the set of quanta within a vortex does not strictly maintain the same members. These vortices represent special wavefronts in the medium known as sonons (think smoke rings) and can therefore propagate without significantly displacing the connectivity of the underlying medium.

  36. Yan Zhiqiang says:

    Hi Thad,

    I am an astrophysics student.

    I find your idea of dark matter and dark energy seems prospective at the first glace. Hope to know more about it. So please send me a copy too.

    Thank you!

  37. arthur says:

    Thad,

    I have just been shown your tedx talk, and listened to the vacuum superfluidity video on this site. Thank you very much for bringing me back into thinking of theoretical physics.

    I have just purchased your audiobook from Audible and will be getting right into it. The softcover is now $75+ on amazon and hardcover $100 on lulu. Congratulations on mastering the 2D geometry of supply and demand!

    I’d kindly request a copy of the pdf, as there is nothing available in the kindle store and I have no ipad. I will be sorry to miss the color visuals, but…

    Alternatively, I’d buy a $100 hardcover signed by you – just don’t tell the wife.

    Thank you for your work and your attention to the commenters here.

    My very best,

    Arthur

    • Thad Roberts says:

      Hi Arthur,

      I’m happy to arrange sending you a signed hardcover book (for $80 plus shipping). That’s the manufacturing cost – at least they tell me. Seems a bit steep to me, but there we have it. Let me know if you want to pursue this option.

      I will eventually make an ePub, and kindle, version. Trying to make the black and white versions of the figures right now. The color really was a valuable part of the book, so I’m trying to figure out how to not have to sacrifice the quality to an unacceptable level.

      I’m emailing you a link for the pdf for now.

      I look forward to your comments as you read. 😉

      Thad

  38. Michael C Grasso says:

    I enjoyed the video. Your findings confirm in some aspects what my research is showing. There are some differences though. I also find that charge (+ and -) IS none other than clock and counter-clock spin. I also believe, given the evidence, that the EU basic theory (to be perfected of course) is the “right” direction to go. My research found that EM is “controlled” by a “numerical matrix” (nothing is random or by chance). Yes, it’s all “quanta”, or numbers as the famous Greeks used to say…
    I’d love to read the PDF, even though I may found it too difficult to understand it in detail.

    • Thad Roberts says:

      I’m sending you a link to the pdf now. You can also order the book in soft back from Amazon, hardback from Lulu, an iBook or and audiobook from Audible. If you find it too difficult to understand any parts, please keep notes for me and let me know which parts you think could be made more clear.

  39. nikhil says:

    hi,
    i am an undergrad student from india. i am very much interested in reading about the new theories related to space time and the origins of this universe.
    i would also like to request a copy of einsteins intuitions.
    i hope these mysteries will be unraveled in time. and i wish youall the best thad.

    • Thad Roberts says:

      Hi Nikhil,
      I’m sending you a link to the pdf vial email. You can also order the book in soft back from Amazon, hardback from Lulu, an iBook or and audiobook from Audible. Thanks for being a part of this journey of curiosity.

  40. Mike Petersen says:

    Hello, Thad…

    I acquired your book in PDF format early in 2014, but did not have occasion to read it until recently. My question for you concerns String Theory. A lot of insight into the true nature of the cosmos has been revealed through various concepts in String Theory, so I think it is close to “being there” for an accurate description of the microscopically small. What is your take on how the “strings” in String Theory fit in with qst?

    Thanks in advance for your reply.

    Mike Petersen

    PS – My PDF copy of the book does not include anything about the discovery of the Higgs boson…does any more recent version of your book delve into this?

    • Thad Roberts says:

      Hi Mike,
      The strings are more generally extended into n-dimensional branes in M-theory, but I don’t have a clear answer for you for how they overlap with qst. I can loosely speculate that the quanta in qst can be taken to represent branes, whose large collection throughout configuration space defines the state of space, and that the resonate modes of the branes code the interactions between quanta and therefore give rise to the various stable distortions that we call matter particles, but that’s a rough and loose alignment. Chapter 21 talks about the Higgs mechanism. Let me know if you need the published version.

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