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Einstein’s Intuition

 

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Einstein’s Intuition‘ is now available in soft cover from Amazon in black and white and full color, hard cover from Lulu in full color, as an iBook from Apple, and an Audiobook from Audible.

About the Book

Presented in clear and accessible language with wonderfully supportive graphics, Roberts offers the reader a voyage through the development of human knowledge. He then examines the outstanding mysteries of modern physics—the phenomena that lie outside the boarders of our current understanding (dark energy, dark matter, the Big Bang, wave-particle duality, quantum tunneling, state vector reduction, etc.) and suggests that the next step in our intellectual journey is to treat the vacuum of space as a superfluid—modeling it as being composed of interactive quanta, which, in a self similar way, are composed of subquanta, and so on. With this proposition Roberts engenders the vacuum with fractal geometry, and opens the door to explaining the outstanding mysteries of physics geometrically.

Roberts’ model, called quantum space theory, has been praised for how it offers an intuitively accessible picture of eleven-dimensions and for powerfully extending the insight of general relativity, eloquently translating the four forces into unique kinds of geometric distortions, while offering underlying deterministic dynamics that give rise to quantum mechanics. That remarkably simple picture explains the mysteries of modern physics in a way that is fully commensurate with Einstein’s intuition. It is a refreshingly unique perspective that generates several testable predictions.

“This work is mathematically beautiful and scientifically priceless, and the kicker is that it comes with a vivid and satisfying picture.”
~ Chris J. Wilshaw

“This book fundamentally changed my understanding of our universe.”
~ Matt Emmi

 

Editorial Reviews

1.”Interweaving personal anecdotes and contemplations on theoretical physics, Thad Roberts takes the reader on a rambunctious adventure as he explores the development of new physics. It’s a captivating read.””

     ~ Garrett Lisi, Ph.D. Director of the Pacific Science Institute Surfer & Physicist, E8 theory

2.”Thad Roberts has taken the cutting edge of science out of the dark caverns reserved for mathematical geniuses, and put it back on the street. This book will change the way we see the universe, ourselves as individuals, and society as a whole.””

     ~ Richard Hitchings

3.“”Presented in clear and accessible language with wonderfully supportive graphics, this book offers the lay reader a voyage through the infinitely small and the macroscopically large. Thad’s geometric postulation enables derivation of hypothesizes that will drive the next generation of experimentation in search of empirical verification. By bringing the lay reader to the forefront of theoretical physics, Einstein’s Intuition is indeed a rare gift.””

     ~ Philip Emmi, Ph.D.

4.”When I explored Thad’s quantum space theory I was amazed to see that it truly offered an understandable way to visualize his proposed model, which, if proven, eliminates the current discontinuity between our fundamental theories. More importantly it defines a grander vision of reality from which our universe naturally arises and evolves, and provides explanations for the great mysteries that currently lie beyond our reach. Furthermore, unlike string theory, qst offers testable predictions. I recommend this book to anyone interested in understanding the grand scope of reality.””

     ~ Wayne Eskridge

5.”Philosophically intriguing, visually stimulating, and best of all a joy to read.””

     ~ Marie Green, Ph.D.

6.”This book stirs new hope that the innermost workings of our universe can be thoroughly knowable. It offers a perspective that has the potential to rock the entire physics community, unlocking secrets that could bring forth radical improvement to our daily lives, and establishing Thad Roberts among the rarest of genius.””

     ~ Chris Tuason

7.“”With care­fully chosen and precisely assembled prose, Roberts opens the door to the next age of human perception by proposing a theory of everything that offers real, intuitive explanations for gravity, dark energy, dark matter, quantum tunneling, entanglement, black holes, the Big Bang, and more.””

     ~ Craig Joiner

8.”‘Einstein’’s Intuition’ will open your eyes and expand your mind to the wonders of the universe. Thad shares his life, his love and his mind, and pours them all into his writing.””

     ~ Paul Brennan

9.”Incredibly lucid. This book made it easy for me to understand scientific ideas I have been coping with all my life. Roberts’ thinking is so vivid and so accessible, that you cannot help but conclude that he has almost certainly uncovered truths about the universe that most of us have never dreamed of.””

     ~ Bruce Penney

10.”Thad’s quantum space theory is a natural idea and has as much to offer the next big leap in our global understanding of who we are and our place in the universe as the idea of the atom did for explaining chemicals and DNA. This work is math­e­mat­i­cally beau­tiful and sci­en­tif­i­cally price­less, and the kicker is that it comes with a vivid and sat­is­fying picture.””

     ~ Chris J. Wilshaw

About the Author

Thad Roberts is a theoretical physicist, philosopher, and adventurer who passionately explores the possibility that quantum mechanics is not exact, but is, instead, an accurate approximation of a deeper deterministic theory. Thad has excavated dinosaur fossils, sailed across the Atlantic in a 55’ sloop, and lived out of a VW Vanagon for 2 years traveling the world for $10 a day. He has worked as an astrophysicist for NASA, and then a flight lead, training astronauts for their EVAs. His life took an infamous twist when, to impress a girl, he literally stole the moon—a story that is captured in the best-selling book “Sex on the Moon”. During his confinement he poured himself into a thorough investigation of Nature’s deepest mysteries—an intellectual adventure that gave form to this book. Thad currently works as a theoretical physicist for a private think tank, and as a motivational speaker for the American Program Bureau, where he shares his story to inspire others to follow their passions and to let their curiosity propel them to a broader horizon.

Comments (10)

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  1. Ralf Westphal says:

    Here are a couple of questions that came to my mind after reading your book:

    Q1: This is probably a silly question after reading all of your book. How could I possibly not gotten it? 😉 Still I’m wondering: Does a certain quantum always represent the same (x,y,z) coordinate in our 3D space? That would mean, when an object moves, it consists at first of quanta q1,q2,q3… and later of quanta q789,q790,q791…

    Also that would mean if at super-time t0 the quanta q1,q2,q3 are aligned like this in super-spatial space, and later at super-time t7 the quanta got mixed up and are in the order q2,q1,q3 this would not make a difference for any object in our 3D world.

    I’m assuming it’s like this, but I’m not sure. It would mean, 3D particles are like waves whose form stays the same, but whose constituents are ever changing while they move.

    Q2: Quantum density differs. But how tightly packed are quanta in super-space in general? For example if I assume an electron to be of spherical form roughly 5*10^59 quanta would fit into it. But then they would be most tightly packed. I guess that’s what a black hole looks like :-)

    If an electron consists of less quanta, how many? Roughly. Any idea?

    Which leads to the question: How many quanta are there per super-spatial volume in a „true” vacuum?

    Q3: What’s between quanta in super-spatial space? You’re talking about quanta being made up of sub-quanta. But you’re not talking about what’s around quanta, what they move through until they bump into each other.

    Q4: You’re depicting quanta as spheres. Why’s that? How come, the sub-quanta stay lumped together in that way? Is there a membrane around them? Hardly. That would introduce another concept/„material“.

    But if there is no membrane around them, then they have to stay together due to some other reason. Are quanta also just patterns of sub-quanta like electrons are patterns of quanta?

    If so, wouldn’t that mean, super-spatial space is made up of sub-quanta? So there’s sub-quanta everywhere: in quanta and between quanta. (Again more or less density.)

    If so, wouldn’t that mean, there is evaporation happening? Sub-quanta evaporating from the surface of quanta upon collision? Or even „condensation“/addition?

    And wouldn’t it mean that sub-quanta need to be treated the same? Which would lead to super-spatial space being constituted by infinitely small sub-quanta, let’s denote them like this: quantum^-∞ :-)

    Those quanta would come together in „quantum swirls“ to form quantum^-(∞-1) quanta and so on and so forth up the quantum hierarchy. „Our” quanta would be quantum^0. But together they form quantum^1 (our universe) etc.

    This picture to me is different from yours. As far as I understand there is total void between your quanta. But in my picture there is no void. Not on any level of the omniverse fractal. Which essentially leads to… a continuum :-) But this continuum is emerging from infinitesimal small quanta.

    Q5: Time ticks when „quanta resonate freely“. Do I remember that correctly?
    „Resonate freely“, i.e. do not bump into each other, to me means something like pulsing. Should I picture quanta pumping like a heart: expanding, contracting, expanding, contracting… until they hit another quantum.

    If so, where does the pulsation come from?

    If not, what does „resonate freely“ mean other than „not being in contact with another quantum“?

    To me this does not feel as simple as it could be 😉

    Let me draw an analogy: As a human I experience time upon change. When I’m sitting all by myself in a dark room time stands still. When I’m standing in the middle of a crowded bus, nobody talking, no movement, time stands still. But when I bump into other people (physically or psychologically) then time progresses. Something is happening, i.e. a change occurs.

    Back to qst this to me would mean: there is no pulsation of quanta, no independent tick of time (10^-44 seconds). Time only progresses upon contact between quanta. No time, when they are packed together (black hole). No time when they are far apart and not colliding (vacuum).

    The beauty of this seems that time (t, not super-spatial time) is going away as a dimension of its own :-) There is only space left. Time may be introduced as a separate dimension for convenience, though :-)

    Which leads to the question: What’s time anyway? Maybe it’s just a by-product of consciousness? An abstraction, a tool – but not reality in a physical sense.

    Q6: If the universe (no, even the omniverse) is deterministic, then all free will is a fundamental illusion. You’re alluding to that in your final chapter, when you’re talking about how everything gets played out in the same way again and again.

    If that’s true, then any talk about „We have to accept that“ or „This will change our view of the world“ is void. Because there is no choice. Me typing this and deciding which word to write next is just happening. I can’t even decide to let go of my illusion of control.

    The illusion of any free will, any opportunity for choice is also a deterministic outcome. Maybe organisms with this illusion are more stable? In any case it’s just happening.

    Q7: If mass is just a geometric distortion of super-spatial space then quanta itself do not have mass. Nor do sub-quanta or super-quanta (our universe). Quanta don’t have mass, they just constitute mass by being arranged in certain densities.

    Mass, like all other forces, is just an effect.

    But how can massless quanta, well, cause any effect at all?
    This question leads me from physics to information technology.
    Have you heard about cellular automata (https://en.wikipedia.org/wiki/Cellular_automaton)? Watch the stable forms of pixel agglomerations move across the picture… They are massless, yet they cause change.

    The secret of this: simple rules (or at least a small set of rules).

    Have a look here:
    http://blog.wolfram.com/2007/09/11/my-hobby-hunting-for-our-universe/
    or here: https://www.youtube.com/watch?v=60P7717-XOQ#t=14m06s

    So are we talking about physics as a result of certain rules executed by some simulation engine?

    • Thad Roberts says:

      Hi Ralf,

      Great questions! Let me know if my responses clear things up enough.

      Q1: This is probably a silly question after reading all of your book. How could I possibly not gotten it? 😉 Still I’m wondering: Does a certain quantum always represent the same (x,y,z) coordinate in our 3D space? That would mean, when an object moves, it consists at first of quanta q1,q2,q3… and later of quanta q789,q790,q791…

      Also that would mean if at super-time t0 the quanta q1,q2,q3 are aligned like this in super-spatial space, and later at super-time t7 the quanta got mixed up and are in the order q2,q1,q3 this would not make a difference for any object in our 3D world.

      I’m assuming it’s like this, but I’m not sure. It would mean, 3D particles are like waves whose form stays the same, but whose constituents are ever changing while they move.

      A1: Great question. First, when an object moves through the vacuum, the label “object” points to a region of the vacuum with a particular configuration. It is this configuration that moves in a coherent sense (if the object is coherently sustained in form) not the specific quanta that make it up. Just as a wave can pass through water without carrying any molecules across the pool, objects in the vacuum can move without transporting quanta through the vacuum. The background state of the vacuum is the equilibrium state where there is maximum disorder and randomness. When an impulse moves through the medium with some order and structure, it is only that order that defines the object, not the specific arrangement of its constituents. That is to say, if you swap the positions of any two quanta anywhere, nothing changes as long as the superspatial velocities of those quanta are also swapped, or as you put it, this would not make a difference for any object in our 3D world.

      Q2: Quantum density differs. But how tightly packed are quanta in super-space in general? For example if I assume an electron to be of spherical form roughly 5*10^59 quanta would fit into it. But then they would be most tightly packed. I guess that’s what a black hole looks like :-) If an electron consists of less quanta, how many? Roughly. Any idea? Which leads to the question: How many quanta are there per super-spatial volume in a „true” vacuum?

      A2: The quantum density goes from maximum packing in a black hole, which can be numerically analyzed by packing theory, but the density of a true vacuum is not a fixed value and is therefore not so easy to answer. For example, a vacuum that is far far away from any mass source still constantly experiences perturbations as photons pass through it, distorting its density. The average kinetic energy of the quanta, which is partly controlled by the flux of light through the region, also controls the density. As the kinetic energy decreases, the relationship options between the quanta change. At high temperature stable close proximity positions of quanta are rare, but at some point the temperature drops enough such that the density of the quanta (in superspace) increases (a phase change). So the density of a true vacuum is not some constant thing even in the “true vacuum” (which I mean to reference being far from any mass). Of course, your question is further complicated by the unknown of scale to begin with. Only once you pick a representative size in superspace for the quanta of space (that is, how many quanta of superspace make up one quanta of space), can you quantitatively start to talk about density of quanta in superspace. For this, I would note that we might rely on our fractal expectations to posit the quanta as stable quantized vortices in the superspatial medium. But I would need a fluid dynamic expert with fully functional analysis of turbulent flow (and stable vortex formation in inviscid fluids) to guide us to any solid claim of what these sizes should be merely from knowledge of the substrate’s properties. My rough idea is that they would follow the dynamic densities of other compressible fluids, like the particle density of air.

      Q3: What’s between quanta in super-spatial space? You’re talking about quanta being made up of sub-quanta. But you’re not talking about what’s around quanta, what they move through until they bump into each other.

      A3: The first resolution of this model is to treat quanta of space as bubbles that move through something like a traditional empty Euclidean stage. This is an oversimplification, but it is the resolution I focused on most in the book. Increasing our resolution by one step (recall Chapter 11) we see that the quanta of space are really just vortices in superspace. The collection of those vortices make up the medium we call space, or the 3D vacuum. These vortices are made up of sub-quanta, and they move through the sub-quanta medium.

      Q4: You’re depicting quanta as spheres. Why’s that? How come, the sub-quanta stay lumped together in that way? Is there a membrane around them? Hardly. That would introduce another concept/„material“. But if there is no membrane around them, then they have to stay together due to some other reason. Are quanta also just patterns of sub-quanta like electrons are patterns of quanta? If so, wouldn’t that mean, super-spatial space is made up of sub-quanta? So there’s sub-quanta everywhere: in quanta and between quanta. (Again more or less density.) If so, wouldn’t that mean, there is evaporation happening? Sub-quanta evaporating from the surface of quanta upon collision? Or even „condensation“/addition? And wouldn’t it mean that sub-quanta need to be treated the same? Which would lead to super-spatial space being constituted by infinitely small sub-quanta, let’s denote them like this: quantum^-∞ :-) Those quanta would come together in „quantum swirls“ to form quantum^-(∞-1) quanta and so on and so forth up the quantum hierarchy. „Our” quanta would be quantum^0. But together they form quantum^1 (our universe) etc. This picture to me is different from yours. As far as I understand there is total void between your quanta. But in my picture there is no void. Not on any level of the omniverse fractal. Which essentially leads to… a continuum :-) But this continuum is emerging from infinitesimal small quanta.

      A4: Depicting quanta as spheres is a low resolution way of representing their vortex essence in superspace. The sub-quanta stay lumped together only as a fluid dynamic stability consequence, in a similar way to how the quanta form vortices that represent stable distortions in the state of the vacuum we call electrons. There is no membrane around them and you are right that if there were that would introduce another “force” that would need explaining. You put it wonderfully in your question, “quanta are patterns of sub-quanta like electrons are patterns of quanta.” Nicely worded ;-). And yes, exactly, the superspatial medium is made up of sub-quanta. If the vortices we are talking about here are truly stable, that is if the medium exhibits true superfluidity, then there will be no evaporation. However, their will be constant exchange between which quanta or sub-quanta actually make up the vortex. And yes, sub-quanta need to be treated the same, hence our fractal construction (revisit Chapter 11 here – and then please send me a note pointing to where you think I could be more clear about this in that chapter). Apparently I failed at properly explaining my picture, but the picture you are describing is the one I have in mind. I only talk about a void between quanta as an 11D approximation of the underlying 30D medium, which is only an approximation of an even richer 85D medium and so on. Hope that helps.

      Q5: Time ticks when „quanta resonate freely“. Do I remember that correctly?
      „Resonate freely“, i.e. do not bump into each other, to me means something like pulsing. Should I picture quanta pumping like a heart: expanding, contracting, expanding, contracting… until they hit another quantum. If so, where does the pulsation come from? If not, what does „resonate freely“ mean other than „not being in contact with another quantum“? To me this does not feel as simple as it could be 😉 Let me draw an analogy: As a human I experience time upon change. When I’m sitting all by myself in a dark room time stands still. When I’m standing in the middle of a crowded bus, nobody talking, no movement, time stands still. But when I bump into other people (physically or psychologically) then time progresses. Something is happening, i.e. a change occurs.

      Back to qst this to me would mean: there is no pulsation of quanta, no independent tick of time (10^-44 seconds). Time only progresses upon contact between quanta. No time, when they are packed together (black hole). No time when they are far apart and not colliding (vacuum). The beauty of this seems that time (t, not super-spatial time) is going away as a dimension of its own :-) There is only space left. Time may be introduced as a separate dimension for convenience, though :-) Which leads to the question: What’s time anyway? Maybe it’s just a by-product of consciousness? An abstraction, a tool – but not reality in a physical sense.

      A5: Okay this question is a bit messy. Let me try to untangle it. First, when we are imagining quanta with our 11D approximation as spheres, time becomes the resonation of those spheres. This tracks change at each location and defines time in a way that matches up with the qualities of time we need to account for. You can think of it as an elastic ball. When another ball collides with it, it rebounds and the shape of the ball undulates in response to the collision. The properties of the ball (its size, surface tension, etc) determine the resonation frequency. If we increase our resolution to the 30D picture, then we see more structure in the quanta, being vortices in superspace made up of a collection of sub-quanta all swirling about in a stable coherent way. When two of these vortices collide without destroying each other the internal dynamics receive a pressure wave that resonates internally, distorting the shape of the vortex which propagates through it with phase succession. This means that even a single “quanta” has a rich encoder of change within it. Now, since (in the model) the media at each level is only approximately a superfluid (differing to a degree that represents the difference in size between the quanta and sub-quanta) there is some transfer of energy to the internal system with each collision, which means that this undulation eventually drains out and time goes slower and slower at each location unless another collision resets things. Time only progresses when these undulations occur because that is the measure of independent change. The collisions mark passing of energy through the medium (change in position) but this passing co-joins the evolutions of the colliding quanta during collision and therefore dissolves the uniqueness of evolution required by time until rebound. Your analogy is quite a bit off in another direction. Your personal feeling of time, or experience of time is not the kind of time we are talking about. We are talking about objective time, the kind science deals with. Time does not objectively stand still when you are sitting all by yourself in a dark room. Your watch still ticks away, your hair still grows, your heart still beats, quanta still resonate.

      Q6: If the universe (no, even the omniverse) is deterministic, then all free will is a fundamental illusion. You’re alluding to that in your final chapter, when you’re talking about how everything gets played out in the same way again and again. If that’s true, then any talk about „We have to accept that“ or „This will change our view of the world“ is void. Because there is no choice. Me typing this and deciding which word to write next is just happening. I can’t even decide to let go of my illusion of control. The illusion of any free will, any opportunity for choice is also a deterministic outcome. Maybe organisms with this illusion are more stable? In any case it’s just happening.

      A6: Yes, free will is fundamentally an illusion, an illusion that seems to give social systems evolutionary advantages. Note that this does not mean that there are no choices, it only means that choices don’t play causal roles as many people want to believe. Of course, something you read today may be fundamental in the evolution of your internal world, the way you see things, etc., and according to determinism you were going to read that and have that response to it. So it is not pointless to have talk about “we have to accept that” or such claims, as these claims may very well be the triggers that led to the change of perspective in your mind. That said, you are right to suspect that there is a better way (more aligned with reality and arguably more moral) to see the world than to be stuck in the illusion of free will all the time. On the other hand, we shouldn’t aim to fully dismiss it in the practical realm as it has clear advantages for the system – underlying our sense of autonomy and individuality (which, if even completely wrong do motivate us to behave in certain ways), and increasing the variety in the group so that the changes of noticing a more successful strategy is possible even when the mass group starts down a specific path.

      Q7: If mass is just a geometric distortion of super-spatial space then quanta itself do not have mass. Nor do sub-quanta or super-quanta (our universe). Quanta don’t have mass, they just constitute mass by being arranged in certain densities. Mass, like all other forces, is just an effect. But how can massless quanta, well, cause any effect at all? This question leads me from physics to information technology.
      Have you heard about cellular automata (https://en.wikipedia.org/wiki/Cellular_automaton)? Watch the stable forms of pixel agglomerations move across the picture… They are massless, yet they cause change.

      The secret of this: simple rules (or at least a small set of rules). Have a look here:
      http://blog.wolfram.com/2007/09/11/my-hobby-hunting-for-our-universe/ or here: https://www.youtube.com/watch?v=60P7717-XOQ#t=14m06s

      So are we talking about physics as a result of certain rules executed by some simulation engine?

      A7: A single quanta represents mass only in a theoretical sense – for example, the amount the state of the vacuum would be distorted if it were absent. In the primary particle sense of mass (mass particles) quanta do not have mass, they just constitute mass by being arranged in certain densities – as you stated. The way this “massless quanta” cause effects are simply in their contributions to the state of the vacuum. This does have much in common with cellular automata, but the lattice points are not fixed here. Your last question, is physics just a result of certain rules executed by some simulation engine? I don’t know where to weigh in here. That seems like a legitimate position to take, but a realist might also take the position that the universe has physical properties to it, that it is real, and that its form and evolution follow rules and it is these rules we mean to parse in physics, not just some hypothetical rules that are being simulated by a computer somewhere.

      Thad

  2. Ralf Westphal says:

    Thanks for your comprehensive and swift answers.

    Q Time: I’m mostly content with them. Just with regard to time I’m not convinced yet. Sure I know my analogy referred to subjective time. But hey, it was an analogy 😉 While subjectively feeling a standstill, objective time keeps ticking. But if objective time is just a construct… then that’s irrelevant.

    So what I hear is: quanta collide, that induces oscillation in both. These oscillations are the tick of time? But why? Viewed from 3D space what happened was passing an impulse from one quantum to another. That way the 3D object moved on. That’s cause and effect.

    We only perceive time by watching cause and effect, I’d argue. And until you set up a clock (which is driven by cause and effect) to compare other cause-effect chains with, there is no time. Time to me is created by observing differences and relating them to each other.

    If we abstract from this by introducing a time dimension… well, that’s a legitimate move. Nevertheless this does not make time a real dimension :-)

    Q Infinity: So I even understood you correctly when I described quanta being made up of sub-quanta and the void between quanta also consisting of sub-quanta.

    And any certain number of dimensions – 11, 30, 85 – is just a simplification.

    But then: How is infinity “created”? Quanta and even sub-quanta etc. are tangible to me. But this ends once there is really no end in sight :-( Not when zooming in, not when zooming out.

    How to solve the “infinity problem”?

    Q Free will: You’re right, there seem to be choices. I could stop writing or keep on writing. But no choosing happens. So maybe it’s better to call it “alternative paths of development” – which only makes sense as long as you have limited knowledge about the omniverse’s state. De facto there are no alternatives, because all quanta movements on all levels are deterministic.

    What will happen tomorrow is already preordained, even though subjectively I see lots of choices.

    For deterministically evolving organisms this probably means some advantage for keeping their entropy low. Consciousness can arise even in a deterministic omniverse.

    -Ralf

    • Thad Roberts says:

      Your approach to time is a time honored one. I won’t try to pull you to my way of thinking because diversity of thinking has value too. For me the fractal connection absolves the mystery or “problem” of infinity you are pointing to here. I would find it far more unsettling if we were being asked to swallow an ontology that includes infinite divergences, or a hard edge to the universe, etc. Self-similarity transforms the usual infinite regress into something palatable. As for your final follow up, I agree. Perhaps the phrase “ignorance options” best applies since these “alternative options” are only extrapolations of our lack of knowledge about the universe’s state. I don’t know what definition you are working with for “consciousness” but if you mean a complex, high-order system, with feedback mechanisms and perhaps even with an identity projection, then of course consciousness can arise in a deterministic omniverse. In fact, at least some of the time (if not all of the time) it must. 😉

      • Ralf Westphal says:

        I like the holarchy, the self-similar structure, viewing the omniverse as a fractal quite a bit.

        However, to me it seems this leads to the omniverse being a black hole. Because there cannot be any space between quanta. Look at this picture:

        https://www.lucidchart.com/publicSegments/view/fe43e396-2150-401d-9bae-1ea83088ef49/image.png (shrink the picture using your browser’s zoom-out key combination)

        It just shows in a simplified manner drilling down into the fractal. The 11D view is an abstraction of the 30D view, which in turn is just an abstraction of the 85D view… and so on until the (∞-1)D view is just an abstraction of the ∞D view :-)

        As you can see the average distance between quanta shrinks with each drill down. The void between quanta on level nD is filled with quanta of level (n+1)D. So in fact there is no void, but quanta as well as non-quantum space filled with sub-quanta of the next lower level.

        That’s fine if it ends somewhere, say on level 10^47D 😉 Then there will be true void between the quanta of that level. And that’s wiggle space for them.

        But as you’re saying, no such end is in sight. There are infinite levels down (and up). Which, to me, inevitably leads to just quanta, and no space between them. Quantum space thus is completely filled up. No wiggle space between quanta, because whenever you think you found some, you need to zoom in one more level and fill it with yet smaller quanta. Each and every time. It’s like Sysiphos 😉 And eternal task. Ad infinitum.

        With no void between quanta all quanta are packed up most tightly in fact they are an infinitely huge perfect monolith. I’d call that the ultimate black hole :-) Or more spiritually: all is just one.

        • Thad Roberts says:

          Great graphic. I think we are talking past each other just a little here. In your explanation, I didn’t see any mention of different media. The quantized vacuum of x, y, z space is made up of quanta, and the collection of those quanta define the state of the vacuum. In other words, the collection of quanta define the medium of space. The quanta are not space. Space is an emergent ingredient that exists only as a collection of the quanta are considered, just like pressure is an emergent property that comes into existence as many molecules are considered. At the scale of one molecule the notion of pressure entirely dissolves. So, while I completely agree that this model gives you access to structure all the way down (or up), it does not allow you to represent space with an infinite density. Space refers only to the collection of quanta, it cannot make mention of the ingredients that make up those quanta. Likewise, intraspace (within each quanta) is an entirely different medium, which is also defined in an emergent way. So, space is a collection of quanta, which are each filled with intraspace. Intraspace is a collection of subquanta, which are each filled with intra-intraspace, and so on. Put in another way, in reference to the medium of space there is a complete void of space at and below the scale of the quanta. There is also a complete void of intraspace at and below the scale of the subquanta, etc. The fractal structure gives us conceptual access to how the pattern repeats, but with each new level of resolution we are talking about a different medium. Consequently, with each new medium we are no longer talking about the previous medium.

  3. B says:

    This helped me understand how the math can equal something as it is fundamentally based on non variables.
    I would like to however understand it in the Form by which it is known. That is to say I don’t believe everything is a perfect sphere or Circle and I do believe that everything is like a glob. I also have noticed we use straight lines to conduct ourselves through a system that clearly has no straight lines. How can we ever understand it with this kind of math?

    • Thad Roberts says:

      It sounds like you’re really going to like studying fractals. Check out the Afterword in my book – I think you’ll find the beginning of a trail you’ll like.

  4. Daniel Levy says:

    I am a fan of your amazing book.
    Quick question. Do your think that something like a carbon atom could form at a different fractal level in the Universe or is there something about the actual size of our fractal level that leads to the possibility of complex carbon chemistry?

    Regards,

    Dan

    • Thad Roberts says:

      In chapter 11 I discuss the fractal hierarchy of the universe, and in Chapter 16 I explain how the constants of Nature depend on the geometry of the vacuum, which extends as an identical argument on each fractal level we examine. This means that on each level we find the same constants of Nature (internally observed) and therefore program in the same propensity for atomic structures and chemistry that we find on our level.

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