Elementary Particles As Elastic Deformations In Space-time

Elementary particles as elastic deformations in space-time: spinning Planck-spheres of temporal curvature coupled with Compton sized electric flux rings Salvatore Gerard Micheal, Faraday Group (altphy.org), 08/NOV/2008 There are four sections to this paper: survey of literature, derivation of core parameters, investigation of core equations, and an intuitive description. The first section has five citations which indicate a desperate need to find an integrated semi-classical theory of elementary particles. The second section is an exposition of the logical steps toward a theory of that order. The third section takes a ‘deep dive’ into the equations which are core to this theory. And the fourth section attempts to provide an intuitive approach to it. Section One – Survey of Literature: Presently, there is some disparate momentum in the literature to create a unified theory of elementary particles based on an elastic-impeding theory of space-time. The purpose of this paper is to conceptually unite that impetus. The motivation for this paper takes the form of various texts produced for they lay-public. These texts are entirely unsatisfactory for theoretical physicists. Ergo, the need for this paper; however, if the reader is inclined to survey one, the most recent text can be provided electronically via email. Please contact the author at micheals at msu dot edu. The text is called N and Ω. The first citation comes from “The gravity of magnetic stresses and energy” by Bimonte, Calloni, and Rosa. Page 2: “We then consider the field near a long solenoid, and we show that the magnetically-generated gravitational field is different from zero, and as expected it is equivalent to the newtonian field generated by a linear mass-density that is equal to the instantaneous magnetic energy per unit length stored in the solenoid.”[italics added] The first italicized statement shows magnetic fields can generate gravitation (the Italians prove it theoretically but state explicitly the need for experimental verification). This is an indicator for the need to integrate electromagnetism with gravity. The second italicized statement highlights the need for the concept ‘per unit length’. We will return to this later. The second citation is from “EINSTEIN-CARTAN THEORY” by Trautman, page 7: “It is possible that the Einstein-Cartan theory will prove to be a better classical limit of a future quantum theory of gravitation than the theory without torsion.” This highlights the need for an integrated theory that includes twist and spin. The third citation comes from “On Dislocations in a Special Class of Generalized Elasticity” by Lazar, Maugin, and Aifantis, page 26: “Unlike the nonlocal theories, where these fields still possess singularities at the dislocation line, the quantities calculated in the gradient theories are nonsingular. All fields calculated in the theories of gradient elasticity or gradient micropolar elasticity have the correct limits to classical elasticity or to micropolar elasticity.” This article indicates a local elastic theory of elementary particles does not employ singularities. They have no place in the theory and hence this reason for convention’s automatic rejection of semi-classical theories becomes invalid. The fourth citation comes from “An elastoplastic theory of dislocations as a physical field theory with torsion” by Lazar, page 27: “Obviously, the dislocation acts as the source of

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an incompatible ‘gravitational’ distortion field and is its own source. Additionally, we can say that a screw dislocation is a topological string with cylindrical symmetry in threedimensional gravity.” Again, this article highlights the need for an integrated theory of elementary particles based on the elasticity of space-time. Conventional physicists may see the article as laden with speculation. This illustrates the need for a concise theory shown to be directly connected to physical reality. The fifth citation comes from “On geometric discretization of elasticity” by Arash Yavari, page 20: “A Discrete Theory of Elasticity”. This section of the text develops a new theory of elasticity “with no reference to the continuous theory”. It’s theoretically and practically very important because we need a rigorous connection between linear and nonlinear elasticity. We also need a theory that is computationally feasible. Yavari’s work provides the basis for this. Section Two – Derivation of Core Parameters: The simplistic theory is based on two quantities: Young’s elastic modulus of space and linear strain of space, extension. We identify them with the symbols Y0 and X respectively. The following derivation comes from N and Ω, pages 20-22. Due to expansion of the Universe, space is under tension. When a particle mutually annihilates with its anti-counterpart, it's as if an ideal stretched string has been plucked – two photons / e-m waves are emitted in opposite directions. Of course, space has more qualities than just being under tension. It has permeability and permittivity. c2 = τ0/λ0 (1) p3 wave propagation rate squared is tension reduced by mass per unit length c2 = 1/μ0ε0 (2) p250 the speed of light squared is the inverse of permeability times permittivity => λ0 = τ0μ0ε0 (3) So, a mass is an element of space (per unit length) under tension (or internal pressure) subject to permeability and permittivity. Perceptive readers should notice (3) is a clever rewrite of E = mc2. But it's more than that – it shows that masses are a product of the three and only three qualities of space – elasticity, permeability, and permittivity: τ0 = Y(Δl/l) (4) p72 tension is linearly related to extension through Young's modulus under the elastic limit => λ0 = Y0μ0ε0(Δl/l) (5) (Page references are from Physics of Waves, Elmore and Heald, 1969, Dover.) .. Until now, we have not made the 'per unit length' explicit. Let's do that and assign the Plancklength: λ0/lP = Y0μ0ε0(Δl/l) (6) This is a place to start and we'll follow a similar convention when the need arises. Let's replace lambda with the standard notation and move lP to the other side: m0 = (Y0lP)μ0ε0(Δl/l) (7) Multiply by unity (where tP is the Planck-time): m0 = (Y0lPtP)μ0ε0(Δl/ltP) (8) Now, the first factor on the RHS is 'where we want it' (units are in joule-seconds). And, the fact we had to 'contort' the extension by dividing it by the Planck-time should not

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prove insurmountable to deal with later. Finally, let's assume the first factor is equal to the magnitude of spin of electrons and protons, ħ/2: m0 = (ħ/2)μ0ε0(Δl/ltP) (9) By our last assumption, Y0 = ħ/2lPtP ≈ 6.0526*1043 N. To simplify and isolate the extension: m0 = (ħ/2c2)(Δl/l)(1/tP) (10) => (Δl/l) = (2c2tP/ħ)m0 = 2(tP/ħ)E0 (11) So, the linear strain of space due to internal stress is directly related to rest-energy through a Planck-measure. Later, if space allows (pun intended), we will show that (11) reduces to an even simpler form involving only two factors. If our assumptions hold, the numerical values for (11), for electrons and protons respectively, are approximately: 8.3700*10-23 and 1.5368*10-19. The values are dimensionless – per the definition of linear strain. The meaning is: 'locally', space is expanded (linearly) by the fractions above (assumed in each dimension). What exactly locally means – will have to be addressed later. The numerical value of Y0 is extremely high as expected. All this says is: space is extremely inelastic. The numerical values for ∆l/l will have to be investigated – perhaps as suggested in the previous paper. Section Three – Investigation of Core Equations: The following text is taken directly from chapter four of N and Ω. In this chapter, we take a deeper dive into the following table – in order to deepen our understanding of space-time and energy: m/(μ0ε0) = ħωm hν ≡ h/Tγ2 ((ħ/2)/tP)X ≡ (h/tP)C Y0lPX = Z0e2ωe ωe ≡ 10.905ωm X ≡ Δl/l = m/lPY0μ0ε0 = 2tPωm The purpose of this book is to show they are not just equations – that they have deep meaning about basic structures in our universe. Anyone can scribble down a list of equations, but it takes years of contemplation to truly understand the fabric of space-time from scratch. What was my inspiration? In junior high, a gym teacher mentioned to me that they thought elementary particles were confined photons. They said they could not prove it, but they were sure it was true. This planted a seed in my mind – itching to explain and understand. After years of paper research (at that time – no internet), I found one man, published in Physics Essays, who seemed able to prove auto-confinement. Of course, he is dismissed and ignored by convention. Since then, I have given up trying to prove elementary particles are trapped photons. But over the years, in the process of trying to prove and understand, I have discovered deeper and more fundamental concepts/relations. Those are listed above.

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The first line is Einstein’s discovery written differently. Some years ago, it was discovered that the speed of light squared is equal to the inverse of space-permeability times spacem/(μ0ε0) = ħωm hν ≡ h/Tγ2 ((ħ/2)/tP)X ≡ (h/tP)C Y0lPX = Z0e2ωe ωe ≡ 10.905ωm X ≡ Δl/l = m/lPY0μ0ε0 = 2tPωm permittivity. And separately, that energy is equal to h-bar times omega, angular frequency. Everyone agrees that h-bar is the fundamental unit of angular momentum. But the physical meaning of omega – convention refuses to say. It’s simply the “amount of hbars”, a coefficient of h-bar, in particles – according to convention. So line one is basically a rewrite of mc2 = E. What does it show? It shows that the energy in mass is directly related to space-permeability and space-permittivity. Those two – are components of Z0, the impedance of space. Line two relates to Einstein’s special theory of relativity. It is a required definition to keep things consistent in that respect. If we divide both sides by h, Planck’s constant, we get frequency is identically equal to the inverse of period times gamma squared. Gamma comes from special relativity and is equal to the square-root of one minus speed over light-speed squared. It is a dimensionless fraction which typically amplifies rest values when we divide those rest values by it. Nu, frequency, is a relativistic quantity – which means it is amplified by speed. Period, T, is also a relativistic quantity. In fact, mass and angular frequency, from line one, are relativistic quantities. We normally write m = m 0/γ, for instance, which means relativistic mass is rest mass divided by gamma. We omit the term ‘relativistic’ to avoid confusion, but it is strictly required to be precise in our statements. Frequency is angular frequency over 2π, but convention ascribes little or no meaning to frequency and period in this context. Normally, period is the inverse of frequency – and this is true for many many systems. But because time slows down for speedy crafts/particles, and because time slows down near strong gravity sources, we must rationally explain this somehow. The causal deterministic perspective asserts they are the same thing. In my theory, I explain them both as curved space-time. Convention assigns no deep meaning to special relativity. Convention typically explains time dilation with a particle bouncing between plates: at rest, it has a fixed distance of travel, frequency, and period; at high speed, it has a longer travel path, lower frequency, and longer period. (The direction of travel is parallel to the plates.) But this conventional perspective sheds no light on the causal mechanism of time dilation. Convention avoids this ‘messy situation’ (having to define the relationship between frequency and period above) by not ascribing any physical meaning to omega, nu, and T. h and h-bar (h-bar is h/2π) are most certainly not relativistic quantities (they don’t change

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with speed). So if omega, nu, and T have any physical meaning, the ‘only room to move’ (the only quantities above that can be relativistic quantities) is in them. We know for a fact that mass increases, energy increases, and time slows down for speedy particles. We know for a fact that m/(μ0ε0) = ħωm hν ≡ h/Tγ2 ((ħ/2)/tP)X ≡ (h/tP)C Y0lPX = Z0e2ωe ωe ≡ 10.905ωm X ≡ Δl/l = m/lPY0μ0ε0 = 2tPωm h, h-bar, and charge don’t change for any speed. So again, if omega, nu, and T have any physical meaning, they must be relativistic quantities. I propose omega-m (m for mass) is the angular spin rate of the core of elementary particles. This is proposed to be a Planck-sphere with diameter of Planck-length. The following is a list of Planck dimensions: Planck-length = lP = 1.61608*10-35 m Planck-time = tP = 5.39067*10-44 s Planck-speed = c = lP/tP = 2.99792*108 m/s They are conventionally considered to be absolute in the sense: nothing can be shorter than Planck-length, no time can be shorter than Planck-time, and no speed can be greater than c, the speed of light. Anything shorter or faster is physically meaningless. h-bar/2 is the conventionally accepted value for spin of elementary particles. That’s why it appears in line three above. (Actually, once you define X and C, the rest become easy to derive.) I arrived at line three by listing and simplifying eight different ways to describe energy. The identity symbol is really between X and C. Once you divide both sides by h and multiply by tP, you find X ≡ 4πC. 4π is conventionally known as ‘a solid angle’. Temporal curvature, C, through a solid angle is linear extension of space. This is a definition. Linear extension is defined in line two of the lower box. It follows from the standard definitions of stress and strain in engineering. Y is the standard symbol for Young’s modulus of elasticity. It is required for an elastic model of space. In practice, once Y is determined, X can be calculated (and vice versa). The ‘per unit length’ must be decided and once it is, the rest pretty much ‘flow’ from that decision; the choice of Y0 and ‘per unit length’ determine X here. Y is normally given in newtons. So, in deriving/defining Y0, I used that as a guide .. I feel like I’ve pretty much lost all of you except the engineers at this point. Let me insert my original derivation here. [Deleted for brevity – deleted text can be found above in section two of this paper.] That concludes my original derivation of Y0 and X. It may help to read it through several times noting the assumptions.

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I could ride the fence like convention and say there is nothing inside Planck-spheres except energy, but if we think about it very carefully – we are somewhat forced into a position of proposing/accepting that there is structure inside. This is what I have been avoiding for twenty-five years! :( Twenty-five years ago, it was suggested to me to employ Planck dimensions. And I believe I understood the danger at that time. That’s why I doggedly pursued a model with Compton dimensions. But it simply doesn’t work with an elastic model of space. Dimensions cannot be so large; force cannot be distributed over large areas because there is not enough energy in e.p.s to balance that. The only model that seems to work is a dual-sized model – Planck-size for mass and Compton size for charge. At this very moment of writing, it occurred to me – the possibility of torii within torii. Bergman and his staff at commonsensescienc.org have developed a quasi-torus model of electro-dynamic flux. In the process of deriving the Planck-sphere model of mass, a step in that process was proposing an ultra-thin torus. But that torus has to be thinner than the Planck-length for that model to work. That’s why I rejected it. I must concede that it is possible e.p.s may be torii within torii. But there are two reasons why I don’t subscribe to that perspective right now: mass as ultra-thin torii requires extra assumptions about geometry – assumptions we cannot prove now. And, do you see Bergman’s staff willing to work with me? No. So what’s the point of me trying to integrate models when the other party refuses to collaborate? They are also currently dismissed by convention. I believe that model would require a similar onion-like structure within the inner torus. (Part of my model of the core is the proposal it is an onion-like spherical standing wave of temporal curvature.) Except that it would have to be torii within torii. Until this geometry can be proven to me and Bergman’s staff becomes willing to work with me, I will defer accepting this model. The simpler model is sphere within torus. m/(μ0ε0) = ħωm hν ≡ h/Tγ2 ((ħ/2)/tP)X ≡ (h/tP)C Y0lPX = Z0e2ωe ωe ≡ 10.905ωm X ≡ Δl/l = m/lPY0μ0ε0 = 2tPωm I suppose we are ready to study the fourth line in the core equation table. Originally, there was not an equal sign. The approximation comes from my discovery ħ ≈ Z0e2. For about fifteen years, I have stared at that ‘≈’ – trying to understand it. The factor that makes equality is 10.905 on the right side. But every time I would try to explain/understand it, required additional assumptions. In order to write and publish this book, I’m required to ‘take a stand’. To me, it’s better to take a stand and be wrong than ride the fence for eternity. At least you have a chance for progress. Riding the fence does not.

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m/(μ0ε0) = ħωm hν ≡ h/Tγ2 ((ħ/2)/tP)X ≡ (h/tP)C Y0lPX = Z0e2ωe ωe ≡ 10.905ωm X ≡ Δl/l = m/lPY0μ0ε0 = 2tPωm Can 10.905 be absorbed into any term on left or right? If on the left, we must modify definitions of elasticity or extension (and justify it). On the right, we basically only have two choices: Z0e2 and omega. If we choose the former, we are implicitly choosing some geometry. If we choose omega, we must understand the consequences and any associated assumptions. If electric flux is a spinning ring with outer dimension of Compton diameter (h = mcλC, where lambda-C is Compton wavelength), and if ωe = 10.905ωm, then tangential speed is 10.905c which is impossible – or is it? There are only two choices at this point: allow flux speeds greater than c or change dimensions. Since allowing speeds greater than c tends to throw a ‘monkey wrench’ into things, we’ll go with the latter. Let’s tentatively change the outer dimension of the flux ring to λC/10.905. That way, the tangential speed is exactly light-speed which agrees with the Bergman model. Why do I bother to conform my model to Bergman’s? Again, it’s because in all my searches, I have found only one complete deterministic model of elementary particles which seems to make any sense .. A member of the Faraday Group, of which I am the founder, worked on this model independently a decade or so earlier than Bergman’s seminal paper. But I won’t give his name here to help readers discover this for themselves. The following are websites for Faraday Group: unc.edu/~gravity/ msu.edu/~micheals/ http://groups.yahoo.com/group/faraday_group/ Please join and contribute if you are so inclined. The group is “an association of physicists and those interested in physics”. They are most definitely NOT working on unifying my model with anything else; everybody’s working on their own thing. For current updates of this theory, please visit: https://www.msu.edu/~micheal/physics/ The reason I organized the table above – the way it is – is for the following reason. Everything in the top box is actually the same thing; they are all equal to energy – they are eight different ways of looking at energy! Mass has spin; it has frequency; it has period; it is curvature; it is extension; it is spinning flux.

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The fact we can look at energy (at least) eight different ways is not a testament to human ingenuity and insight – it’s a statement about the elegance of our universe. Our universe is a beautiful and wonder-full place. Just look up on a clear night. Section Four – An Intuitive Description: The following text is taken directly from chapter five of N and Ω. True understanding does not come from regurgitation of facts; it comes from internalizing concepts. It took me years to understand the electromagnetic wave, the photon. And I still cannot bridge the gap between photons and e.p.s if they are indeed the same thing. My original proposal was that radiation propagates through space by changing form: from electromagnetic to gravitational and back.. In gravitational form, the wave is much like a 3D soliton. The e-m part is well understood by engineers. In my searches on the net, I could find only one other who developed a similar model of photons. But as I mentioned before, focusing on a trapped-photon model of e.p.s is a ‘dead end’; physicists will autoreject that idea faster than you can say “reject”. It’s better to focus on a model with the minimum number of assumptions. That way, there’s at least a small chance for consideration. I visualize the core with layers – much like an onion. In a way, we must ascribe some structure to the inside – or there is no way to differentiate between protons and electrons. Electrically, there is no difference between a positron and proton; there is no electrical difference between an electron and antiproton. The difference is about mass. If we can accept that masses are spherical standing waves of temporal curvature, then the difference between masses is simply a difference in wave number inside the sphere. The real (next) question becomes: why are there only two stable (forms of) elementary particles? (Why are there only two stable wave numbers inside the sphere?) If I could answer that, to the satisfaction of convention, I would have the Nobel Prize. For me, a more important question is about the physical link between core and ring of flux. At this point, I can only speculate. If the core was distributed as a torus within a torus, the physical connection between core and ring of flux would be easier to visualize: one would be part of the other. Unless the core generates the ring of flux (or vice versa), I see no other way to comprehend it (if the true situation is sphere within torus). The differing spin rates is somewhat alarming. It would seem to make the physical connection somewhat tenuous. I would expect the outer rate to be less than inner – if outer ‘dragged’ inner .. As you can see, even I – the theory’s discoverer, have trouble comprehending it. From the core equations, spinning flux is an equal expression for energy of elementary particles. It is just as important as core energy. For e.p.s, they are inseparable. Whether the core is a torus or sphere, its spin rate is less than that of the flux ring. It must ‘drag’ the flux ring in a way. Or else spin rates would be the same. So imagine an elementary particle as a new couple: the flux ring is the vibrant and energetic new bride; the core is her dull and boring new husband. He drags his feet; he slouches (boy, does this sound familiar;). He acts as if space impedes his way ;). His bride zips around – she moves at

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the speed of light. All he can do to ‘keep up with her’ is spin around himself – watching her. But he can’t; space impedes his very spin. Of course, I don’t imagine e.p.s as ice skating newlyweds (maybe an old married couple – hobbling around;). The problem with trying to visualize the system is that we don’t have good macroscopic analogies for the electromagnetic field. We don’t have good macroscopic analogies for charge flux. It’s difficult to connect to the model viscerally when we don’t have everyday experiences to connect to it. If e.p.s are torii within torii, imagine them as donuts within donuts. The inner donut is very very thin and resides in the center – inside the flux-outer donut. Inside the very very thin inner donut – it has layers and layers. Now imagine them spinning. But the spin rates are different. The inner donut lags behind the outer donut. Its spin is impeded somehow. Just today in a dream, an elderly black man asked me a kind of ‘trick question’: “A building is falling off a cliff. What holds it up?” I replied “Gimme a minute; I need to think about this.” Then he said “You’re supposed to answer these on the fly.” I heard him talking to another guy about more questions – something about complex numbers. (If you and I have the same amount of imaginary numbers, what do we have? Answer: the same complex number.) And then I realized what he was looking for: “Oh I know what it is!” (He raised an eyebrow toward me.) “Inertia! Inertia holds the building up!” What keeps e.p.s spinning? Inertia. What keeps the disk drive inside your computer spinning? (other than the motor to overcome friction and accelerate the disk initially) Inertia. Inertia is the quality of matter that resists acceleration (whether it be linear or angular). The deep question that ‘no one’ has been able to answer: what causes inertia? No one is in quotes because many have tried to answer that question – just no one has succeeded to satisfy convention with their answer. Some time ago, I explained inertia as the smeared extension. But if we think about mass as confined temporal curvature, inertia is simply the lack of energy to add or take away from the core. Accelerating a mass adds relativistic energy to the core; decelerating a mass takes away. A particle at rest has a fixed minimum amount of energy in the core. What could be more elegant than that? Convention’s resistance to positive change is like the inertia inside a baby – refusing to grow up .. One of my theories of personality is about ‘emotional inertia’. When something makes us angry, really angry, it takes time to cool down. When we love, truly love, it’s usually for a long time. Our emotions have a kind of inertia. Of course, I’ve watched my baby change from crying to laughing in a blink of an eye, but adults rarely do this. I believe the concept of inertia is important not just to physics and engineering .. It could be said that the field of physics is all the teachers, students, and researchers that care about physics. Their collective belief system is important to the field. Their resistance to change, their ‘philosophical inertia’, is important: if a new idea is wrong, take time to confirm it – and reject it; if a new idea is right, take time to confirm it – and accept it. The central problem with accepting my ideas is not the lack of math-lattice supporting them; it’s the fundamental disagreement in approach. Convention has accepted the random-wave model of matter. It uses reduction

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to break a problem into parts – then tries to solve them separately. Because of my training in systems, I have a holistic approach to solving problems. Sometimes, problems are so complex, you need the systems approach to solve them. In my book on systems, I define complexity to be “the property of a system with the following features: a generous frequency of distinct types of components, a non-trivial arrangement of those components – in order for the system to function nominally, and some quantitative evidence of a system-wide synergy.” Now strictly speaking, e.p.s are not complex structures, but their behavior inside atoms and molecules suggests we need the systems approach to understand them. Convention cannot accept my ideas because it cannot integrate them into the current framework – ideas clash. I’m not asking them to discard reduction – just amplify it with the systems approach. But I am asking them to take a hard long look at the random-wave concept, compare it to the elegance of temporal curvature, and decide. If they decide to keep random-wave, that’s their business – their problem. They will find more and more compelling evidence against it (such as exact atomic control – we can do it now). Uncertainty in physics is becoming a relic of the past (the uncertainty relations used to hold prime importance in physics). When I was in university, it was my conviction that problem solving is a matter of perspective: achieve the right perspective, the problem ‘solves itself’. What this means in practice is: reformulate the problem in a clever way and the solution usually becomes obvious. The book called Heuristics confirms this. It’s an excellent resource for problem solving. I haven’t finished reading it; it’s very ‘heavy’ mathematically. The first two or three chapters can be digested by science students; try it. After years of conventional problem solving, I’m convinced the systems approach is absolutely required for some types of problems: space systems engineering (in order to avoid the Shuttle type disasters), human systems engineering (on a global scale such as suggested by my book Humanity Thrive!), and ‘microscopic’ systems analysis. In the first two cases, we are designing systems. In the last case, we are trying to understand it. Microscopic is in quotes because the systems we are trying to understand are much smaller than what’s viewable with a microscope. That’s part of the problem. We cannot view them directly. We can only infer properties from various kinds of experiments. The only technique that has any chance of viewing them directly is electron interferometry. And that technique is currently in dispute .. So, a chapter on the systems approach is advisable here. Salvatore Gerard Micheal, Faraday Group (altphy.org), 08/NOV/2008

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