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The Wave Structure of Matter (WSM) and the origin of the Natural Laws.


The WSM interests every curious person who has puzzled over the meaning of matter, space and the Universe. Until recently the origin of the Natural Laws have been unknown although many persons have sought a Theory of Everything. Only two scientists, William Clifford and Nobel Laureate Irwin Schroedinger have proposed a successful origin of matter and the Natural Laws based upon waves in space. The mathematical proof awaited the current Wave Structure of Matter described below. The unique feature of the Wave Structure of Matter (WSM) is that it replaces the concept of a discrete material particle, and is simple--Only the wave medium, space, and two properties, Principles I and II, are needed to obtain a wave equation of matter in space; nothing more. The unique pairs of solutions are found to have all the properties of electrons and positrons. The resulting wave electrons contain the laws of Nature that underlie all science.

Applications have appeared in industries where their bottom line depends on scientific truth, such as the development of computer chips by Hitachi Corp. and by Professor Carver Mead at the California Institute of Technology for Intel Corp. [Reference 8].

History of Wave Structures as the origin of Natural Laws.

The first knowledge of the Wave Structure of Matter (WSM) began with the Greek philosophers such as Democritus and Pythagoras and were further developed in the last two centuries by William Clifford, Irwin Schroedinger, Albert Einstein and Paul Dirac. These pioneers had to courage to leave the popular mainstream of physics and astronomy.

Many people followed the Greek philosophers, seeking to understand the structure of atoms and molecules. Most ideas have been analogies to objects around us; like baseballs and grains of sand. Electrons were imagined to move like moons around planets and spinning toy tops. Einstein and Schrodinger realized that these analogies were wrong. Instead, experimental measurements showed that the structure of matter was related to the properties of the apparently empty space around us, and that the elements of matter had to be spherical waves extended in space.


Until recently, most concepts of matter were speculations in analogy to objects around us; like baseballs and bullets, and grains of sand. Particles were imagined to move like moons around planets and toy tops spinning on a table. These analogies made most scientists feel comfortable so they ignored conflicting evidence.. As Churchill said, "We often stumble onto the truth but most of us brush ourselves off and pretend it did not happen!" Only a few persons like Einstein, Clifford and Schrodinger looked beyond the discrete point particle.

William Kingdon Clifford [References 1-3] the famous English geometer spoke [1870] before the Cambridge Philosophical Society saying: All matter is simply undulations in the fabric of space. In Clifford's concepts, the assumed mass and charge substances do not exist but are properties of a wave structure in space. In short, space waves are real, while mass and charge points are mere appearances of the wave structure.

Nearly a half-century before Einstein developed his general theory of relativity, and before quantum mechanics, Clifford discussed (1876) the geometry of space at astronomical distances and in space too small (i.e. atom-sized) to be observed, stating:

I hold: 1) That small portions of space are in fact analogous to little hills on a surface which is on the average flat, namely that the ordinary laws of geometry are not valid in them. 2) That this property of being curved or distorted is continually being passed on from one portion of space to another after the manner of a wave. 3) That this variation of the curvature of space is what really happens in that phenomenon which we call the motion of matter, whether ponderable or ethereal. 4) That in this physical world nothing else takes place but this variation subject to the law of continuity.

The fundamental element of space curvature in Clifford's mathematical model was the twist, which he planned to use to describe electromagnetic and atomic phenomena by viewing matter as space curvature. Clifford's work preceded general relativity by two generations.

In 1873, Clifford published "Preliminary Sketch on Biquaternions," which described a calculus of twists and screws; a space-theory of matter. Clifford published his magnum opus, the 'Elements of Dynamics' in 1878. The book described an elastic medium interpreted as the whole of curved space. Thus if the expansion and the spin are known at every point, the whole motion can be determined with the result that every continuous motion of an infinite body can be built up of squirts and vortices.

Unfortunately, Clifford's ideas were difficult to grasp in the 1870's. Einstein's curved space was not seen as radical in 1915 as were Clifford's in 1870. The scientific community did not receive Clifford's geometry very well; it was too advanced for a community that was just beginning to cope with non-Euclidean geometries. The rapid acceptance of relativity was made easier, by J.K.F. Gauss' measurements of space curvature from three mountaintops in Hanover in the 1820's made long before relativity theory was introduced.

Ernst Mach (1838-1916) and Bishop Berkeley (1685-1753) proposed that the law of inertia depended on all the matter of the universe. This is known as Mach's Principle [Reference 6]. It was the first recognition that a natural law F=dp/dt = ma, depends on cosmology. That is, the stars determine the absolute reference frame of rotary motion. It is very strange that the stars, so far away through empty space, seem to dictate the operation of the most basic law of the Universe. The Austrian physicist-philosopher Ernst Mach first noticed this. But before the Wave Structure of Matter, no one had gone beyond his speculative proposal that the distant matter of the universe determines this law of inertia.

Ernst Mach's concept arose from two fundamentally different methods of measuring the speed of rotation. First, without looking at the sky, one can measure the centrifugal force on a mass m and use Newton's Law in the form F = ma = [mv.sup.2]/r to find circumferential speed v. The second method compares the object's angular positions with the fixed (distant) stars. Both methods give exactly the same result. Mach reasoned that there must be a causal connection between the distant matter in the universe and inertia. He asserted: Every local inertial frame is determined by the composite matter of the universe. Tom Phipps rephrased Mach, "When the railway jerks, it is the fixed stars that throw you down.

Mach's Principle, in a mathematical form, has become Principle II of the Wave Structure of Matter where inertia is an interaction with the universal medium space, not with the distant stars. Space, is established by the distant bodies of the Universe and surrounds us at all times. This explains why the distant bodies appear to create inertia.

Albert Einstein [Reference 7] was greatly influenced by Mach when he deduced both Special Relativity and the General Theory of Relativity (GTR). Einstein, adopted an extended-in-space concept of matter simply because he realized the point-particle model was impossible. He studied the mechanism of the transmission of force from one particle to another and concluded that particles must possess a property that extends throughout space to connect particles. His knowledge of Nature told him that discrete particles couldn't exist because their borders would be an abrupt discontinuity; instead particles and space must be continuous.

Both Einstein's General Theory of Relativity (GTR, 1915) and Principle II of the Wave Structure of Matter (WSM) are based upon the properties of space. Both are correct and represent the physical reality of the universe. However General Relativity primarily examines the large scale, cosmic properties of space and matter in it, whereas the WSM begins with the quantum micro-structure of matter itself. Although his medium and the medium of WSM are identical, he did not concern himself with quantum waves or the micro-structure of matter. They use different mathematical methods but they produce the same results.

Calculating the GTR. Einstein's general theory is based upon the existence of a space medium that contains the matter of the universe. Then his 4D math calculates how energy and matter determine space density everywhere in the Universe, and how density changes with time. Finally his theory calculates space-density on an astronomical scale to find the paths of light rays. These light-paths define the 4D coordinates of space just as grid-lines on graph paper define 2D coordinates. If matter and energy are evenly distributed, all the coordinate lines are parallel. But if not parallel the space is said to be curved.

In our real Universe, matter and energy are distributed almost perfectly evenly and the curvature of space is very tiny. In order to find experimental proof of his theory, Einstein had to search exhaustively to find where the small curvature was big enough to measure. He found that close to the Sun light rays would be deflected enough.

His complex mathematical procedure has caused the study of GTR to be misunderstood and used only by mathematical scientists. In contrast, the use of 3D waves for each mass 'particle' in the WSM greatly simplifies the calculation.

Nobel Laureate Erwin Schrodinger a co-discoverer of quantum mechanics and Nobel Laureate adopted the view of Clifford and wrote in 1937: What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen (appearances). He believed that quantum waves were real, not probability distributions with a particle hidden inside. He saw that abolishing the discrete point particle would remove the paradoxes of 'wave-particle duality' and the 'collapse of the wave function'.

He sided with Einstein opposing the Bohr school that believed in probability functions for 'discrete particles'. Like Einstein and Clifford he recognized that discrete 'point particles' were impossible. He wrote that the puzzle of matter will be found in the structure of space, not in point-like bits of matter, and that the physical world is based upon the geometry of space. "During discussions with Neils Bohr concerning the probability interpretation of his own Schrodinger's Equation, he firmly disagreed with Bohr and mainstream quantum mechanics and wrote: Let me say at the outset, that in this discourse, I am opposing not a few special statements of quantum mechanics held today (1950s), I am opposing as it were the whole of it. I am opposing its basic views that have been shaped 25 years ago, when Max Born put forward his probability interpretation, which was accepted by almost everybody.... I don't like it, and I'm sorry I ever had anything to do with it." [Reference 10.]. His thinking was ignored for sixty years.

Paul Adrianne Maurice Dirac [Reference 4] received a Nobel Prize for his work (1923) predicting the spin of the electron and the existence of the positron. Dirac developed much of the theory describing the quantum waves of the electron, but was never satisfied with its point-particle character so that the Coulomb electron required a mathematical correction termed "renormalization". In 1937, he wrote, "This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it turns out to be small--not neglecting it because it is infinitely large and you do not want it! "Like Schrodinger, he had confidence in what his mathematics was telling him and refused to go along with the speculations and approximations of mainstream science.

The Quest for a Theory of Everything. In recent decades, there has been a partial success of Quantum electrodynamics (QED), which united quantum theory and electromagnetism and explained some behavior of electrons and photons. Quantum mechanics explained the wave-like aspects of electrons surrounding atomic nuclei, and knowledge of electromagnetism has culminated in the astounding computer revolution.

Some scientists hoped the same methods could be applied to other particles and forces to obtain a "Theory of Everything". Unfortunately most attempts began with the impossible discrete material 'particle'. For several decades there have been many proposals but no winners. As Freeman Dyson of Princeton said, "The paths of physics are littered with the corpses of unified theories". For a physicist who believes that Nature should be elegant and simple, this notion is the supreme challenge. A theory that condenses all of physics into a single concept has profound consequences for science and its future.

In years before 1990 the 'particle' attempts became increasingly bizarre: Multiple universes, microscopic strings, tiny tops, quarks, we live in a black hole, or a white hole, a universe made of worm-holes, the big-bang, and so on and on. Any incredible scheme, with any number of dimensions seemed to be a valid model of matter, provided the algebra was correct and it did not violate the conservation of energy. Many predicted that the solution to the deep puzzles would be strange. Niels Bohr commented, "We all agree that your theory is crazy. The question which divides us is whether it is crazy enough."

Viable theories, however crazy, should: 1) raise much less questions than the answers it provides. 2) introduce many fewer new constants than the natural constants it explains, and 3) the number of assumptions required should be much less than the properties of Nature it reveals; in short: simplicity is the goal. But often the zeal to publish overrules logic so eternal hope has given almost eternal life to many useless theories.

How is matter 'particles', constructed of waves?

Answering this question requires a change of concept from a discrete material, like a grain of sand, to a wave structure in space. The physics and math are very simple but the main task is to change old ideas embedded in our minds.

Matter is a wave structure propagated in a quantum space medium. Figure 1. There are two solutions of the wave equation: an inward moving spherical wave that rotates spherically [Reference 9] at the waves center, producing spin h/4[pi] to become an outward spherical wave. The wave center is the apparent location of the electron/positron formed by pairs of the wave solutions. See Wolff [10-13] This structure satisfies experimental observation and displays a beautiful tapestry of the universe that connects matter, the cosmos and ourselves. [Wolff 14,15]

This Spherical Standing Wave Structure of Matter (WSM) applies to cosmology, the big bang, the red shift, and the structure of the universe. On the practical side, the WSM improves devices in nanotechnology, computers, and micro circuits; and may in the future, apply to biology and the transmission of electric energy.

1. Solutions of the Wave Equation (Principle I)

The conservation of energy in the medium of space yields only one wave equation:

Potential energy - kinetic energy = 0


-- -(1/c-) -- t- = 0 (1)

where -- = wave amplitude. The wave equation (1) must be written in spherical coordinates because cosmological space has spherical symmetry. If uniform density of the space medium is assumed, this yields a constant speed, c, of the waves and light. There are only two spherical solutions:

Outward moving wave = [[PHI].sub.out] =(1/r) [[PHI].sub.max] exp(iwt-ikr) (2)

Inward moving wave =

[[PHI]] =(1/r) [[PHI].sub.max] exp(iwt+ikr) (3)

where wave number k = mc /h, frequency w = 2[pi]f, r = radius from the wave center, and energy = E = hf = [mc.sup.2] These two waves form the complete wave-structure of charged matter: the electron, positron, proton, and anti-proton. Superposition of the inward wave and the outward wave produces a standing wave called a space resonance (SR) There are two SR combinations: an electron and a positron,

An electron is: -in -- out_with CW spin (4)

A positron is: - out -- in_with CCW spin (5)

At the center the inward wave undergoes a rotary transformation to the outward wave. This phase-reversal, called spherical rotation, can proceed in two ways termed CW or CCW producing the electron and the positron with opposite spins [+ or -]h/4[pi].

The spherical in-wave is coming from all directions in spherical 3D space and changes phase to form an out-wave in 3D spherical space. This is not a 'stop-and-reverse' which is impossible; it violates momentum conservation. The only possible way is a 3D mechanism called spherical rotation. This 720 degree rotation requires that the entire wave resonance structure (in-wave plus outwave) acquire a quantum angular momentum spin of value [+ or -]h/4[pi]. This is easy to calculate! Try it using E = mc -= hf and 720 - rotation.

It is philosophically sobering that spherical rotation is a property of only 3D space, not 2D, 4D, or other space. Thus, proposls that postulate 5D, 10D, 11D space, etc. are patently invalid; they cannot describe real matter with spin. Further, if spherical rotation did not exist, we and our Earth--all matter in the atomic table could not exist.

CPT inversions. It is known experimentally that different particles have patterns of behavior that depend on the charge, direction in time, and LH-RH handedness. Their behaviors are called CPT inversions: Charge inversion changes a particle to an anti-particle by switching the in-waves to out-waves and changing the direction of spin. To perform a Time inversion, change t to -t, which converts the positron into an electron. To perform a Parity inversion imagine that the waves are viewed in a mirror. A positron is the mirror image of the electron. To make particle inversions you change the + or signs as needed in the equations (2) and (3) of the particles (4) and (5).

There is an empirical rule that successive C->P->T inversions of a particle always return to the initial state. The physical reason for this was not found using the material particle model, however you can use equations (2 & 3) to show that the origin of CPT is a property of the wave structure.

Time travel? These CPT relations describe Feynman diagrams that show the behavior of electrons and positrons in experimental labs. Feynman wrote a cryptic statement, "A positron is an electron traveling backward in time." This statement led to many sci-fi films about time travel, but the positron does not go backwards. Only its inward and outward waves are opposite to those of the electron. It is a normal particle.

2. The Doppler effect: Special Relativity & the DeBroglie Wavelength.

A very important property of the in-out waves is the Doppler effect between two space resonances(SR). Doppler shows the origins of special relativity and the de Broglie wavelength, the basis of the Schroedinger Equation. This result is a wave property and cannot be found using a discrete particle model.

Examine the Doppler Effect by writing the equation [4] of a SR, as seen by an observer with relative velocity b = v/c. The relative velocity causes the in-waves to be red shifted and the out-waves to be blue shifted using the relativistic Doppler factors D and 1/D, D = g(1 - b), 1/D = g(1 + b), where g= [(1 -[b.sup.2]).sup.-1/2] = [[1-[v.sup.2]/[c.sup.2]].sup.-1/2]

Insert the Doppler factors, D, 1/D and g above into Eqn [4] to get the Doppler shifted wave amplitudes received at either particle:

- (electron) = [A.sub.max] exp[i(ct + r)k/D + [A.sub.max] exp[i(ct - r)kD

After multiplying out and rearranging terms, the amplitudes received by the moving observer are,

Received amplitude - = (1/r){(2[[PHI].sub.max])exp[ikg(ct+br) ]sin[kg(bct+r)]} (6)

The RH side of [6] is an exponential oscillator modulated by a sine factor. Examine these factors and see they contain the de Broglie wavelength that underlies QM, and relativistic energy and momentum that is the mass increase of special relativity. The terms of the factors are:

In the exponential oscillator factor:

Wavelength = h/mvg. This is the de Broglie wavelength, [Reference 5] with relativistic momentum.

Frequency = kgc / 2[pi] = [gmc.sup.2] / h. This is mass frequency with relativistic energy.

And in the sine factor:

Wavelength = h/mcg. This is the Compton wavelength with relativistic momentum.

Frequency = b [gmc.sup.2]/h = b x (mass frequency). This is relativistic momentum frequency.

QM and special relativity are the result. You see that the Doppler effect causes the correct de Broglie wavelength and relativistic mass increase to appear in the observed waves, as a function of the relative velocity. This corresponds exactly to experimental observation. This result removes the mystery of the discrete particle model where mass is a fixed property and then later it is a changing property depending on motion v/c. But you never know why. We also see that energy, mass and frequency are equivalent - with different units: E = [mc.sup.2] = hf. You can also see that if an electron and positron are super-imposed, the waves will cancel; they annihilate, as experimentally observed.

It is important to note that the Doppler is symmetrical; it does not depend on whether the relative velocity is +v or -v. Thus the origin of QM and relativity requires both in-and out-waves.. This is exactly as observed.

The space resonance displays all physical properties of an electron, viz: electric charge, QM, SRT, forces, annihilation, spin, and CPT relations between Charge, Parity, and Time. The origin of these physical properties is the spherical wave structure of the electron and the wave medium of space.

2. The second Principle II of the WSM is used to calculate the density of the quantum wave medium--the space all around us. The role of the medium was foreseen in 1883 by Ernst Mach who noticed that the inertia of a body depended on the presence of the visible stars as written above. The energy exchange of inertia actually takes place with the space medium not with the fixed stars. It appears to be the fixed stars because they establish the density of the space medium.

Principle II is:

Density of space is proportional to:

SUM of {(waves from all matter)/ (each distance squared)}

or, [mc.sup.2] = hf = k'- N-[n.sup.2] (1/[rn.sup.2])

where m and f are the mass and frequency of that electron, c is the velocity of light and h is Planck's constant. This SUM includes all the matter in a sphere with the Hubble Radius. This density determines c, and is almost constant everywhere because there are so many particles (N = about [10.sup.80]) contributing waves. Nevertheless, space density and c vary slightly near large masses like the Sun. Accordingly space is not empty; it is a energy-dense quantum wave medium created by waves from every particle in the universe. Inertia, charge, and other forces are mediated by the pervasive space medium.

Principle II contains the origin of the inertial energy exchange F=ma. The exchange is the interaction of waves from accelerated matter with the universal space medium. This agrees with laboratory experience using gyroscopes and the laser gyros that navigate aircraft. Before the WSM space medium was known, inertia was a paradox stated by Newton as: action-at-a-distance.

Principle II contains a strange feedback loop in Nature, as follows:

The matter of the universe tells the space medium what it is and in turn space tells matter how it must move. The reader may disbelieve this strange result. But one confirmation is Einstein's General Relativity (GTR) that contains the same feedback.

Similar to WSM, GTR calculates the density of space-time at each point in space using the density of matter and energy everywhere in the universe. A varying density is referred to as curvature of space. This space density determines the paths of moving matter and light which follow the curvature. The feed back loop is the same.


William Clifford, English mathematician at the Royal Philosophical Society, first suggested that matter was composed of pure waves in space, as ff:

(1.) William Kingdon Clifford, The Common Sense of the Exact Sciences, Ed. Karl Pearson, New York: Dover, (1955) = Reprint of the third edition of 1899; First English edition, London: Macmillan (1885), New York: (1885).

(2.) William Clifford, (1876) "On the Space Theory of Matter" in The World of Mathematics, p568, Simon and Schuster, NY (1956).

(3.) William K. Clifford, "On the Space-Theory of Matter," 2 February (1870), Trans Cambridge Phil Soc., 1866/1876, 2: 157-158. Reprinted in William K. Clifford, Mathematical Papers, Ed. Robert Tucker, New York: Chelsea, (1968).

(4.) Paul Dirac "Quantum Electrodynamics" Nature, 174, 321 London, (1937), {This is the pioneer treatment of Quantum Mechanics.}

(5.) Louis Duc de Broglie, PhD thesis, "Recherce sur la Theorie des Quanta", U. of Paris, (1924).

(6.) Albert Einstein, Generalized Theory of Gravitation, Crown Books (1950).

(7.) Ernst Mach, (German-1883). English: The Science of Mechanics, Open Court (1960).

(8.) Carver Meade, Collective Electrodynamics, MIT Press (1999).

(9.) Charles Misner, Kip Thorne, and John Wheeler, Gravitation, W.H. Freeman Co. San Francisco, p. 1149 (1973). {Describes a classic study of 'spherical rotation'.}

(10.) E. Schroedinger, in Schroedinger Life and Thought [Moore], p 327, Cambridge U. Press (1989).

(11.) Milo Wolff, Exploring the Physics of the Unknown Universe, Technotran Press, (1990).

(12.) Milo Wolff, "Microphysics, Fundamental Laws and Cosmology, in" Sakharov Memorial Lectures on Physics, Moscow, May 2131, 1991. Nova Sci. Pub. NY (1992).

(13.) Milo Wolff, "Exploring the Universe," Temple University Frontier Perspectives, 6, No 2, pp. 44-56, (1997).

(14.) Milo Wolff "Spin, the Origin of the Natural Laws, and the Binary Universe", Temple University Frontier Perspectives 10, No 2 (2001).

(15.) Milo Wolff, 'Gravitation and Cosmology' in From the Hubble Radius to the Planck Scale, R. L. Amoroso et al (Eds.), pp 517-524, Kluwer Acad. Publ. (2002).


"Quantum Science Corner"

"Wave Structure of Matter": This most complete site broadly discusses the WSM, its history and philosophy. By Geoff Haselhurst.

Dean Dauger: http://daugerres Beautifully shows in 3D animation, the correct H atom waves computed from Schroedinger's Equation.

Mike Weber: /mike/StandingWave3D/ An insightful 3D animation of the wave-center of the electron. User can choose values of time, Doppler speed, and other electron interaction parameters.

By Milo Wolff, MIT (retired), and Geoff Haselhurst,
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Author:Wolff, Milo
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Date:Sep 22, 2008
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