The apparent inconsistencies between the point particle theory and the observed wave behavior of the electron are reconciled by an electron structure, the Space Resonance. Electrons or positrons can be described as a pair of spherical scalar waves diverging and converging at their center. This simple structure produces the observed properties of electrons. This basic charged-particle structure is then found to be the origin of the basic laws of physics, including quantum theory, relativistic mass increase, inertia, charge and electromagnetism.
The Space Resonance structure is obtained from three assumptions or principles: (1) a
laws of nature and Principles of nature
. The distinction between them is tied to their generality. Principles are considered to be more general and by implication more basic. For example, the Principle of
Least Action is inferred from several of the force laws and the principle of Conservation of Energy expresses all the various heat and energy flow laws.
Since laws are obtained by measurement of nature rather than derived from other knowledge, they are by definition
empirical and "of unknown origin". Therefore if we seek to find the origins of laws we cannot use the existing laws
themselves but must use other observed facts together with logical deduction and established mathematics. Rarely a law is found contained within another law. For example the gas law When seeking origins, it is important not to inadvertently use existing laws to deduce themselves. Although the quantum laws of quantum particles can be extrapolated to large macro-objects, the inverse is not possible. Such circular reasoning can occur if, for example, an e-m field or mechanical model from macro-physics is assumed to be the structure of a quantum particle. Logically, finding the origins of existing laws requires forming new concepts that nevertheless satisfy observed data. It is a major result of this article to further deduce that most of the natural laws originate from the properties of the quantum waves of the charged particles (electron, proton,etc) , and the properties of the space (ether, vacuum,etc.) which is formed from the totality of all those particle quantum waves. One such effect is already known as Mach's Principle which asserts that inertia is a result of an inertial reference frame established by all matter in the universe. The discovery of these origins from the work of this article creates a radical new picture of the physical world: quantum mechanics and relativity are in a sense united, origins of forces are understood, puzzles and paradoxes are explained and, most important, relationships between microphysics (electrons and particles) and the universe (cosmology) are seen to be a result of an all-pervading "space" (the vacuum or ether) filled with oscillating quantum (particle) waves. The reader should be aware that he is evaluating a new basic proposal that all natural science results from just three assumptions about the properties of space. The search for the structure of the electron started over a century ago, in H.A. Lorentz's book [2]
Many have suggested that a wave-structured electron plays a fundamental role in nature. The famous geometer-mathematician Clifford [3] suggested in 1876 that all physical laws were the result of undulations (waves) in the
fabric of space. Nobel laureate Paul Dirac, who developed much of the theory describing the quantum waves of the
electron, was never satisfied with its point-particle character because the Coulomb electron required a mathematical correction termed "renormalization". In 1937, he wrote, Weyl, Clifford, Einstein, and Schroedinger [4] agreed that the puzzle of matter will be found in the structure of space, not in point-like bits of matter. They speculated that the physical world is based upon a geometry of space. What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. The complexity of physics and cosmology is just a special geometry. This idea had an enduring appeal because of its economy of concepts and simplicity of design.
In 1945, Wheeler and Feynman [5] represented charge by assuming a pair of spherical inward and outward Phipps [6] put forth a This paper shows that these scientists' visions have come true. Dirac was correct. The electron is a wave structure without particle substances. The medium of the waves is space, still unexplored but related to "vacuum" and "ether"; terms increasingly used as the wave nature of matter becomes unmistakable.
Furthermore, an Energy Exchange Mechanism can be seen to underly the force laws and even special relativity, the
DeBroglie wavelength, and Conservation of Energy. For example, the force laws describe force as the change in energy over distance,
And the opposite is true. We cannot identify a particle without the force laws to locate and measure it. Thus our perception
of particles depends on the form of the natural laws. These three, particles, laws, and the universe are an interdependent
We deduce that the waves of an electron structure are the means of the communication between particles of matter. Below in Section III we shall see that the mathematical solutions of the wave equation indeed allow for two-way continuous communication by means of waves which form the the electron structure. This reasoning underlying measurement yields boundary criteria on the structure of the electron summarized in the two corollaries below :
^{2}
/r, to find circumferential speed v. The second method compares the object's angular positions with the fixed (distant) stars. Mysteriously, 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. (This wave structure of the electron now proves that Mach was right.) Mach's Principle of Inertia is the clearest evidence that very distant bodies can affect us instantaneously. Phipps [6] quotes Mach, "When the subway jerks, it is the fixed stars that throw you down." Mach's Principle is criticized because it appears to violate causality: "Events cannot occur before the causes which produce them." but this does not actually occur as will be seen below where Mach's Principle is used to find the energy exchange mechanism of the electron.
Three assumptions about the properties of space determine the space resonances. In return for this investment, the theory obtains a physical and mathematical origin for natural laws plus relationships between particles and cosmology.
^{2}/h. Two solutions of the wave equation shown in Figure 1 describe the physical structure of the electron. Equation (2) below shows that an electron is comprised
of two spherical scalar waves traveling in space with velocity c; one inward to a center and the other outward. The two superimposed waves form a standing wave,
termed a space resonance (SR). The center of the wave structure is the nominal location of the electron. These space resonances are perpetual spherical oscillators.
Each resonance extends throughout space and interacts with other resonances so that the natural laws result from the properties of the waves and the medium they travel in, 'space' or the The Wave-equation for the electron, in spherical coordinates, is: d where
A standing wave results by combining them with their amplitudes opposing at r = 0 , to get The equation, Energy = mc This equation becomes clearer when changed to a simpler exponential function, The exponential factor is an oscillator. The sine function modulates the rapid oscillator waves with a standing wave of
wavelength 1/k which surprisingly is the Compton wavelength of the electron. The intensity is the envelope of ^{2}
away from its centers This equation is simulated in the animation of the electron on this web-site. The amplitude,
To examine this requirement we first make a quantitative assumption, similar to Mach's Principle, which establishes the
density of space (ether or vacuum). Then we will examine the density formula seeking a means of intereaction.
Assume that the mass (wave frequency) and propagation speed of an SR wave in space depends on the sum of all SR wave intensities in that space; a superposition of the intensities of waves from all
particles inside the Hubble (H) Sphereof radius R = c/H, including the intensity of a particle's own waves.
Now examine the homnogeneity of the space. The universe contains so many particles that the density of space is nearly
constant everywhere. But close to the center of an electron, the amplitude of an electron's own waves following the 1/r
INPUT = Acos(w then the output will be: OUTPUT = AB[ cos(w The non-linear element produces sum and difference frequencies of the original w Similarly in space, different waves passing through the dense, non-linear region at the particle center will mix. If an input frequency and a particle frequency are similar, resonance can occur. An example of this is a tuned radio receiver. An energy (frequency) exchange between resonances behaves like two coupled oscillators in a circuit, or like two pendulums joined with a spring.
where V is the volume inside the Hubble Sphere and R its radius. The integral, from r = 0 to R = cT = c/H, extends over a
sphere whose expanding radius R depends on the age T of the particle. Thus T is the maximum range of the particle's spherical waves. This reduces to Inserting values from astronomy measures, R = 10 e Equation (5) is a relation between the size r
1. Charge and mass interactions occur at the center (lump). The electron resonance extends throughout space but
energy exchanges take place in the non-linear bump at the center. Thus the SR "looks" like a point particle but no mass or
charge substance is required to produce this experimental appearance. It is all waves.
_{1}+AMP_{2}+ AMP_{3} +... AMP_{n} }^{2 }
dx dy dz = a minimum (7) or,
The total amplitude of particle waves in space always seeks a minimum.In other words, all the waves of the total number n of particles inside the Hubble Sphere adjust themselves at each point to make total amplitude a minimum. To accomplish this, energy (frequency) exchanges take place, or wave-centers move in order to minimize the total amplitude. This principle is very powerful and predicts many observations. For example, waves of two electrons close together will have a higher intensity than electrons farther apart. Therefore two electrons must repel in order to satisfy the MAP. A positron and an electron will attract. It also creates the Pauli Exclusion Principle, forces between atomic nuclei, and gravitation.
2. The electric charge force between two resonances is F = k/r ^{2}, where k = e^{2}/4 pi e_{o}
. It is the same as Coulomb force everywhere except at the center. This force arises as a result of the Minimum Amplitude Principle which attempts to minimize wave amplitudes near the resonances. The 1/r^{
2} factor is the result of the 3D geometry of ordinary space. The electric constant k is a measured parameter which can be approximated from Equation (6) which shows it to be a property
of space. Thus only one value of charge occurs in nature.The complex amplitude AMP can be regarded as the electric potential of the electron.
The structure of the SR leads to new applications that solve puzzles of physics and cosmology. The examples below are important applications.
Consider two SRs moving with relative velocity b = v/c. Each receives the same Doppler shifted waves from the other.
They are symmetrical. Their IN waves are red-shifted and their OUT waves are blue-shifted according to the usual Doppler factors, g(1+b) and g(1-b) which shift frequency and wavelength.
Equation (8) is composed of an exponential carrier wave modulated by a sine function. The relativistic term, g = [1- (v/c)
frequency = kgc/(2 pi) = gmc ^{2}/h = mass-energy frequency. velocity = c/b = phase velocity.
frequency = gmc ^{2}
b/h = b x (mass frequency) = "momentum frequency". velocity = bc = v = relative velocity of the two resonances. The above matching results are remarkable! They clearly show the origin of mass increase and quantum mechanics in the wave structure of matter. It is instructive to compare Equation (8) for moving electrons with Equation (2) for a stationary electron. They are of the same form but (8) contains the velocity b = v/c and the related quantum and relativistic properties for moving particles.
_{o} = e^{2}/mc^{2}. Eliminate r_{o}and obtain e^{2} = mc^{2}
R/SQRT{3N}. This shows that the charge e^{2} is dependent on the total of all N particles. We also recall that charge always occurs in natural laws as e^{2}
, never as e alone. Thus, charge is a property of space and total matter, not of particles, and there is only one value of charge in nature e^{2}
. Conservation of charge follows from the anti-symmetrical structures of the SR and anti-SR described in Section III above.
^{2}
, the geometric property of distance in 3D space.
Other types of space inhomogeneities also appear as force laws including Mach's Principle, gravity, and magnetism, which are discussed in IIIE and IIIF. Rotation, angular momentum, spin and the Dirac Equation are discussed in References [8, 9, 11].
To analyze this, examine the IN/OUT wavelength change from acceleration and calculate the forces caused by acceleration
relative to the masses of the universe. This change disturbs the local balance with waves from other matter in the universe. The MAP corrects the imbalance by readjusting frequencies of the accelerated resonance: electric Force = e' x
In analogy, mass Force = m' x
The E field of an accelerated charge e is computed from the magnetic vector potential electric field = For the analogous particle m, assume an analogous mass field derived from an analogous vector potential, mass field = Following the analogy, the gravity constant G has replaced the electric constant 1/4pi e m' = (d where d = {(8pi Gd Now if we choose d
electric/gravity force = F Compare this with the measured ratio = e One can regard this perturbation as an induction of a gravity force by the changing space property. It is analogous to the induction of an electric field by a changing current. Like Lenz's law, the force opposes the change.
^{2}
between twocharges. This little known result was found about the year 1910. Lorrain and Corson [12] use it
to derive the magnetic force equation beginning with Coulomb's law and special relativity, with the result:
where special relativity creates the coss product, q is the current producing charge with relative velocity
_{o} of the electron, the big and the small. Remarkably, it describes how all the mass of
the universe acts together to create the "charge" and mass of each electron as a property of space. To see how the electron mass depends on other matter, combine Equation (5) with the Compton wavelength r mc Again, confirming our logical deduction, we see that the electron mass like the charge is a property of the universe, that is the total particles N and its size R.
Ordinarily we observe communication as two energy-exchange events: an energy shift at a source particle and later an absorbtion event at a receiver particle. We calculate the message velocity (c ) using the time between the events. We used to think of this as a moving photon but this leads to confusion. The correct picture uses the IN-OUT waves traveling at space-wave velocity c. Before two potential partners can undergo those energy shifts, the IN/OUT waves must exchange information (boundary conditions) of their respective particle energy states so that energy exchanges can take place in a way that minimizes wave amplitudes in accordance with the MAP (Assumption III) . If minimization is not possible no exchange can take place. Is this respect, the Minimum Amplitude Principle is similar to other physics principles such as the Principle of Least Action, and "Energy flows down-hill". It underlies them.
These prior information exchanges do not produce energy changes visible to us. The mysterious EPR experiments use two
separated photo-detectors which appear to have instantaneous knowlege of each other's state of polarization. We are not
aware of the prior information exchanges because they are hidden from our laboratory instruments since they are not energy
shifts but are carried by the IN-OUT quantum waves. After we understand the role of the quantum waves we recognize
that Nature is a puppet-master who allows us to see the puppets but not the quantum wave ensemble behind the curtain.
A second World of Scalar Waves forms the structure of the basic particles, electron, protons, and neutrons which compose the material objects and the space(ether) of our world of energy-exchange. These waves in space are unseen by us. We only know of their existence when an energy (frequency) exchange occurs to stimulate our senses. Nevertheless this unseen scalar wave world is basic and determines the real action in both worlds. The waves obey the rules of superposition and interference and are governed by Assumptions I, II, and III. The behavior of the particles (space resonances) in their interactions is largely due to their oscillating scalar waves which reveal their behavior to us via the rules of quantum mechanics and relativity. These waves (inward and outward) fulfill the requirements of matter inter-dependence discussed in Sections III and IV above.
One role of the scalar waves is inter-particle information exchange of their quantum states. This is usually unseen in our
world but it is conspicuous in the mysterious EPR effect (Einstein et al, 1935). Information must be exchanged because
partners of a future energy exchange cannot act until they have "knowledge" of each other's state. This is necessary so that
the MAP (Assumption III) can determine whether an exchange will minimize net wave amplitudes. These information
exchanges are usually hidden from our laboratory instruments because they are not energy shifts. Nature is a puppetmaster who allows us to see the puppets but not the orchestration behind the curtain.
2. The lifetimes of atomic and nuclear decays are not constants as once thought but depend on their quantum-wave states and the distance between partners of the energy exchange. Such variable lifetime atomic decays have been investigated by Walther et al [16] and Greenberger et al [15]. 3. Inertial and gravity forces are predicted to be of the action-at-a-distance type as originally stated by Newton. This agrees with action-at-a-distance gravity as recognized by astronomers to account for planetary motions. Lorrain & Corson [12] and Graneau [17, 18] verify action-at-a-distance for magnetism confirming the SR electron but not conventional older physics. [1] Galeczki, G. 1994, Physical Laws and the Special Theory of Rerlativity, Apeiron 20, 26-31. |