2.1 GENERAL NATURE OF THE (BU) THEORY
An attempt will be made in the following sections to outline qualitatively how some basic Newtonian, (SR), (GR) and (QM) concepts can be ‘reverse engineered’ – i.e. their results are first separated from their original theoretical and mathematical frameworks, then reconstructed using the premises and interactions of (BU) theory.
While (BU) theory is causal and local, it is not classical, since no continuous integral processes are possible: the nodes are discrete with units of action h, and other than the spin of individual nodes in situ, absolutely nothing else actually moves. Unlike classical theories, no preconceived ideas about mass or motion are used, but these concepts are developed from first principles. Assuming neither flexible spacetime nor the constancy of the speed of light, the theory is not relativistic (SR) or (GR) either. The speed of light is the maximum speed between nodes, so a simple Galilean relativity does not apply. There are no inherent time and space dimensions in (BU), but to aid keeping track of the changes of the state of the universe, a fixed time dimension can be defined as described above. Even so, this time dimension should not be thought of as a standard universal time zone, since all interactions are measured locally, and signals from various distances arrive at various times relative to their distance and velocity of the source. Three fixed space dimensions can be defined from the geometry of the nodes, but again such directions are not absolute in the universe as a whole. Nor does (BU) depend on concepts of probability so it is not a variation on (QM) in its Copenhagen interpretation.
A curious aspect of (BU) is that concepts that were simple in classical physics becomes complex, while (SR) and (GR) on the other hand become simple. Motion, which was considered a simple change of position of a whole mass in time, now involves the complex process of self-convolution. This involves all the nodes making up the mass as well as those in its own gravitational field in which it is moving. Conversely, (SR) and (GR) can be derived simply from the model without using complex equations of differential geometry to describe a physically unrealistic flexible spacetime dimension. There are the usual relativistic effects in (BU) but they can be derived from the model using classical concepts. Similarly the results of (QM) can be re-formulated on the basis of the electromagnetic waves transferred within a field of nodes. It is speculated that only two basic constants co and h are necessary to describe nature, and that all other constants, including the constant of universal gravitation G can be derived from them.
If these expectations are confirmed, then all the laws of physics can be derived systematically and quantitatively from the handful of a priori premises of (BU), revised as necessary. If successful, this would be the basis of a unified theory of physics. Such a systematic ‘theory of everything’ (TOE) is too ambitious a task for this speculative paper and will be left for future work if the (BU) concepts are found feasible.
2.2 A DISCRETE CALCULUS FOR (BU)
The reductionist nature of BU demands matching mathematical methods. Newton developed the calculus to describe concepts such as acceleration. Einstein adapted the language of differential geometry and tensors to describe his notions of flexible space and time. No new or difficult mathematics is necessary to describe (BU) interactions. The node structure in (BU) resembles that of 3-dimensional arrangements of atoms in crystals or metals, so some of the well-developed notation to describe the various orientations of facets might be useful in developing (BU) interactions. Unlike crystals however, (BU) has no free electrons transporting electricity or diffusing heat, so this comparison should not be taken too far.
Rather, in (BU) a field or action is described by a summation of discrete intervals or stepwise changes. The summation symbol ∑ of discrete calculus now appears instead of the integeral . It is only on the scale of relatively large distances on the atomic or molecular scale and larger that the incremental nature of BU can be ignored, and phenomena can then be treated with continuous integrals. Continuous integral fields only apply when the Xmax the maximum physical dimensions considered are much larger than the node-to-node distance do. A scaling factor Sc is proposed to judge when (BU) interactions warrant a discrete treatment.
An interaction would be quantum in nature if Sc is, say, between zero and one, and classical for larger values. (BU) functions are complete in themselves, but for the sake of comparison with current models, they may be regarded as a regular sampling at the nodes of such continuous functions. In (BU) there is no conflict between descriptions of the macroscopic world of large objects and the quantum world (FIG. 21).
If each node is given a label axyz then the very geometry of the lattice resembles a sort of matrix, and matching mathematical matrices can be developed to describe various interactions. It will be discussed in section 2.7 how Heisenberg’s matrices in QM might be derived from this geometry. Similarly the tensors of general relativity describing the local deformation of spacetime can also be reinterpreted within (BU), using the moments of the nodes to define local density.
Since there is no space between the nodes, a signal travels between two nodes A and B within a volume of space in (BU) only via the network of intervening nodes. A ‘straight line’ will actually be a jagged zigzag of segments, not a smooth diagonal crossing over an infinitely divisible space. The total path length of, say a ray of light, will be larger by a factor of 1=<FL =<√3 depending on the direction of the line within the cubic lattice in three dimensional space. For example, in the case of the line AB in Figure 21(c), aligned exactly diagonally across the cubic lattice, FL =√3 .
FIG. 21. Discrete Calculus in (BU). (a) A function in the x-y plane of a volume of nodes centered on an arbitrarily chosen node (0) is described by summation functions ∑ showing discrete quantum behavior from node to node. The maximum function value Xmax is of the same order of magnitude as the node-to-node distance do. Distances are not measured in straight lines such as OC, but along zigzag paths connecting the nodes. (b) In macroscopic systems in (BU), Xmax>>do and the same function can be described by integrals (c) Multiple paths are possible from node A to node B in a two or three dimensional volume of space.
Vectors too will describe zigzag paths on the scale of the nodes. A macroscopic vector from any node A to node B will be identical to the summation of smaller node-to-node vectors starting from A along any path or paths to B. This concept is useful in expressing treatments such as Feynman’s sum over histories of an interaction.
Another significant aspect of (BU) is that functions such as the gravitational potential containing inverse distances never explode into infinity as in the case of (GR), because in (BU) a distance can never be zero, i.e. less than do.
2.3 AN ETHER TO CARRY ALL INTERACTIONS
(BU) is a new type of ether theory, a substance that was supposed to fill all of space and argued over since antiquity. The crucial difference between (BU) and earlier concepts of ether is that in (BU) everything is made up of the ether. The distinction between solid matter, energy, and empty space that has confused most of the earlier theories does not occur in (BU). Descartes had speculated that light is transmitted in space by the action of tiny vortices (FIG 22), not too different from the nodes of (BU).
|FIG. 22 Descartes’ vortices||
FIG. 23 The ether mechanism envisioned by J. C. Maxwell in 1861
Thomas Young theorized that diffraction of light is due to its refraction in a dense medium adjacent to matter. Faraday assumed the existence of lines of force in space to carry magnetic effects. At one time Maxwell had assumed such a mechanical model of an ether for his electromagnetic field, and imagined a system of gears surrounded by particles interacting together to carry the field along (FIG. 23).
When Michelson and Morley’s experiments showed that light is not retarded by its passage through a supposed ether, it caused a crisis in physics. How was light transmitted? Thompson (Lord Kelvin) was a firm believer in the ether, and that atoms were knots in it. As the discoverer of the electron he believed that both atoms and the ether were electrical vortices, but failed to translate this idea into a complete theory. It is interesting that recent topological researches now show that aspects of knot theory are closely linked to gauge fields and gravity and to quantum field theory . By adopting the two postulates of the constancy of the speed of light in a flexible space and time, and the principle of equivalence of all inertial frames, Einstein’s (SR) succeeded in describing the electrodynamics of moving bodies without recourse to the concept of an ether. The ether seemed to have evaporated forever.
Ironically it was Einstein himself who lectured in 1922 on the need for an ether, some years after the results of (SR) and (GR) were experimentally proven. He needed a medium to carry his mesh of ‘clocks and measuring rods’. In 1954 Dirac said “...the failure of the world’s physicists to find such a (satisfactory) theory, after many years of intensive research, leads me to think that the aetherless basis of physical theory may have reached the end of its capabilities and to see in the ether a new hope for the future.” . Recently there has been speculation that the fifth dimension in the Kaluza-Klein solution for Einstein’s equations is a lattice of ether nodes.
FITZGERALD’S, LORENTZ’S, AND EINSTEIN’S (SR)
EMERGE DIRECTLY IN (BU)
In the second half of the 19th Century it was discovered that Maxwell’s equations failed to account for events in frames of reference moving relative to each other. Soon afterwards Heaviside, Fitzgerald, Lorentz and Poincare, put forward various classical theories proposing length contraction and time dilation to correct problems in applying Maxwell’s equations in moving frames of reference, and to explain why such transformations make it impossible to detect the ether.
Unfortunately instead of extending these earlier results, Einstein chose to recast them using a mathematically equivalent model. He proposed, without relying on any experiment or observation from nature, that it is space itself that contracts, and time itself that dilates in a moving frame; not merely the length of the measuring rod, and clock time used by an observer in a relatively moving frame. This allowed him to assign a fixed velocity of light c=contracting space / dilating time. Einstein’s arbitrary postulates imposed an elegant abstract unity in the laws of physics, which then become independent of frames of reference, but at the cost of a loss of physical realism. This does not belittles his lasting contribution in (SR) 8 : that electromagnetic radiation with a maximum velocity of c has a fundamental role in defining space and time. FIG. 24 compares the concept of
(SR) with its multiple moving frames of reference, to a realistic frameless universe where meaningful physical events only occur locally at the smallest scale possible.
FIG. 24. Special and General Relativity describe the motion of bodies with a separate frame of reference for each moving object. Within each object a spacetime grid is distorted differently according to its motion (arrows). Beautiful Universe Theory describe such motions within a regular fixed lattice geometry made up of nodes of varying energy and orientation exchanging momentum locally, simplifying the description.
(BU) the results of (SR), but not its premises, can be adapted
from any of the many and various available classical derivations
Lorentz transformations, the earliest being Heaviside’s55 analysis of how a sphere of charges contracts in the direction of
become an ellipsoid (FIG. 25). Of course it is not the individual
themselves that change shape, but the energy pattern they define in the
lattice. LaFreniere explains length contraction in classical fields as a consequence of
shift in electron spherical standing waves making up matter.
FIG. 25. The Heaviside Ellipsoid. A spherical arrangement of charges will contract in the direction of its motion to become an ellipsoid. In (BU) this will be the simple consequence of a Doppler shift in the de Broglie electron standing waves making up an atom.
Heaviside concluded that a charge moving at a velocity v is equivalent to an electric field following the form:
where E is evaluated at a point with displacement r from the center of the charge distribution and q is the angle between r and the direction of motion. The length contraction in (BU), however, is a combination of a ‘real’ contraction combined with the effects of a contraction due to measurement from an outside frame. Because of Heaviside contraction, the number of nodes the matter spans lengthwise during its motion is smaller than those when it is stationary. An outside observer then attempt to measure this length of a moving body for example by sending light signals to mirrors attached to the front and the back of the body, and comparing the signal arrival times. Because of a Doppler shift in these signals, the frequency increases, and this is equivalent to a time dilation. In (BU) it is these physical effects of length contraction due to the compression at impact, multiplied by the dilation in the timing factor that should explain the (SR) length contraction.
Similar ‘physical’ arguments about the gain of mass of a moving body can be made in (BU): it is just the momentum added to its internal energy upon impact that affects this increase. Using the classical Lorentzian transformations featuring, the mass, length and measured clock time of a body ‘moving’ at a velocity v= cs= c0 /n can be derived in (BU). The body’s energy pattern is transmitted across the lattice at a velocity v. And as we have seen, is a fundamental property of node, its potential energy or ‘density’, whether the node is found within matter, in a radiation field, or in empty space.
useful way to analyze the (SR) transformations in (BU) is
the following. The cores of atoms are an assemblage of locked nuclear
size is insignificant, as compared to the overall size of the atom’s
shells, defined by the electrons oscillating in standing de Broglie
inelastic force impinges on
momentum is added to it, which travels like a wave from node to node.
standing waves making up the shells are compressed into Heaviside
and the energy pattern is transferred within the object in this
until the force’s momentum is expended. This can be
developed into a
formalism whereby a force F of nodes with forward momentum first causes
contraction of the stationary object it collides with. Then, after the
stationary object contracts, it moves forward with a velocity v. This
ideas of force and motion with the Lorentz transformation of length.
effects appear in the abstract formulation of (SR) because length
actually occurs in nature, as explained in (FIG. 26). Similarly the
of time dilation is explained as an actual delay in the time of arrival
light signals used by an outside observer, in the act of measuring the
once the body starts to move.
FIG. 26. Force, Momentum, Motion and Lorentz transformations. At time to momentum arrives as a force F on a molecule made up of four atoms of length Lo (circles, at bottom). The momentum is absorbed and two of the atoms are contracted into Heaviside ellipsoids (middle). By time t1 all the momentum has been absorbed by three atoms (top). The Lorentz contraction is Ls and the final length of the molecule is Lv. At time t2 the entire contracted molecule starts its motion at a velocity V. Anytime after t2 an outside observer from a fixed point O attempts to measure the length of the molecule by sending light beams (dashed lines) to attached mirrors. The Doppler-shifted times of arrival of the light are equivalent to a time dilation, and the estimate of length Lv is further contracted.
2.5 THE HAMILTONIAN ANALOGY, (GR),
AND SCHRÖDINGER’S EQUATIONS IN
The second unique contribution of Einstein in relativity theory was his discovery of the equivalence of gravity with acceleration, a result admired by Lorentz himself. Again Einstein used the concept of flexible spacetime to describe the resulting deformations, using complicated tensor mathematics. Eddington, who proved (GR) experimentally by measuring the predicted deviation of starlight by the sun’s gravity, hinted that GR could be explained in simple classical terms: Eddington argued that gravity affect the density of space, causing its index of refraction (n) to increase and what he called the ‘coordinate velocity’ of light to slow down.
In the (BU) model the strength of the gravitational field is described by nxyz the local relative ‘density’ of the nodes. As (n) changes from node to node, the velocity of signals there changes- i.e. signals accelerate as (n) changes. In this way (BU) provides a physical explanation for the famous equivalence of gravity with acceleration in GR. A description of signals in such a field of variable n reduces to the Hamiltonian Analogy, an enduring idea mentioned by Ibn Al-Haytham (Hazen) in the 10th Century, that the path of a particle in a potential field resembles that of a ray of light traveling in a medium of variable index of refraction (FIG. 27). The Analogy was systematically developed in the 18th Century by Hamilton, who posited that a particle’s energy is always constant made up of variable potential and kinetic energy
(17) E = P.E. + K.E
an equation known as the Hamiltonian. In (BU) P.E. is the node’s internal energy, its spin, while its K.E. is its forward momentum, i.e. how it affects its immediate environment. In optics the eikonal equation relates (n) to the potential:
FIG. 27. The Hamiltonian Analogy in (BU). Variable potential energy (indicated by the shades of the nodes) implies that volumes of space transmit node-to-node signals at different velocities and will have different indices of refraction (n). The laws of geometrical optics then apply to both radiation streamlines (S) and the paths of moving particles (P). Along these paths the transmitted energy is constant, equaling the potential energy plus the kinetic energy at any given point. (a) Snell’s law applies to a geodesic crossing an interface between a field of energetic (i.e. dense) nodes of index of refraction n1 to one with n2<n1. (b) A dipole field has a radial distribution of n causing streamlines S to curve in circular paths. A particle crossing this field curves accordingly. (c) A Schwarzschild metric for the gravity of a particle at the center, is interpreted in (BU) in terms of local density variations without invoking spacetime distortions. The curvature of a geodesic (P) for a particle is similar to the bending of light passing through the dense gravitational field of a star.
In electromagnetic fields the paths along which the energy is transmitted (normal to the equipotential surfaces) are the streamlines S. According to (GR) test particles in a potential field always travel along straight-line geodesics in a curved spacetime. In classical physics and in (BU), and in accordance with the Hamiltonian Analogy, an inhomogeneous gravitational potential causes light and test particles to accelerate along curved streamlines S in ‘straight’ space and time coordinates. This agrees with Euler’s result relating acceleration a=dv/dt with a change in curvature, d/dt . Accelaration can also be expressed as in Eq. 19 .
Using a result from optics, the curvature k can also be expressed in terms of the index of refraction n
(20) k= n grad log n
Where n is the unit normal to the equipotential (ie tangent to the streamline S orthogonal to it) at a point in the field. The description above should yield the same results as (GR), except that in (BU) the physical situation would be much simpler, merely requiring an iterative incremental linear solution of Snell’s law for the deflection of light in adjacent media of different indices of refraction. This was demonstrated by Tamari for a simple dipole field. These effects are linear in (BU), and can be applied numerically to any configuration of matter, however complex its shape, inhomogeneities in its composition, or a mixed pattern of motions (linear, rotational, etc.) of its various parts. This is in contrast to (GR) where solutions to Einstein’s complicated tensor equations are only known for a few simple cases such as a sphere.
(BU) also provides a physical explanation of why there is no dipole solution for Einstein’s (GR) equations, while solutions exist for quadrupoles and higher terms: The smallest piece of matter in (BU) is made up of two nodes, each node being a dipole. Two adjacent dipoles make up a quadrupole.
The Hamiltonian operator, which is related to (Eq. 17) is a fundamental part of Schrödinger’s Equation , the basis of (QM), reinforcing the belief that in (BU), (GR) and (QM) can be unified in a single theory. Conversely it should be possible to derive Schrödinger’s equation in (BU) by equating the mass of a particle with the total momentum (in multiples of (h)) of the nodes it is made up of, and considering their mutual interactions as standing spherical waves in the shell of an atom.
Maxwell’s equations can be derived directly in (BU) from the fact that along the streamlines in free space the electric and magnetic effects generated by each node propagate as a sinusoidal wave at a velocity c0/n. along streamlines S. Maxwell’s continuity equation can also be derived directly because the energy transmitted along any given streamline is a constant. A small volume of space which encloses a bundle of such streamlines transmits equal amounts of current in and out of that volume. Maxwell deduced the velocity of electromagnetic radiation c0 from the square root of the permittivity of free space divided by its permeability. In (Eq. 4) the vacuum node’s spin in units of (h) decides the speed of propagation c0, suggesting a relation between all these quantities.
2.6 NO DUALITY IN (BU): THE PHOTON IS A WAVE PATTERN OF NODES
Using statistical arguments, Einstein showed that light is not a mere wave, but comes in photons as he called energy quanta, multiples of Planck’s constant h. Regrettably Einstein conceived of the photon as a point particle containing all of its energy like a spinning billiard ball, similar to the then recently discovered electron. This single supposition alone is responsible for all the conceptual troubles that have plagued (QM) ever since. Now de-Broglie and Schrödinger had a wave-particle duality to deal with when trying to explain how a particle of mass m can have a wave-like frequency: a wave of what? Born’s introduction of the probability function, avoided the necessity of finding a physically realistic answer to all these new questions. A ‘particle’ such as the photon was assumed to have a probability of being anywhere until it was detected, when it ‘collapsed’ in one position only. Quantum weirdness was born.
The Compton Effect has been widely interpreted as experimental proof that the photon can act like a particle. Recent work however shows that a wave interpretation is equally valid . In (BU) the reason for the particle-wave duality becomes clear: The photon starts out with the ordered release of energy from all the nodes making up electrons surrounding the nucleus, creating a pattern of energy transfer that has both forward and radial momentum. It spreads thereafter from node to node as an electromagnetic wave-like pattern. The photon is always a wave pattern made up of particle-like nodes. There is no need to puzzle over an elusive duality that shows up according to how the photon is observed.
2.7 (BU) EXPLAINS QUANTUM PROBABILITY AND THE UNCERTAINTY RELATIONS
has shown that a classical dipole’s far- field spreads as a bow-wave
contains both forward and radial momentum from which the basic elements
and GR can be derived directly and simply (FIG.28).
FIG. 28 The static and time- harmonic Electric field component parallel to the dipole’s z axis on any line -AA normal to that axis follows the form of a Gaussian probability distribution, providing a physical interpretation of the quantum probability wave function. The value for j was chosen to fit the probability curve to Ez of the field of a simple dipole, for z=B=100.
components of the electric field of any cross-section
of the dipole field normal to the dipole axis closely resemble a normal
distribution, i.e. a probability function. Another way to see how the
of node interactions can be studied probabilistically based on an FCC
is shown in (FIG. 29 a.) Each node transfers its energy to
the 13 immediately
adjacent nodes in the FCC lattice. Had each node interacted with only
nodes, a binomial probability distribution would have resulted (FIG. 29
13 nodes in each branch of the tree the normal distribution is reached
as the energy spreads in the lattice.
FIG. 29 Diffusion of energy between nodes creates a normal distribution resembling probability. (a) In an actual 3 Dimensional FCC lattice momentum arriving at a given node A is transferred to nine neighboring nodes. (b) In a 2-D lattice the energy from A is transferred as a binomial distribution, so that the energy levels of the top row of nodes lie on a probabilistic normal curve P.
Heisenberg used diffraction blurring the image in a microscope as an example of his uncertainty relations.10 In Tamari’s united dipole paper22 the uncertainty relations, for example between momentum direction and position, emerge from this physical dipole model simply and naturally: the photon wave starts out from a single node but can diffract in all directions (albeit at discrete angles which get finer as the wave spreads far in the network). Far away from the source, the photon is now a wave of energy spread over a wide area, but with the node orientation concentrated mostly in the forward direction (FIG. 30).
FIG. 30. Heisenberg’s Uncertainty Relations are a direct consequence of the geometry of a diffracting, i.e. an expanding dipole wave. The momentum range is indirectly proportional to the width of the wave x measured either along a streamline S or an equipotential surface of the field. A (BU) node rotating through pi in one second, by definition, is half a unit of action (h).
This model adapts itself easily in (BU), but instead of a single dipole with a classical wave spreading in vacuum, the bow wave radiates via a field of other dipoles.
It now becomes possible to think that the wave function solutions of Schrödinger’s equation 9describe the angular momentum pattern of nodes oscillating in a standing-wave pattern. This is something that has yet to be proved rigorously, but is made plausible because this wave equation contains the constant (h), which in (BU) is the unit of angular momentum for each node. On the other hand, the infinite number of plane-wave Fourier components making up Heisenberg’s matrices now has a physical explanation from the lattice geometry of (BU): Considering the lattice packing as a crystal, a straight lines radiating from a node A to B can have a plane orthogonal to it containing a number of nodes. The orientation of each of these planes can be adapted from its Miller index, a convention used to define facet angles in crystals. The infinity of such lines that can radiate from A, each at a unique orientation constitutes the plane wave components of the matrix (FIG. 31).
FIG. 31. Heisenberg’s matrices have been interpreted as the infinite plane waves of the Fourier components of a wave. A 2D (a) and 3D (b), (c) interpretation of this concept in (BU) theory. The planes are considered as crystal-like facets, i.e. planes intercepting the lattice at different angles . These planes are defined by their Miller indices which are the intercepts of the plane on the x, y, and z coordinates .
2.8 QUANTUM ENTANGLEMENT IS LOCAL AND CAUSAL IN (BU)
In (BU) the photon is a wave-like pattern of energy states within the fixed nodes of the lattice, and not a point particle, making it unnecessary to use imaginary ‘probability waves’. Of course there are genuinely random physical processes in nature, for example in the timing, phase or polarization involved in the emission and absorption of incoherent photons. These are the end result of complex and chaotic interactions which are in themselves linear, local and causal.
In (BU) a causal, local and physically realistic explanation of quantum effects banishes the whole range of conceptual mysteries, weirdness or magic that have plagued (QM) for most of the past century. From the point of view of (BU) theory, Einstein and his colleagues posed the wrong challenge to (QM) in their ‘EPR Paradox’ paper: The authors questioned how mutually random spins of the entangled pair of electrons arriving at distant locations, can have any correlation between them outside the light cone allowed by (SR), assuming that only local interactions are possible. Bell’s Theorem and Clauser’s experiments, using photon polarization as a variable, successfully challenged this view: there is a correlation although there were no signals exchanged between the distant photons prior to or after their alleged ‘collapse’ when they were sensed. What should have been questioned in the EPR paper instead was the (QM) notion that an electron’s spin (or a photon’s polarization) direction is inherently random in all possible circumstances.
In (BU) all of these suppositions reduce to this simple scenario: the two photons emitted by the same atom start out in opposite directions having identical polarization, which is retained intact when they arrive at the sensors at their respective distant locations. They are entangled because they are identical from start to finish. Their polarization states are faithfully transmitted from node to node across the network, and when the sensor data is compared, of course their polarization states are highly correlated. There is no need to conjure either ‘spooky’ instantaneous action-at-a-distance or hidden variables to explain what is happening. All the interactions are causal and local, as is everything else in (BU). There is no need to appeal to scenarios involving backwards travel in time, multiple universes, or mental processes in the mind of the observer to explain why the photon ‘chooses’ one path or the other.
Something quite similar is involved when trying to explain the double-slit interference experiments. Again, the photons and particles involved are not imbued with a supernatural sense that can tell if the other photon or particle has passed through a particular slit or not. In (BU) either one of two scenarios applies: In the case of radiation, the wave always passes through both slits at once and different parts of the wave front interfere with each other, just as in a water-ripple experiment. This explains how faint-light single-photons produce this interference effect, although in the sensing screen individual atoms with random states accumulate the radiation randomly until a quanta is absorbed, giving the impression of point-like photons arriving there to make up the pattern. Dirac’s maxim that ‘a photon interferes only with itself’ has a clear physical explanation in the context of (BU).
Double-slit interference experiments involving particles such as electrons or protons require another explanation: the particle has an electrostatic or gravitational field, it is speculated that in (BU) the particle passes through one slit, while it’s accompanying gravitational or electrostatic waves pass through the other slit. The particle arrives at the sensor and interferes with its own field arriving there at the same time (FIG. 32).
FIG 32. Double-slit
radiation and particles in (BU). (a) A plane wave-front approaches the
and passes simultaneously from the two slits, interfering at the sensor
top. (b) A particle passes through the slit to the right while
gravitational waves diffracts through the other slit. The particle and
gravity interfere at the sensor.
REFERENCES FOR THIS SECTION
 Witten, E. Quantum Field Theory and the Jones Polynomial. In Communications in Math. Physics. 121,No.3 pp.351-399 (1989).
Drezet, A.The physical origin of the Fresnel drag of light by a moving dielectric medium, http://tw.arxiv.org/PS_cache/physics/pdf/0506/0506004.pdf
 Miller indices are explained at: http://scienceworld.wolfram.com/chemistry/MillerIndex.html
 Balakrishnan, V. K. Introductory Discrete Mathematics. New York: Dover, 1997.
 Benedetto, J. and Ferreira, P. eds, Modern Sampling Theory. Birkhauser Boston 2001
 Feynman, R. P. 1948. Spacetime Approach to Non-relativistic Quantum Mechanics. Rev. Mod. Phys. 20 pp. 367-387
 Cantor, G. et al, eds. Conceptions of Ether, Cambridge Univ. Press (1981)
 Descartes, R. Principia Philosophiae (1644).
 Cantor, G., Was Thomas Young a Wave Theorist? American Journal of Physics, (1984) 52, Issue 4 305-308
 Faraday, M. A speculation touching Electric Conduction and the nature of Mater, 1844 Royal Institution, London
 Maxwell, J.C., The Scientific Papers of James Clerk Maxwell (Ed. W.D. Niven, 1890) were reprinted by Dover Publications in 1965.
 A. A. Michelson and E.W. Morley, Philos. Mag. S.5, 24 (151), 449-463 (1887)
 Thompson, W. T. On Vortex Atoms. Philos. Mag. 34, 15-24, 1867.
 Baez, J. Gauge Fields, Knots and Gravity (World Scientific 1994
 Einstein, A. in an an address delivered on May 5th, 1920, in the University of Leyden.
 Dirac, P. A. M., Scientific Monthly, March 1954
 Appelquist, T., Chodos, A., Peter, G. Freund, O., Modern Kaluza-Klein Theories, Addison-Wesley (New York), 1987.
 O. Heaviside (1888), ‘The electro-magnetic effects of a moving charge’, Electrician 22,147–148.
 Lorentz, H. The Theory of Electrons (1915) 2nd ed. Reprinted Dover N.Y. 1952
 De Broglie, L. Recherches sur la théorie des quanta (Researches on the quantum theory), Thesis Paris, 1924.
 Eddington, Arthur Space Time and Gravitation, Camb. Univ. Press 1920, pp. 107-109
 Born,M. and Wolf, E. Principles of Optics (6th Ed.) pp. 738-746 Pergamon Press Oxford, 1980
 Ronchi, V. 1983 Storia della luce (Roma-Bari Laterza) pp46-56
 Hamilton, W. Theory of A System of Rays, Transactions of the Royal Irish Academy, vol. 15 (1828), pp. 69-174.
 Ambrosini, D., et al, Bouncing Light Beams and the Hamiltonian Analogy Eur. Journal of Physics. 18 (1997) 284-289
 Born,M. and Wolf, E. Principles of Optics (6th Ed.) pp. 112,133 Pergamon Press Oxford 1980
 Williams, B. G. (Ed.). Compton Scattering New York: McGraw-Hill, 1977.
 Tamari, V. Bow Wave Geometry late contribution sent to the Conference "Huygens' Principle 1690-1990: Theory and Applications" Scheveningen, The Hague, The Netherlands. November 1990. http://home.att.ne.jp/zeta/tamari/Bow%20Wave%20Geometry.htm
 Heisenberg Op.cit Ref. 10 , p.109,ff.
 Wood, E. Crystals and Light, Dover, NY, (1977). p. 30,ff.
 A. Einstein, B. Podolsky, and N. Rosen, Can Quantum-mechanical Description of
Physical Reality be Considered Complete?, Phys. Rev. 47, 777-80 (1935).
 Bell, On The Einstein-Podolsky-Rosen paradox Physics 1 pp195-200. 1964
 J.F. Clauser, Experimental Investigation of a Polarization Correlation Anomaly,
Phys. Rev. Lett. 6, 1223-6 (1976).
 Colin, B. Schrodinger’s rabbits Academic Press 2004
 Pinch, T. The Hidden Variable Controversy in Quantum Physics. Physics Education 14 1979 48-52
 Deutsch, D. The Fabric of Reality, Penguin Press 1997
 Rae, A. Quantum Physics: Illusion or Reality? Cambridge 1986
 Taylor, G. 1909 Interference fringes with feeble light Proceedings of the Cambridge Philosophical Society 15 114-115
 Dirac, P. Quantum Mechanics, 9 (Oxford) 1930 .