Scalars, Part I
Eldon A. Byrd

 PART I DEALS with the historical background (beginning in 1900 with the discovery of inconsistencies between deductions and experimental data concerning Planck's constant) leading to the concepts supporting scalars as information carriers. A brief review of the development of Einstein's space-time continuum, the nature of reality, classical mechanics, fields and waves, quantum mechanics, and the general and special theories of relativity set the stage for the emergence of scalars as a form of information transfer. In the process, some of what physics is, and is not, is clarified.

Part II [to appear in the next issue of this Journal] provides the equations linking vector mechanics with scalars and concludes with how scalars can act as information carriers at infinite velocity.

Introduction

One of the purposes of science is to provide order from the chaos of our sense-experience. This is very difficult because the same brain that experiences the chaos has to make up theories that try to make sense. Physics, in particular, is (and always has been) in a state of evolution. Its basis cannot be distilled from experience by inductive methods and its truth content can only be verified by human consciousness.

In 1927 the physical universe was described by Arthur Webster as consisting only of x, y, z, and time. Underlying this description were a myriad of philosophical assumptions.¹ Thus, the foundation of mathematical physics is philosophical in nature.

Science is concerned with the analysis of parts—assumed to be independent of the whole. Recent advances in science refute this assumption. We are coming back to Newtonian "action at a distance" ideas, but from a different and more sophisticated point of view. Interconnectedness now appears to be a more viable viewpoint than ever before. However, interconnective forces seem to be subtle and not subject to measurement by conventional devices and techniques. Bohm² called the interconnective force the "quantum potential."

Space-Time

Einstein³ so completely connected space and time in our "physical" universe that the concepts of action at a distance, potential energy, and simultaneity were destroyed. This was compatible with Maxwell's equations, but not with classical mechanics.

However, in another view, the Pauli Exclusion Principle squeezes an infinity of space-time out of a single point creating a variance of virtual states; whereas Maxwell's equations stem from squeezing an infinity of space-time into a point. We can imagine that we live in a sea of virtual (i.e., unobservable) particles of energy. These energy states may be stimulated by "real" energy to the point of "kicking" virtual particles from negative to positive energy states, making the particles "real." The Dirac equation predicts this and describes the "Dirac Sea" of virtual particles. The Dirac Sea is the matrix of space-time itself.

The Nature of Reality

Science is based on the concept that an external world exists independent of the perceiving subject. Thus, "reality" is based on speculation; or at least is reduced to indirect observation. Therefore, we must be willing to alter our perception of reality.³ The father of real science was not Euclid—or anyone else before Galileo. Pure logical thinking cannot yield any knowledge of the empirical world; all knowledge of reality starts and ends with experience. Together, however, they form a more complete system than either separately.

I propose (as have others) a new paradigm for science: "Physical reality" cannot be described at all in terms of mathematics dealing with the physical because there is no "objective reality." If we start with the premise that there are only fields and that fields generate what we perceive as physical reality—not the other way around—a whole new way of dealing with so-called "reality" will emerge. The balance of this paper deals with this concept, demonstrating why the idea that "matter" creates field does not work as well as the idea that field creates "matter."

Classical Mechanics

Over the past 75 years, it has become apparent that classical mechanics cannot describe our experience with the physical universe. Max Planck dethroned classical physics by showing that quantum mechanics applies to small masses at slow speeds but high acceleration; thereby overcoming the limiting laws of Newtonian physics.

In 1900 it was discovered that there were inconsistencies between deductions from mechanics and experimental facts concerning Planck's constant (ħ). The theory dictated that heat and radiation density of solids would decrease proportionally to decreasing temperature; experience revealed a much more rapid decrease than predicted. No causal laws could be determined before quantum mechanics. Heisenberg, Dirac, de Broglie, and Schrodinger showed that discrete frequencies must be assigned to the energy values.

H. Schrodinger developed a partial differential equation relating a complex scalar to position and time in a discrete way. This led to the theory of the atom and explained why gases radiate and absorb only light of sharply defined frequencies. Thus, quantum physics was born.

Fields and Waves

At first, a mechanical interpretation of a medium (motion or stress of the ether) was advanced in an attempt to explain "field." This gave way to the electromagnetic field as a final irreducible constituent of physical reality. Force was replaced by field (as described by differential equations). Only the field was allowed to interact. Hertz relegated the ether to obscurity of claiming that the concept of field was fundamental and required no mechanical propagation medium.³ However, this required the introduction of two new vectors connected by relations dependent on the nature of the medium—therefore, inaccessible to theoretical analysis. The vectors added complexity to the concept of magnetic field and the relationship between electric current density and field. Lorentz simplified things for electrodynamics by considering the case where fields are the results of particles in motion. This profoundly transformed physics because waves were no longer tied to the ether; they were the result of other factors and were independent of a medium for their existence. Freeing the electromagnetic field from a material substratum paved the way for the idea of force without matter. At this point no one believed in immediate action at a distance—not even gravity effects. It was assumed that if electromagnetic waves propagated with a finite velocity, then so did electrostatic fields.

De Broglie conceived the idea of standing waves, using Planck's constant. However, Born discovered that de Broglie-Schrodinger wave fields were not mathematical descriptions of how an event actually takes place in time and space, but of what we can know about the system. These wave fields make only statistical statements and predictions of the results of all possible measurements. This introduced quantum mechanics into the "real" world.

According to Einstein,³ space-time has an existence independent of matter or field; however, there is no such thing as "empty" space—space without field. Space-time does not exist on its own, but is a structural quality of the field. There is no such thing as "nothing." The field is the representation of reality. As Descartes put it, "There exists no space empty of field."³

Current field laws have meaning only in regard to inertial systems. Remove matter and field, and inertia and time remain. The Minkowski-space is a carrier of matter and field.³ There is no "now" in Minkowski space.

Consider the possibility of replacing "matter" with "field." A dynamic field with areas of low energy density and areas of high energy density—always in a state of flux and manifesting itself in various ways, subject to local organization, having the property of interaction with itself, etc.—can explain most of the questions science has been pondering for centuries. What would be the relationship of the field to "condensed energy" (matter)? An electron is supposed to be an electrically charged particle; so is a proton. If this is true, where are the magnetic masses? Absurdity has run rampant in physics for decades. The "duality" of waves and particles represents the lengths to which physics has gone to in order to "explain" things.

No one believed Maxwell until Hertz demonstrated waves.³ Later, however, it was noted that Maxwell's equations do not allow for their solutions to avoid the inherent singularities that keep them from explaining the total electromagnetic inertia of particles. There are no regular solutions to Maxwell's equations that do not contain singularities—points or spaces where there are no solutions to the equations. Thus, a pure electromagnetic field theory of matter has never been attained. Einstein pointed this out emphatically with the generalized field equation:

R_ik – 1/2(g_ikR) = -T_ik

where R = the scalar of the Riemannian curvature, and T_ik = the energy tensor of matter.

Taking the divergence of both sides:

div [R_ik - l/2(g_ikR)] = 0 = div (-T_ik) = equations of motion of matter in the form of partial differential equations.

Field theory fails in the molecular sphere. Quantum mechanics does not relate to any semblance of reality; physics has been relegated to a game of chance. The possession of the truth has been replaced by the search for it.

Quantum Mechanics

Experiments have shown that it is possible to transition a system from one quantum state to another with external forces consisting of small time-varying additions to the potential energy. The non-linearity and probabalistic nature of this process allows for changes of any magnitude as a function of probability. Hence, Schrodinger proved that Uri Geller can exist.

In spite of the expansion of understanding of physical events quantum mechanics provided over classical mechanics, it is still an incomplete representation of "reality" because it is built out of force and material points. Quantum mechanics does not describe in any way the state of a single function, but rather, an ensemble of systems (in a statistical sense). The results are not measurable and therefore, by definition, are outside the realm of "science"—because science requires measurement. Note that the statistical methods of quantum mechanics cannot be applied to fields! Today's physics is not about the nature of reality, but concerned with possibilities. Therefore, there is not now, and never has been, any sound general theoretical basis for physics, because of the apparent uncertainty of everything.

Links

Capsulizing the sequence of progression in physics:

Maxwell changed the notion of physical reality from material points in motion (described by total differential equations) to continuous fields (described by partial differential equations). Quantum mechanics went a step further and stated that, indeed, we cannot describe reality in terms of absolute differential equations of any kind, but rather, in terms of the probability of the occurrence of a physical reality.

It is only out of ignorance that some still believe that the laws of physics are somehow tied to the structure of the atom and others still believe that the mechanics of a system are determined by potential energy that is a function of its configuration. Arbitrary rules give rise to arbitrary results. Newtonian physics fails utterly to provide a foundation for physics, yet it still occupies a central position in our thinking. Why? Because there is no foundation that is, as yet, complete.

Theory does not come inductively from experience. Logical thinking is deductive, and it is rash to think that a confirmation of consequences would spring from it. The dilemma is that no inductive method of thinking can lead to the fundamental concepts of physics (or of anything else). Only a combination can provide the synergy necessary; experiences suggest theory and vice versa. A new approach should be based on the notion that field gives rise to matter, not the other way around.

General and Special Theories of Relativity

The General Theory of Relativity is concerned mainly with gravitational fields and cannot predict either the existence or the structure of any other field—including the electromagnetic (EM) field. The "giants" (Weyl, Kaluza, and Eddington) failed to extend the theory to EM fields.³ According to the theory, space is a continuous field composed of four independent variables—space and time-without particles, or material points, or motion. Both the General and Special Theories of Relativity assume no instantaneous action at a distance; however, the Special Theory does not exclude massless information transfer. It is from this concept the notion of scalars as information carriers emerges.

References

1. Webster, Arthur. Partial Differential Equations of Mathematical Physics, 1955: Dover Publications.

2. Bohm, D. J. and Hiley, B. J. "On the Intuitive Understanding of Nonlocality as Implied by Quantum Theory," 1975: Foundations of Physics, 5, p. 93.

3. Einstein, A. Ideas and Opinions, 1954: Bonanza Books.

Scalars, Part II
by Eldon Byrd

 Not only are Maxwell's equations shown to be incomplete, they are shown to be inadequate to describe scalar information transfer in either the steady state or non-steady state cases, even though both cases can be written as scalars. The characteristics of scalars are explored, and tables of definitions and relationships of electromagnetic quantities are compiled. The contrast between scalars and vectors is elucidated, and examples are given.

It is concluded that although the space-time matrix limits the physical world, the mind is scalar in nature and, as such, is not bounded.

Introduction

Scalars as information carriers are allowed in mathematical physics much in the same way that ideas are: Ideas cannot be measured, but their effects can.

Electric fields exert a force on stationary as well as moving charges. However, magnetic fields exert a force only on a moving charge (because a magnetic field can be produced by moving charges but not by static charges, whereas an electric field can be produced by either). One big problem: Magnetic quantities were defined in electrical terms. The source of electrical flux is the coulomb charge. No such source for magnetic flux is known or defined (SiUitto).

The following is an attempt to define scalars from the viewpoint of established math and physics. Because current math and physics are inadequate for the task, I suggest that the next step should be to develop an entirely new set of physics and math to explain scalars, independent of what currently exists.

Maxwell's Equations

Maxwell's equations do not describe the behavior of electrical densities, they describe only the effects of a combination of electrical densities on a continuous field with material points that are discontinuous in space. This indicates the incompleteness of the theory; a complete theory requires the continuity of all elements in time and all points in space. In order to deal with this problem from a mechanistic point of view under the assumption that matter causes field, great complexity is added and paradoxes emerge. For example. Maxwell's equations in free space are only useful for the case of real electromagnetic (EM) energy propagation (they ignore the complex conjugate). They cannot describe instantaneous scalar information transfer in space-time because they predict an infinite amount of energy to do so. It takes no EM energy to accomplish a scalar information transfer, as becomes apparent with a shift in thinking to the concept that field gives rise to "matter."

In a non-steady state condition. Maxwell's equations are all scalars. Then, in textbooks, boundary conditions are imposed and the solutions become non-wave solutions. In order to make them work as waves an unknown factor was added to the equations to get them to come out right. Scientists will go to great lengths to prove the universe works the way they think it does, whether they can figure it out or not.

Maxwell's first equation was developed by assuming a charge, Q, was contained in a volume and a flux was passing through the volume's surface:

The electric flux coming out of the surface (S), integrated over the entire surface of the volume was defined to be equal to the charge inside:

However, this says that the flux is infinite for a finite volume, because there are an infinite number of flux lines emanating from the charge. The only way around this was to shrink the surface and volume to zero, and set the result equal to zero. Terrific! Now our physical interpretation of Maxwell's first equation is that the only place in the universe where there is a finite amount of electrical charge is where there is no space!

There is nothing wrong with the non-steady state integral form of Maxwell's equations—it is the absurd boundary conditions that were imposed that make them useless for all practical purposes when discussing scalars. However, the preceding equation and:

are all scalars. They are the non-steady-state form of Maxwell's equations.

Characteristics of Scalars

Electromagnetic fields were theorized "125 years ago and discovered a few years later. Potential fields were theorized 50 years ago and discovered only a few years ago. Scalar fields have been theorized, and recently there is reason to believe their interaction with a laser beam and living human neuronal tissue has been discovered.

Scalars are more fundamental than potential fields because they are derived from them, just as potential fields are derived from electromagnetic fields. Scalar fields replace potential fields when E and B are zero. Scalars are longitudinal in nature; they are derived from potential fields capable of supporting longitudinal signals in the total absence of electric and magnetic fields.

Longitudinal waves have been observed in physical non-linear conducting media, such as plasmas.

Because "propagation" of scalars is independent of the two physical quantities electric permitivity and magnetic permeability (which are linked with the speed of light), scalar information is not limited to the speed of light. Scalar potential is an instantaneous potential, although scalar information can ride piggy-back on EM waves, thus slowing it down from infinity to 3xl0⁸ cm/sec. Thus, it is possible that we live in a universe filled with information fields operating at all frequencies; subtle fields not yet detected by instrumentation; fields that link all life forms. These fields were described by the great mathematician, Dirac.

The superposition of two scalar fields can only yield more scalar fields, not EM or potential fields. Therefore, scalars cannot be used for power transmission—only information transfer. Information may be transmitted using scalar fields and detected by some process like electron interferometry. Biological systems are highly non-linear and also can detect and interact with scalars. Because all "matter" is electromagnetic phenomena, there is an interconnectedness through the scalar fields. All biological organisms communicate with each other, and therefore affect each other.

It is obvious that electrical energy can be stored in a capacitor (anyone who has touched the terminals of a large charged capacitor can attest to this fact). Yet, where is the energy stored? In the "charges" themselves? On the plates? In the dielectric? Or in the field between the plates? EM field theory makes it look as if it is in the field, but no one knows for sure. If it is in the field, where in the field? Scalar energy just is; it isn't anywhere.

When Magnetic and Electrical Fields are Zero

David Bohm in England described m 1975 a subtle effect when both E and B fields were non-existent. When the fields are zero, there are no physical results observed because there is no physical energy flow. However, when E and B fields are zero, under certain conditions, their sources (the scalar potential, V_m, and the magnetic vector potential, A) can produce physical consequences. The observable is the probability density of electron phase shifts occurring under the influence of potential fields while no magnetic or electrical forces exist. This effect has been demonstrated by a number of experiments (Aharonov, Bohm, Chambers, Jaklevic, Lanke, Olariu, and Popescu). Because there is no energy transfer to objects when the electric and magnetic fields are zero, A fields are decoupled from E and B and become scalars which penetrate all objects and also transfer information instantaneously. This makes detecting them with currently available instrumentation virtually impossible. However, generating a scalar field is simple. At extremely low frequencies, all B and E fields are contained within a toroid:

A is external but not directly measurable. In a mobius, the E and B and A fields are contained; however, a scalar as a function of time varying A is generated (not directly measurable by standard electric and magnetic equipment—all of which requires a transfer of energy to register).

Vector Math

Vector math has been defined and manipulated by college professors and students for a long time. Any good textbook can provide details; however, for purposes of the next section a few relationships will be reiterated.

A vector is defined as a scalar that is moving in time and/or space. A vector of zero order is a point with a direction. Vectors can be added, subtracted, multiplied, divided, and operated upon. Operations on vectors are of particular interest. Vectors that are invariant under coordinate transformations are called tensors.

The divergence (div) of a vector. A, is:

The divergence operation on a vector yields a scalar and is known as the del () operation. Thus, •A = div A. This operation is also known as the gradient (grad). Thus,

•A = div A = grad A

The gradient of a scalar is a vector; the gradient of a vector is a scalar.

There are basically two types of vector multiplication—the dot and the cross product. The dot (scalar) product is defined as the magnitude of A times the magnitude of B times the cosine of the smaller angle between A and B (i.e., |A| |B| cos<_AB = A • B = a scalar).

The cross product is defined as the magnitude of A times the magnitude of B times the sine of the smaller angle between them times the unit vector, a_n, perpendicular to A and B:

A x B = |A| |B| sin<_ABa_n

There are many combinations of scalar and vector products; e.g.: 

•A x B.

² x A is a scalar/ where A is any vector field.

² = 0 satisfies every field and provides unique solutions as a function of boundary conditions we make up/ so it is useless for scalar considerations.

Vector and Scalar Math Applied to Electromagnetics

When a scalar (•A) is integrated over a three-dimensional space, it becomes a two-dimensional surface:

                    represents the flux.

Scalars are invariant in any coordinate system. Converting the steady state Maxwell equations into scalars is easy. Take the divergence of each: 

• x E = 0        

• x H = 0         

••D = • ρ = 0

••B = 0            

 Math and physics are satisfied, everything equals 0, and we have again proven we know a whole lot about nothing.

 B = μH =  x A and •  E = ρ

B and H are linked with μ, and E and ρ are linked with , μ and  are defined by a linkage to the speed of light. Therefore, all the manipulation in the world will not allow these physical quantities (and therefore Maxwell's equations) to describe instantaneous scalar information transfer.

Conclusions

This paper has shown that the foundations of mathematical physics, as applied to the classical and quantum mechanical basis of electromagnetic field theory, fail to account for an entire area of theoretically available signals termed "information scalars." For example, suppose a molecular structure possesses an inherent field quality that "broadcasts" its presence to all the universe. The "information" about the structure is omnipresent—there is no electromagnetic energy transfer associated with this process, and time does not even enter into it.

Cause and effect have been established between scalars and biological processes empirically. It behooves us to come up with math and physics to explain what's going on; it has to be outside of established math and physics, which has failed to provide a complete basis for observation, and even a complete basis for its own theoretical self.

Summary

Reality is not based on measurement. Science is; therefore, reality is not based on science. Science is metaphor.

Fields produce "matter."

Newtonian mechanics is incomplete.

Quantum mechanics is incomplete.

Maxwell's equations are incomplete.

Scalars are information.

Particles (including protons, electrons, and sub-atomic particles) are really just fields that manifest themselves to our senses and instruments in such a way that we define them as "matter."

References

The following were used in the preparation of this paper:

Einstein, A., Ideas and Opinions, 1954: Bonanza Books.

Webster, A., Partial Differential Equations of Mathematical Physics, 1955: Dover Publications.

Sillitto, R., Non-Relatiavistic Quantum Mechanics, 1960: Quadrangle Books, Chicago.

Hayt, W., Engineering Electromagnetics, 1958: McGraw Hill

Hawkins,G., Multilinear Analysis for Students in Engineering and Science, 1963: John Wiley and Sons.

Konopinski, E., "What the electromagnetic vector potential describes," May 1978: Am. J. Phys., 46 (5).

Dea, Jack, Private communications. 1987 (U. of Arizona)

Aharonov, Y. and Bohm, D., "Significance of Electromagnetic Potentials in the Quantum Theory," 1959: Phys. Rev., 115, pp. 485-491.

Chambers, R., "Shift of an Electron Interference Pattern by Enclosed Magnetic Flux," 1960: Phys. Rev. Lett., 5, pp. 3-5.

Jaklevic, R., and Lanke, A., and Mercerau, J., "Quantum Interference from a Static Vector Potential in a Field-free Region," 1964: Phys Rev. Lett., 12, pp 274-275.

Olariu, S. and Popescu, I., "The Quantum Effect of Electromagnetic Fluxes," 1985: Rev. Mod. Phys., 57, pp 339-435.

Bohm, D. and Hiley, B., "On the Initiative Understanding of Nonlocality as Implied by Quantum Theory," 1975: Foundations of Physics, 5, p. 93.