# PesWiki.com

## PowerPedia:Scalar field theory

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Scalar waves are There was an error working with the wiki: Code[17]s and associated Zero-point energy (in contrast to "vector energies" which sums to zero). Scalar field theory (SWT) is a set of There was an error working with the wiki: Code[18] in a abstract model which posits that there is a basic There was an error working with the wiki: Code[19].

In conventional fields, the scalar field associates a scalar value, which can be either mathematical in definition, or physical, to every point in space. Scalar fields are often used in physics, for instance to indicate the temperature distribution throughout space, or the air pressure. In mathematics, or more specifically, differential geometry, the set of functions defined on a manifold define the commutative ring of functions. Just as the concept of a scalar in mathematics is identical to the concept of a scalar in physics, so also the scalar field defined in differential geometry is identical to, in the abstract, to the (unquantized) scalar fields of physics.

#### Introduction

A scalar in mathematics is a number as opposed to a vector, function, or other object. It is a quantity having magnitude but not direction. A scalar in physics is a physical quantity that has the same value under any coordinate system. A scalar in computing is an atomic quantity that can hold only one value at a time. a quantity that has magnitude but not direction. This is compared to a vector which is a directed quantity, one with both magnitude and direction an element of a vector space. Scalar waves are hypothetical elektromagnetic Longitudinal waves. It is one of the theories or concepts of Nikola Tesla, Tom Bearden, There was an error working with the wiki: Code[28] and others.

In mathematics and physics, a scalar field associates a scalar value, which can be either mathematical in definition, or physical, to every point in space. Scalar fields are often used in physics, for instance to indicate the temperature distribution throughout space, or the air pressure. In mathematics, or more specifically, differential geometry, the set of functions defined on a manifold define the commutative ring of functions. Just as the concept of a scalar in mathematics is identical to the concept of a scalar in physics, so also the scalar field defined in differential geometry is identical to, in the abstract, to the (unquantized) scalar fields of physics.

#### Mathematics and geometery

In mathematics, the scalar product, also known as the dot product, is a binary operation which takes two vectors over the real numbers R and returns a real-valued scalar quantity. It is the standard inner product of the Euclidean space.

##### Properties

The following properties hold if a, b, and c are spatial vectors and r is a scalar in mathematics. The dot product is commutative:

: {a} \cdot {b} = {b} \cdot {a}.

The dot product is bilinear:

: {a} \cdot (r{b} + {c}) = r({a} \cdot {b}) +({a} \cdot {c}).

The dot product is distributive:

: {a} \cdot ({b} + {c}) = {a} \cdot {b} + {a} \cdot {c}.

When multiplied by a scalar value, dot product satisfies:

: (c_1{a}) \cdot (c_2{b}) = (c_1c_2) ({a} \cdot {b})

(these last two properties follow from the first two). Two non-zero vectors a and b are perpendicular if and only if a · b = 0. If b is a unit vector, then the dot product gives the magnitude of the projection of a in the direction b, with a minus sign if the direction is opposite. Decomposing vectors is often useful for conveniently adding them, e.g. in the calculation of net force in mechanics. Unlike multiplication of ordinary numbers, where if ab = ac, then b always equals c unless a is zero, the dot product does not obey the cancellation law:

If a · b = a · c and a ? 0:

Then we can write: a · (b - c) = 0 by the distributive law and from the previous result above:

If a is perpendicular to (b - c), we can have (b - c) ? 0 and therefore b ? c.

In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra). Note that scalar multiplication is different than scalar product which is an inner product between two vectors.

More specifically, if K is a field and V is a vector space over K, then scalar multiplication is a function from K × V to V. The result of applying this function to c in K and v in V is cv.

Scalar multiplication obeys the following rules:

Left distributivity: (c + d)v = cv + dv

Right distributivity: c(v + w) = cv + cw

Associativity: (cd)v = c(dv)

Multiplying by 1 does not change a vector: 1v = v

Multiplying by 0 gives the null vector: 0v = 0

Multiplying by -1 gives the additive inverse: (-1)v = -v.

Here + is addition either in the field or in the vector space, as appropriate and 0 is the additive identity in either. Juxtaposition indicates either scalar multiplication or the multiplication operation in the field. Scalar multiplication may be viewed as an external binary operation or as an action of the field on the vector space. A geometric interpretation to scalar multiplication is a stretching or shrinking of a vector. As a special case, V may be taken to be K itself and scalar multiplication may then be taken to be simply the multiplication in the field. When V is Kn, then scalar multiplication is defined component-wise. The same idea goes through with no change if K is a commutative ring and V is a module over K. K can even be a rig, but then there is no additive inverse. If K is not commutative, then the only change is that the order of the multiplication may be reversed from what we've written above.

##### Geometric interpretation

In the Euclidean space there is a strong relationship between the dot product and lengths and angles. The geometric properties rely on the basis in linear algebra of vectors being perpendicular and having unit length: either we start with such a basis, or we use an arbitrary basis and define length and angle (including perpendicularity) with the above. As the geometric interpretation shows, the dot product is invariant under isometric changes of the basis: rotations, reflections, and combinations, keeping the origin fixed. In other words, and more generally for any n, the dot product is invariant under a coordinate transformation based on an orthogonal matrix. This corresponds to the following two conditions:

the new basis is again orthonormal (i.e. it is orthonormal expressed in the old one)

the new base vectors have the same length as the old ones (i.e. unit length in terms of the old basis)

#### Conventional physics scalars

In physics, a scalar is a simple physical quantity that does not depend on direction, and therefore does not depend on the choice of a coordinate system. In physics, for a vector a, a·a is the square of its magnitude, and if b is another vector

: {a} \cdot {b} = a \, b \cos \theta \,

where a and b denote the magnitude of a and b, and ? is the angle between them. The magnitude is a scalar of physics in the physical sense, i.e. a physical quantity independent of the coordinate system, expressed as the product in mathematics of a numerical value and a physical unit, not just a number. The dot product is also a scalar in this sense, given by the formula, independent of the coordinate system. The formula in terms of coordinates is evaluated with not just numbers, but numbers times units. Therefore, although it relies on the basis being orthonormal, it does not depend on scaling.

For example, the distance between two points in space is a scalar, as are the mass, charge, and kinetic energy of an object, or the temperature and electric potential at a point inside a medium. On the other hand, the electric field at a point is not a scalar in this sense, since to specify it one must give three real numbers that depend on the coordinate system chosen. The speed of an object is a scalar (e.g. 180 km/h), while its velocity is not (180 km/h north). The gravitational force acting on a particle is not a scalar, but its magnitude is. Another example is the mechanical work is the dot product of force and displacement vector.

A physical quantity is expressed as the product of a numerical value and a physical unit, not just a number. It does not depend on the unit distance (1 km is the same as 1000 m), although the number depends on the unit. Thus distance does not depend on the length of the base vectors of the coordinate system. Also, other changes of the coordinate system may affect the formula for computing the scalar (for example, the Euclidean formula for distance in terms of coordinates relies on the basis being orthonormal), but not the scalar itself. In this sense, physical distance deviates from the definition of metric in not being just a real number however it satisfies all other properties. The same applies for other physical quantities which are not dimensionless.

In the theory of relativity, one considers changes of coordinate systems that trade space for time. As a consequence, several physical quantities that are scalars in "classical" (non-relativistic) physics need to be combined with other quantities and treated as four-dimensional vectors or tensors. For example, the charge density at a point in a medium, which is a scalar in classical physics, must be combined with the local current density (a 3-vector) to comprise a relativistic 4-vector. Similarly, mass density must be combined with momentum density and pressure into the energy tensor. Examples of scalar quantities:

electric charge and charge density (the latter nonrelativistically in relativity it must be combined with current density to comprise a 4-vector)

relativistic distance

mass and mass density (the latter nonrelativistically in relativity it must be made part of the energy tensor in combination with momentum density and pressure)

speed, but not velocity or momentum

temperature

energy and energy density (the latter nonrelativistically)

A related concept is a pseudoscalar, which is invariant under proper rotations but (like a pseudovector) flips sign under improper rotations. One example is the scalar triple product (see vector), and thus the signed volume. Another example is magnetic charge (as it is mathematically defined, regardless of whether it actually exists physically).

##### Scalar potential

In physics, a scalar potential is, mathematically, a scalar field whose negative gradient is a given vector field. If the scalar potential is denoted by the Greek letter ? and the vector field it generates as v, then

The vector field can be a velocity field or a force field. The equation therefore means a movement or acceleration towards the direction in which there will be a decrease of potential. Physically, the scalar potential is similar or identical to potential energy. Any conservative force field can be represented as the negative gradient of some scalar potential. Any lamellar field can be represented as having a scalar potential, but a solenoidal field generally does not have a scalar potential (except the degenerate case when it is Laplacian).

If \vec F is an irrotational vector field (aka conservative, curl-free, or potential) vector field with continuous partial derivatives, the potential of \vec F with respect to a reference point r_0 is defined in terms of a line integral:

:V(r) = - \int _{r_0} ^{r} \vec F \cdot d r'

where r' is a dummy variable of integration. It can be shown that such a scalar field exists for any curl-free vector field. By the Fundamental Theorem of Calculus, we can alternatively define V as the scalar field that satisfies the following condition:

:\vec F = -\nabla V

This does not give a unique definition of V. In terms of definition (1), the ambiguity lies in the choice of the reference point. In terms of definition, V can change by a constant value throughout all space without changing its gradient.

Altitude as gravitational potential energy

An example is the (nearly) uniform There was an error working with the wiki: Code[29] near the Earth's surface. It has a potential energy

: U = m g h

where U is the gravitational potential energy and h is the height above the surface. This means that gravitational potential energy on a contour map is proportional to altitude. On a contour map, the two-dimensional negative gradient of the altitude is a two-dimensional vector field, whose vectors are always perpendicular to the contours and also perpendicular to the direction of gravity. But on the hilly region represented by the contour map, the three-dimensional negative gradient of U always points straight downwards in the direction of gravity F. However, a ball rolling down a hill cannot move directly downwards due to the normal force of the hill's surface which cancels out the component of gravity which is perpendicular to the hill's surface. The component of gravity which remains to move the ball is parallel to the surface:

: F_S = - m g \ \sin \theta

where &theta is the angle of inclination, and the component of FS perpendicular to gravity is

: F_P = - m g \ \sin \theta \ \cos \theta = - {1 \over 2} m g \sin 2 \theta

This force FP, parallel to the ground, will be greatest when &theta is 45 degrees.

Let &Deltah be the uniform interval of altitude between contours on the contour map, and let &Deltax be the distance between two contours. Then

: \theta = \tan^{-1}{\Delta h \over \Delta x}

so that

: F_P = - m g { \Delta x \Delta h \over \Delta x^2 + \Delta h^2 } .

However, on a contour map, the gradient will be inversely proportional to &Deltax, which is not similar to force FP: altitude on a contour map is not exactly a two-dimensional potential field. The magnitudes of forces are different, but the directions of the forces are the same on a contour map as well as on the hilly region of the Earth's surface represented by the contour map.

Pressure as buoyant potential

In fluid mechanics, a fluid in equilibrium but in the presence of a uniform gravitational field will be permeated by a uniform There was an error working with the wiki: Code[20] which will cancel out the gravitational force: that is how the fluid maintains its equilibrium. This buoyant force is the negative gradient of pressure:

: {f_B} = - \nabla p .

Since buoyant force points upwards, in the direction opposite to gravity, then pressure in the fluid will increase downwards. Pressure in a static body of water increases proportionally to the depth below the surface of the water. The surfaces of constant pressure are planes which are parallel to the ground. The surface of the water can be characterized as a plane with zero pressure.

If the liquid has a vertical vortex (whose axis of rotation is perpendicular to the ground), then the vortex will cause a depression in the pressure field. The surfaces of constant pressure will be parallel to the ground far away from the vortex, but near and inside the vortex the surfaces of constant pressure will be pulled downwards, closer to the ground. This will also happen to the surface of zero pressure: therefore, inside the vortex, the top surface of the liquid is pulled downwards into a depression, or even into a tube (a solenoid).

The buoyant force due to a fluid on a solid object immersed and surrounded by that fluid can be obtained by integrating the negative pressure gradient along the surface of the object:

: F_B = - \oint_S \nabla p \cdot \, d{S}.

A moving airplane wing makes the air pressure above it decrease relative to the air pressure below it. This creates enough buoyant force to counteract gravity.

Calculating the scalar potential

Given a vector field E, its scalar potential can be calculated to be

: \phi({R_0}) = {1 \over 4 \pi} \int_\tau {\nabla \cdot {E}(\tau) \over \| {R}(\tau) - {R_0} \|} \, d\tau

where &tau is volume. Then, if E is irrotational vector field (Conservative),

: {E} = -\nabla \phi = - {1 \over 4 \pi} \nabla \int_\tau {\nabla \cdot {E}(\tau) \over \| {R}(\tau) - {R_0} \|} \, d\tau .

This formula is known to be correct if E is a continuous function and vanishes asymptotically to zero towards infinity, decaying faster than 1/r and if the divergence of E likewise vanishes towards infinity, decaying faster than 1/r2.

#### Conventional scalar fields

A scalar field is a function in mathematics from R'n to R. That is, it is a function defined on the n-dimensional Euclidean space with real number values. Often it is required to be continuous function, or one or more times differentiable, that is, a function of smooth function class Ck. The scalar field can be visualized as a n''-dimensional space with a real or complex number attached to each point in the space. The derivative of a scalar field results in a vector field called the gradient. In differential geometry, where it is applicable to differential forms, a scalar field on a C''k-manifold is a Ck function to the real numbers. Taking R'n as manifold gives back the special case of vector calculus. A scalar field is also a 0-form. The set of all scalar fields on a manifold forms a commutative ring, under the natural operations of multiplication and addition, point by point.

Examples found in physics

A potential field, such as the Newtonian gravitational potential field for gravitation, or the electric potential in electrostatics.

A temperature, humidity or pressure field, such as those used in meteorology. Note that when modeling weather on a global basis, the surface of the Earth is not flat, and thus the general language of curvature in differential geometry plays a role.

Examples in quantum theory and relativity

In quantum field theory, a scalar field is associated with spin 0 particles, such as mesons or bosons. The scalar field may be real or complex valued (depending on whether it will associate a real or complex number to every point of space-time). Complex scalar fields represent charged particles. These include the Higgs field of the Standard Model, as well as the pion field mediating the strong nuclear interaction.

In the Standard Model of elementary particles, a scalar field is used to give the leptons their mass, via a combination of the Yukawa interaction and the spontaneous symmetry breaking. This mechanism is known as the Higgs mechanism. This supposes the existence of a (still hypothetical) spin 0 particle called Higgs particle.

In scalar theories of gravitation scalar fields are used to describe the gravitational field.

scalar-tensor theories represent the gravitational interaction through both a tensor and a scalar. Such attempts are for example the Jordan theory as a generalization of the Kaluza-Klein theory and the Brans-Dicke theory.

Scalar fields like the Higgs field can be found within scalar-tensor theories, using as scalar field the Higgs field of the Standard Model. This field interacts gravitatively and Yukawa-like (short-ranged) with the particles that get mass through it.

Scalar fields are found within superstring theories as dilaton fields, breaking the conformal symmetry of the string, though balancing the quantum anomalies of this tensor.

Scalar fields are supposed to cause the accelerated expansion of the universe (inflation), helping to solve the horizon problem and giving an hypothetical reason for the non-vanishing cosmological constant of cosmology. Massless (i.e. long-ranged) scalar fields in this context are known are inflatons. Massive (i.e. short-ranged) scalar fields are proposed, too, using for example Higgs-like fields.

#### Pseudoscalars

In mathematics and physics, a pseudoscalar is a quantity that behaves more or less like a scalar, except that it transforms oddly under the action of a discrete group. Typically, the discrete group is the parity operation on three-dimensional space, and pseudoscalars change sign under a parity inversion. The notation used in geometric algebra provides a mathematically cleaner, less ambiguous notation for the concept, as compared to the traditional physics notation. The prototypical example of a pseudoscalar is the scalar triple product. A pseudoscalar, when multiplied by an ordinary vector, becomes a pseudovector or axial vector a similar construction creates the pseudotensor.

##### Physics

In physics, a pseudoscalar denotes a physical quantity analogous to scalar. Both are physical quantities which assume a single value which is invariant under proper rotations. However, under the parity transformation, pseudoscalars flip their signs while scalars do not.

Examples

the magnetic charge (as it is mathematically defined, regardless of whether it exists physically)

the pion, the charged particle that mediates nuclear forces. Most mesons are pseudoscalars. Curiously, the pion forms a isospin triplet the current associated with the pion is an axial vector, known as the axial vector current.

##### geometric algebra

A pseudoscalar in a geometric algebra is the highest-grade basis element of the algebra. For example, in two dimensions there are two basis vectors, e1, e2 and the highest-grade basis element is e1e2 = e12. This element squares to ?1 and commutes with all elements — behaving therefore like the imaginary scalar i in the complex numbers. It is these scalar-like properties which give rise to its name. Pseudoscalars in geometric algebra correspond to the pseudoscalars in physics. Indeed, the language of the geometric algebra provides for a cleaner notation for the concept of the pseudoscalar than does the traditional physics notation this is one of the claimed strengths of the geometrc algebra notation.

#### Other kinds of fields

There was an error working with the wiki: Code[30]s are associate a vector to every point in space. Some examples of vector fields include the electromagnetic field and the Newtonian gravitational field. There was an error working with the wiki: Code[31]s are associate a tensor to every point in space. For example, in general relativity gravitation is associated with a tensor field (in particular, with the Riemann curvature tensor). In Kaluza-Klein theory, spacetime is extended to five dimensions and its Riemann curvature tensor can be separated out into ordinary four-dimensional gravitation plus an extra set, which is equivalent to Maxwell's equations for the electromagnetic field, plus an extra scalar field known as the "dilaton".

#### Scalar field theory

As stated above, scalar waves are hypothetical waves, which differ from the conventional electromagnetic transverse waves by one oscillation level parallel to the direction of propagation they thus have characteristics of longitudinal waves.

##### Terminology

The basic understanding of scalar field theory begins with several definition of terms within the theory, which are also used in academic physics, but assigns them other meanings. A "scalar field" is a set of assigned observable magnitudes at every point in n-dimensional space (compare this with the the scalar field of the current academic definition n is also 4 or greater). There was an error working with the wiki: Code[1] An "There was an error working with the wiki: Code[21] and, is any ordering (static or dynamic) in the vacuum (eg., the position of the object relative to other objects). A "scalar potential" is the stationary ordering in the virtual particle flux of the vacuum (compared with the scalar potential of the current academic definition). A "vector potential" is any nonstationary ordering in the virtual particle flux of vacuum (compare with the scalar potential of the current academic definition). Scalar potentials and vector potentials are thus defined as: "contained" inside the energy domain. There was an error working with the wiki: Code[2]

##### Magnetic fields interaction

SFT is based on "non-symmetrical regauging" potentials, demonstrated by the interaction of two magnetic fields.

When the field lines oppose each other, the magnets are pulled together. When the fields are aligned in the same direction, the magnets push apart. When two magnets strongly oppose each other but are not permitted to move apart, the force between them is said to create a "scalar bubble" between the magnets. The greater the repulsive force, the larger this scalar bubble becomes. As the magnets move away and the pushing force decreases, the scalar bubble shrinks in size and strength.

In a similar manner, two magnets that are strongly attracted create a "scalar void" between them that grows larger the closer the two magnets become. Two magnets powerfully attracted to one another create a very large scalar void, that decreases as the attracting magnets are moved apart.

Despite the claims of its proponents, no repeatable experiments were able to show the existence of the scalar field. All observed effects were shown to comply to the standard physical laws of There was an error working with the wiki: Code[32]. As not only classical electromagnetics but also There was an error working with the wiki: Code[33] are a field of physics, where the observations are in spectacular agreement with the theoretical predictions, currently the case for Scalar field theory looks bleak.

##### Field effects of scalar energy

SFT suggests that scalar energy can move through space much like an electromagnetic wave. However, the operating principles are different. The regular expansion and contraction of a scalar bubble/void is like rythmicly splashing water on a pond. It sends out ripples through the general scalar field that can subtly affect the size and strength of distant scalar bubbles/voids. This means that a pair of magnets that are rhythmically opposing/attracting each other are sending out scalar ripples through space that will slightly perturb the scalar bubble/void between a second pair magnets nearby. The net effect is that the attraction and/or repulsion between the second pair of magnets exhibits a change in strength, even though the magnets and fields themselves are motionless. According to skeptics, the following description given for an application to a communication system reportedly failed to give reproduceable results.

##### Basic scalar system

The scalar communications antenna does not make any sense according to normal electromagnetic theory. The goal of a scalar antenna is to create powerful repulsion/attraction between two magnetic fields, to create large scalar bubbles/voids. This is done by using an antenna with two opposing electromagnetic coils that effectively cancel out as much of each other's magnetic field as possible. An ideal scalar antenna will emit no electromagnetic field (or as little as possible), since all power is being focused into the repulsion/attraction between the two opposing magnetic fields. Normal electromagnetic theory suggests that since such a device emits no measurable electromagnetic field, it is useless and will only heat up. A scalar signal reception antenna similarly excludes normal electromagnetic waves and only measures changes in magnetic field attraction and repulsion. This will typically be a two-coil powered antenna that sets up a static opposing or attracting magnetic field between the coils, and the coils are counter-wound so that any normal RF signal will be picked up by both coils and effectively cancel itself out.

##### Scalar antennas and detectors

Various proponents have developed instrument with characteristics and specifications for different designs. Scalar antenna and detector examples include:

TypesThere was an error working with the wiki: Code[3]

There was an error working with the wiki: Code[22] Detectors

Electrostatic Detectors

There was an error working with the wiki: Code[23] Detector

WindingsThere was an error working with the wiki: Code[4]

single-wire There was an error working with the wiki: Code[34]

dual-wire bifilar

pancake bifilar

cone bifiliar

Proponents of the theory have constructed bifiliar test antennas as There was an error working with the wiki: Code[35]s. These have taken the form of a ferrite rod, ferrite ring, an air core, or the common square transformer shape.

#### Other claims, theories, and suggestions

There was an error working with the wiki: Code[24] suggests that scalar energy could be used as a directed-energy weapon. He says that if two scalar "energy beams" are created that collide with each other, the two scalar fields will nullify each other and create a burst of electromagnetic energy in its place, that can continue on forward in the direction the two scalar beams were heading. A point within the framework from Bearden rests on the allegation that during the reformulation of the There was an error working with the wiki: Code[25] a key elements was lost in the original theory.

It has been suggested that scalar fields do not follow the same rules as electromagnetic waves, and can penetrate through materials that would normally slow or absorb electromagnetic waves. If true, a simple proving method is to design a scalar signal emitter and a scalar signal receiver, and encasing each inside separate shielded and grounded metal boxes, known as There was an error working with the wiki: Code[36]s. These boxes will absorb all normal electromagnetic energy, and will prevent any regular non-scalar signal transmissions from passing from one box to the other.

Some people have suggested that organic life may make use of scalar energies in ways that we do not yet understand. Therefore caution is recommended when experimenting with this fringe technology. However, keep in mind that if scalar fields do exist, we are likely already deeply immersed in an unseen field of scalar noise all the time, generated anywhere two magnetic fields oppose or attract. Common scalar field noise sources include AC electric cords and powerlines carrying high current, and electric motors which operate on the principle of powerful spinning regions of repulsion and attraction.

#### External articles and references

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General

P.W. Higgs Phys. Rev. Lett. 13(16): 508, Oct. 1964.

P. Jordanm Schwerkraft und Weltall, Vieweg (Braunschweig) 1955.

C. Brans and R. Dicke Phis. Rev. 124(3): 925, 1961.

A. Zee Phys. Rev. Lett. 42(7): 417, 1979.

H. Dehnen et al. Int. J. of Theor. Phys. 31(1): 109, 1992.

H. Dehnen and H. Frommmert, Int. J. of theor. Phys. 30(7): 987, 1991.

C.H. Brans "The Roots of scalar-tensor theory", arXiv:gr-qc/0506063v1, June 2005.

A. Guth Pys. Rev. D23: 346, 1981.

J.L. Cervantes-Cota and H. Dehnen Phys. Rev. D51, 395, 1995.

{WPcite}}

http://www.cheniere.org/books/ferdelance/

T. E. Bearden

T. E. Bearden, "Scalar electromagnetics". Fer de Lance, 1986.

T. E. Bearden, "Founders of Scalar Electromagnetics".

T. E. Bearden, "Method, System, and apparatus for conditioning electromagentic potentials, fields, and waves to treat matter". Provisional Patent Application.

Scalar field theory

There was an error working with the wiki: Code[9]"Scalar Wave FAQ". The TEP Project, JLN labs, 19/08/97.

There was an error working with the wiki: Code[10]" T. E. Bearden, "Scalar field". A partial glossary for scalar electromagnetics and subtle phenomena, 1988 (updated 2000).

There was an error working with the wiki: Code[11] T. E. Bearden, P. K. Anastasovski, C. Ciubotariu, et al., "Operator derivation of the gauge invariant Proca and Lehnert equations elimination of the There was an error working with the wiki: Code[26]", Foundations of Physics, 30, 1123 (2000).

There was an error working with the wiki: Code[12] Myron W. Evans, et al., "Classical electrodynamics without the Lorenz condition: Extracting energy from the vacuum". Physica Scripta 61(5), May 2000, p. 513-517.

There was an error working with the wiki: Code[13] T. E. Bearden, "Clean Electrical Energy from the Active Vacuum". Jan. 2002. (ed. explained in end reference 32)

T. E. Bearden, "EM Energy from the vacuum: Ten questions with extended answers". September 2000. (There was an error working with the wiki: Code[37])

There was an error working with the wiki: Code[14] T. E. Bearden, "On extracting electromagnetic energy from the vacuum".

Scalar antenna examples

There was an error working with the wiki: Code[15] " More Electromagnetism : Scalar Waves". RMCybernetics, 2005.

There was an error working with the wiki: Code[16] Robert Shannon, "Notes on Scalar Detector Designs". 1996.

"Electromagnetics Researches". JLN Labs, 01-31-05.

Journal articles

T. E. Bearden and There was an error working with the wiki: Code[38] , "Utilizing Scalar Electromagnetics to Tap Vacuum Energy". Proceedings of the 26th Intersociety Energy Conversion Engineering Conference (IECEC '91).

T. E. Bearden, "Background for Pursuing Scalar Electromagnetics". Assoc. Dist. Am. Sci., 1992.

Books

Tom E. Bearden, "Scalar technology". Michels 2002, ISBN 0914119052

Marco bishop, "There was an error working with the wiki: Code[27] - scalar waves". RK publishing house 2002, ISBN 3855027862 (German)

Konstantin Meyl, "Scalar wave technology". 2001, ISBN 3980254267 (German)

Myron W. Evans, "Modern Nonlinear Optics, Part III". (Second Edition) John Wiley & Sons, Inc 19 Mar 2002. ISBN 0471389323 ISBN 0471231495 (Online)

Other

"More Electromagnetism". RMCybernetics, 2005. (ed. Discusses electromagnetics and scalar wave theory.)

Bill Morgan, "Scalar Wars The Brave New World of Scalar Electromagnetics".

Koen van Vlaenderens "''Generalised Classical Electrodynamics for the prediction of scalar field effects".

Konstantin Meyl, "Longitudinalwellen-Experiment nach Nikola Tesla". (German)