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## Field (physics) – Wikipedia

In physics, a field is a physical quantity, represented by a number or tensor, that has a value for each point in space and time. For example, on a weather map, the surface wind velocity is described by assigning a vector to each point on a map. Each vector represents the speed and direction of the movement of air at that point. As another example, an electric field can be thought of as a “condition in space” emanating from an electric charge and extending throughout the whole of space. When a test electric charge is placed in this electric field, the particle accelerates due to a force. Physicists have found the notion of a field to be of such practical utility for the analysis of forces that they have come to think of a force as due to a field. The sloppy use of language to which physicists are prone may lead to confusion in the student as to whether field here means “region” or “single point force vector” within a given region or “a set of point force vectors” within a given region or “all point force vectors” within a given region (bear in mind the fact that Gravitational and Electromagnetic Forces have ranges that are theoretically infinite).

The concept of field started out as a mathematical device to describe fluid flows at every point in space, such as on a weather map. Later it was used to describe electric and magnetic fields by their lines of forces at every point in space. Now it is being used to describe force vectors due to gravitation at every point of a theoretically infinite space.

It is only recently that the electromagnetic field has come to be looked upon as a basic substance on its own right that has dimensions. An example of such a field is light. The concept of substance as an electromagnetic field is yet to be sorted out fully. As a physical substance, this field has extensions and varying degrees of solidity. We may now divide substance into “matter” and “field”.

In the modern framework of the quantum theory of fields, even without referring to a test particle, a field occupies space, contains energy, and its presence precludes a classical “true vacuum”. This led physicists to consider electromagnetic fields to be a physical entity, making the field concept a supporting paradigm of the edifice of modern physics. “The fact that the electromagnetic field can possess momentum and energy makes it very real … a particle makes a field, and a field acts on another particle, and the field has such familiar properties as energy content and momentum, just as particles can have.” In practice, the strength of most fields has been found to diminish with distance to the point of being undetectable. For instance the strength of many relevant classical fields, such as the gravitational field in Newton’s theory of gravity or the electrostatic field in classical electromagnetism, is inversely proportional to the square of the distance from the source (i.e., they follow Gauss’s law). One consequence is that the Earth’s gravitational field quickly becomes undetectable on cosmic scales.

This brings a revolution to the concept of “space”. Space has always been conceived in the context of physical extensions. We have been measuring space as if it were rigid like matter. Now we can conceive of space differently as the extensions of the invisible “field”. A “true vacuum” may be free of substance as “matter”, but it may not be free of substance as “field”. We notice that as we see light travel through the intergalactic space. What we think of “empty space” may just be the invisible “field”. This would explain dark matter and dark energy quite nicely.

We may now explain space itself as the extensions of the field. We come to see space as a property of substance rather than as the absence of substance. We no longer see space existing in the absence of substance. It now seems absurd to talk about “matter occupying space” or “field being a condition in space”. The context of “space” is replaced by the concept of emptiness. Space is the property of extension of field that exists in emptiness. We can experience space because we can experience substance. That is how substance is defined. But we cannot experience emptiness, which is an absence of substance.

An electric field is, therefore, a condition in emptiness and not a “condition in space”. This shift in viewpoint makes “energy” of field comparable to “mass” of matter. The electric charge can now be viewed as a condensed region within the electric field and not merely a mathematical entity of a “single point force vector”. The density of the field may be defined in terms of the compactness of cycles due to higher frequencies.

Force is expressed as a gradient of momentum. In case of the field, this momentum is proportional to frequency. Therefore, force exists in a field as a gradient of frequency. Thus, forces arise due to gradients in frequency around the condensed regions of the field. “Strength” of the field diminishes as frequency gradients diminish in the field.

A field can be classified as a scalar field, a vector field, a spinor field or a tensor field according to whether the represented physical quantity is a scalar, a vector, a spinor, or a tensor, respectively. A field has a unique tensorial character in every point where it is defined: i.e. a field cannot be a scalar field somewhere and a vector field somewhere else. For example, the Newtonian gravitational field is a vector field: specifying its value at a point in spacetime requires three numbers, the components of the gravitational field vector at that point. Moreover, within each category (scalar, vector, tensor), a field can be either a classical field or a quantum field, depending on whether it is characterized by numbers or quantum operators respectively. In fact in this theory an equivalent representation of field is a field particle, namely a boson.

The classification of fields as scalar, vector, spinor, or tensor is mathematical. In reality, the primary field is electromagnetic. The secondary field is gravitational, which is made of frequency gradients.

An electromagnetic field is much more than either electric or magnetic field. An electromagnetic field consists of dynamic cycles in which electric and magnetic energies are rapidly interchanging just like kinetic and potential energies interchange during the oscillations of a pendulum. Thus we may compare electric to kinetic energy, and magnetic to potential energy. Each cycle of the electromagnetic field is composed of energy equal to the Planck’s constant ‘h’. The properties of these cycles change as they get compressed with increasing frequency. This is observed in the electromagnetic spectrum.

The cycles in the gamma region start to become so compacted that they start to display the property of mass. This part of spectrum is displayed in the structure of the atom in which the gradient of frequency (or density) rapidly increases towards the center. Quantum particles appear in rapidly condensing field like eddies appear in a rapidly moving flow. All quantum particles are manifestations of the condensed regions of the electromagnetic field in the gamma range of frequencies. The fundamental quantization occurs in terms of the energy of cycle and its frequency.

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## History

To Isaac Newton his law of universal gravitation simply expressed the gravitational force that acted between any pair of massive objects. When looking at the motion of many bodies all interacting with each other, such as the planets in the Solar System, dealing with the force between each pair of bodies separately rapidly becomes computationally inconvenient. In the eighteenth century, a new quantity was devised to simplify the bookkeeping of all these gravitational forces. This quantity, the gravitational field, gave at each point in space the total gravitational force which would be felt by an object with unit mass at that point. This did not change the physics in any way: it did not matter if all the gravitational forces on an object were calculated individually and then added together, or if all the contributions were first added together as a gravitational field and then applied to an object.

The gravitational force is more accurately defined in the context of a field. It is more than just a mathematical convenience. The gravitational force is the cumulative effect of all the gradients of field density between any two bodies.

The development of the independent concept of a field truly began in the nineteenth century with the development of the theory of electromagnetism. In the early stages, André-Marie Ampère and Charles-Augustin de Coulomb could manage with Newton-style laws that expressed the forces between pairs of electric charges or electric currents. However, it became much more natural to take the field approach and express these laws in terms of electric and magnetic fields; in 1849 Michael Faraday became the first to coin the term “field”.

The independent nature of the field became more apparent with James Clerk Maxwell’s discovery that waves in these fields propagated at a finite speed. Consequently, the forces on charges and currents no longer just depended on the positions and velocities of other charges and currents at the same time, but also on their positions and velocities in the past.

The field is naturally bound by emptiness, whose frequency is zero. The field, therefore, develops from a frequency of zero to higher frequencies in a continuous fashion. The first quantization occurs in terms of the cycles of frequency.

The field acquires different properties throughout its frequency range in the electromagnetic spectrum. The electrical properties are part of it. The forces depend on three dimensional frequency gradients rather than on linear distances. Waves in the field propagate at a finite speed because field has inertia. This inertia occurs in the form of permittivity and permeability. This inertia produces the finite characteristic of the velocity of light ‘c’.

Maxwell, at first, did not adopt the modern concept of a field as a fundamental quantity that could independently exist. Instead, he supposed that the electromagnetic field expressed the deformation of some underlying medium—the luminiferous aether—much like the tension in a rubber membrane. If that were the case, the observed velocity of the electromagnetic waves should depend upon the velocity of the observer with respect to the aether. Despite much effort, no experimental evidence of such an effect was ever found; the situation was resolved by the introduction of the special theory of relativity by Albert Einstein in 1905. This theory changed the way the viewpoints of moving observers should be related to each other in such a way that velocity of electromagnetic waves in Maxwell’s theory would be the same for all observers. By doing away with the need for a background medium, this development opened the way for physicists to start thinking about fields as truly independent entities.

An electromagnetic wave is a disturbance in the electromagnetic field in the form of a ripple.  There is no other substance. Underlying this field is “emptiness”, which is complete absence of substance. At lower frequencies the field comes very close to being “no substance” with its inertia reduced to zero and its wavelength and duration expanded to infinite.

The “velocity” of light is not infinite because field has inertia. As the density of the field increases with frequency, the magnitude of this “velocity” decreases. The velocity of the quantum particles in the gamma region is a fraction of ‘c’. This velocity may be plotted against inertia of the field. This velocity approaches infinity as inertia approaches zero. This velocity is independent of the observer (the frame of reference) of the theory of relativity. The theory of relativity does not take inertia into account. It works only in those cases where the differences in inertia are extremely large, such as, between light and planetary body. The Michelson-Morley’s experiment failed only because it lacked the accuracy to compare the inertia of light to the inertia of earth.

Einstein assumed the inertia of light to be zero, but if that were the case, the velocity of light would be infinite. This inconsistency underlies the theory of relativity. We are dealing here with a range of inertia that is mind boggling.

In the late 1920s, the new rules of quantum mechanics were first applied to the electromagnetic fields. In 1927, Paul Dirac used quantum fields to successfully explain how the decay of an atom to a lower quantum state lead to the spontaneous emission of a photon, the quantum of the electromagnetic field. This was soon followed by the realization (following the work of Pascual Jordan, Eugene Wigner, Werner Heisenberg, and Wolfgang Pauli) that all particles, including electrons and protons, could be understood as the quanta of some quantum field, elevating fields to the status of the most fundamental objects in nature. That said, John Wheeler and Richard Feynman seriously considered Newton’s pre-field concept of action at a distance (although they set it aside because of the ongoing utility of the field concept for research in general relativity and quantum electrodynamics).

In atomic interactions, energy always changes in terms a certain number of frequency cycles. Therefore, such change appears to be quantized. Quanta relates to a packet of energy involved in an energy interaction among fields. All quantum particles consist of quanta.

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These are the comments inspired by the rest of Wikipedia article.

Classical fields are mathematical only. They represent vector force, an idea based on the mass property of matter. The gravitational and electric fields have been looked upon as emanating from matter.

#### Newtonian gravitation

According to Disturbance theory mass is a very condensed region of the field in the upper gamma range. There is no emptiness between two bodies. There is only a continuation of much less dense field between them.

The distance between the two bodies is the sum of all the wavelengths of the field cycles between them. These cycles are not rigid like matter. They can also vary in their wavelengths and frequency.

The attractive force of gravitation between two bodies is the summation of all frequency gradients between them. The highest frequency gradient exists at the surface of the bodies. Newton’s law of gravitation provides an approximation of this force.

A mass particle moves as a high inertia ripple in a very low inertia field. Its natural velocity is based on the interaction of its inertia with the surrounding inertia. Inertia depends on the density of the field.

#### Electromagnetism

A charge particle is a condensed region of the field in lower gamma range. Its frequency gradient is also steep but less condensed compared to the gradient in the upper gamma range.  Therefore, the two ends of the gradient appear to be separated as negative and positive.

The relationship between electric and magnetic energy is similar to the relationship between kinetic and potential energy.

#### Gravitation in general relativity

In general relativity, mass-energy warps space time. Per Disturbance theory it is the other way around. Fundamental reality is the electromagnetic field, which condenses into energy-mass. The condensation creates frequency gradients that act as force. The nature of this force differs depending on its position on the electromagnetic spectrum.

#### Waves as fields

Waves are part of the electromagnetic field in which they move as a three-dimensional ripple. They have finite propagation speed because of inertia intrinsic to the field. Their 3D nature results in the inverse-square law.

#### Quantum fields

All physical phenomena start with electromagnetic field. The electromagnetic field consists of cycles, and, therefore, it is quantized. Only when it condenses into mass that it is no longer quantized. All that changes from classical to quantum is the mathematics.

#### Field theory

Field theory deals with the dynamic aspects of the field.

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• vinaire  On November 27, 2017 at 6:48 AM

11/27/17 – The above comments have been updated in a major way.

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• vinaire  On November 28, 2017 at 7:11 AM

11/28/17 – I have added comments on the HISTORY section of the Wikipedia article.

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• vinaire  On November 28, 2017 at 2:25 PM

11/28/17 – I have added comments on the rest of the Wikipedia article.

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