Scaler Waves Page 1 Scalar Waves and the Human Möbius Coil System Scalar field Scalar wave create a scalar field such as temperature or pressure, where intensity of the field is graphically represented by intensity of the color. In mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate- independent. This implies that any two observers using the same units will agree on the value of the scalar field at the same point in space (or spacetime). Examples used in physics include the temperature distribution throughout space, the pressure distribution in a fluid, and spin-zero quantum fields, such as the Higgs field. These fields are the subject of scalar field theory.
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Scaler Waves Page 1
Scalar Waves and the Human Möbius Coil System
Scalar field
Scalar wave create a scalar field such as temperature or pressure, where intensity
of the field is graphically represented by intensity of the color.
In mathematics and physics, a scalar field
associates a scalar value to every point in a space. The scalar may either be a
mathematical number, or a physical
quantity.
Scalar fields are required to be coordinate-independent. This implies that any two
observers using the same units will agree on the value of the scalar field at the same
point in space (or spacetime).
Examples used in physics include the temperature distribution throughout space,
the pressure distribution in a fluid, and spin-zero quantum fields, such as the
Higgs field. These fields are the subject of scalar field theory.
Scalar Waves and Human Mobius Coil System
Scaler Waves and Fields Page 2
Definition
Mathematically, a scalar field on a region U is a real or complex-valued function or
distribution on U. The region U may be a set in some Euclidean space, Minkowski
space, or more generally a subset of a manifold, and it is typical in mathematics
to impose further conditions on the field, such that it be continuous or often
continuously differentiable to some order. A scalar field is a tensor field of order zero,
and the term "scalar field" may be used to distinguish a function of this kind with a
more general tensor field, density, or
differential form.
Physically, a scalar field is additionally distinguished by having units of
measurement associated with it. In this context, a scalar field should also be
independent of the coordinate system used to describe the physical system—that is,
any two observers using the same units must agree on the numerical value of a
scalar field at any given point of physical space. Scalar fields are contrasted with
other physical quantities such as vector fields, which associate a vector to every
Scalar Waves and Human Mobius Coil System
Scaler Waves and Fields Page 3
point of a region, as well as tensor fields
and spinor fields. More subtly, scalar fields are often contrasted with pseudoscalar
fields.
Uses in physics In physics, scalar fields often describe the
potential energy associated with a particular force. The force is a vector field,
which can be obtained as the gradient of the potential energy scalar field. Examples
include:
Potential fields, such as the Newtonian
gravitational potential, or the electric potential in electrostatics, are scalar fields
which describe the more familiar forces. Temperature, humidity or pressure field,
such as those are used in meteorology as well.
Quantum theory and relativity
Scaler Field is used in Quantum Field Theory. A scalar field is associated with
spin-0 particles. The scalar field may be real or complex valued. Complex scalar
fields represent charged particles. These
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include the charged Higgs field of the
Standard Model, as well as the charged pions mediating the strong nuclear
interaction. In the Standard Model of elementary
particles, a scalar Higgs field is used to give the leptons and massive vector bosons
their mass, via a combination of the
Yukawa interaction and the spontaneous symmetry breaking. This mechanism is
known as the Higgs mechanism.[5] The Higgs boson is still the subject of searches
at particle accelerators.
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-
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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, 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 as
inflatons. Massive (i.e. short-ranged) scalar fields are proposed, too, using for
example Higgs-like fields.
Other kinds of fields
Vector fields, which associate a vector to
every point in space are examples of other kind of fields. Some examples of vector
fields include the electromagnetic field and the Newtonian gravitational field.
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Tensor fields, which associate a tensor to
every point in space are another example. 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". The dilaton scalar is also found among the
massless bosonic fields in string theory.
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‘The Heart of Health; The Principles of Physical Health and Vitality,’ By Stephen Linsteadt, NHD, CNC