Figure 6. Symmetries of nature determine the properties of forces in Gauge theories. The symmetry of a snowflake can be characterized by noting that the pattern is unchanged when it is rotated 60 degrees; the snowflake is said to be invariant with respect to such rotations. In physics, non-geometric symmetries are introduced. Charge symmetry, for example, is the invariance of the forces acting among a set of charged particles when the polarities of all the charges are reversed. Isotopic-spin symmetry is based on the observation that little would be changed in the strong interactions of matter if the identities of all protons and neutrons were interchanged. Hence proton and neutron become merely the alternative states of a single particle, the nucleon, and transitions between the states can be made (or imagined) by adjusting the orientation of an indicator in an internal space. It is symmetries of this kind, where the transformation is an internal rotation or a phase shift, which are referred to as Gauge symmetries. The first Gauge Theory with local symmetry was the theory of electric and magnetic fields, introduced in 1868 by James Clerk Maxwell. The character of the symmetry that makes Maxwell?s theory a Gauge Theory is that the electric field is invariant with respect to the addition or subtraction of an arbitrary overall electric potential. However, this symmetry is a global one because the result of experiment remains constant only if the new potential is changed everywhere at once (there is no absolute potential and no zero reference point). A complete theory of electromagnetism requires that the global symmetry of the theory be converted into a local symmetry. Just as the electric field depends ultimately on the distribution of charges, but can conveniently be derived from an electrical potential, so the magnetic field generated by the motion of these charges can be conveniently described as resulting from a magnetic potential. It is in this system of potential fields that local transformations can be carried out leaving all the original electric and magnetic fields unaltered. This system of dual, interconnected fields has an exact local symmetry even though the electric field alone does not(9). Maxwell?s theory of electromagnetism is a classical one, but a related symmetry can be demonstrated in the quantum theory of EM interaction (called quantum field theory). In the quantum theory of electrons, a change in the electric potential entails a change in the phase of the electron wave and the phase measures the displacement of the wave from some arbitrary reference point (the difference is sufficient to yield an electron diffraction effect) . Only differences in the phase of the electron field at two points or at two moments can be measured, but not the absolute phase. Thus, the phase of an electron wave is said to be inaccessible to measurement (requires a knowledge of both the real and the imaginary parts of the amplitude) so that the phase cannot have an influence on the outcome of any possible experiment. This means that the electron field exhibits a symmetry with respect to arbitrary changes of phase . Any phase angle can be added to or subtracted from the electron field and the results of all experiments will remain invariant. This is the essential ingredient found in the U(1) Gauge condition. Although the absolute value of the phase is irrelevant to the outcome of experiment, in constructing a theory of electrons, it is still necessary to specify the phase . The choice of a particular value is called a Gauge convention. The symmetry of such an electron matter field is a global symmetry and the phase of the field must be shifted in the same way everywhere at once . It can be easily demonstrated that a theory of electron fields, along with no other forms of matter or radiation, is not invariant with respect to a corresponding local Gauge transformation. If one wanted to make the theory consistent with a local Gauge symmetry, one would need to add another field that would exactly compensate for the changes in electron phase . Mathematically, it turns out that the required field is one having infinite range corresponding to a field quantum with a spin of one unit. The need for infinite range implies that the field quantum be massless. These are just the properties of the EM field, whose quantum is the photon. When an electron absorbs or emits a photon, the phase of the electron field is shifted (9). The gauge symmetry case of our interest in this white paper is the one where we have two unique levels of physical reality as indicated in Equation 1. In one, we have electric atoms and molecules restricted to travel at velocities less than that of c, the velocity of EM light. In the other, we have magnetic information waves restricted to travel at velocities greater than c. Our main interest, here, is how one describes the EM gauge symmetry state for the two cases (1) these two levels of physical reality are almost completely uncoupled and (2) these two levels are strongly coupled so that the second level is instrumentally accessible via the measuring instruments of the first. In the first case, one could define a generalized potential function, , and EM gauge symmetry state where = D (x, y, z, t) + R (kx, ky, kz, kt) (6a) and EM gauge state: Ue(1) + Um(1) (6b) However, our commercial measurement devices, cannot access the phenomena associated with R so it doesn?t exist to us. In the second case, a strong coupling coefficient, eff, exists between e and m substances so we have Consider the top drawing in figure 7, it shows a unique space that combines an internal space (ordinate) with a two-dimensional representation of spacetime (abscissa). In this unique space, the spatial location of a particle is represented by a dot at a coordinate point in the horizontal, spacetime plane while the phase-value for the field in the internal space is specified by angular coordinates in this unique space. As the particle moves through spacetime (the sequence of dots), it also traces out a path in the internal space (the dashed line) above the spacetime trajectory at a distance proportional to the instantaneous phase angle for the electron wave. Mathematicians call this internal space distance a fiber. When there is no external gauge potential acting on the particle, the internal space path is completely arbitrary. When this particle interacts with an internal gauge field (E or H), the dashed path in the internal space is a continuous curve determined by the gauge potential. In mathematical jargon, the unique space formed by the union of our four-dimensional spacetime with an internal space is called a “fiber bundle space”.(5) When there is only one internal space variable, like the electron wave function, the internal space is designated as a U(1) EM gauge symmetry space because the state looks like the interior of a flat ring with the phase value represented as the angle, , of the point on the ring seen in figure 7 (top).