The magnetic and electric fields are force fields. They exert forces on magnetic or charged particles. We can measure these fields easily with instruments that respond to such forces. Magnetic and electric fields therefore have a very real and tangible existence. But these force fields themselves are merely higher order expressions of something more fundamental known as potential fields. Potential fields form an underlying substrate in which certain distortions give rise to magnetic or electric fields. But even without such distortions, and hence without any measurable magnetic or electric fields, the potential field can still exist in its distortion-free state.
There are three main potential fields: magnetic vector potential `vec(A)`, scalar electric potential `V`, and gravitational potential `varphi`. These respectively give rise to the three main force fields: magnetic field `vec(B)`, electric field `vec(E)`, and gravitational field `vec(g)`. The following equations show how these relate:
`grad xx vec(A) = vec(B)`
`-grad V = vec(E)`
`-grad varphi = vec(g)`
The first equation is pronounced “del cross A equals B” or “curl of A equals B.” This means that curl (vorticity, circulation, twist) in the magnetic vector potential gives rise to a magnetic force field. For instance, if `vec(A)` uniformly circulates counter-clockwise around your computer screen, the equivalent magnetic field `vec(B)` points out of the screen toward you; `vec(B)` is always at right angles to the curled parts of `vec(A)`. A magnetic field line may be visualized as the central axis of a vortex made of vector potential. But if the vector potential has zero vorticity, then no magnetic field arises, yet it can still distort in other ways by fluctuating, diverging, or compressing.
The second equation is pronounced “minus grad V equals E” or “negative gradient of V equals E”. Gradients are inclines, increases in some quantity over some distance. When the scalar electric potential `V`, also known as voltage, changes over some distance, that establishes an electric field. For example, if electric scalar potential is lower at the left side of your screen and increases steadily toward the right, the electric field from this will point toward the left, down the slope. A positive charged particle released in this field will be propelled toward the left. But if there is no gradient in the scalar potential, meaning if the voltage everywhere on your screen is uniform, then there is no associated electric field. The charged particle will just sit there experiencing no force. However, the voltage can still vary over time, fluctuating everywhere at the same rate, and still the charged particle experiences no force. Modern scientific instruments cannot measure such a field because the electrons within the instruments do not move in a way that creates detectable current.
The third equation is similar to the second. It says that the gravitational force field `vec(g)` we are all familiar with, which points down toward the center of the earth and accelerates falling masses at an average rate of 9.8 `m/s^2`, is itself simply the negative gradient of the gravitational potential `varphi`. Or to put it another way, the gravitational potential increases with height, forming a gradient whose downward slope points toward the ground. But again, theoretically if the gravitational potential did not have a slope, there would be no measurable gravity force, and yet the potential field could still vary in other ways such as varying uniformly everywhere within a certain area over time. Once more, such a field cannot be measured with standard scientific instruments because without there being any forces, no reading can be made.
A fourth equation relates the magnetic vector potential to the electric field:
`(del vec(A))/(del t) = -vec(E)`
This equation says that if `vec(A)` increases over time, an electric field will arise pointing opposite the physical direction of `vec(A)`. This is why changing magnetic fields are said to give rise to electric fields and vice versa; magnetic fields consist of curled vector potential, and a change in the latter manifests an electric field. What is not taught in physics classes, however, is that a curl-free vector potential that varies over time can induce a dynamic electric field without its corresponding dynamic magnetic field.
So what is the significance of potential fields? Well, aside from giving rise to phenomena that we can detect and measure, they can also do things that we cannot detect using standard methods, things that may have effects we might not even imagine possible. What if the frequency of an oscillating but uniform scalar potential (voltage) can affect our mood? Then our mood could be manipulated by such fields without us — being limited to mainstream modern technology — ever finding out what the true cause might be. Same can be said for curl-free magnetic vector potential fields, or gradient-free gravitational potential fields.
Well it turns out that technology does exist to detect some of these exotic potential fields that lack any measurable force field components. However, these are out of reach for the average person. See for instance a list of patents dealing with the vector potential. Most of these employ what are known as Josephson junctions, which are quantum mechanical devices that allow direct measurement of the vector potential regardless of whether or not a magnetic force field is present. But good luck to anyone who desires to build or buy a Josephson junction; these require superconducting materials assembled with precision. They can be found in a less effective configuration in medical MRI machines, employed as the core components of SQUID (Superconducting QUantum Interference Devices) detectors designed to measure very weak magnetic fields.
The important thing to know about all this is that force-free potential fields have subtle effects on reality at the quantum level. Whereas magnetic and electric fields play a greater role in physical processes involving energy transfers, potential fields work more on the quantum level as phase selectors, probability shapers, and spacetime torsion inducers. This is what scalar physics is all about, using those more exotic aspects of electromagnetic theory that are unknown or ignored by mainstream science.
For further discussion and several diagrams concerning the vector potential and its role in electromagnetism, please see my research notes on transverse and longitudinal waves. And if you feel comfortable with the math, then read about one important appplication of all this: Portal Physics (also known as space-time engineering). For a non-mathematical diagram-based explanation of potential fields in relation to electricity, gravity, magnetism, and non-Maxwellian wave phenomena, see The Etheric Origins of Gravity, Electricity, and Magnetism