The Problem of Field


Reference: Disturbance Theory


Faraday, from his extensive experimentation with electric and magnetic phenomena, conceived the notion of field as “lines of force” that originated from and terminated at material points. To Faraday, field provided a resolution to the mystery of “action at a distance” that troubled Newton.

Maxwell formulated the mathematical basis that supported the results from Faraday’s extensive experimentation and his notion of the field. He developed the mathematical equations that showed light to be electromagnetic in nature. Maxwell confirmed that Faraday’s field, which carried force, was real. This put many discoveries of radiative phenomena into perspective as electromagnetic spectrum of increasing frequency.


Maxwell’s Equations

Maxwell’s equations describe the electromagnetic cycle of the basic space as follows.

  1. ∇⃗⋅ E = ρ/ϵ0
  2. ∇⃗⋅ B = 0
  3. ∇⃗× E = −∂B /∂t
  4. ∇⃗× B = c−2E /∂t + μ0J


E is the electric field

B is the magnetic field

J is the displacement current

∇⃗ ⋅ is the divergence operator that provides measure of the flow of a vector field.

∇⃗ × is the curl operator that provides measure of the rotation of a vector field.

The Maxwell’s equations may be interpreted as follows:

  1. Charge generates Electrical lines of force that flow out linearly.

  2. The magnetic lines of force appear as circles around the electrical lines of force.

  3. The linear flow of electrical lines of force converts into rotating magnetic lines of force.

  4. The rotating magnetic lines of force convert back into linear flow of electrical lines of force.


The Electromagnetic Cycle

Thus the dynamics within an electromagnetic cycle of the basic space may be interpreted as follows:

Something called “charge” triggers the electromagnetic cycle. This cycle is an oscillation between electrical flow and magnetic rotation. The electrical flow winds up as magnetic rotation. The magnetic rotation then unwinds back as electrical flow.

Thus, there is an oscillation between electric flow and magnetic rotation that acquires increasing frequency as one moves up the electromagnetic spectrum.


Einstein’s Light Quanta

Einstein’s discovery of light quanta simply means that the continuous wave like characteristics of electromagnetic cycles starts to appear more particle-like at higher frequencies. This established the field as a real substance besides matter.

In the widespread low frequency field, areas of high frequency appear to be more compact and substantial. Thus high frequency areas appear as “particles” within the low frequency “wave” background. Neither the “particle” nor the “wave” aspect of the field is absolute or separate. Both aspects are part of the same field continuum. They are simply the manifestation of different frequencies that exist side by side.

The quantization of electromagnetic field appears mostly in the gamma range of the electromagnetic spectrum. All quantum particles including electrons and the nucleons of the atom appear in this range. Such particles are not separate in themselves. They exists in continuum with the background field. This field model seems to resolve the wave and particle confusion and the results from the double slit experiment.


Further Research

The de Broglie hypothesis may be used to show the gradual quantization throughout the electromagnetic spectrum and beyond.



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