Deep Thinking on Circuits

Understanding Resistors as Field Disruptors through Poynting Theory and Tugboat Theory

Resistors as Field Disruptors

In the traditional view of electric circuits, resistors are passive elements that “oppose” current and convert energy into heat. But if we examine them through the lens of Poynting theory (PT), and integrate insights from Tugboat Theory, a much deeper picture emerges.

According to Poynting theory, energy flows through the space around a circuit via the Poynting vector:

\[ \vec{S} = \vec{E} \times \vec{B} \]

This vector describes how electromagnetic energy moves in space, determined by the electric field \( \vec{E} \) and magnetic field \( \vec{B} \). Crucially, energy doesn't travel through the wire — it moves alongside it, guided by the field structure.

A resistor, then, does not merely block this energy — it acts as a coherence damper. When the field energy enters the region of the resistor, the synchronized relationship between \( \vec{E} \) and \( \vec{B} \) begins to break down. The fields still exist, but they lose the structured wavefronts necessary for forward energy propagation. Instead, the energy becomes thermal motion, i.e., heat.

In this sense, resistors are localized decoherence zones: places where the coherent memory of the electromagnetic field is deliberately erased.

Does a Resistor Slow Propagation?

A natural question follows: if resistors disrupt the fields, do they also slow the speed of energy propagation?

The answer is nuanced.

• The speed of field propagation in space is given by: \[ v = \frac{1}{\sqrt{\varepsilon \mu}} \] where \( \varepsilon \) and \( \mu \) are the permittivity and permeability of the medium. In vacuum or air, this speed is close to the speed of light, and it is not directly affected by the resistor.
• However, a resistor reduces the amplitude of the energy flux and disrupts phase coherence. It transforms structured field energy into unstructured heat, which slows the effective delivery of usable energy.
• In other words, the wavefront speed remains constant, but the energy transmission efficiency drops significantly.

In Tugboat Theory terms, the resistor acts like a place where the tugboats forget which direction to pull. The synchronization is lost, and the field stops “handing off” energy in a coordinated way.

Conclusion

Resistors are more than components that oppose current. They are field disruptors — devices that take coherent, synchronized electromagnetic energy and convert it into disorganized thermal motion. While they don't reduce the speed of electromagnetic field propagation in the surrounding space, they dampen the ability of the field to carry coherent energy forward.

This behavior aligns beautifully with Tugboat Theory's view that current and energy transfer are not about particles flowing like water, but about field memory and phase synchronization. A resistor is where that memory ends.

By reinterpreting circuit elements in this way, we open the door to a more unified understanding of classical and quantum electrical behavior, where fields — not wires — carry the truth.

References and Further Reading

• John H. Poynting (1884), “On the Transfer of Energy in the Electromagnetic Field,” Philosophical Transactions of the Royal Society A. https://doi.org/10.1098/rsta.1884.0016
• MIT OpenCourseWare – Lecture on Poynting Vector and Energy Transfer https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-fall-2005/resources/lecture-20-electromagnetic-energy-and-poynting-vector/
• Griffiths, D. J., Introduction to Electrodynamics, 4th Ed. Cambridge University Press.
• Veritasium: “Where Does the Energy Go in an Electric Circuit?” (YouTube) https://www.youtube.com/watch?v=bHIhgxav9LY
• James Redgewell, “Tugboat Theory and Vacuum Memory,” 2025 https://jredgewell.blogspot.com/