Transverse Sensitivity Scale of Photons
Inferred from Classical Diffraction Experiments
David Allen LaPoint
PrimerField Foundation
January 22, 2026
Plain English Version
Abstract
Scientists have studied how light bends around edges for over 200 years. These experiments are called "diffraction" experiments. This paper looks at those experiments to answer a simple question: How far sideways does a photon (a single particle of light) seem to "reach" when it passes near an edge?
Using standard math that scientists have used for centuries, we find that for visible light traveling about 8 inches (20 cm), the answer is roughly 2 millimeters—about the thickness of a credit card. That might sound small, but it's actually huge compared to the wavelength of light itself. It represents about 4,000 wavelengths.
This means whatever a photon actually is, it can't be a tiny point. Something about the photon must extend outward by millimeters in order for edges that far away to affect where the photon lands. In PrimerField (PF) theory, we interpret this as direct evidence that photons have extended magnetic field structures.
1. Introduction
When light passes by a sharp edge or through a narrow opening, it doesn't just travel in straight lines like you might expect. Instead, it spreads out and creates patterns of light and dark bands. This behavior is called diffraction, and scientists have studied it for hundreds of years.
The math that describes these patterns is extremely accurate. But here's the thing: the equations tell us what patterns to expect, but they don't really tell us why light behaves this way.
This paper asks a simple question that's often overlooked: How far away from the geometric path can an edge or boundary be and still affect where a photon ends up?
We're not making up new physics here. We're just taking the standard, well-tested math and asking what it tells us about how far a photon's influence extends sideways.
Throughout this paper, the word "sensitivity" means only this: the photon detection pattern changes when an edge is within a certain distance. We're not claiming the photon physically touches that distance or that any force acts across it. We're simply measuring when the edge matters and when it doesn't.
2. How We Did This
2.1 The Setup We're Analyzing
To make meaningful comparisons, we need to keep certain things constant. Here are the conditions we use throughout this paper:
Wavelength: 500 nanometers (nm). This is green light, roughly in the middle of the visible spectrum.
Distance from edge to detector: 20 centimeters (about 8 inches). This is the distance the light travels after passing the edge before we detect it.
Single photon conditions: We're thinking about what happens one photon at a time. The patterns we see are built up from many individual photon detections.
These choices let us calculate specific numbers that anyone can verify.
2.2 The Fresnel Scale
The math of diffraction uses a natural length scale that combines wavelength and distance. This is called the Fresnel length, and it tells us roughly where the transition happens between "edge matters a lot" and "edge barely matters."
For our conditions (green light at 20 cm), this Fresnel length works out to about 0.22 mm. But that's just the starting point—it tells us where significant effects begin, not where they become negligible.
2.3 How We Define 'Negligible'
Here's a tricky thing about diffraction: as you move away from the edge, the light intensity doesn't smoothly approach its final value. Instead, it wobbles up and down around that final value, with the wobbles getting smaller and smaller.
So you can't just say "the intensity is within 5% of the final value" because it might cross that threshold multiple times.
Instead, we use an "envelope" approach. We ask: at what distance do ALL the subsequent wobbles stay within our threshold? This gives us a single, reproducible number.
For this paper, we chose a 5% envelope threshold. This means we find the distance where the maximum deviation from the final intensity stays below 5% forever after.
3. Edge Diffraction Results
3.1 The Basic Math
When light passes by a sharp straight edge (like a razor blade), the resulting pattern is described by mathematical functions called Fresnel integrals. These have been known and tested for over 200 years.
The key result is that light intensity approaches its final value in an oscillating way. The envelope of these oscillations decreases roughly as 1 divided by the distance from the edge.
3.2 What the Numbers Tell Us
Table 1 shows how the light intensity varies at different distances from the geometric edge. Notice how the deviation bounces around rather than smoothly decreasing.
| Distance (mm) | Intensity Ratio | Deviation |
|---|---|---|
| 0.67 | 1.108 | 10.8% |
| 1.12 | 1.065 | 6.5% |
| 1.79 | 0.961 | 3.9% |
| 2.24 | 0.969 | 3.1% |
| 3.35 | 1.021 | 2.1% |
| 4.47 | 0.984 | 1.6% |
| 6.71 | 0.989 | 1.1% |
| 11.18 | 0.994 | 0.6% |
Table 1. Light intensity at various distances from the geometric edge (green light, 20 cm distance).
3.3 The Sensitivity Distance
Using the envelope approach with a 5% threshold, we find that all subsequent intensity variations stay within 5% once you're about 2.0 mm from the geometric edge.
This is our main result for edge diffraction: at this specific geometry (green light, 20 cm travel distance), the presence of an edge still measurably affects photon detection patterns out to about 2 millimeters.
| Threshold | Sensitivity Distance |
|---|---|
| 10% | ~1.0 mm |
| 5% | ~2.0 mm |
| 3% | ~3.4 mm |
| 2% | ~5.1 mm |
| 1% | ~10.1 mm |
Table 2. Sensitivity distance for different threshold choices (green light, 20 cm).
3.4 Different Colors of Light
The sensitivity distance depends on wavelength. Longer wavelengths (redder light) give larger distances; shorter wavelengths (bluer light) give smaller distances. The relationship follows a square-root pattern. Table 3 shows the results across the visible spectrum.
| Color | Wavelength | 5% Distance |
|---|---|---|
| Violet | 400 nm | 1.8 mm |
| Blue | 450 nm | 1.9 mm |
| Green | 500 nm | 2.0 mm |
| Yellow | 580 nm | 2.2 mm |
| Red | 700 nm | 2.4 mm |
Table 3. Sensitivity distance across visible wavelengths (20 cm propagation, 5% threshold).
3.5 Thousands of Wavelengths
Here's what makes this result striking: for green light at 500 nm, a 2 mm sensitivity distance represents about 4,000 wavelengths. The boundary influence extends across a distance four thousand times larger than the wavelength of the light.
For different colors, this ratio ranges from about 3,400 wavelengths (red) to 4,500 wavelengths (violet). Any way you slice it, that's a huge number.
4. Single-Slit Diffraction
A single slit (a narrow rectangular opening) has two edges instead of one. The full diffraction pattern involves both edges working together.
A useful rule of thumb: if the slit is wide enough that each edge is outside the sensitivity range of the other (meaning the slit is wider than about 4 mm for our conditions), then the center of the slit behaves roughly as if no edge were present.
This is just a rough guide—the actual two-edge math is more complicated—but it shows how the edge diffraction results give us intuition about finite openings.
5. Double-Slit Interference
Double-slit experiments involve different physics than edge diffraction. The interference fringes depend on how well the light source is "coherent"—meaning whether the light waves at the two slits stay in a fixed relationship.
The sensitivity distance we calculated for edges doesn't directly apply to double-slit fringe visibility. Double-slit experiments probe source preparation rather than boundary proximity.
6. How Distance Affects the Result
An important feature: the sensitivity distance depends on how far the light travels after passing the edge. This follows directly from the Fresnel math.
The relationship is a square root: double the travel distance, and the sensitivity distance increases by about 41% (square root of 2). Table 4 shows this effect.
| Travel Distance | 5% Sensitivity Distance |
|---|---|
| 2 cm | 0.64 mm |
| 20 cm | 2.0 mm |
| 2 m | 6.4 mm |
| 20 m | 20.1 mm |
Table 4. How travel distance affects sensitivity distance (green light, 5% threshold).
This tells us the sensitivity distance isn't a fixed property of the photon alone. It depends on the geometry of the experiment. However, the scale factor (the 4,000 wavelengths worth of distance) is inherent in the physics.
7. What This Means
What we've done here is take well-established physics—Fresnel diffraction formulas that have been tested and confirmed for over two centuries—and extract a specific distance scale that's usually left implicit.
The math shows that the approach to geometric optics (light traveling in straight lines) is oscillatory, not smooth. This is why we needed the envelope approach.
To be clear about what we are and aren't claiming: we're NOT saying the photon physically extends 2 mm. We're NOT saying there's a force acting over 2 mm. We ARE saying that if you place an edge within 2 mm of the geometric path, the detection pattern changes measurably. That's an empirical fact embedded in the standard math.
Any physical theory that claims to describe what photons actually are must account for this. If single photons build diffraction patterns statistically, and if edges within millimeters affect those patterns, then whatever a photon is must have some property that extends across that distance.
8. Conclusions
This paper had one goal: to extract a real-space distance scale from the mathematics of diffraction.
Using green light (500 nm wavelength) traveling 20 cm, with a 5% envelope threshold for negligibility, we get approximately 2.0 mm. This corresponds to about 4,000 wavelengths.
For reference purposes going forward, we establish this as a "canonical anchor": under these specific conditions, the transverse sensitivity scale is 2.0 mm.
Within PrimerField (PF) theory, this result has a direct interpretation: photon fields extend transversely over millimeter scales under these propagation conditions. If boundary conditions millimeters away can change where individual photons are detected, then the photon cannot be a dimensionless point. Something about the photon—which PF theory identifies as its field structure—must extend across that distance.
This isn't speculation added on top of the math. It's the physical implication of the math itself. The Fresnel predictions are experimentally validated. This sensitivity distance is therefore a constraint that any realistic description of light must satisfy.
References
[1] M. Born and E. Wolf, Principles of Optics, 7th ed., Cambridge University Press (1999). The classic textbook on optical physics.
[2] J. W. Goodman, Introduction to Fourier Optics, 3rd ed., Roberts & Company (2005). Standard text for diffraction theory.
[3] E. Hecht, Optics, 5th ed., Pearson (2017). Widely used undergraduate textbook.
[4] A. Sommerfeld, Optics, Academic Press (1954). Advanced treatment of wave optics.
[5] A. Fresnel, original memoirs on diffraction (1818-1826). The foundational work on this subject.
[6] R. P. Feynman, QED: The Strange Theory of Light and Matter, Princeton (1985). Popular explanation of quantum electrodynamics.
[7] P. Grangier et al., "Experimental evidence for photon anticorrelation," Europhysics Letters (1986). Key single-photon experiment.
[8] L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge (1995). Comprehensive treatment of coherence.
Appendix: The Math Behind the Numbers
For readers interested in the technical details, here's a brief explanation.
The Fresnel integrals C(u) and S(u) are defined as integrals of cosine and sine functions with a quadratic argument. The variable u is a "normalized coordinate" that packages together the physical distance, wavelength, and propagation distance.
For the knife-edge case, the intensity formula involves squaring the sum of these functions. As u gets large, the intensity approaches 1 (the unblocked value), but it does so in an oscillating way.
The envelope of these oscillations decreases approximately as 0.45/u. Setting this equal to our 5% threshold and solving gives u ≈ 9.0.
Converting back to physical distance: at 500 nm wavelength and 20 cm propagation, u = 9.0 corresponds to x ≈ 2.0 mm.
All the numbers in this paper can be verified using standard Fresnel integral calculators, including the scipy.special.fresnel function in Python.