Transverse Sensitivity Scale of Photons
Inferred from Classical Diffraction Experiments
David Allen LaPoint
PrimerField Foundation
May 13, 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—a small but easily visible distance. That might sound small, but it’s actually huge compared to the wavelength of light itself. It represents about 4,000 wavelengths.
This result is a constraint on any physical theory: whatever a photon is, it cannot be fully described as a dimensionless point when it comes to predicting diffraction statistics. Standard physics (quantum electrodynamics, QED) accommodates this through the non-local spread of probability amplitudes. In PrimerField (PF) theory, it is interpreted as direct evidence that photons have extended magnetic field structures. Both interpretations are discussed in the conclusions.
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 2.0 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 large 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 and on the threshold chosen. What remains stable is the Fresnel scaling pattern: the distance grows with the square root of wavelength and travel distance. Under the 5% threshold used here, the reference result is about 4,000 wavelengths for green light at 20 cm.
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 are NOT saying the photon physically extends 2 mm.
• We are 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. Different theories do so differently. Standard quantum physics (QED) accounts for it through the non-local spread of probability amplitudes—mathematical quantities that extend across space and govern where detections are likely to occur. PF theory accounts for it through the physical extent of the photon’s field structure. Both accommodate the same numerical result; they differ in what they say about the underlying physical reality.
7.1 What About Beam Splitters?
You might ask: if a photon has an extended field structure, what happens when it hits a beam splitter (a half-silvered mirror that sends light either straight through or off to the side)? Shouldn’t the field split, sending part to each detector?
Experiments show definitively that a single photon never triggers two detectors at once. It always goes one way or the other, never both simultaneously. This is called “antibunching” and it’s one of the best-confirmed results in optical physics.
This seems to conflict with an extended structure. But it doesn’t—because physical extent and divisibility are different things. Think of a bowling ball. A bowling ball is large—it takes up real space—but when it reaches a fork in the road, it goes one way, not both. You wouldn’t say the bowling ball is a point just because it doesn’t split.
PF theory proposes that a photon’s field is extended but indivisible. The entire field configuration goes one way at a beam splitter. This is fully consistent with all known single-photon experiments. The antibunching result tells us a photon can’t be split, not that it must be a point.
7.2 What About the Detector Distance Question?
Since the sensitivity distance depends on the detector distance (it grows with the square root of z), you might ask: how does the photon “know” how far away the detector is when it passes the edge?
It doesn’t. The sensitivity distance x* doesn’t describe a property of the photon at the edge. It describes a property of the experimental setup as a whole. After you’ve fully specified where the detector is, you can calculate x*. It’s a geometric descriptor of the arrangement, like the focal length of a lens system—not something that exists inside the photon in flight.
8. Conclusions
This paper had one goal: to extract a real-space distance scale from the mathematics of diffraction, and to show how photon detection statistics respond to boundary conditions in physical space. 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 x* = 2.0 mm (one-sided). The two-sided span is 4.0 mm (approximately 8,000 wavelengths).
The scaling law x* ∝ √(λz) is independent of the threshold convention. The geometry dependence of x* means it characterizes the experimental configuration, not an intrinsic photon property. The results are fully consistent with standard physics.
8.1 The PrimerField Interpretation
The preceding analysis doesn’t depend on any specific physical theory. It’s a mathematical result from well-tested formulas. What follows is specifically the PrimerField interpretation of that result. Readers who don’t accept the PF framework can set this subsection aside without affecting the validity of the math above.
Within PF theory, the results above are interpreted through five foundational ideas:
1. Photons have real structure. A photon is not a mathematical abstraction or a point of probability. It possesses a real, deterministic field configuration—not as an average or expectation value, but as a fundamental physical property. This differs from standard quantum physics, where the photon has no classical field in a single-particle state.
2. That structure extends far beyond the wavelength. The transverse sensitivity distance x* = 2.0 mm, under the reference geometry used here, gives PF theory a measurement-derived way to estimate where that structure remains detectable through boundary effects. The field doesn’t end at one wavelength—it extends thousands of wavelengths out.
3. The field fades out, it doesn’t stop. There is no hard edge to a photon’s field. The sensitivity distance marks where the influence becomes practically undetectable—not where the field ends. This is analogous to how a magnet’s field extends without a sharp cutoff; you just get to a distance where it’s too weak to measure.
4. The photon is indivisible despite being extended. An extended structure can still be a single unit. The whole field configuration goes one way at a beam splitter and cannot be partitioned by optical elements. This is consistent with the antibunching experiments described in Section 7.1.
5. The structure exists before any measurement. The photon’s field doesn’t grow or change as it travels. The geometry of the experiment determines which portion of that pre-existing structure is probed—like adjusting a window to see more or less of a landscape that was already there.
These five ideas define the PF ontological framework and represent a foundational departure from standard quantum field theory—not an error within it. Both frameworks accommodate the same numerical diffraction results. The question of which framework better describes the underlying physical reality is what PF theory is designed to investigate.
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, G. Roger, and A. Aspect, “Experimental evidence for photon anticorrelation,” Europhysics Letters (1986). Key single-photon experiment cited in Section 7.1.
[8] L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge (1995). Comprehensive treatment of coherence.
[9] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover (1972). Section 7.3 provides the Fresnel integral asymptotic expansions underlying the envelope calculation in the Appendix.
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. Using standard asymptotic expansions of the Fresnel integrals (Abramowitz & Stegun [9], Eq. 7.3.27), the envelope of these oscillations can be shown to decrease as approximately 0.45/u. This result has been verified numerically—at u = 9.0, the computed envelope is 0.0500 ± 0.001, confirming the 5% threshold assignment.
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.