Axial Alignment, Multiple Redshift Systems,
and Einstein Ring Formation

Why Face-On Galaxies Produce Complete Einstein Rings, Why Every Examined Ring System Shows Multiple Redshifts, and Why PF Theory Unifies These Patterns as One Axial Structural Phenomenon

David Allen LaPoint

PrimerField Foundation

May 15, 2026

Abstract

Einstein rings are circles of light that appear around certain galaxies when everything lines up just right between a distant light source, a foreground galaxy, and our telescopes. This paper presents three separate lines of evidence from published astronomical surveys that together point to a new explanation for how these rings form — one based on the magnetic field structure of PrimerField (PF) Theory rather than on Einstein's theory of gravity bending space.

First, the most complete, nearly perfect rings are seen around galaxies that appear nearly circular in our sky — meaning we are looking straight down their central axis. This is the opposite of what Einstein's gravity-based lensing theory predicts for disk-shaped galaxies. Second, every ring system in this analysis where detailed light measurements exist shows multiple distinct speed signatures, consistent with the six energy flow zones of a dual-bowl PF magnetic field structure viewed straight-on from the end. Third, galaxies with jets pointed directly at Earth — called blazars — show about twice as many absorbing gas systems along their line of sight compared to randomly oriented galaxies, while galaxies with jets at intermediate angles show no such excess.

A new prediction is presented: the probability of forming a complete Einstein ring should decrease steadily from near-circular galaxies (E0 type) to highly elongated galaxies (E7 type). The PrimerField dual-bowl magnetic field geometry, confirmed in laboratory plasma experiments, provides a single unified explanation for all three patterns. The Equatorial Null Zone — a ring-shaped zone where opposing magnetic fields cancel — acts as a magnetic guide, directing light to a specific ring radius set by the field's own geometry. The PrimerField geometry underlying these predictions was established from physical experiments before this literature analysis was conducted. The pattern in the data was not the source of the hypothesis.

1. Introduction

Einstein rings are among the most striking sights in astronomy. When a distant glowing object sits almost exactly behind a large foreground galaxy from our point of view, its light wraps all the way around that galaxy and reaches us as a complete circle of light. The first Einstein ring was discovered in the 1980s. Roughly fifty confirmed examples are now known.

The standard explanation treats each ring as light being bent by the gravity of the foreground galaxy, which warps the surrounding space according to Einstein's General Relativity. Under this view, the ring's size depends on how massive the foreground galaxy is and how far apart everything is. When multiple distance measurements (called redshifts) appear from the same patch of sky, the standard explanation says these are simply unrelated galaxies at different distances that happen to line up by coincidence.

This paper challenges both of those interpretations. It presents three independent lines of evidence — from galaxy shape, from multiple speed signatures, and from absorption patterns along jet-aligned sightlines — that together point to a single structural explanation grounded in PrimerField Theory's dual-bowl magnetic field geometry.

A critical note on how we arrived here: The dual-bowl PrimerField field shape described in this paper was established through physical laboratory experiments with magnetic arrays and confirmed through plasma confinement experiments — before any astronomical data was examined. The orientation predictions, the ring formation mechanism, and the multiple-speed-signature structure were all derived from that geometry first. The pattern in the data was not the source of the hypothesis. This matters: predicting something before finding it is a different — and stronger — kind of evidence than fitting an explanation to data after the fact.

2. What Gravity Theory Predicts vs. What We Actually See

Studies of how disk-shaped spiral galaxies bend light — particularly the well-known Keeton and Kochanek (1998) and Maller, Flores, and Primack (1997) analyses — predict that tilted, edge-on disk galaxies should be better light-benders than face-on ones. Think of it this way: an edge-on coin concentrates more of its mass along your line of sight than a face-on coin does. These studies apply specifically to disk and spiral galaxies, not all galaxy types.

What disk-lensing models predict: For disk-dominated galaxies, Einstein's gravity-lensing calculations favor more highly tilted, edge-on galaxies as more effective ring-formers, with the predicted efficiency increasing several times over for edge-on versus face-on views.

What is actually observed: The opposite pattern appears in the data. The most complete, cleanest Einstein rings are associated with foreground galaxies that appear nearly circular in our sky. The Jackpot (SDSS J0946+1006), the Euclid ring in NGC 6505, the double ring system FOR J0332-3557, and most rings in the SLACS survey all involve foreground galaxies with nearly circular projected shapes. When the measured elongation of lens galaxies is reported, it consistently trends toward low values — consistent with looking straight down their axis — not the elongated profiles expected from highly tilted galaxies.

This is not a small discrepancy. The standard gravity-lensing calculations predict that tilted galaxies should be better lenses. Yet the cleanest complete rings come from face-on, nearly circular galaxies. Standard gravity theory can accommodate this by invoking selection effects, dark matter halo orientation, or background source positioning — but each of those requires a separate add-on explanation for each case. PF Theory predicts complete-ring formation from face-on geometry as a direct, first-principles consequence of its field structure, as explained in Section 5.

3. Multiple Speed Signatures in Einstein Ring Systems

When astronomers analyze the light from Einstein ring systems in detail, they find something surprising: every system in this analysis where detailed measurements exist shows multiple distinct speed signatures — meaning the light carries marks of material moving at several different speeds in several different directions. This claim applies only to the specific systems examined in this paper; it is not stated as a conclusion about every known Einstein ring system.

To understand this, you need to know about two ways these speed signatures are detected:

Source-plane redshifts are spectroscopically identified background galaxies lensed by the foreground system. In the Jackpot system, these are detected at redshifts of z = 0.222 (the foreground galaxy itself), 0.609, 2.4, and approximately 6. Standard astronomy treats each redshift as a completely separate, unrelated galaxy at a different cosmological distance that happens to lie along the same line of sight.
Absorption-line redshifts are patterns in light from blazars (galaxies with jets pointed at Earth) and quasars, where intervening gas absorbs specific colors of light. Each absorption pattern tells us the speed and direction of the absorbing gas.

Standard astronomy treats these two categories separately. PF Theory proposes that both may reflect the same underlying structure: distinct energy flow zones within a single PF dual-bowl field system, each zone producing its own characteristic speed signature when the system is viewed straight-on along its axis.

The probability problem for standard theory: The standard interpretation of the Jackpot requires four separate, unrelated objects to be aligned within arcseconds across billions of light-years — a probability the discoverers themselves described as extraordinarily small under a chance-alignment model.

A key clarification about redshift and distance: When we look at a very distant galaxy, all of its light is already shifted toward the red end of the spectrum by the expansion of the universe over billions of years. This is the cosmological redshift baseline. Any internal motion within the PF field structure that points toward us would appear as a reduced redshift relative to that baseline — not as an actual blueshift. Any motion pointing away would appear as an increased redshift. The result is a spread of redshift values at different magnitudes, all positive — which is exactly what is observed in systems like the Jackpot.

Furthermore, each energy flow zone produces a range of speed values rather than one single sharp value. Material at the outer edge of each zone moves at a different angle than material near the center. This means the number of distinct signatures that can be detected is limited by the precision of our instruments, not by the actual number of flows. Better instruments are predicted to resolve additional components that currently appear blended together.

4. The Blazar Excess: An Orientation Test

Blazars are active galactic nuclei — extremely energetic galaxy cores — whose jets happen to point almost directly toward Earth. In PF terms, this means we are looking straight down the axis of the galactic dual-bowl field structure. This makes blazar sightlines a natural test: if axial alignment causes excess absorption signatures, they should appear in greater numbers along blazar sightlines than along randomly oriented sightlines.

4.1 The Bergeron et al. (2011) Finding

Bergeron, Boissé, and Ménard (2011) analyzed spectroscopic data for 45 blazars and measured the number of magnesium absorption systems along their lines of sight, compared to a control sample of normal quasars. The result was a statistically significant excess — approximately double — the number of absorption systems toward blazars compared to the control group.

This was described as unexpected because, under the standard model, intervening absorbers should be completely independent of which way the background source's jet points. Standard gravity provides no mechanism by which jet orientation should correlate with the number of absorption systems along the line of sight.

Caveat: A follow-up study by Mishra et al. (2018) with a larger blazar sample found the excess less statistically clear when the sample size was increased. This result is included here in the interest of scientific honesty. The Bergeron et al. finding remains the most directly relevant published result, and the control case described below provides independent orientation evidence. The uncertain status of the blazar excess is acknowledged rather than hidden.

4.2 The Control Case: Chand and Gopal-Krishna (2012)

The key control experiment was provided by Chand and Gopal-Krishna (2012), who analyzed approximately 115 flat-spectrum radio-loud quasars (FSRQs). FSRQs have jets oriented at intermediate angles to the line of sight — not directly at us like blazars, but not sideways either. Under the PF framework, intermediate orientation should produce reduced or no excess absorption compared to blazars.

Result: No statistically significant excess was found for FSRQ sightlines compared to normal quasars. The authors explicitly attributed the blazar excess to the extreme axial orientation of blazar jets. When the jet is not pointed at us, the excess disappears.

This provides a useful check: look straight down the axis and excess absorbers appear. Do not look down the axis and the excess disappears. Under the standard model, this correlation has no explanation. Under PF Theory, it is a direct consequence of looking into versus across the internal flow zone structure.

A prediction extending this result: if FSRQ sightlines were analyzed at sufficient precision and sorted by jet angle, the excess absorption should appear as a continuous gradient — increasing steadily from random quasars through FSRQs to blazars — tracking the degree of axial alignment. This would convert a binary (blazar vs. non-blazar) comparison into a continuous test of the orientation-absorption relationship.

4.3 Summary of Orientation Evidence

The pattern is consistent across all examined categories. Axial alignment — whether measured by galaxy shape, jet orientation, or ring completeness — is the common factor in enhanced Einstein ring formation and excess multiple speed signatures. No standard model mechanism predicts this correlation. PF Theory predicts it from the geometry of the dual-bowl field structure.

5. How PrimerField Theory Explains All Three Patterns

PrimerField Theory describes a universal field architecture based on two opposing bowl-shaped magnetic field regions, with their narrow ends facing each other and their wide ends facing outward. This geometry — derived from physical laboratory experiments and confirmed through plasma confinement experiments — produces characteristic internal structures and external field boundaries that scale from laboratory to galactic dimensions.

Figure 1. Labeled cross-section of the dual-bowl PrimerField field structure. EJ = Ejection Jets (outflows from the narrow ends); CD = Confinement Dome; FR = Flip Ring; CR = Choke Ring; FP = Flip Point; ENZ = Equatorial Null Zone (a ring-shaped zone at the equator where opposing field lines cancel each other out); CZ = Compression Zone; CZB = Compression Zone Boundary; EP = Equatorial Plane.

5.1 Six Energy Flows and Their Speed Signatures

A dual-bowl PF system contains six distinct energy flow paths, each moving at a different speed and in a different direction relative to an observer looking straight down the axis. Critically, each flow zone produces a range of speeds, not a single fixed value. The flow angle and speed vary continuously within each zone, producing a corresponding range of Doppler speed signatures along any axial line of sight. (The Doppler effect is the same reason a siren sounds higher as it approaches and lower as it moves away — motion affects the apparent frequency of waves.)

Flow Zone 1 — Outer bowl circulation (Bowl 1): Energy flowing away from the equatorial plane along the outer region of the first bowl. Speed is mostly sideways at the rim, becoming more aligned with the axis near the center entrance. Produces a moderate redshift range, smallest at the outer rim.
Flow Zone 2 — Central flow inward (Bowl 1): Energy flowing toward the center region through the central column. This flow is most directly aligned with the axis and accelerates toward the center, producing the widest redshift range — from moderate at the entrance to maximum near the center.
Flow Zone 3 — Central flow inward (Bowl 2): Mirror of Flow Zone 2 from the opposing bowl. Produces an equivalent redshift range along the same line of sight, overlapping spatially with Flow Zone 2.
Flow Zone 4 — Outer bowl circulation (Bowl 2): Mirror of Flow Zone 1. Overlaps spatially with Flow Zone 1 in the projected axial view.
Flow Zone 5 — Ejection Jet (Bowl 1): High-speed outflow along the axis from the narrow end of Bowl 1, directed toward the observer. Produces a reduced redshift signature relative to the cosmic baseline — the single flow in the system moving toward the observer.
Flow Zone 6 — Ejection Jet (Bowl 2): High-speed outflow from Bowl 2 in the opposite direction, moving away from the observer. Produces the maximum redshift contribution in the system. Both ejection jets operate at the highest speeds and most direct axial angles, making them the dominant speed signatures.

Figure 2. Cross-section energy flow diagram showing the circulation pattern within a dual-bowl PF structure. Magenta arrows indicate energy flow direction. The outward leg of each bowl and the inward central flow are both visible. Each leg produces a distinct speed signature for an observer looking straight down the axis. The near-side and far-side bowls both contribute simultaneously, producing the full set of six overlapping speed signatures along any axial line of sight.

5.2 Axial Alignment and Multiple Speed Signatures

When an observer's line of sight is aligned with the axis of a dual-bowl PF system, the combined light received from the galactic face carries contributions from multiple distinct flow zones — not because any single photon passes through all six zones one after another, but because different positions across the face of the structure sample different flow environments simultaneously.

Figure 3. Computed magnetic field intensity (side view cross-section) of a dual-bowl PrimerField array at 15.5 cm bowl spacing, with predicted energy flow zones indicated. Green arrows show flow direction within each zone; arrow length is proportional to predicted Doppler speed contribution. Zone A (central column, innermost) carries the longest arrows — highest velocity, most axial, widest speed range. Zone B (bowl circulation, intermediate) carries medium arrows. Zone C (outer circulation) carries shortest arrows. Blue circles mark the cross-sectional location of the Equatorial Null Zone (ENZ) where opposing field lines cancel.

Figure 4. Computed magnetic field intensity, top-down view at the midplane of the same dual-bowl PrimerField array — the view an observer looking directly down the galactic axis would see. The dark ring at approximately 12–13 cm radius is the Equatorial Null Zone (ENZ); viewed face-on it becomes a complete dark ring. Letters A, B, and C identify the same speed gradient zones from Figure 3, now seen as concentric ring-shaped regions. The ENZ ring is where PF Theory predicts an Einstein ring forms.

A photon traveling along the central axis passes through the ejection jet columns and the central flow region. A photon at an intermediate distance from the axis passes through the bowl circulation zones. A photon at the ENZ radius is deflected into the ring. The detector integrates across all of these positions simultaneously, producing a spectrum with multiple absorption components at different redshift values — not because the photons passed through separate galaxies, but because they sampled distinct velocity environments at different spatial positions within one structure.

When the observer's line of sight is perpendicular to the axis — as with an edge-on galaxy — the six flows are not separated along the line of sight. They blend into a single broader signature. This is why edge-on and intermediate-orientation systems do not show the same clean multiple speed structure as axially aligned systems.

An important observational limitation: Current instruments measure absorption line positions (speed values) but cannot determine where along the line of sight each absorption occurred relative to the Einstein ring radius or galactic center. The mapping of speed zones to spatial positions shown in Figures 3 and 4 is a prediction of PF Theory that current instruments cannot yet verify directly. This is an open experimental prediction, not a confirmed observation.

5.3 Face-On Orientation and Einstein Ring Formation

In PF Theory, a face-on galaxy orientation corresponds to the observer being aligned with the structural axis of the galactic PF field. The axially symmetric field geometry produces a specific boundary structure — the Equatorial Null Zone (ENZ) — at a characteristic equatorial radius determined by the field architecture of the system.

Figure 5. Three-dimensional view of the dual-bowl PF structure showing the equatorial plane (grey disc) intersecting the field geometry. The ENZ forms as a ring at the equatorial radius where opposing field lines from both bowls cancel. A face-on observer — looking straight down the vertical axis — sees this structure as a ring at a specific projected radius. An edge-on observer sees only the side profile and cannot produce the symmetric ring geometry required for a complete Einstein ring.

5.4 The ENZ as a Magnetic Guide: How Einstein Rings Form

PF Theory proposes a specific mechanism for Einstein ring formation that differs fundamentally from Einstein's gravity mechanism. In the PF framework, light is an electromagnetic field structure that propagates through and interacts with the surrounding magnetic field geometry. Incoming photons traveling along or near the galactic axis do not experience curved spacetime — they follow the magnetic field line geometry of the galactic PF structure.

In the side view (Figure 3), the field lines curve and converge toward the equatorial plane from both above and below, funneling toward a specific equatorial radius. In the top-down view (Figure 4), this convergence appears as a dark null ring — the ENZ — at a well-defined radius. An incoming photon following these field lines is guided to the ENZ radius and deflected into a circular path, producing the ring.

Both Einstein's General Relativity and PF Theory predict a ring. They disagree on the cause and therefore on the predicted ring size. General Relativity predicts ring size from mass and distance geometry. PF predicts ring size as an emergent property of the galactic field architecture — bowl curvature, field strength, bowl spacing, and gap geometry all contribute. The current paper does not attempt quantitative ring radius predictions, as this requires detailed field characterization of each system. This is a direction for future work.

6. Case Study: SDSS J0946+1006 ("The Jackpot")

6.1 Observed Structure

This system consists of a massive foreground galaxy at a redshift of z = 0.222, surrounded by two concentric partial ring structures. The inner ring, at an angular radius of 1.43 arcseconds, corresponds to a source at z = 0.609. The outer ring, at 2.07 arcseconds, corresponds to a source at approximately z = 2.4. A subsequent analysis identified a third lensed source at z ≈ 6, with an angular radius of approximately 2.5 arcseconds. Additionally, standard modeling of the system requires a "dark substructure" — something with the mass of a small galaxy but no detected light.

The rings are partial — not complete circles — indicating that the system is not perfectly face-on but slightly tilted relative to our line of sight. This is consistent with the PF interpretation that complete rings require near-perfect axial alignment, and partial rings indicate a slight offset from the axis.

Figure 6. Hubble Space Telescope image of SDSS J0946+1006, the "Jackpot" gravitational lens system. Two concentric partial rings are visible at different radii, both incomplete in the same upper-left quadrant. Under PF Theory, both rings are arcs rather than complete circles because the system is viewed slightly off-axis. The identical angular interruption in both rings is interpreted under PF Theory as evidence of one unified tilted axial geometry rather than unrelated source planes at different cosmological distances. Image credit: NASA/ESA/Hubble.

6.2 What Standard Astronomy Requires

The standard interpretation requires three separate background source galaxies behind the foreground lens, each independently lensed to produce the observed ring structure. The discoverers noted that the probability of this specific alignment configuration is extraordinarily small under a chance-alignment model, even accounting for lens selection effects. Additionally, the dark substructure detected in lens modeling has no obvious luminous counterpart — it appears as mass without corresponding light-emitting material.

6.3 What PF Theory Predicts

In PF Theory, the Jackpot is a single dual-bowl PF system viewed slightly off-axis. The multiple redshift components correspond to the six energy flow zones of the field structure. Not all six flows produce separately resolvable absorption components at current spectral resolution — the near-side and far-side equivalents of each zone overlap in velocity space, and gradient flows blend into broader features. The four observed components reflect the resolution limit of current instruments, not the total number of flows.

PF interprets the modeled "dark substructure" as internal PF field architecture — a non-luminous field structure rather than a separate dark-matter clump or faint satellite galaxy. The lens model requires invisible structure; PF interprets that as field architecture.

The probability of this configuration under PF Theory is not extraordinarily small. Every sufficiently luminous dual-bowl system viewed near its axis should present the field geometry capable of producing concentric structures and multiple speed components. The rarity under the standard model reflects the inadequacy of the chance-alignment model, not an unlikely event.

6.4 Redshift Ordering and the Gradient Prediction

The observed pattern in the Jackpot shows redshift increasing with angular distance from center. The central region has the lowest observed redshift, and the outermost partial ring corresponds to the highest. This ordering is consistent with the PF flow zone geometry: the central column zone produces flow components that partially cancel the cosmological redshift for near-side flows, while the outer zones produce flows at larger angular radii with different net Doppler contributions.

The key prediction is not the exact ordering of the components, but the existence of a structured, orientation-dependent set of absorption components whose number and velocity distribution reflect the flow zone geometry — and whose detection is enhanced by axial viewing and suppressed by non-axial viewing.

7. Ring Completeness and Viewing Angle: The Core Visual Argument

Among the most visually compelling evidence in this paper is a pattern visible across a survey grid of sixteen lens systems reproduced below. The pattern is immediately apparent even before any formal analysis.

Figure 7. Sixteen gravitational lens systems from the Sloan Lens ACS (SLACS) Survey, imaged by the Hubble Space Telescope. Orange: foreground lens galaxies. Blue: lensed background sources. The most complete, nearly circular rings are associated with lens galaxies that appear nearly circular — consistent with near-axial or face-on orientation under the PF interpretation. Partial rings and arcs are associated with lens galaxies showing elongated projected shape — consistent with tilted orientation. PF predicts this correlation will persist monotonically — a falsifiable test using existing data. Image credit: NASA/ESA/Hubble/SLACS Survey Team.

In General Relativity lensing, any preferred axis in the ring morphology must come from outside the field theory itself — through the projected mass distribution of the lens, external gravitational shear, background source position, or detection effects. There is no intrinsic connection between the lens galaxy's orientation relative to the observer and ring completeness. In PF Theory, the preferred axis is intrinsic to the field structure itself. Face-on: complete ring. Tilted: arc. Edge-on: nothing.

What the data shows: Ring completeness scales directly and systematically with face-on orientation of the lens galaxy. The most complete rings are associated with lens galaxies whose projected shape is nearly circular. The least complete rings are associated with lens galaxies showing elongated projected shapes. This pattern is visually apparent across the grid and has been noted qualitatively in the SLACS literature without a mechanism being offered.

Think of it this way: hold a hula hoop directly in front of you and it looks like a perfect circle. Tilt it and it looks like an ellipse or an arc. Tilt it all the way to edge-on and you see only a thin line. The ENZ behaves the same way — and the pattern in Figure 7 is the expected result of that geometry.

The pattern in Figure 7 calls for systematic measurement: a formal audit of ring completeness versus projected lens elongation across the full SLACS catalog would test whether the correlation is stronger than expected from General Relativity lens modeling, source alignment, and selection effects alone. PF Theory predicts the correlation will hold monotonically — a falsifiable test using existing published data.

7.5 Are the Rings from a Background Galaxy or from the Foreground Galaxy's Own Field?

A foundational question deserves explicit examination: in Einstein ring systems, is the ring light actually coming from a separate galaxy located billions of light-years behind the foreground galaxy, or could it originate within the field structure of the foreground galaxy itself? This question is rarely posed directly in mainstream literature because the background-source interpretation is assumed as the starting framework. But the assumption is worth examining.

Complete near-axial rings may include light produced within the ENZ field structure rather than from a background galaxy.
Short arcs and partial rings may still involve redirected light from a genuine background source.

PF Theory's claim is that the same field geometry controls both cases — the ENZ determines where light concentrates or is redirected, whether that light originates inside or outside the field structure.

What is directly detected: Rings and arcs of light at specific angular positions around certain foreground galaxies, with speed measurements showing different values in the same direction of sky. The ring morphology is detected. The cause — whether the light originated from behind the galaxy or within its field structure — is inferred, not directly measured.

This distinction has implications for the multiple redshift components observed in systems like the Jackpot. If some of the redshift components reflect Doppler velocities within PF flow zones rather than cosmological distances of background sources, the number of truly independent source planes required drops substantially — and with it, the extraordinarily small probability that standard modeling requires for the chance alignment.

8. Predictions and Falsifiability

8.1 Maximum Component Count

The six-flow model predicts that a single dual-bowl system viewed along its axis can produce a maximum of six distinct velocity signatures — four from bowl circulations and two from ejection jets. At current instrument resolution, fewer components are typically resolved because gradient flows blend and near-side/far-side equivalents overlap in velocity space.

Prediction: As instrument resolution improves, the number of resolved absorption components in axially aligned systems will increase. Systems currently showing two or three components will resolve into four, five, or six components. No single system will show more than six distinct redshift signatures attributable to internal flows.

8.2 Orientation Dependence

Prediction: A systematic survey of Einstein ring systems will confirm that complete or near-complete rings are produced preferentially by galaxies whose projected shape is near-circular — consistent with face-on orientation. The fraction of complete rings will decline continuously as lens galaxy elongation increases, reaching near zero for highly elongated projected shapes.

This prediction is opposite to General Relativity-based disk-lensing cross-section predictions. If confirmed statistically, it supports axial field structure as the organizing principle over projected mass concentration.

8.3 Blazar-Quasar Absorption Gradient

Prediction: When blazar and FSRQ samples are sorted by estimated jet inclination angle, the absorption excess should scale continuously with alignment. Blazars at the tightest alignment show the highest excess. FSRQs at intermediate angles show reduced but non-zero excess. Random quasars show baseline. This continuous gradient prediction is more precise and more falsifiable than the binary comparison, and it follows directly from the PF flow zone geometry.

8.4 Galaxy Shape and Einstein Ring Probability: The E0–E7 Prediction

The Hubble classification system for elliptical galaxies ranges from E0 (apparently circular) to E7 (highly elongated, with about a 3:1 axis ratio). PF Theory predicts a direct relationship between Hubble ellipticity subtype and Einstein ring formation probability: an E0 galaxy appears circular when projected onto the sky, consistent with axial viewing; an E7 galaxy appears highly elongated, meaning the observer is viewing it at a large angle to its symmetry axis. Einstein ring formation becomes geometrically impossible as the viewing angle increases toward edge-on.

E0 — highest Einstein ring formation probability. The circular projected shape is directly consistent with the face-on axial alignment required for ring formation.
E1 through E3 — declining probability. Rings may form but will be incomplete, appearing as arcs rather than full circles.
E4 through E7 — near-zero probability. A 1966 finding in the mainstream literature also established that most E4–E7 classified galaxies are misclassified lenticular (S0) galaxies. The true elliptical population capable of producing Einstein rings may be concentrated almost entirely at E0–E3.

No systematic survey has compiled the E0–E7 subtype distribution of Einstein ring host galaxies. The SLACS catalog data exists and could in principle be analyzed to test this prediction directly. Such an analysis would produce a distribution that either confirms the monotonic decline from E0 to E7 predicted by PF Theory, or shows a flat or inverted distribution consistent with General Relativity-based disk-lensing cross-section predictions.

This prediction is stated here as a Guided Extrapolation — derived by applying PrimerField's established axial geometry to the existing Hubble classification system. The underlying PF geometry is the established framework; the connection to E0–E7 probability is the extrapolation.

9. Discussion

The three observational patterns documented in this paper — face-on ring formation, multiple speed signatures in every examined ring system, and orientation-dependent absorption excess — have each been noted separately in the mainstream literature. What has not been done, until now, is to connect these three findings into a single coherent picture. Standard cosmological theory has no structural framework that naturally produces all three simultaneously. PF Theory has exactly such a framework.

A single dual-bowl magnetic field geometry, viewed along its axis, simultaneously produces all three effects: axial symmetry creates the face-on orientation that enables ring formation; the six flow zones create the multiple speed components; and the axial enhancement of absorption systems explains the blazar excess. Three independent observational patterns explained by one geometric structure.

On the Event Horizon Telescope imaging of M87: The EHT image of M87 shows a bright ring with a dark central region at a specific angular radius. The top-down magnetic field computation shown in Figure 4 shows a structurally similar pattern at the ENZ — a dark null ring at a defined radius, with a brighter field interior. Both General Relativity and PF predict a ring. GR attributes the ring to the photon sphere around a singularity. PF attributes it to the ENZ of the galactic dual-bowl field structure. A definitive discrimination requires either precise ring radius predictions from PF field modeling or detection of observational signatures that one mechanism predicts and the other does not. This comparison is noted here as a direction for future analysis, not as a confirmed result.

On central density: If the PF field geometry organizes matter at galactic scales, and the ENZ, jets, and circulation zones are all field-determined rather than gravity-determined, then the apparent mass concentration at the galactic center is not a singularity accumulating infinite density. It is a center region defined by the field geometry, with a maximum density set by the point at which the field structure itself can no longer compress matter further. The extreme density estimates derived from General Relativity orbital mechanics assume a point mass model. If orbital velocities are set by field structure rather than point mass gravity, the inferred central density from GR models is an artifact of an incorrect model.

10. Laboratory Confirmation of the Dual-Bowl Field Geometry

The dual-bowl field geometry described throughout this paper is not a theoretical construct. It has been physically realized at laboratory scale using arrays of permanent magnets arranged in bowl-shaped configurations, and tested in plasma experiments under vacuum conditions. The plasma self-organizes in response to the field geometry, providing experimental confirmation of the field's confinement and organizational properties.

Figure 8. Laboratory Confirmation: Dual-Bowl Plasma Confinement. Plasma confined in a spherical ball at the nuclei region of a dual CERN-bowl magnetic array in a laboratory vacuum chamber. The plasma self-organizes into a sphere at the focal point between the two bowls — behavior predicted by PrimerField field geometry and confirmed experimentally. This is not a simulation or theoretical construct. The ejection jets visible as pink/red columns above and below the plasma sphere correspond directly to the EJ structures identified in the field architecture diagrams throughout this paper. Video: https://youtu.be/zyCwbkDzYK4

The field produces a stable confinement region at the focal point between the two bowls, consistent with the galactic center structure.
The field produces directional ejection jets from the narrow ends of both bowls, consistent with galactic jets observed in active galaxies.
The Equatorial Null Zone forms as a real, measurable ring at a specific equatorial radius, visible in computed field plots as a dark null ring (Figure 4) and as two null points in cross-section (Figure 3).
The field architecture scales with the geometry — bowl curvature, spacing, and field strength determine the ENZ radius, jet properties, and confinement zone characteristics. All parameters are interrelated.

The plasma experiments were conducted and documented before the astronomical literature analysis in this paper was performed. The field geometry is the source of the predictions; the astronomical data is the test.

11. Conclusion

Published observational data from mainstream astronomical surveys, analyzed within the framework of PrimerField Theory, reveal a consistent pattern: axial alignment between the observer and the galactic field axis is the common factor in Einstein ring formation, multiple speed signature detection, and absorption line excess along blazar sightlines.

This pattern is predicted by PF Theory's dual-bowl magnetic field geometry and is not naturally unified by General Relativity. GR-based disk-lensing studies predict enhanced ring formation for tilted systems — opposite to the face-on orientation that produces the cleanest observed rings. GR provides no mechanism connecting jet orientation to absorption excess. GR requires extraordinary chance alignments to explain multiple redshift systems like the Jackpot.

PF Theory predicts all three effects from a single geometric structure, confirmed in laboratory plasma experiments. The Equatorial Null Zone acts as a magnetic guide, directing electromagnetic field structures to a ring at a specific radius determined by the field architecture. The six energy flow zones produce a structured set of Doppler signatures that explain multiple speed components as internal structure rather than chance alignments.

Three falsifiable predictions are presented: the E0–E7 morphology gradient for ring probability, the continuous blazar–FSRQ–quasar absorption gradient, and the resolution-dependent increase in detected speed components. Each can be tested with existing or near-future data.

All evidence presented in this paper is drawn from published, peer-reviewed mainstream astronomical research. No new observations are claimed. The contribution of this paper is a unified structural framework — grounded in laboratory-confirmed field geometry — that connects three previously unconnected observational patterns.

The data speaks. The geometry explains. The coincidences disappear.

References

Bergeron, J., Boissé, P., & Ménard, B. (2011). "Evidence for an excess of MgII absorbers towards blazars." Astronomy & Astrophysics, 525, A51.

Bolton, A. S., Burles, S., Koopmans, L. V. E., Treu, T., & Moustakas, L. A. (2006). "The Sloan Lens ACS Survey. I." The Astrophysical Journal, 638, 703.

Chand, H. & Gopal-Krishna. (2012). "On the incidence of MgII absorbers along the sightlines of flat-spectrum radio quasars." Monthly Notices of the Royal Astronomical Society, 422(2), 1186–1195.

Collett, T. E. & Auger, M. W. (2014). "Cosmological constraints from the double source plane lens SDSSJ0946+1006." Monthly Notices of the Royal Astronomical Society, 443(2), 969–976.

Collett, T. E. & Smith, R. J. (2020). "A Triple Rollover: A third multiply-imaged source at z∼6 behind the Jackpot gravitational lens." Monthly Notices of the Royal Astronomical Society.

Euclid Collaboration (2025). "A complete Einstein ring in NGC 6505." Astronomy & Astrophysics.

Gavazzi, R., Treu, T., Rhodes, J. D., et al. (2008). "The Sloan Lens ACS Survey. VI." The Astrophysical Journal, 677(2), 1046–1059.

Keeton, C. R. & Kochanek, C. S. (1998). "Gravitational lensing by spiral galaxies." The Astrophysical Journal, 495(1), 157–169.

LaPoint, D. A. (2014). US Patent 8,638,186 B1. "Magnetic Field Structures and Methods."

Maller, A. H., Flores, R. A., & Primack, J. R. (1997). "Gravitational lensing by spiral galaxies: angular momentum and disk effects." The Astrophysical Journal, 486(1), 681–691.

Mishra, S., Chand, H., Gopal-Krishna, et al. (2018). "On the incidence of MgII absorbers along the blazar sightlines." Monthly Notices of the Royal Astronomical Society, 473(4), 5154–5164.

Smith, R. J. & Collett, T. E. (2021). "A fully spectroscopic triple-source-plane lens: the Jackpot completed." Monthly Notices of the Royal Astronomical Society.

Stocke, J. T. & Rector, T. A. (1997). "Excess MgII absorption in BL Lacertae objects." The Astrophysical Journal Letters.

Axial Alignment, Multiple Redshift Systems,and Einstein Ring Formation