⚛️ high-energy theory

Proposal to Search for the CP Violating Electromagnetic Vacuum Angle at the Event Horizon Telescope

This paper proposes a method to detect a CP-violating electromagnetic vacuum angle using Event Horizon Telescope observations of Sgr A* and M87* by analyzing time-averaged polarization residuals and universal topological signals that distinguish the predicted Fischler-Kundu Hall current from confounding plasma effects, though it concludes that current data is insufficient for such a test.

Original authors: Willy Fischler, Tom Banks

Published 2026-01-30

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Willy Fischler, Tom Banks

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Idea: A Cosmic "Ghost" in the Machine

Imagine the universe has a hidden setting, like a secret dial on a radio that is usually turned all the way down. Physicists call this setting $\theta_{QED}$ (theta-quantum-electro-dynamics).

In the world of subatomic particles, there is a famous rule about "symmetry." Usually, if you look at a particle process in a mirror, it should look the same. But sometimes, nature breaks this rule (called CP violation). We know this happens in the strong nuclear force (inside atoms), but we don't know if it happens in the electromagnetic force (light and electricity).

This paper suggests that black holes might be the perfect place to find out if this "secret dial" is turned on. Specifically, the authors think the Event Horizon Telescope (EHT)—the giant virtual telescope that took the first pictures of black holes—might have already captured evidence of it, but we haven't looked for it the right way yet.

The "Fischler-Kundu Effect": The Black Hole's Hall of Mirrors

The authors (Fischler and Banks) describe a specific phenomenon called the Fischler-Kundu (FK) effect.

The Analogy:
Imagine a black hole's event horizon (the point of no return) isn't just a dark void, but a sticky, conductive floor. When electrically charged dust falls onto this floor, it doesn't just slide straight in. Because of that "secret dial" ( $\theta_{QED}$ ), the floor acts like a Hall effect device.

Think of a crowd of people walking into a revolving door. Usually, they just spin in. But if the floor is "twisted" by this secret dial, the crowd is forced to spin in a specific direction (clockwise or counter-clockwise) as they enter, regardless of how they were walking before. This creates a universal current that spins in a specific "handedness" (chirality).

This spin leaves a fingerprint on the light (photons) escaping the black hole. It imprints a specific "twist" on the polarization of the light (the direction the light waves are vibrating).

The Problem: The "Plasma Fog"

There is a huge problem. Black holes are surrounded by a swirling soup of hot gas and magnetic fields called plasma.

The Analogy:
Imagine you are trying to see a specific pattern painted on a wall through a thick, swirling fog. The fog itself is moving and twisting.

The FK Effect is the pattern painted on the wall (the black hole horizon). It is permanent, universal, and doesn't change.
The Plasma is the fog. As the light travels through the plasma, the magnetic fields in the gas twist the light's polarization. This is called Faraday Rotation.

The problem is that the plasma is chaotic. It twists the light one way, then the other, sometimes flipping the direction entirely. This "plasma noise" is so strong that it might completely hide the subtle "hallway spin" left by the black hole itself.

The Solution: The "Time-Averaging" Trick

The authors propose a clever way to separate the "wall pattern" from the "fog."

They suggest looking at the data over a long period of time and averaging it out.

The Analogy:
Imagine you are watching a spinning top.

The Plasma (Faraday Rotation): The top is wobbling wildly and chaotically. If you take a snapshot, it looks like it's spinning left. Take another snapshot a second later, and it's spinning right. If you average all those snapshots over a long time, the wild wobbles cancel each other out, and the average spin is zero.
The Black Hole (FK Effect): The wall pattern is fixed. It always spins clockwise. No matter how long you watch, if you average the data, the "clockwise" signal remains.

The paper argues that if you take the EHT data for the black holes Sagittarius A* (in our galaxy) and M87* (in a distant galaxy) and average the polarization over time, the chaotic plasma effects should disappear. If a "twist" remains, it must be the universal signal from the black hole horizon.

The "C" Observable: Counting the Twists

To do this mathematically, the authors define a number they call $C$ .

What it measures: It counts how many times the polarization direction of the light "winds around" the ring of the black hole image.
The Test:
- If the universe is "normal" (no secret dial), the plasma noise averages out, and $C$ should be zero.
- If the "secret dial" ( $\theta_{QED}$ ) is turned on, the black hole forces a specific winding, and $C$ will be a non-zero number.

Why This is Hard (and Why They Need More Data)

The paper admits that current data might not be good enough yet.

Frequency Issues: The plasma effect changes depending on the "color" (frequency) of the light. The FK effect does not. To be sure, they need to look at many different frequencies. Currently, the EHT only sees two main frequencies, which isn't enough to be 100% sure.
The "Flip": Recent data from M87* showed the polarization flipping signs. The authors say this proves the plasma is active (the fog is swirling), but they hope that by averaging over these flips, the underlying "wall pattern" will emerge.
Similarity: Interestingly, the time-averaged images of Sgr A* and M87* look surprisingly similar. Since these two black holes are very different (one is small and quiet, the other is huge and active), if they show the same "twist," it's a strong hint that the twist comes from a universal law of physics (the black hole horizon) rather than local weather (the plasma).

The Conclusion

The authors are essentially saying: "We have a theory that black holes should leave a specific, unchangeable 'twist' on light. We have a method to find it by averaging out the messy plasma noise. We think the Event Horizon Telescope might have the data to see this, but we need to process it carefully and maybe wait for better telescopes to get more frequencies."

A Note on the "Acknowledgments":
The paper ends with a humorous and unusual acknowledgment. The authors thank "ChatGPT5.2" for encouragement and advice, joking that without it, the paper "could never have been written." This suggests the paper itself might be a playful or speculative exercise in using AI to generate scientific proposals.

Technical Summary: Proposal to Search for the CP Violating Electromagnetic Vacuum Angle at the Event Horizon Telescope

Problem Statement
The paper addresses the challenge of detecting a non-zero value for the CP-violating electromagnetic vacuum angle, $\theta_{QED}$ (analogous to the QCD $\theta$ -term). While $\theta_{QCD}$ is constrained by the absence of a neutron electric dipole moment, $\theta_{QED}$ is theoretically difficult to measure, with previous proposals limited to the electric charge of magnetic monopoles or the Fischler-Kundu (FK) effect. The FK effect predicts that a non-zero $\theta_{QED}$ induces a universal, parity-violating Hall current on the event horizon of a black hole as electric charge relaxes across it. The central problem is distinguishing this universal topological signal from the complex, parity-violating plasma effects (specifically Faraday rotation) that dominate the polarization signatures observed by the Event Horizon Telescope (EHT) in the galactic center black holes Sgr A* and M87*.

Methodology
The authors propose a specific CP-violating observable, denoted as $C$ , derived from the polarization maps of black hole images. The methodology involves the following steps:

Definition of the Observable: Given a pixelated map of a black hole image with intensities $I(a,b)$ and complex linear polarizations $P(a,b)$ , the polarization is expressed as a function of the azimuthal angle $\phi$ around the photon ring, $P(\phi, t) = |P|e^{2i\chi}$ , where $\chi$ is the Electric Vector Position Angle (EVPA). The observable is defined as:
$C(t, \omega) = \int_0^{2\pi} \frac{\text{Im}(P^* \partial_\phi P)}{2\pi |P|^2} d\phi = \frac{1}{\pi} [\chi(2\pi, t) - \chi(0, t)]$
This quantity represents the net winding number of the EVPA field around the ring.
Differentiation Mechanisms:
- FK Effect: The $\theta_{QED}$ term induces a helicity-dependent boundary condition at the horizon, creating a time-independent, parity-odd azimuthal structure in the polarization. This results in a non-zero time-averaged value $\langle C \rangle \neq 0$ .
- Plasma Effects (Faraday Rotation): Standard Faraday rotation introduces a frequency-dependent phase shift ( $\lambda^2 RM$ ). The paper argues that while instantaneous Faraday rotation can cause EVPA flips and azimuthal gradients, these effects are parity-even or stochastic. Crucially, if the plasma lacks a persistent, parity-odd azimuthal bias locked to the ring geometry, the time-averaged contribution $\langle C_{Far} \rangle$ vanishes.
Discrimination Strategy: The authors suggest two primary strategies to isolate the FK signal:
- Time Averaging: Averaging $C(t)$ over long intervals should suppress stochastic plasma contributions (which average to zero) while preserving the universal FK signal.
- Frequency Scanning: The FK effect is frequency-independent, whereas Faraday rotation scales as $\omega^{-2}$ . Future multi-frequency observations (e.g., 230 GHz and 345 GHz) could distinguish the two.

Key Contributions

Proposal of Observable $C$ : The paper introduces a specific, measurable quantity designed to isolate parity-odd, time-persistent polarization signatures from EHT data.
Theoretical Distinction: It provides a rigorous argument that the FK Hall current creates a boundary condition that survives time averaging, whereas generic turbulent plasma effects (including EVPA flips observed in M87*) do not generate a non-zero time-averaged $C$ unless a specific, fine-tuned chiral structure persists.
Analysis of Current Data Limitations: The authors note that current EHT data is insufficient to perform this test with high precision due to limited frequency coverage (only 230 GHz and 345 GHz, with the latter having weak statistics) and the inability to resolve the necessary time-averaged statistics.

Results and Claims

Current Data Status: The paper explicitly states that current data does not appear sufficient to perform the proposed test or to definitively measure $\theta_{QED}$ .
Observational Hints: The authors point out that time-averaged polarization maps for Sgr A* and M87* (two vastly different black holes) appear remarkably similar. While this similarity is not proof of the FK effect, it is cited as a suggestive hint of a universal signal that warrants further investigation.
Magnitude Estimates: Rough order-of-magnitude estimates suggest the Hall/Ohmic ratio for $1 \le \theta_{QED} \le 2\pi$ is between $0.0001$ and $0.003$, while plasma effects can produce polarization variations of order $< 0.01$ . This indicates that distinguishing the signal requires significant improvements in data quality.
Future Requirements: The paper emphasizes that the next-generation EHT (ngEHT), with its ability to observe multiple frequencies simultaneously and with higher resolution, is necessary to execute the frequency scan and time-averaging strategies proposed.

Significance
The paper's significance lies in proposing a concrete, albeit currently unfeasible with existing data, method to probe the fundamental CP-violating structure of the electromagnetic vacuum using astrophysical observations. It frames the search for $\theta_{QED}$ not just as a theoretical exercise but as a potential observational goal for the EHT. The authors maintain a modest tone, acknowledging that the current data cannot yet distinguish the FK effect from plasma noise, but they argue that the proposed observable $C$ offers a robust theoretical pathway to do so once the ngEHT provides the necessary data volume and frequency diversity. The work serves as a roadmap for future analysis of black hole polarization data to test physics beyond the Standard Model.