⚛️ quantum physics

Quantum correlation tests at cosmic distances

This paper proposes and analyzes the feasibility of conducting quantum correlation tests between Earth and the Moon to extend the verified distance of entanglement by a factor of 300, thereby providing a more stringent test of quantum mechanics and constraints on alternative theories.

Original authors: Thomas Durt, Jean Schneider

Published 2026-04-17

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Thomas Durt, Jean Schneider

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: Testing "Spooky Action" on a Cosmic Scale

Imagine you have a pair of magic dice. You give one to your friend on Earth and keep the other for yourself. You both roll them at the exact same time.

In the normal world, the result of your roll has nothing to do with your friend's roll. But in the quantum world, these dice are "entangled." If you roll a 6, your friend instantly rolls a 6, no matter how far apart you are. This connection happens faster than light. Albert Einstein famously called this "spooky action at a distance."

Scientists have proven this works over long distances (like 1,200 km, roughly the distance from Paris to Berlin). But a big question remains: Does this spooky connection last forever, or does it fade away if you get too far apart?

This paper proposes a new experiment to test this by stretching the distance from 1,200 km all the way to 390,000 km (the distance from Earth to the Moon).

1. The Mystery of the "Hidden Speed"

For decades, physicists have argued about how these magic dice know what the other is doing.

The Standard View: They are connected by an invisible thread that snaps instantly (infinite speed).
The "Old School" View (Louis de Broglie): Maybe there is a hidden "speed limit." Maybe the connection travels through space like a wave, but it's just really, really fast.

Louis de Broglie, a famous physicist from the early 20th century, always felt that quantum mechanics was missing something. He thought particles should move through real, 3D space, not in some abstract mathematical "cloud" (called configuration space). He wondered: What if the connection takes a tiny bit of time to travel?

If the connection has a speed limit, and we separate the dice far enough apart, the message might arrive too late to coordinate the rolls. The "spooky action" would break, and the dice would stop behaving magically.

2. The Experiment: Earth vs. The Moon

The authors suggest a bold experiment:

Setup: Place a source of entangled photons (the "magic dice" made of light) on the Moon.
Detectors: Put one detector on the Moon and another on Earth.
The Goal: Measure the correlation between the two.

Why do this?
Current records are held by satellites orbiting Earth (about 500 km up). By moving the source to the Moon, we increase the distance by a factor of 300.

Think of it like testing a radio signal. If you can hear a radio station clearly from 10 miles away, that's good. But if you can hear it clearly from 3,000 miles away, you know the signal is incredibly powerful. If the signal fades at 3,000 miles, you've discovered a limit to how far the radio waves can travel.

3. The "Speed of Collapse"

The paper tries to calculate a "lower bound" for the speed of this connection.

The Analogy: Imagine two people trying to high-five. If they are standing next to each other, they can high-five instantly. If they are on opposite sides of a football field, they have to run to meet in the middle.
The Math: If the "high-five" (the quantum connection) happens instantly, the speed is infinite. But if we assume the measurement takes a tiny fraction of a second (like 5 picoseconds, which is a trillionth of a second), we can calculate how fast the "message" must have traveled to coordinate the result.

By moving the detectors to the Moon, the authors hope to prove that this "message" travels at least 700,000 times faster than light. If they find a limit, it would be a massive discovery, proving that quantum mechanics isn't as "spooky" as we thought, but rather follows a hidden, ultra-fast rulebook.

4. Why It Matters (Beyond the Science)

A. The Philosophical Win:
If the connection breaks at the Moon's distance, it would mean that the universe has a "memory" or a "medium" (like an old-fashioned ether) that stores quantum information. It would validate the ideas of Louis de Broglie and show that the universe is built on real, physical space, not just abstract math.

B. The Technological Win:
If the connection doesn't break, it opens the door to Quantum Key Distribution (QKD).

What is QKD? It's a way to send unbreakable secret codes using entangled particles.
The Future: If we can send these codes from Earth to the Moon (and eventually Mars), we could build a global (or even planetary) secure internet. No hacker could ever crack these codes because the act of eavesdropping would break the entanglement and alert the users.

5. The Challenges

The paper admits this is hard.

Atmosphere: Earth's atmosphere is like a foggy window that distorts laser beams. Sending a laser from Earth to the Moon is tricky.
The Solution: They suggest putting the laser source on the Moon and sending it to detectors in space (at Lagrange points, which are stable spots in space between Earth and Moon) to avoid the Earth's "fog."

Summary

This paper is a proposal to take a famous quantum physics experiment and scale it up to the size of the solar system.

Current Status: We know quantum entanglement works over 1,200 km.
The Proposal: Test it over 390,000 km (Earth to Moon).
The Question: Does the "spooky connection" survive the trip?
The Stakes: If it breaks, we find a new speed limit for the universe. If it holds, we pave the way for a super-secure, planet-wide internet.

It's a quest to see if the universe's "magic glue" is strong enough to hold the Earth and Moon together, or if it eventually runs out of steam.

1. Problem Statement

The paper addresses two fundamental issues in quantum physics:

The Nature of Non-Locality: While Bell's theorem and subsequent experiments confirm that entangled subsystems exhibit instantaneous statistical correlations regardless of distance, the orthodox interpretation relies on the "collapse of the wavefunction," a non-deterministic and non-local process often described in abstract configuration space rather than physical 3D space.
The Speed of Quantum Correlations: It remains experimentally unproven whether quantum correlations propagate at infinite speed or at a finite (but extremely high) speed through a physical medium (e.g., a "quantum ether" or 3D space). Current experimental bounds on the speed of these correlations are limited by the maximum distance over which Bell's inequalities have been violated (currently ~1,200 km).
Distance Dependence: There is a theoretical possibility (shared by Louis de Broglie) that quantum correlations might decay or disappear at macroscopic cosmic distances, a hypothesis that cannot be tested with current terrestrial or near-Earth satellite experiments.

2. Methodology

The authors propose a methodology to drastically increase the distance scale of Bell tests to derive tighter lower bounds on the speed of quantum correlations and test the persistence of entanglement.

A. Theoretical Framework for Speed Estimation

The paper refines the method for calculating the lower bound of the speed of quantum correlations ( $v_Q$ ).

Standard Approach: Previous estimates (e.g., by Gisin) divided the distance between detectors by the measurement duration.
Proposed Modification: The authors argue that if correlations propagate as waves through a physical medium (following the trajectory of particles), the relevant distance is twice the maximum trajectory length from the source to the farthest detector.
Time Constraint: They assume a measurement duration ( $\Delta t$ ) of 5 picoseconds (based on Gisin's 1999 experiment).
Formula: $v_Q \geq \frac{2 \times D_{max}}{\Delta t}$ .
Relativity Note: The authors acknowledge that simultaneity is frame-dependent but argue that testing simultaneous measurements provides the most constraining scenario for finite-speed models.

B. Proposed Experimental Configurations

The paper evaluates several configurations to extend the test distance from the current record (~1,200 km) to cosmic scales:

Earth-Moon Configurations (Target: ~390,000 km):
- Case 1: Source on Earth, detector on the Moon.
- Case 2: Source on Earth, one photon reflected off a lunar mirror back to Earth (similar to lunar laser ranging).
- Case 3 (Preferred): Source on the Moon, detectors on Earth. This avoids atmospheric turbulence for the source and allows for a gain factor of ~300 over current satellite experiments.
- Case 4 (Lagrange Points): Source and detectors placed at Earth-Moon Lagrange points (L4/L5). This offers a distance gain of ~20 over Earth-Moon but avoids atmospheric interference for both ends.
Interplanetary Configurations:
- Mars: A proposal to test correlations between Earth and a Martian base. This would offer a distance gain of ~1,000 but is deemed technologically unfeasible for decades.

C. Technical Challenges & Solutions

Atmospheric Turbulence: The authors note that Earth's atmosphere causes timing perturbations and beam dispersion. Placing the source on the Moon (Case 3) or using Lagrange points (Case 4) mitigates this.
Gravitational Time Dilation: The paper calculates the General Relativistic correction for proper time ( $\alpha = 1 - GM/Rc^2$ ) between Earth and Moon. For detection cadences exceeding ~12 photons/sec, this correction must be accounted for to maintain synchronization.
Signal Loss: Unlike fiber optics (exponential attenuation), satellite links suffer from geometric optics losses ( $L^{-2}$ ) due to beam divergence. The authors suggest that while difficult, this is a solvable engineering challenge similar to the LISA project.

3. Key Contributions

Proposal for a 300x Distance Increase: The paper formally proposes moving Bell tests from the 1,200 km scale (Cao et al., 2017) to the Earth-Moon distance (~390,000 km).
Refined Speed Bound Calculation: By redefining the distance metric to include the full trajectory (source to detector) and assuming a 5 ps measurement window, the authors demonstrate that an Earth-Moon experiment would push the lower bound on the speed of quantum correlations to approximately $10^7 c$ to $10^8 c$ (depending on the specific configuration), significantly tightening constraints on alternative theories.
Testing the "Disappearance" Hypothesis: The proposal offers a unique opportunity to test Louis de Broglie's hypothesis that entanglement might not survive at large distances, a question current technology cannot answer.
Technological Roadmap: The paper connects fundamental physics to the development of planetary-scale Quantum Key Distribution (QKD), suggesting that successful long-distance entanglement is a prerequisite for a global quantum internet.

4. Results and Predictions

Current Status: The paper reviews existing records (Cao et al., 1,203 km) which set a lower bound on correlation speed of roughly $10^7 c$ .
Projected Outcomes:
- If Bell's inequalities are violated at the Earth-Moon distance, the lower bound on the speed of quantum correlations will increase by a factor of ~300.
- If correlations disappear or weaken significantly at this distance, it would imply a breakdown of standard quantum mechanics or the existence of a distance-dependent decoherence mechanism not accounted for in current theory.
- The paper notes that no current theoretical model (using constants $h, c, G$ ) predicts a deviation scale specifically at the Earth-Moon distance; thus, any deviation would constitute a discovery of a new fundamental constant.

5. Significance

Foundational Physics: This experiment would be a decisive test for "realistic" interpretations of quantum mechanics (like de Broglie-Bohm or Vigier's quantum thermostat) that posit correlations propagate through physical 3D space at finite speeds. It challenges the necessity of abstract configuration space.
Technological Impact: Successfully maintaining entanglement over 390,000 km would validate the feasibility of Planetary-Scale QKD, enabling secure communication networks between Earth, the Moon, and eventually other planets.
Legacy of de Broglie: The paper honors Louis de Broglie's lifelong quest to describe quantum phenomena in real physical space rather than configuration space, framing this experiment as the ultimate test of his "double solution" and non-locality concepts.

In conclusion, Durt and Schneider argue that extending Bell tests to the Earth-Moon distance is both a critical test of the foundations of quantum mechanics and a necessary step toward a future interplanetary quantum communication infrastructure.