An Improved Torsion Balance Test of the Equivalence Principle Towards the Sun

This paper reports a fourfold improvement in testing the Equivalence Principle towards the Sun using a rotating torsion balance with beryllium and aluminum test bodies, achieving a 95%-confidence limit of $\eta_{\odot, Be-Al} \leq 2.1 \times 10^{-13}$.

The Gist

Imagine gravity as a giant, invisible magnet that pulls everything toward massive objects. For over a century, physicists have believed a fundamental rule: gravity pulls on everything exactly the same way, no matter what it's made of. Whether you drop a feather, a brick, or a piece of gold, they should all fall at the exact same speed if there's no air resistance. This rule is called the Equivalence Principle, and it's the foundation of our understanding of how the universe works.

But what if that rule isn't perfectly true? What if gravity treats a piece of aluminum slightly differently than a piece of beryllium?

The Experiment: A Cosmic See-Saw

A team of scientists at the University of Washington decided to test this idea with extreme precision. They built a super-sensitive "cosmic see-saw" called a torsion balance.

• The Setup: Imagine a very thin, nearly invisible glass thread (made of fused silica) hanging from the ceiling. At the bottom, they attached a horizontal bar with weights on the ends.
• The Weights: On one side of the bar, they placed weights made of aluminum. On the other side, they placed weights made of beryllium.
• The Goal: They wanted to see if the Sun's gravity pulled harder on the aluminum than the beryllium (or vice versa). If the Sun pulled differently, the bar would slowly twist, just like a see-saw tipping to one side.

To make the test even more sensitive, they spun the entire apparatus slowly on a giant, friction-free air bearing (like a hovercraft). As it spun, the aluminum and beryllium weights swapped places relative to the Sun. If gravity treated them differently, the bar would wiggle in a specific rhythm as it turned.

The Challenge: Listening for a Whisper

The signal they were looking for was incredibly tiny. The paper compares the sensitivity to measuring a change in speed so small it's like a snail moving a distance smaller than the width of an atom.

To hear this "whisper," the scientists had to block out the "noise" of the world:

• Earthquakes: Even tiny tremors could shake the sensitive thread.
• Construction: They had to pause their experiment when nearby construction work was happening.
• Temperature: They kept the machine in a temperature-controlled vault because heat makes things expand and contract, which could mimic a gravity signal.

The experiment ran for a full year (from July 2024 to July 2025), but due to construction and hardware glitches, they only had about 186 days of "high-quality" data.

The Result: Gravity is Still Fair

After crunching the numbers, the scientists found no wiggle. The aluminum and beryllium weights were pulled by the Sun's gravity in exactly the same way, within the limits of their measurement tools.

They calculated that if there is a difference, it is smaller than 2.1 parts in 100 trillion.

Why This Matters

This isn't just a "no news is good news" story. It's a massive upgrade in precision:

1. Four times better than any previous test looking specifically at the Sun.
2. 20% better than any previous test of this type, regardless of what object was doing the pulling.

The scientists chose the Sun as their test subject because it is made mostly of hydrogen and helium, which is similar to the makeup of most of the normal matter in the universe. By proving that the Sun doesn't play favorites between different materials, they have tightened the rules of the universe even further.

In short: The universe's gravity rulebook remains intact. The Sun pulls on aluminum and beryllium with the exact same hand, confirming that the Equivalence Principle holds up even under the most rigorous scrutiny we can currently offer.

Technical Summary

Technical Summary: An Improved Torsion Balance Test of the Equivalence Principle Towards the Sun

Problem Statement
The Equivalence Principle (EP), a cornerstone of General Relativity, posits that gravitational acceleration is independent of an object's composition. While numerous experiments have tested this principle using the Earth as a source mass, such tests are limited in their ability to probe interactions that do not couple to the specific elements comprising the Earth. Consequently, there is a need to test the EP using a source mass with a composition representative of the broader baryonic universe—specifically hydrogen and helium. This paper addresses the search for violations of the EP towards the Sun, motivated by the potential existence of long-range interactions between normal matter and dark matter, as well as couplings to ultra-light vector dark matter.

Methodology
The authors employed an upgraded rotating torsion balance apparatus located in an underground laboratory at the University of Washington. The core of the experiment involved a pendulum suspended from a 22-µm thick, 1-meter long ultra-low loss fused silica torsion fiber. The pendulum carried eight test bodies arranged in a dipole orientation: four made of beryllium and four made of aluminum.

The entire apparatus was mounted on an air-bearing turntable rotating at 0.46 mHz. This rotation effectively interchanged the test bodies in the laboratory frame with each revolution, allowing for the detection of differential accelerations. The system was housed in a vacuum chamber with thermal enclosures, magnetic shielding, and active gravity gradient compensation. Tilt sensors and thermal expansion feet maintained the apparatus's alignment, while an autocollimator measured the pendulum's angular position relative to the vacuum chamber.

Data collection spanned from July 7, 2024, to July 7, 2025. To minimize systematic effects, the pendulum was rotated 180° on three separate occasions during this period. Due to local construction and hardware failures, the duty cycle was restricted, yielding 186 days of high-quality data out of a 366-day span.

The analysis involved splitting the measured differential acceleration into two-day segments. Each segment was fitted to sinusoidal functions representing harmonics of the turntable frequency and the torsional resonance. The authors extracted complex numbers ($\Delta a_{TT}$) representing the amplitude and phase of the differential acceleration occurring once per turntable revolution. These data were subsequently fitted to "solar basis functions," which modeled the Sun's projected location in the lab's horizontal plane and an orthogonal component, accounting for daily Earth rotation and annual orbital variations. Data sets exhibiting misfit-squared values exceeding four times the thermal noise or falling outside the 95% confidence interval were discarded.

Key Contributions and Results
The experiment successfully isolated the differential acceleration towards the Sun, distinguishing it from the orthogonal (out-of-phase) direction to verify experimental sensitivity. The final measurement of the differential acceleration towards the Sun was determined to be:
$$\Delta a_{\odot} = 0.66 \pm 0.61 \, \text{fm/s}^2 \, (1\sigma)$$

Based on the known gravitational acceleration of the Earth towards the Sun ($\sim 5.9 \, \text{mm/s}^2$), the authors established a 95%-confidence limit on the Eötvös parameter for beryllium and aluminum test bodies:
$$\eta_{\odot, \text{Be-Al}} \leq 2.1 \times 10^{-13}$$

Significance
The paper claims that these results represent a factor of four improvement over previously reported tests of the Equivalence Principle specifically directed towards the Sun. Furthermore, this represents a $\sim 20\%$ improvement over all previous torsion balance tests of the EP, regardless of the source mass or distance scale.

The authors conclude that while the Equivalence Principle remains foundational, this study significantly extends the reach of torsion balance tests. They note that with future improvements—specifically faster turntable rates, enhanced turntable control, and interferometric angle readout—the apparatus has the potential to match or exceed the sensitivity of state-of-the-art satellite tests. The raw data and analysis code are made available to the community to support further verification and study.