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Torsional Pendulum

Torsional Pendulum

A torsional pendulum involves the oscillation of a rigid body in which the restoring force is provided by the torsion in the string from which the rigid body is suspended. Ideally, the string should be massless; practically, its mass is much smaller than the rigid body's mass and is neglected.
As long as the rigid body's angular displacement is small, its oscillation can be modeled as a linear angular oscillation. The amplitude of the oscillation is an angle. The role of mass is played...

Simple Pendulum

Simple Pendulum

A simple pendulum consists of a small diameter ball suspended from a string, which has negligible mass but is strong enough to not stretch. In our daily life, pendulums have many uses, such as in clocks, on a swing set, and on a sinker on a fishing line.
The period of a simple pendulum depends on two factors: its length and the acceleration due to gravity. The period is completely independent of any other factors, such as mass or maximum displacement. For small displacements, a pendulum is...

Physical Pendulum

Physical Pendulum

When a rigid body is hanging freely from a fixed pivot point and is displaced, it oscillates similar to a simple pendulum and is known as a physical pendulum. The period and angular frequency of a physical pendulum are obtained by using the small-angle approximation and drawing parallels with a spring-mass system. The small-angle approximation (sinθ=θ) is valid up to about 14°.
When dealing with complicated systems, the mass moment of inertia is an important parameter, as it...

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

Measuring Acceleration Due to Gravity

Measuring Acceleration Due to Gravity

Consider a coffee mug hanging on a hook in a pantry. If the mug gets knocked, it oscillates back and forth like a pendulum until the oscillations die out.
A simple pendulum can be described as a point mass and a string. Meanwhile, a physical pendulum is any object whose oscillations are similar to a simple pendulum, but cannot be modeled as a point mass on a string because its mass is distributed over a larger area. The behavior of a physical pendulum can be modeled using the principles of...

The de Broglie Wavelength

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...

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Related Experiment Video

Updated: Mar 10, 2026

Experimental Methods for Trapping Ions Using Microfabricated Surface Ion Traps

Experimental Methods for Trapping Ions Using Microfabricated Surface Ion Traps

Published on: August 17, 2017

One-milligram torsional pendulum toward experiments at the quantum-gravity interface.

Sofia Agafonova¹, Pere Rosselló¹, Manuel Mekonnen¹

¹Institute of Science and Technology Austria, Klosterneuburg, Austria.

Communications Physics

|March 9, 2026

Summary

This summary is machine-generated.

Researchers explored quantum gravity by generating entanglement with a microgram-scale torsional pendulum. Laser cooling achieved record-low temperatures, paving the way for quantum-gravity interface studies.

Keywords:

General relativity and gravity Imaging and sensing Optomechanics Quantum mechanics

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Last Updated: Mar 10, 2026

Experimental Methods for Trapping Ions Using Microfabricated Surface Ion Traps

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Published on: August 17, 2017

In Situ Measurement of Vacuum Window Birefringence using 25Mg+ Fluorescence

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Published on: June 13, 2020

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

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Published on: April 4, 2017

Area of Science:

Quantum physics
Gravitational physics
Precision measurement

Background:

Investigating quantum properties of gravity is crucial for unifying physics.
Systems with low-frequency dynamics at microgram-to-milligram scales are promising for probing quantum gravity.

Purpose of the Study:

To explore entanglement generation via gravity.
To assess the potential of milligram-scale torsional pendulums for quantum gravity research.

Main Methods:

Developed a figure-of-merit for entanglement generation through gravity.
Utilized a 1-milligram torsional pendulum operating at 18 Hz.
Employed laser cooling to reduce the pendulum's motion to 240 microkelvins.

Main Results:

Achieved a 20-fold improvement in cooling compared to existing oscillators.
Demonstrated the effectiveness of milligram-scale torsional pendulums for precision measurements.
Quantified the utility of this approach against other platforms.

Conclusions:

Milligram-scale torsional pendulums are a powerful platform for quantum gravity research.
The achieved low temperatures and performance show significant potential for future studies at the quantum-gravity interface.