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How to Measure the Gravitational Field of a Quantum Object

Measuring devices have become sensitive enough to detect the gravitational forces between tiny objects and may soon cross the quantum threshold.

At the end of the 18th century, the British scientist Henry Cavendish measured the force of gravity between two objects for the first time in a laboratory. The objects in question were lead balls, one the size of a watermelon, the other the size of a baseball. The force between them, he discovered, was tiny—roughly the weight of a grain of sand.

Since then, the experiments have become more accurate but still generally involve relatively large  objects—the smallest gravitational field ever measured was between two cylinders weighing 90 grams. But fields between smaller masses are so tiny that nobody has come up with a way to measure them.

That looks set to change thanks to the work of Jonas Schmole and pals at the University of Vienna in Austria. They’ve come up with a way to measure the gravitational attraction of millimeter-scale objects that are three orders of magnitude less massive than anything measured before. 

Such an experiment would allow scientists to probe gravity on scales that have never before been possible and opens the door to a new era of experiments  that explore of the relationship between gravity and quantum mechanics for the first time. 

The new method for measuring gravitational forces is simple in principle. At its heart, it exploits the way tiny objects resonate when they are repeatedly nudged. One way of doing this is to carve tiny springboards out of silicon, so that the electronics necessary for monitoring them can be built into a single chip. These so-called microelectromechanical devices have become common in recent years—they are the technology behind airbags and accelerometers in smartphones, for example.

Now Schmole and co want to use them to measure gravitational forces. Their idea is to make a springboard and place a milligram-scale sphere on the end of it. This is the test mass whose movement under the force of gravity they hope to measure.

At the same time, they place another similar sphere on the end of a bar that can be ratcheted back and forth like a piston. This is the source mass that generates a moving gravitational field. 

When these two spheres are placed close to each other, the resulting gravitational field should create an attractive force between them. That should pull the test mass on the springboard toward the source mass. As the source mass moves away, the attraction will drop, allowing the test mass to drop away. 

That causes the springboard to vibrate. And if the movement of the source mass matches a certain critical frequency, the springboard will resonate, and this motion can be measured by bouncing a laser off the springboard.

Adjusting the way the source mass moves back and forth will allow Schmole and co to explore the way the resonance occurs and to measure the force that is causing it—the gravitational attraction between the two bodies.

And that’s it—a simple way to measure the gravitational force between two milligram-sized objects that is possible today with state-of-the-art MEMs devices.

Of course, there are some important subtleties in the experiment. For example, the test mass and source mass have to be isolated so that the movement of one doesn’t influence the other, except by gravitational attraction. That’s a significant challenge. Another is isolating the entire device from external vibrations that might swamp the signal of interest. 

But Schmole and co say these are manageable and that the experiment is eminently doable. “Current state of the art technology should allow for a proof-of-concept demonstration for objects on the scale of millimeters and tens of milligrams, which already improves the current limit for sensing the gravitational field of a small source mass by three orders of magnitude,” they say.

That’s interesting work and not just because of the experimental challenges involved. Millimeter-scale objects are close to the scale at which the strange laws of quantum mechanics become observable. These lead to bizarre phenomenon such as a single object being in two locations at the same time.

The exciting opportunity that Schmole and co hint at is the ability to measure the force of gravity associated with quantum objects. How will the gravitational force manifest itself when associated with an object that exists in two locations at the same time? 

That’s a question many physicists would give their right arms to know the answer to. They may not have long to wait!

Ref: : A Micromechanical Proof-Of-Principle Experiment for Measuring the Gravitational Force of Milligram Masses

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