Can a Measurement Be Undone? Recovering the State of a Measured Microscopic System with a Reversible Measuring Apparatus

In the quantum world, the act of measuring something is often described as a violent interruption. Before a measurement, a tiny particle can exist in a state of superposition, effectively being in two places or two conditions at once. This is a delicate, invisible harmony known as coherence. However, the moment we try to find out which state the particle is in, this harmony seems to shatter. The particle "collapses" into a single, definite state, and the ability to be in two places at once vanishes. For decades, physicists have debated whether this collapse is a fundamental law of nature—a hard stop where reality forces a choice—or if it is merely an illusion caused by the measuring device getting tangled with the particle. If the latter is true, and if the laws of physics are perfectly reversible, then the lost harmony should be recoverable if we could somehow undo the measurement and return the measuring device to its original state.

A new proposal by Peter Renkel of The MathWorks suggests a way to test this directly. The idea is to build a measuring device that is reversible, one that can store information about a microscopic particle and then be wiped clean, returning to exactly how it was before the measurement began. If standard quantum mechanics is the whole story, the microscopic particle should regain its lost harmony once the device is reset. But if a mysterious physical process causes the collapse to happen permanently, even after the device is reset, the harmony will remain broken. This experiment aims to catch that permanent break, distinguishing between a reversible entanglement and an irreversible collapse of reality.

The proposed experiment uses a specific setup involving two very different objects: a single, tiny molecule and a charged nanoparticle. The molecule acts as the microscopic system, prepared in a superposition of two internal states. Because these two states have slightly different electrical properties, they exert different forces on the nearby nanoparticle. As the molecule interacts with the nanoparticle, the nanoparticle moves in response, effectively recording which state the molecule was in. This movement is the measurement; the nanoparticle now holds the "which-state" information.

Crucially, the experiment does not stop here to read the result. Instead, the researchers propose a precise sequence of forces that guides the nanoparticle back along a path that undoes its movement. The nanoparticle is returned to its exact starting position and momentum, erasing the information it just stored. In the language of physics, the measuring apparatus is restored to its pre-measurement state. If the universe follows standard quantum rules, the molecule should not care that it was measured and then "un-measured"; its original quantum harmony should return, and it should behave as if the interaction never happened.

However, if a physical collapse mechanism exists—one that permanently destroys quantum coherence the moment information is created—the molecule will not fully recover. Even though the nanoparticle has been reset, the molecule will retain a "scar" of the measurement, showing a permanent loss of harmony. The experiment is designed to detect this tiny, residual loss. By repeating this cycle of measurement and reversal hundreds of thousands of times, the researchers hope to see if a small, unexplained amount of coherence is missing.

The paper outlines a concrete design for this test using a molecule similar to calcium hydroxide and a charged nanoparticle. The molecule is held in a trap, and the nanoparticle is suspended nearby. During a single cycle lasting about 4.19 milliseconds, the nanoparticle moves enough to clearly distinguish the two states of the molecule, effectively recording the information. Then, the system reverses, bringing the nanoparticle back to zero displacement. The researchers calculate that if they run this cycle 500,000 times, they could detect a loss rate as small as 5.51 per second. This sensitivity would allow them to set a new, direct limit on theories that predict a permanent collapse, such as Continuous Spontaneous Localization, a model suggesting that gravity or mass causes quantum states to break down.

The significance of this approach lies in its directness. Previous experiments have tried to infer collapse by looking for side effects, such as unexpected heating or radiation emitted by collapsing particles. This proposal, by contrast, looks at the measurement process itself. It asks a simple, operational question: if we store information in a machine and then delete that information by returning the machine to its original state, does the quantum system recover? The answer to this question does not depend on the details of any specific theory but rather on the fundamental nature of how information and reality interact.

The researchers acknowledge that building such a device is challenging. It requires extreme control over electric fields and the ability to keep the nanoparticle stable while it moves and returns. They have mapped out the necessary conditions, including the need to cancel out stray electric fields that could mimic the signal of a collapse. They also note that while their design uses a specific molecule and nanoparticle, the logic applies to any system where a microscopic object can push a larger, mesoscopic object and have that object pushed back.

If this experiment is built and finds no residual loss, it would provide strong evidence that quantum mechanics is complete and that the collapse of the wave function is not a physical event but a consequence of how we interact with the world. If it does find a loss, it would be a revolutionary discovery, proving that there is a fundamental, irreversible limit to how much information can be erased, even in a perfectly controlled laboratory setting. For now, the paper stands as a detailed blueprint for a test that could finally settle whether the quantum world can truly be undone.