Impossibility paradox: Calculating the incalculable in the quantum realm

A new theory has emerged from the theoretical realm of quantum physics, offering a glimpse into the behavior of the fundamental particles that makes up our world.

This breakthrough, which defies previous assumptions, has the potential to revolutionize the design of quantum computers and pave the way for room-temperature superconductors.

Pulci the cat meets quantum dynamics

Berislav Buca, a researcher at the Niels Bohr Institute of the University of Copenhagen, is the architect behind this mind-bending theory. Published in the prestigious journal Physical Review X, Buca’s work delves into the nearly impossible using “exotic” mathematics.

His muse, a white cat named Pulci, perhaps a cousin of Schrödinger’s famous cat, adorns the illustrations of his research, with arrows through the cat’s body symbolizing the quantum mechanical origin of its movements.

“Many physics disciplines are ultimately about explaining and predicting the world by understanding the laws of physics and calculating the behavior of the smallest particles. In principle, we would be able to answer any possible question about how all sorts of things behave if we were able to,” says Buca.

Schrödinger’s Cat: A thought experiment in quantum mechanics

For a moment, let’s revisit the most famous cat in quantum physics and how it relates to Buca’s work. Schrödinger’s Cat is a thought experiment proposed by Austrian physicist Erwin Schrödinger in 1935.

It was designed to illustrate the paradoxical nature of quantum superposition, a fundamental principle of quantum mechanics.

The thought experiment involves a hypothetical cat, a flask of poison, a radioactive source, and a Geiger counter, all placed inside a sealed box.

The radioactive source has a 50/50 chance of decaying within an hour, which would trigger the Geiger counter. If the Geiger counter detects the radioactive decay, it shatters the flask, releasing the poison and killing the cat.

The paradox

According to quantum mechanics, the radioactive source is in a superposition of decayed and non-decayed states until it is observed. Consequently, the cat is said to be simultaneously alive and dead until someone opens the box and observes its state.

This contradicts our everyday understanding of reality, where an object can only be in one state at a time.

The Copenhagen Interpretation suggests that the cat is neither alive nor dead until it is observed, and the act of observation collapses the superposition into a definite state.

The Many-Worlds Interpretation posits that the cat is both alive and dead, existing in parallel universes that split at the moment of observation.

Objective Collapse Theories propose that the superposition collapses spontaneously due to some objective physical process, such as gravity, without the need for observation.

Misconceptions and significance

Schrödinger’s Cat is often misunderstood as a real experiment. However, it is purely a thought experiment and has never been conducted in reality.

The experiment was not meant to suggest that cats can be both alive and dead, but rather to highlight the counterintuitive nature of quantum superposition when applied to everyday objects.

This thought experiment — which, undoubtedly inspired Buca’s to create his cat, Pulci — has sparked ongoing debates about the nature of reality and the role of observation in quantum mechanics.

It has also inspired various philosophical discussions about the relationship between the observer and the observed, as well as the nature of consciousness.

Complexity of quantum particles

Turning our attention back to Buca, despite the potential to understand the behavior of everything in the universe from the microscopic laws governing particle dynamics, he emphasizes the need for caution.

The interactions and movements of quantum particles in their systems are incredibly complex, with even the world’s most powerful supercomputers only able to perform calculations on a dozen particles at a time.

“So in practice, it isn’t possible. Not currently. However, my theory is a significant step in the right direction,” explains Buca.

“This is because it takes a kind of mathematical shortcut to understanding the dynamics of the whole, without computing power being lost in the details for a broad class of systems with many quantum particles. That is, without the need to calculate all of the individual particles in a system,” he continued.

Guiding the hunt for quantum particles

Buca’s theory has already made a name for itself by providing the first mathematical proof of the eigenstate-thermalization hypothesis — a long-held assumption in theoretical physics that had yet to be explained mathematically. This hypothesis concerns the ability of mathematics to describe the motions of quantum systems as wholes.

The implications of this research extend beyond the realm of theoretical physics. The knowledge gained from Buca’s theory could potentially lead to the discovery of quantum materials with unique properties that could transform our world. These materials are crucial for the development of stable quantum computers and room-temperature superconductors.

“We are looking for a material for quantum computers that can withstand entropy — a law of nature that causes complex systems — e.g., materials — to decay into less complex forms. Entropy destroys the coherence needed for quantum computers to be stable and keep working,” Buca explains.

Road map for researchers

Buca’s theory provides a road map for researchers, guiding them across the vast landscape of possible materials by allowing for predictions of how these materials would behave under experimental conditions.

This breakthrough gives researchers a way to target their search for quantum materials equipped with special properties.

“Until now, the hunt for these materials has been governed by chance. But my results can, for the first time, provide a guiding principle to navigate by when searching for unique properties in materials,” says Buca.

Accomplishing the impossible with quantum particles

In summary, Berislav Buca’s pioneering theory in theoretical physics opens up a world of possibilities, offering a mathematical shortcut to understanding the dynamics of quantum systems and guiding researchers in their search for quantum materials with extraordinary properties.

As we stand on the brink of a new era in quantum computing and materials science, Buca’s work provides a roadmap for navigating the complex landscape of quantum particles and their interactions.

With the potential to revolutionize fields ranging from computing to superconductivity, this research brings us one step closer to unlocking the secrets of the universe and transforming our world through the power of quantum mechanics.

The full study was published in the journal Physical Review X.

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