Analyzing an event from the perspective of different observers has led to several theoretical breakthroughs in classical physics. In the quantum world, however, switching between different reference frames is much more complicated. Physicists at the Institute of Quantum Optics and Quantum Information Vienna of the Austrian Academy of Sciences and the Université Libre de Bruxelles have developed a new, general mathematical framework that can be used to analyze quantum systems from the perspective of the particles involved. The result was recently published in the journal Communications Physics and could enable new advances in the unification of quantum mechanics and general relativity.

New method

Albert Einstein's thought experiments have shown that a beam of light reflected back and forth between mirrors on board a spaceship describes a different path for observers on board than for observers watching the experiment from Earth with a telescope. However, the different perspectives can always be unambiguously converted into one another using fixed mathematical rules. For the quantum world, in which the spaceship could in principle exist in superpositions, such changes between different reference frames were previously only possible with severe restrictions. Theoretical quantum physicists Esteban Castro-Ruiz from IQOQ in Vienna and Ognyan Oreshkov from the Université Libre de Bruxelles have developed a new method that eliminates these limitations.

"Quantum reference frames have been researched since the 1960s. However, until now it has not been possible to switch between frames without having to take the state of the entire universe into account. That is, the way we describe a particle from the point of view of a quantum reference frame would in general depend on whether there are two, three of several million other particles “out there”. Our method, in contrast, splits the system we want to analyze into subsystems and allows us to precisely describe the perspective of the quantum particles involved without additional information," says Esteban Castro-Ruiz. For a simple system of three electrons, for example, this means that particle one can be fully described from the perspective of particles two and three. 

Clues to Quantum Gravity?

"Because these are quantum particles, we cannot describe complementary properties such as momentum and location independently of each other. Our quantum reference system is therefore a composite system composed of two particles, one that serves as a reference for momentum and one for location. A specific subsystem of the full system under consideration, which contains information about the relationships between all the elements involved, is the key to our method. When the reference frame is in a classical state, this subsystem contains no information, but in the quantum world it is essential for fully describing the perspective of the quantum reference frame. In this way, this subsystem also functions like a test that tells us whether our reference frame is classical or follows the quantum rules," says Ognyan Oreshkov.

The physicists can effortlessly switch back and forth between different perspectives of quantum particles, even if the properties of the particles are in superposition states and are not clearly defined. As a result, they obtain the complete wave function of the entire system from the perspective of a quantum refernce frame and thus a complete description. The new method is extremely general and should be applicable to any quantum system, which will open up new possibilities for both experimental physicists and their theoretical colleagues. "The unification of quantum mechanics and general relativity is one of the great open challenges in physics. Our new approach could provide new clues as to how quantum mechanics and general relativity can be put together," says Esteban Castro-Ruiz.