Anyone with a high school diploma knows Newton’s universal law of gravitation: According to it, gravity is inversely proportional to the square of the distance separating a mass from a heavy mass. And nowadays, almost everyone has heard of quantum mechanics as well, thanks to the advent of quantum computers, which even the Prime Minister of Canada can explain.
The fascinating behavior of quantum systems is that they can allow an element to assume two states (if not more) simultaneously. A particle with positive rest mass (“massive particle”) can land in two places at the same time. This isn’t science fiction: in fact, atomic interferometers regularly arrange cesium or rubidium atoms in such a way that the quantum state of the atom is split and present in two locations, where those two locations can be up to several centimeters apart.
Such states are very gravitationally sensitive, resulting in the most accurate measurements scientists have been able to make of the Earth’s gravitational field, say, equivalent to 1/1015. But the question is: what gravitational field creates a massive particle in such a quantum state?
To answer this question, particle physicists Richard MacKenzie and Manu Paranjape from the Université de Montréal have been working with their colleague Urjit Yajnik from the Indian Institute of Technology Bombay in India since 2012, benefiting from a cooperation granted by the Québec-Maharashtra Minister of International Relations and the Francophonie of Quebec.
Together with numerous students and other collaborators, they have produced significant research in theoretical particle physics, and their latest study, just published in Physical Review Letters, the journal of the American Physical Society, asks this question: what is the gravitational field of a particle Mass in a Spatially Nonlocal Quantum Superposition? Their startling discovery is as follows: While it does not reveal that a massive particle is fissioned and exists in two places simultaneously, given the position average of the massive particle, the gravitational field appears to come from only one place.
To reach this conclusion, the team studied scattering experiments conducted by other particle physicists, such as those at the Large Hadron Collider, experiments aimed at looking inside atoms themselves, nuclei and other subatomic particles. Deep inelastic scattering experiments performed in the late 1970s also revealed the presence of quarks in the nucleus, confirming the strong interaction theory or quantum chromodynamics.
Manu Paranjape
Credit: Photo courtesy
“It was obvious to us that we had to calculate the behavior of the gravitational diffusion of other particles compared to the spatially non-local massive particle,” says Manu Paranjape. This calculation would allow to study the nature of the gravitational field created by the non-local massive particle. In doing so, we found very clearly that the scattering behaves as if the massive particle were at its central position and not as if half a particle were at each of two spatially separate locations. In truth, this result was quite unexpected.”
Now comes the tedious phase of the work, namely the experimental verification of the theoretical calculations of the scientists.
Richard MacKenzie
Credit: Photo courtesy
“Currently, the gravitational field of a given atom is far too weak to be observed experimentally, even with the most sensitive gravitational field detectors, namely atomic interferometers,” Richard MacKenzie points out. However, it is within the realm of possibility to measure the gravitational field of a mass of about a billion atoms.
Although it represents much less than a microgram of matter, that number of atoms is roughly the same as that found in the quantum state at the macroscopic level, in what is known as a Bose-Einstein condensate. It would be possible to shape a spatially non-local superposition of a Bose-Einstein condensate of this size, which could produce measurable gravitational fields.
If the scientists’ theory could be verified experimentally, “the result would be spectacular,” says Manu Paranjape. So we invite you to keep an eye out for this question… wherever you are.
About this study
“What is the Gravitational Field of a Mass in a Spatially Nonlocal Quantum Superposition?”, by Urjit Yajnik and colleagues, was published in Physical Review Letters on March 7, 2023.