Anyone with a high school diploma knows Newton’s universal law of gravitation: according to this law, the force of gravity is inversely proportional to the square of the distance separating a mass from a gravitational mass. And nowadays, almost everyone has also heard of quantum mechanics thanks to the advent of quantum computing, which even the Prime Minister of Canada is able to understand.explain.
The fascinating behavior of quantum systems is that they can allow an element to assume two states (if not more) simultaneously. Thus, a particle with a positive rest mass (“massive particle”) can end up in two places simultaneously. This is not science fiction: indeed, atomic interferometers regularly arrange cesium or rubidium atoms in configurations such that the quantum state of the atom is split and present in two placesthese two places being able to be separated from each other up to several centimeters.
Such states are very sensitive to gravitation, resulting in the most accurate measurement scientists have been able to make of Earth’s gravitational field, corresponding to 1/1015 for exemple. But the question is: what gravitational field does a massive particle create in such a quantum state?
To answer this question, particle physicists from the University of Montreal Richard MacKenzie et Manu Paranjape have been working since 2012 together with their colleague Urjit Yajnikfrom the Indian Institute of Technology Bombay, India, with a scholarship from Quebec-Maharashtra cooperation granted by the Ministry of International Relations and La Francophonie of Quebec.
Along with numerous students and other collaborators, they have produced a significant body of research in theoretical particle physics, and their most recent study, which has just been published In Physical Review Letters, the journal of the American Physical Society, asks this question: what is the gravitational field of a mass in a spatially nonlocal quantum superposition? Their surprising discovery is as follows: while it would not allow to know that a massive particle is split and present in two places at the same time, the gravitational field seems to come from only one place, in view of the position mean of the massive particle.
To come to this conclusion, the team looked at scattering experiments conducted by other particle physicists, such as in the Large Hadron Collider, experiments that aimed to peer into the very interior of atoms, nuclei and other subatomic particles. The experiences of deep inelastic scattering carried out at the end of the 1970s also demonstrated the presence of quarks in the nucleus and confirmed the theory of strong interaction, or quantum chromodynamics.
Manu Paranjape
Credit: Courtesy Photo
“It seemed 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 make it possible to probe the nature of the gravitational field created by the non-local massive particle. In doing so, we established very clearly that the scattering behaves as if the massive particle were in its mean position and not as if there were a half-particle at each of two spatially distinct locations. In truth, this result was rather unexpected.”
Now comes the arduous phase of the work, namely the experimental verification of the scientists’ theoretical calculations.
Richard MacKenzie
Credit: Courtesy Photo
“At the moment, 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, points out Richard MacKenzie. However, it is within the realm of possibility to measure the gravitational field of a set of regarding a billion atoms.
Although it represents much less than a microgram of matter, this number of atoms is approximately equivalent to that which intervenes in the quantum state at the macroscopic level corresponding to what one qualifies as condensat de Bose-Einstein. It would be possible to shape a spatially nonlocal superposition of a Bose-Einstein condensate of such size, which would allow measurable gravitational fields to be created.
If the scientists’ theory might be verified experimentally, “the results would be spectacular,” says Manu Paranjape. We therefore invite you to stay on the lookout for this question… wherever you are.
About this study
The article “What is the gravitational field of a mass in a spatially nonlocal quantum superposition?”, by Urjit Yajnik and colleagues, was published on March 7, 2023 in Physical Review Letters.
