Distinguishing classical from quantum gravity through measurable stochastic fluctuations

In a new Physical Review Letters study, researchers propose an experimental approach that could finally determine whether gravity is fundamentally classical or quantum in nature.

The nature of gravity has puzzled physicists for decades. Gravity is one of the four fundamental forces, but it has resisted integration into the quantum framework, unlike the electromagnetic, strong, and weak nuclear forces.

Rather than directly tackling the challenging problem of constructing a complete quantum theory of gravity or trying to detect individual gravitons—the hypothetical mediator of gravity—the researchers take a different approach.

Phys.org spoke to the researchers behind the study to gain insight into their unique approach.

“Several proposals have appeared in the past years that, in principle, allow us to determine gravity’s nature experimentally, but their experimental requirements are extraordinarily challenging. So our motivation was to come up with a more feasible experiment that would have the power to at least falsify that gravity is classical,” explained Serhii Kryhin, a third-year graduate student at Harvard University and a co-author of the study.

The researchers aimed to rephrase the age-old question into one that could provide more concrete results: “What measurable differences would tell us whether gravity needs to be quantized?”

Quantum vs. classical fluctuations

“The idea is very simple yet remained unnoticed all this time. If gravity is quantum, as a long-range force, it should be able to induce quantum entanglement of distant matter. However, if gravity is fundamentally classical, no entanglement can be produced,” said Vivishek Sudhir, Associate Professor at MIT and co-author of the study.

The insight is that if gravity is classical, it must exhibit irreducible stochastic fluctuations. These fluctuations are a necessity, stemming from a fundamental inconsistency that would arise without them—the deterministic nature of gravity (due to being classical) would violate the principles of quantum mechanics.

The brilliance comes in recognizing that these fluctuations would leave behind a signature in the cross-correlation spectrum as a phase shift, differing from what would be produced if gravity was quantum.

“Quantum fluctuations always arise as quantum fluctuations of dynamic degrees of freedom of general relativity. From a practical perspective, the main difference between quantum and classical gravity fluctuations comes in the magnitude. Being relativistic effects, quantum fluctuations are notoriously weak and thus incredibly challenging to measure,” said Kryhin.

“On the other hand, classical fluctuations, if they exist and have to remain consistent with everything else we know, appear to be much larger,” added Prof. Sudhir.

Mathematical framework

The researchers propose a theoretical framework for this quantum-classical interaction in the Newtonian limit of gravity. In this framework, classical gravity and quantum matter co-exist.

They created a quantum-classical master equation describing how quantum matter and classical gravity evolve together. They also derived a Hamiltonian for Newtonian gravity’s interaction with quantum masses through two complementary approaches—Dirac’s theory of constrained systems and the Newtonian limit of gravity.

Next, they formulated a modified quantum Newton’s law that accounts for stochastic gravitational effects and finally calculated the distinctive correlation patterns between two quantum oscillators interacting gravitationally.

This mathematical framework led them to a closed Lindblad equation (Markovian master equation) for quantum matter interacting with classical gravity. This equation includes a term proportional to the parameter ε, which distinguishes between classical gravity (ε ≠ 0) and quantum gravity (ε = 0).

Identifying measurable quantities

The researchers derived several crucial results. They showed that, contrary to previous claims, a consistent theory of classical gravity interacting with quantum matter is indeed possible.

Their calculations reveal that classical gravity would induce fluctuations distinct from its quantum counterpart. Crucially, they identify an experimentally measurable signature.

When two quantum harmonic oscillators interact gravitationally, their cross-correlation spectrum shows a characteristic phase shift of π or 180 degrees at a specific detuning from resonance if gravity is classical.

To test these predictions, the researchers propose what amounts to a quantum version of the historic Cavendish experiment, using two highly coherent quantum mechanical oscillators coupled gravitationally.

The researchers could observe the characteristic phase shift by precisely measuring the cross-correlation of their motions.

What distinguishes this approach from previous proposals is its experimental feasibility. Unlike other tests that might require creating massive objects in quantum superposition states, this experiment relies on correlations between quantum oscillators within the reach of current or near-future technology.

Prof. Sudhir noted, “Semiclassical models of gravity usually explicitly neglect the backaction of quantum fluctuations of matter onto the classical gravity dynamics. In contrast, our theory allows self-consistent dynamics of classical gravity field and quantum matter.”

Jury’s still out

An experimental confirmation that gravity is classical would have profound implications for our physical theories.

“At present, it is taken as a self-evident fact that gravity has to be quantum, although nobody precisely knows what that means!” said Kryhin.

“Immense effort has been made to understand the behavior of quantized general relativity and construct a complete theory of quantum gravity, which resulted in the construction of string theory as one of the byproducts. If experimentally proven that gravity is classical, we will have to start from the beginning in a search for a satisfactory ontological picture of the world.”

While the study offers a fresh perspective on a question that has plagued physicists for decades, they acknowledge the many problems to be addressed, from formalism development and model-building to demonstrating the technologies required for the experiment.

“From an experimental standpoint, we need two gravitating masses, noise isolation, and measurement techniques, all of which need to come together to realize the sensitivity needed for a decisive experiment,” concluded Kryhin.

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