Universality of Free Fall Survives Planck-scale Deformed Newtonian Gravity Investigation

The fundamental principle that all objects fall with the same acceleration, known as the universality of free fall, underpins much of our understanding of gravity, and its potential breakdown at extremely small scales remains a central question in physics. Giuseppe Fabiano from Lawrence Berkeley National Laboratory and the University of California, Berkeley, Domenico Frattulillo from INFN, Sezione di Napoli, and Christian Pfeifer from ZARM, University of Bremen, along with Fabian Wagner, investigate this principle within a theoretical framework that incorporates potential modifications to gravity at the Planck scale. Their work represents the first detailed examination of how deformed relativistic symmetries, arising from a doubly-special-relativity setting, affect the free fall of test particles in a gravitational field, such as that of the Earth. The team demonstrates that, generally, these deformations violate the universality of free fall, yet they also identify specific theoretical models where this cherished principle holds, predicting a measurable alteration to the familiar Newtonian gravitational potential.

The approach involves modifying the standard Newtonian potential with terms related to the incredibly small Planck mass, effectively introducing a short-range alteration to gravity. This deformation allows scientists to investigate potential violations of the weak equivalence principle, which states that all objects fall with the same acceleration in a gravitational field, regardless of their composition. The research specifically examines how these Planck-scale modifications affect the relative acceleration between test bodies with differing mass-energy densities, employing a mathematical approximation to calculate this acceleration and identify terms that could lead to a measurable violation.

The analysis demonstrates that any differential acceleration is proportional to the difference in mass-energy density between the test bodies and inversely proportional to a very high power of the Planck mass. This scaling behaviour is crucial for assessing the potential detectability of these effects in future experiments. The results show that, despite the deformation of the Newtonian potential, the universality of free fall remains approximately valid to a high degree, as the calculated differential acceleration is extremely small due to the very small value of the Planck mass. This suggests that detecting violations of the weak equivalence principle arising from Planck-scale deformations of gravity will be exceedingly difficult with current or foreseeable technology, though the research provides a quantitative framework for understanding the interplay between Planck-scale physics and gravitational interactions.

Lorentz Violation and High Energy Physics

This research explores the possibility that Lorentz symmetry, a fundamental principle of special relativity, may not be exact at extremely high energies, such as those approaching the Planck scale. This motivation stems from attempts to formulate a consistent theory of quantum gravity, where spacetime may not be smooth at the smallest scales, leading to modifications of the usual rules of relativity. A key mathematical framework used is the κ-Poincaré algebra, a deformation of the standard Poincaré algebra that incorporates a fundamental length scale, potentially related to the Planck length, and is closely linked to noncommutative geometry. The concept of relative locality is introduced to address potential issues with causality that can arise in theories violating Lorentz symmetry, proposing that observers in different states of motion perceive events differently, and their perceptions are related by a deformed symmetry described by a mathematical structure called a bicrossproduct.

The research explores how the Poincaré algebra can be deformed to incorporate a fundamental length scale, leading to modified kinematic properties of particles, utilizing mathematical techniques such as mixing coproducts and quantum R-matrices to construct integrable systems. The team also investigates extended Galilei algebras, combining Galilean and relativistic symmetries, potentially providing a bridge between non-relativistic and relativistic physics in the context of Lorentz violation, and pathways to relativistic curved momentum spaces where Lorentz violation can affect particle propagation. This work connects theoretical predictions to real-world observations, emphasizing the need for experimental tests. Modern variations of the Michelson-Morley experiment, using highly sensitive interferometers, are used to search for violations of Lorentz symmetry, while experiments like MICROSCOPE test the equivalence principle with high precision and lunar laser ranging searches for variations in the gravitational constant.

Observations of high-energy cosmic rays, gamma-ray bursts, and the detection of gravitational waves by LIGO and Virgo provide further opportunities to test general relativity and search for Lorentz violation, as do atomic clocks used to search for variations in fundamental constants. The research presents a comprehensive overview of a program exploring the possibility that Lorentz symmetry may not be exact at very high energies, emphasizing the importance of combining theoretical developments with experimental tests to constrain these theories and search for evidence of new physics. The work highlights the potential for Lorentz violation to provide insights into the nature of quantum gravity and the structure of spacetime at the Planck scale, grounding the theoretical work in observable reality.

Universal Free Fall And Modified Gravity

This research investigates the universality of free fall, a cornerstone of classical physics, within the framework of theories proposing modifications to established physics at the Planck scale. By considering test particles falling freely within the gravitational field of Earth, while incorporating principles of deformed Galilean relativity, the team demonstrates that the universality of free fall is not generally maintained, and identifies specific models where it is preserved, predicting a corresponding alteration to the standard Newtonian gravitational potential. Notably, the researchers developed a method to analyze deviations from universal free fall using an effective Eötvös factor, which provides a more accurate means of comparison with experimental measurements than previous approaches. They found that, for certain “distinguished” models exhibiting no time delay in experiments like the leaning tower of Pisa, this effective factor vanishes, indicating adherence to the universality principle, but only in conjunction with a modified Newtonian potential, acknowledging that further investigation is needed to fully understand the implications of this modified potential on other observable phenomena and potentially opening new avenues for testing these theoretical modifications to gravity.