Lorentz violation (or Lorentz invariance violation) is the hypothetical idea that the fundamental laws of physics can change depending on orientation or speed. It breaks a core pillar of Einstein’s theory of relativity, which states that physical laws remain the same for all observers, regardless of their reference frame.  The two prime theories — the Standard Model of particle physics and General Relativity (GR) — are completely built on Lorentz symmetry.  However, these two theories are incomplete and fail at extremely high, microscopic energies.  Theories attempting to bridge this gap, such as string theory or loop quantum gravity, often predict microscopic deviations from Lorentz symmetry at extremely high energies.  Because Lorentz violation would create tiny, subtle effects, scientists hunt for them in precise, large-scale experiments including astrophysical observations and high-precision laboratory tests.  For example, scientists can track light or neutrinos from distant gamma-ray bursts to see if high-energy particles travel at slightly different speeds over millions of light-years.

Einstein-æther gravity was proposed to provide a framework in which Lorentz violations are implemented through a dynamical unit time-like vector field, allowing one to analyze their degrees of freedom and phenomenology using standard gravitational tools.  In Einstein-æther theory, Lorentz violations can lead to several observable consequences.  Pulsars in binary systems serve as high-precision cosmic clocks that allow for some of the most stringent tests of GR and constrain possible deviations from it. Pulsars with white dwarf (WD) companions are, however, particularly valuable for testing alternative theories of gravity: their strong asymmetry in gravitational self-energy enhances predicted beyond-GR effects, most notably dipole gravitational radiation, which vanishes for equal-mass binaries. They currently provide the tightest constraints on the parameter space of alternative theories of gravity.

PSR J1738+0333 is a millisecond pulsar (P = 5.9 ms) in a short period (8.5 hours) and nearly circular orbit around a low-mass WD companion. The observed time derivative of the orbital period is large and has been determined with great precision. The high precision measurements of the system distance, through VLBI observations, and of the proper motion allow for the determination of the contributions to the measured period derivative that are due to the real acceleration imparted to this system by the gravitational potential of the Milky Way, and to the apparent acceleration due to the transverse motion (the Shklovskii effect), as seen from the observer. PSR J1738+0333 is also characterized by a remarkable timing stability and precision (∼ 2µs), which led to its inclusion into pulsar timing array programs. Thanks to all of these properties, PSR J1738+0333 has provided some of the best constraints on scalar-tensor theories and quadratic scalar-tensor gravity, has set the best limit on dipole radiation.

Vaglio et al. compiled 25,054 Time of Arrival measurements between September 2001 to February 2021 from the Arecibo, Jodrell Bank, Nançay, Effelsberg, Westerbork, Murriyang/Parkes, and Green Bank radio-telescopes. They obtain a bound on a parameter which represents the most robust constraint derived from a single binary pulsar system to date. The key parameters are the preferred-frame parameters α1 and α2 which introduce secular changes in the orbital elements that are absent in GR. This leads to a formula for the orbital period derivative of an eccentric binary with masses m1, m2 given by the equation above. It brings to mind a famous quote from the 1986 movie Crocodile Dundee, in this case, “That’s not an equation — THIS is an equation!”