LorentzInvariance - crowlogic/arb4j GitHub Wiki

Lorentz invariance is a principle stating that the laws of physics are the same for all observers, regardless of their relative motion. This principle is a cornerstone of the theory of special relativity, formulated by Albert Einstein, and it deeply incorporates the constancy of the speed of light across all inertial frames.

The concept originates from the transformations derived by Hendrik Lorentz, which describe how the measurements of time, space, and simultaneity between events change for observers moving relative to each other at constant velocities. These transformations ensure that the speed of light remains constant at ( c ) (approximately 299,792 kilometers per second) in all inertial frames. This invariance implies that no matter how fast an observer is moving relative to a light source, they will always measure light's speed as ( c ).

Lorentz invariance has profound implications across physics, influencing everything from the behavior of particles at high velocities to the structure of the laws governing electromagnetism and other fundamental forces. It is also a required property for any fundamental physical theory, including quantum field theory, to be consistent with the framework of special relativity.

Lorentz-violating theories

Models that explain phenomena through a slight breaking of Lorentz invariance, rather than invoking a Higgs field, typically fall under the category of Lorentz-violating theories. These theories are part of broader attempts to reconcile quantum mechanics with general relativity or to explore new physics beyond the Standard Model.

One prominent framework for these theories is the Standard Model Extension (SME), developed by theoretical physicists such as Don Colladay and Alan Kostelecký. The SME includes all possible Lorentz-violating terms that could be added to the Standard Model of particle physics. It systematically categorizes how Lorentz invariance can be broken in various fields and interactions, providing a comprehensive approach to test for Lorentz violation in experiments.

The motivation for considering Lorentz-violating theories can include:

• Quantum Gravity: Some approaches to quantum gravity, such as certain versions of string theory and loop quantum gravity, suggest that Lorentz invariance might not hold at very high energies close to the Planck scale.
• Dark Matter and Dark Energy: Lorentz-violating models have been proposed as explanations for dark matter and dark energy, where modified dispersion relations or altered vacuum properties could account for observed phenomena without needing additional fields.
• Cosmological Inflation: Models of inflation that incorporate Lorentz-violating elements can provide different mechanisms for rapid expansion without relying on traditional scalar fields like the Higgs.

These models usually suggest that Lorentz invariance is an approximate symmetry that holds true at accessible energy scales but might be violated subtly or overtly at much higher energies or under extreme conditions. The empirical search for Lorentz violation is a vigorous area of research in experimental physics, utilizing various systems ranging from high-energy particle accelerators to astrophysical observations.