SUMMARY
The discussion centers on the existence of an invariant definition of acceleration in Newtonian physics, akin to proper acceleration in General Relativity (GR). Participants highlight that while Newtonian mechanics traditionally relies on the concept of inertial frames, Newton-Cartan gravity offers a framework where gravity is treated as a fictitious force, similar to GR. Key points include the distinction between coordinate acceleration and proper acceleration, and the assertion that Newtonian acceleration is invariant under Galilean transformations. The conversation also touches on the complexities of defining inertial motion and the implications of using accelerometers in different gravitational contexts.
PREREQUISITES
- Understanding of Newtonian mechanics and its limitations.
- Familiarity with General Relativity and the equivalence principle.
- Knowledge of Newton-Cartan gravity and its mathematical framework.
- Concept of inertial frames and their role in defining motion.
NEXT STEPS
- Study the mathematical formulation of Newton-Cartan gravity.
- Explore the implications of the equivalence principle in both GR and Newtonian contexts.
- Learn about the differences between coordinate acceleration and proper acceleration.
- Investigate the role of accelerometers in measuring inertial motion in various gravitational fields.
USEFUL FOR
Physicists, students of theoretical physics, and anyone interested in the foundational concepts of gravity and motion in both Newtonian and relativistic frameworks.