That hinges on how you want to define local.paweld said:Is it possible to deifine local inertial frame which is Poincare invariant (in general relativity)
(every manifold is locally flat, so we can chose coordinates which are
almost pseudoeuclidean, but in what sense they might be Poincare invariant)
Thanks.
A local inertial frame is a coordinate system in which the laws of physics take on their simplest form. In this frame, objects at rest remain at rest and objects in motion continue to move at a constant velocity unless acted upon by an external force. This frame is used to describe the behavior of objects in the absence of any external forces.
Poincare invariance is a fundamental principle in physics that states that the laws of physics should remain the same regardless of the observer's inertial frame of reference. This means that the laws of physics should be invariant under translations, rotations, and boosts (changes in velocity). It is a key concept in both classical and modern physics.
Local inertial frames are directly related to Poincare invariance. Poincare invariance requires that the laws of physics remain the same in all inertial frames, including local inertial frames. In other words, the laws of physics should be the same in a local inertial frame as they are in any other inertial frame. This principle is crucial in understanding the behavior of physical systems and making accurate predictions.
Considering local inertial frames and Poincare invariance is important because it allows us to accurately describe and understand the behavior of physical systems. By using local inertial frames, we can simplify complex physical phenomena and make accurate predictions about their behavior. Poincare invariance ensures that our observations and predictions are consistent regardless of the observer's frame of reference.
The theory of general relativity is built upon the principles of local inertial frames and Poincare invariance. In general relativity, the laws of physics are described in the context of curved spacetime, which is locally inertial. This means that in small regions of spacetime, the laws of physics take on their simplest form, allowing us to make accurate predictions about the behavior of objects. Additionally, the theory is Poincare invariant, meaning that it is consistent regardless of the observer's frame of reference.