- #1
wbandersonjr
- 68
- 1
What is a non-inertial reference frame? how is it defined?
Does Mach mean he can notice a motion of the stars when he's accelerating inside his car?vanhees71 said:The physicist Ernst Mach came up with the idea that the reference frame, which is at rest with respect to the fixed stars around our galaxy determines such an inertial frame, but that's as much a postulate as is the more abstract formulation about the existence of an inertial frame, but at least it's an assumption, one can check experimentally in principle.
fluidistic said:Does Mach mean he can notice a motion of the stars when he's accelerating inside his car?
Or does he mean that as long as you don't see stars moving then you can consider yourself over an inertial frame? Or neither of these sentences and I'm not understanding what Mach said.
vanhees71 said:Now the issue of inertial frames is pretty clear! In general you cannot define a global inertial reference frame (except in an empty universe, where nothing can cause gravity), but only in a small four-dimensional space-time interval. Any body that is free falling, i.e., for which no other forces than gravity act, defines a local inertial frame. E.g., the International Space Station (ISS) is to a good approximation freely falling in the gravitational field of the Earth, the Sun etc. That's why within this quite small environment inside the ISS, one feels no gravity, and thus the interior of the ISS is (to a good approximation) a local inertial frame.
But they can't be sewn together to form a Minkowski coordinate chart on an extended region of space-time.RedX said:So can't local inertial frames be defined at each spacetime point,
vanhees71 said:Then, after a long struggle over about 10 years, Einstein came to the conclusion that not only three-dimensional space is non-Euclidean at presence of a gravitational field but four-dimensional space-time as a whole! This lead to the final theory, namely the General Theory of Relativity (GTR).
Now the issue of inertial frames is pretty clear! In general you cannot define a global inertial reference frame (except in an empty universe, where nothing can cause gravity), but only in a small four-dimensional space-time interval. Any body that is free falling, i.e., for which no other forces than gravity act, defines a local inertial frame. E.g., the International Space Station (ISS) is to a good approximation freely falling in the gravitational field of the Earth, the Sun etc. That's why within this quite small environment inside the ISS, one feels no gravity, and thus the interior of the ISS is (to a good approximation) a local inertial frame.
A non-inertial reference frame is a coordinate system that is accelerating or rotating with respect to an inertial reference frame. In this type of frame, objects appear to experience fictitious forces that are not present in an inertial frame.
The main difference between the two is that an inertial reference frame is not accelerating or rotating, and therefore obeys Newton's laws of motion. In a non-inertial frame, objects appear to experience additional forces due to the acceleration or rotation of the frame.
One example of a non-inertial reference frame is a car that is driving around a circular track. The car and the passengers inside experience a centrifugal force that is not present in an inertial frame, due to the circular motion of the car.
In a non-inertial reference frame, the laws of physics, such as Newton's laws of motion, still hold true. However, additional fictitious forces must be taken into account in order to accurately describe the motion of objects in the frame.
Non-inertial reference frames are important in physics because they allow us to accurately describe the motion of objects in accelerating or rotating systems. They also help us understand the effects of forces on objects in these types of frames and how they differ from inertial frames.