Local Reference Frame: Explaining What It Is?

[surajt88]

According to this, if someone spins around at 2 revs per second when the moon is in the horizon, the moon seems to move at 4 times the speed of light. And this implies the moon is not in our local reference frame. And per this, local inertial frame applies to "small regions of a gravitational field". So the moon and Earth are not in a "small region of a gravitational field"? I know all this boils down to the explanation what a reference frame is. Can someone clarify?

 

[Dale]

A frame which is spinning at 2 rev/s is not inertial even locally.

Essentially, a reference frame is a coordinate system*. You can imaging putting accelerometers at rest at each point in the coordinate system. If those accelerometers all read 0 all the time and are not changing distance wrt each other, then the reference frame is inertial. In GR, that can only be done locally.


*Technically, it is sloppy usage and a reference frame is what is called a "frame field", but the distinction is not usually important.

 

[harrylin]

According to this, if someone spins around at 2 revs per second when the moon is in the horizon, the moon seems to move at 4 times the speed of light. And this implies the moon is not in our local reference frame. And per this, local inertial frame applies to "small regions of a gravitational field". So the moon and Earth are not in a "small region of a gravitational field"? I know all this boils down to the explanation what a reference frame is. Can someone clarify?

You seem to refer to reference frames in general relativity. However, special relativity is easier to understand although it ignores some small effects due to gravitational fields - effects that are of little relevance for your issue. SR uses the same "reference frames" as the reference systems that Newton's theory referred to: coordinate systems with clocks that are in rectilinear, uniform motion. The laws of physics (such as about the speed of light) do not refer to a spinning reference system.