Local Reference Frame: Explaining What It Is?

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SUMMARY

The discussion centers on the concept of local reference frames in the context of general relativity (GR) and special relativity (SR). It establishes that a spinning reference frame, such as one rotating at 2 revolutions per second, is not inertial, leading to the conclusion that celestial bodies like the moon do not reside within a local inertial frame. The conversation clarifies that an inertial reference frame is defined by accelerometers reading zero and remaining stationary relative to each other, which can only be achieved locally in GR. The distinction between reference frames in GR and SR is also highlighted, noting that SR simplifies the concept by focusing on uniform motion without gravitational effects.

PREREQUISITES
  • Understanding of general relativity (GR) and special relativity (SR)
  • Familiarity with the concept of inertial and non-inertial reference frames
  • Knowledge of coordinate systems and their application in physics
  • Basic grasp of gravitational fields and their effects on motion
NEXT STEPS
  • Study the principles of general relativity, focusing on local inertial frames
  • Explore the differences between general relativity and special relativity
  • Learn about the implications of non-inertial reference frames in physics
  • Investigate the role of accelerometers in defining reference frames
USEFUL FOR

This discussion is beneficial for physicists, students of theoretical physics, and anyone interested in the foundational concepts of relativity and reference frames.

surajt88
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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"?:confused: I know all this boils down to the explanation what a reference frame is. Can someone clarify?
 
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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.
 
surajt88 said:
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"?:confused: 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.
 

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