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Local reference frame

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Title: Local reference frame  
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Subject: Frames of reference, Local coordinates, Redshift, General relativity, Inertial frame of reference
Collection: Frames of Reference
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Local reference frame

In theoretical physics, a local reference frame (local frame) refers to a coordinate system or frame of reference that is only expected to function over a small region or a restricted region of space or spacetime.

The term is most often used in the context of the application of local inertial frames to small regions of a gravitational field. Although gravitational tidal forces will cause the background geometry to become noticeably non-Euclidean over larger regions, if we restrict ourselves to a sufficiently small region containing a cluster of objects falling together in an effectively uniform gravitational field, their physics can be described as the physics of that cluster in a space free from explicit background gravitational effects.

Einstein and general relativity

When constructing his general theory of relativity, Einstein made the following observation: a freely falling object in a gravitational field will not be able to detect the existence of the field by making local measurements ("a falling man feels no gravity"). Einstein was then able to complete his general theory by arguing that the physics of curved spacetime must reduce over small regions to the physics of simple inertial mechanics (in this case special relativity) for small freefalling regions.

Einstein referred to this as "the happiest idea of my life".

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