Fundamentals of Time and Relativity

Inertial frame

  • In an inertial frame of reference Newton's first law of motion is obeyed by all objects and fields within the frame. Homogeneity and isotropy are assumed.
  • Although the concept of an inertial frame is an abstraction, it works well enough in many situations.

In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration. It is a frame in which an isolated physical object — an object with zero net force acting on it — is perceived to move in a straight line at constant speed (which might be zero) or, equivalently, it is a frame of reference in which Newton's first law of motion is obeyed by all objects and fields within the frame.

Although usually not stated explicitly, homogeneity and isotropy are assumed. These fundamental symmetries are, and always have been, defining attributes of inertial coordinate systems. Moreover, it can be shown by mathematical argument that any reference frame moving uniformly and rectilinearly with respect to a given inertial frame is also inertial. Given that some frame is inertial, any frame that rotates or otherwise accelerates relative to this first frame is non-inertial.

Newton’s first law can be thought of as providing a definition of the concept of zero total external force; no force acts on an object if it is moving with constant velocity. However, in the real world no objects behave this way; all objects are subject to the force of gravity. So, strictly, the first law is more of a theoretical concept than actual fact and the same goes for inertial frames.

Even though Newton’s first law, and the associated notion of an inertial frame, is an abstraction, it works well enough in many situations. It holds in any infinitesimal region. In larger regions, if gravity can be ignored for a certain phenomenon of interest, one can find a usable inertial frame. Two examples:

  • The “Earth-Centered Earth-Fixed” frame (ECEF), in which the Earth rotates about a fixed axis. This reference frame is not inertial but will serve as such locally. However, synchronization of distant clocks in this frame would lead to errors.
  • The “Earth-Centered Inertial” frame (ECI), which is effectively the frame of the distant stars is, to a high degree of precision, a global inertial frame, provided it is used to describe phenomena far from any of those distant stars and other massive objects.