# Inertial frame of reference

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 with a constant velocity (it might be a zero velocity) or, equivalently, it is a frame of reference in which Newton's first law of motion holds. All inertial frames are in a state of constant, rectilinear motion with respect to one another; in other words, an accelerometer moving with any of them would detect zero acceleration.

It has been observed that celestial objects which are far away from other objects and which are in uniform motion with respect to the cosmic microwave background radiation maintain such uniform motion.

Measurements in one inertial frame can be converted to measurements in another by a simple transformation, the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity.

In analytical mechanics, an inertial frame of reference can be defined as a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner.

• in any region small enough for the curvature of spacetime and tidal forces to be negligible, one can find a set of inertial frames that approximately describe that region.
• the physics of a system can be described in terms of an inertial frame without causes external to the respective system, with the exception of an apparent effect due to so-called distant masses.

In a non-inertial reference frame, viewed from a classical physics and special relativity perspective, the interactions between the fundamental constituents of the observable universe (the physics of a system) vary depending on the acceleration of that frame with respect to an inertial frame. Viewed from this perspective and due to the phenomenon of inertia the 'usual' physical forces between two bodies have to be supplemented by apparently sourceless inertial forces. Viewed from a general relativity theory perspective appearing inertial forces (the supplementary external causes) are attributed to geodesic motion in spacetime.

In classical physics, for example, a ball dropped towards the ground does not move exactly straight down because the Earth is rotating. This means the frame of reference of an observer on Earth is not inertial. As a consequence the science of physics has to take into account the Coriolis effect—an apparent force—to predict the respective small horizontal motion. Another example of an apparent force appearing in rotating reference frames concerns the centrifugal effect, the centrifugal force.