Inertial frame of reference

In physics, an inertial frame of reference (also inertial reference frame or inertial frame ) is a frame of reference which describes time homogeneously and space homogeneously, isotropically, and in a time independent manner. This allows motion and interactions to be described without the presence of fictitious forces. Special relativity states that there are actually infinitely many such frames, and the physical laws takes the same form as they do in any other inertial frame of the same handedness. In flat spacetimes, all inertial frames are in a state of constant, uniform motion with respect to one another.

By contrast, in non-inertial reference frames, the laws of physics depend upon the particular frame of reference, and the usual physical forces must be supplemented by what are called fictitious forces. All non-inertial frames are accelerating with respect to all inertial frames.

Within the realm of Newtonian mechanics, an inertial frame of reference, or inertial reference frame, is one in which Newton's first law of motion is valid. However, the principle of special relativity generalizes the notion of inertial frame to include all physical laws, not simply Newton's first law.

Newton viewed the first law as valid in any reference frame that is in uniform motion relative to the fixed stars; that is, neither rotating nor accelerating relative to the stars. Today the notion of "absolute space" is abandoned, and an inertial frame in the field of classical mechanics is defined as:

An inertial frame of reference is one in which the motion of a particle not subject to forces is in a straight line at constant speed.

Hence, with respect to an inertial frame, an object or body accelerates only when a physical force is applied, and (following Newton's first law of motion), in the absence of a net force, a body at rest will remain at rest and a body in motion will continue to move uniformly that is, in a straight line and at constant speed. Newtonian inertial frames transform among each other according to the Galilean group of symmetries.

Accelerated reference frame

In theoretical physics, an accelerated reference frame is usually a coordinate system or frame of reference, that undergoes a constant and continual change in velocity over time as judged from an inertial frame.

An object in an accelerated frame will usually be compelled to move relative to the frame by a fictitious force. If this force is opposed mechanically, the transmission of this "holding force" through the object will make the object seem to feel accelerational "g-forces" as if it were suspended in a gravitational field, otherwise the force will be not directly detectable (not "felt") except by the motion it creates.