## The Local Frames of Reference

##### Reference: A Logical Approach to Theoretical Physics

In contrast to the Universal Frame of Reference there are local frames of reference. A local frame of reference is like a viewpoint attached to a body within the universe as compared to the viewpoint of the whole universe.

The local frames of reference may be outlined as:

• Inertial frame of reference
• Inertial frame of reference (Newtonian)
• Inertial frame of reference (Relativistic)
• Non-inertial frame of reference

.

## Inertial Frame of Reference

An inertial frame of reference is defined as one in which all laws of physics take on their simplest form. In this frame of reference, a body does not accelerate unless force is applied to it. In the absence of force, the body either stays at rest or moves at a constant speed in a straight line. Conceptually, the physics of a system in an inertial frame have no causes external to the system.

The inertial frame of reference describes time and space as homogeneous, isotropic, and independent of each other. In other words, it assumes space to be filled with matter that is homogeneous and isotropic throughout. (see Matter, Void and Space). It does not consider any variations in its density. The inertial frame of reference applies to the material domain only from the perspective of MATERIAL-VOID duality. It is not universal because it does not include the motion associated with electromagnetic radiation and gravitational force.

Conceptually, a body will move freely at a constant speed relative to another body only when there is a density differential (see The Universal Frame of Reference). But such differential is so small in the material domain that it is ignored. Therefore, all inertial frames are in a state of constant, rectilinear motion with respect to one another irrespective of density. 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).

.

## Inertial Frame of Reference (Newtonian)

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.

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 transformation.

The Newtonian frame of reference was the original inertial frame of reference that used Earth as its reference point for the motion of material objects on Earth; and Sun as its reference point for the motion of planets in the solar system. It was local because the basis of reference were local bodies.

.

## Inertial Frame of Reference (Relativistic)

The principle of special relativity generalizes the notion of inertial frame to include all physical laws, not simply Newton’s first law. It, like Newtonian mechanics, postulates the equivalence of all inertial reference frames. However, because special relativity postulates that the speed of light in free space is invariant, the transformation between inertial frames is the Lorentz transformation, not the Galilean transformation which is used in Newtonian mechanics.

The special theory of relativity measures the material velocities from the basis of the velocity of light. The large density differential between matter and light makes the material velocities closer to being absolute as in the universal frame of reference. This gives more accurate results as in the calculation of the precession of the perihelion of Mercury’s orbit.

The invariance of the speed of light leads to counter-intuitive phenomena, such as time dilation and length contraction, and the relativity of simultaneity. But this is similar to the shrinking of period and wavelength as frequency increases in the electromagnetic spectrum. This indicates increasing density. This effect continues in the material domain. When external force is applied to matter its density increases by an infinitesimal amount (see The Electromagnetic Spectrum).

The Lorentz transformation reduces to the Galilean transformation as the speed of light approaches infinity. But those Galilean transformation require velocities to be measured relative to the stars as in the Universal Frame of Reference. Error comes about when velocities are measured relative to local bodies.

The Relativistic frame of reference uses a universal basis, but it still limits itself to the material domain. It is local in that sense.

.

## Non-Inertial Frame of Reference

In contrast to the inertial frame, a non-inertial frame of reference is one in which fictitious forces must be invoked to explain observations. In other words, when there are curved paths, or rotation, in the inertial reference frame and no forces are visible, then fictitious forces of inertia are assumed.

These fictitious forces come about because of the frame of reference itself is accelerating. This makes the frame of reference non-inertial. For example, Coriolis effect occurs due to Earth’s rotation. This is accounted for by a fictitious force. Another example of such a fictitious force is the centrifugal force associated with rotating reference frames (see video). All of these forces including gravity disappear in a truly inertial reference frame, which is one of free-fall.

Both inertial and non-inertial frames are local because they are limited to the material domain. The Newtonian version uses a body within the universe from which to observe the motion of other bodies. The Relativistic version, however, uses a near universal basis that allows more accuracy but for the material domain only (see The Universal Frame of Reference).

.