Galilean principle of relativity

The problem relates directly to the constancy of c, which implies that the velocity of light is independent of both the motion of its source and the direction of propagation, a condition that cannot hold in more than one Newtonian inertial frame if the Galilean principle of relativity applies. Since there is no evidence that the laws of physics are not identical in all inertial frames of reference the only conclusion is that the prescription for Galilean transformations needs modification to be consistent, not only with simple mechanics, but also with electromagnetic effects. 

The Newtonian laws of motion have been formulated for inertial frames of reference only, but no special IS has been singled out so far, since classical nonrelativistic mechanics relies on the Galilean principle of relativity ... 

In the last chapter the basic framework of classical nonrelativistic mechanics has been developed. This theory crucially relies on the Galilean principle of relativity (cf. section 2.1.2), which does not match experimental results for high velocities and therefore has to be replaced by the more general relativity principle of Einstein. It will directly lead to classical relativistic mechanics and electrodynamics, where again the term classical is used to distinguish this theory from the corresponding relativistic quantum theory to be presented in later chapters. 

For the reasons discussed above we have to abandon the Galilean principle of relativity and accept that Newton s laws cannot be fundamental laws of Nature. We thus consider Maxwell s equations for electromagnetic fields to be valid in all inertial frames of reference and consequently obtain the relativity... 

Principle of relativity.- All of the laws of nature are identical in all Galilean frames of reference it follows that the equation of a law retains its form in time and space when we change the inertial frame of reference. The rate of propagation of the interactions is the same in all inertial frames of reference. 

This invariance defines the principle of (Galilean) relativity, once thought to be universally valid. However, the situation for electromagnetic waves is different and the form of equation (22) is destroyed3 under a transformation... 

The fictitious forces are conventionally derived with the help of the framework of classical mechanics of a point particle. Newtonian mechanics recognizes a special class of coordinate systems called inertial frames. The Newton s laws of motion are defined in such a frame. A Newtonian frame (sometimes also referred to as a fixed, absolute or absolute frame) is undergoing no accelerations and conventionally constitute a coordinate system at rest with respect to the fixed stars or any coordinate system moving with constant velocity and without rotation relative to the inertial frame. The latter concept is known as the principle of Galilean relativity. Speaking about a rotating frame of reference we refer to a coordinate system that is rotating relative to an inertial frame. 

Transformations that preserve the relativity principle are called Lorentz transformations. The form of these looks complicated at first (see diagram). However, they arise from the simple requirement that there can be no experiment in dynamics or electromagnetism that will distinguish between two different Galilean frames of reference. 

Of course, in Eq. (6) the contraction form factor p is valid only in the arm that is parallel to the velocity vector. Equation (6) was interpreted by Lorentz and Fitz-Gerald as a real contraction [17]. It is important to see that in Eq. (6) the hidden parameter p is only one possible solution for the contradiction, but the result of the M-M experiment allows numerous other solutions based on the inner properties and features of the light. The M-M experiment destroyed the world picture of classical physics, and it required a new physical system of paradigms. Thus, for example, the applicability of Galilean relativity principle was rendered invalid. 

Because of zero inertial acceleration (3.48), we can see from these general results (3.78)-(3.83), that the balances (3.70), (3.74)-(3.77) are valid in any inertial frame and not only in the one fixed with the distant stars. This assertion expresses the Galilean relativity principle about the impossibiUty of preference of any inertial frame. 

This remarkable result also has implications for the measurement of spatial intervals. The measurement of a spatial interval requires the time coincidence of two points along a measuring rod. The relativity of simultaneity means that one cannot contend that an observer who traverses a distance X m per second in the train, traverses the same distance x m also with respect to the embankment in each second. In trying to include the law of propagation of light into a relativity principle, Einstein questioned the way in which measurements of space and time in different Galilean frames are compared. Place and time measurements in two... 

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