What is Equal Apriori Probability?

A fundamental postulate of statistical mechanics is that a macroscopic system in equilibrium is equally likely to be in any of its accessible microscopic states satisfying macroscopic conditions of system. It is called the postulate of equal apriori probability.

According to this postulate, the probability of finding the phase point for given system in any region of phase space is identical with that for any other region of equal extension or volume. This may also be stated as for a system in equilibrium, all accessible microstates corresponding to a given microstate are equally probable.

The basis for the postulate of Equal Apriori Probability is ergodic hypothesis. The constancy of volume element in phase space with time indicate validity of postulate of Equal Apriori Probability.

Explanation of words in "The Special Theory of Relativity"

Special: The word "Special" in name arises because we employ only unaccelerated reference frames, not all reference frames  that one can think of. In other words, we "specialize" to the way things appear when observed from uniformly moving reference frames.

Relativity: The word "Relativity"  comes from a phrase coined by Henry Poincare, an eminent French Physicist and Mathematician.

In 1904, Poincare was invited to address the international congress of Arts and Science, held in St. Louis to commemorate the 100th Anniversary of Losiana purchase. "Poincare" spoke of "Principle of Relativity".

In his words.....

Assume that you are in plane on its way from Chicago to Pheonix, another plane making the return flight, over wheat fields of Kansas. A farmer, looking up, notes that you are flying south-west at 500 miles/hr relative to his wheat fields. The pilot of return flight notes that the distance between the two planes is decreasing at about 1000 miles/hr. So far as the pilot is concerned, you are travelling at about 1000 miles/hr relative to his plane.

The essence is this:

Statements about uniform motion relative to a specified reference frame-wheat fields or another air plane are meaningful.

       A quantitative statement about uniform motion with out specification of a reference frame is not meaningful. Why? because our principle 1 says we cannot discern uniform motion with out recourse to some reference frame.

Take first the colloquial form of that principle: If we are in unaccelerated vehicle, its motion has no effect on the way things happen inside it. So by just doing experiments inside the vehicle, we have no way to assign a velocity to the vehicle. Only if we look out of window and there by use wheat fields of Kansas as an outside reference frame- we can decide on velocity (relative to that outside reference frame).    

Theory: It appears because principle 1 &2 are generalizations from observation and experiment.