-1632, Galileo proposed his thought experiment, called “Galileo’s Ship“:

“…That is why I said you should be below decks; for if this took place above in the open air, which would not follow the course of the ship, more or less noticeable differences would be seen in some of the noted effects…”

-This is the point which I wish to drive my shoulder into. Focusing on the air as a medium for the transmission of sound waves, I want to transmutate these noticeable differences into mathematically measurable phenomena.

-In Galileo’s Ship once again:

“…have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that, you discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still…”

-It is this not being able to tell whether the ship is moving, or at rest, which is the critical point. This is the foundation of Galilean invariance, or his principle of relativity. It is reiterated by Newton, and appears in the axioms of Einstein; no experiment can be done to detect absolute motion. The laws of physics are the same from the point of view from a reference frame, or within the reference frame.

-However, it has already been observed by scientists that sound waves violate this invariance, or relativity. Sound waves seem to cross this wall of separation between two reference frames, one at rest and one in relative motion (at a constant velocity). An observer within the ship cabin, shares the motion of the ship, along with the air molecules. This observer is at rest within the ship’s reference frame. The laws of physics take on their simplest form.

-An observer on the shore sees the ship observer and air molecules following the translatory motion of the ship as it travels through the water. This shore observer factors this translation into a formula, but realizes that he cannot communicate any of this mathematical information to the ship observer.

-If the cabin observer moved to the open air of the main deck, I think she would have a different set of experiences than she had had below decks. If a sailor is set to ring a bell at the aft end of the ship, then the sound waves would travel to the fore end of the ship where the ship observer could be positioned. The fore and aft positions are at rest relative to each other; but are moving in tandem relative to the still air. This is a critical point; so she proposes to perform a thought experiment.

-If she were to send a light signal -- a lantern maybe -- to a sailor at the bell, then this sailor would ring the bell (disregarding reaction times). This light signal would effectively be instantaneous over this short distance, D. If she started her chronometer at this exact same moment, then she would measure the time, t₁, for the sound wave to return to her. However, because the ship is in translatory motion, with the air at rest (windless day), then the formula she would use is not t = D / c, as below decks; instead, she would use t₁ = (D - vt₁) / c in the open still air.

-This would be identical in form to the shore observer’s mathematics (from the Michelson-Morley experiment to detect the Aether). He would simply factor in the translatory motion of the ship in his calculations. The ship observer can safely assume that, because she knows of the violation of invariance by sound waves, that the time she measures would be associated with the formula that includes the ship’s velocity, v. This unknown can then be solved for.

-This counterclaims the principles of relativity. A certain kind of motion is revealed; it is somewhere between absolute and relative motion. This intermediary motion spins silken threads between reference frames.

-It seems counterintuitive that the mere addition of four solid walls and the introduction of very slow sound waves can produce more insight into scientific phenomena than super fast light waves. This may be more Philosophy than Physics; what rides on a narrow gauge rail, is our perception of reality.

http://en.wikipedia.org/wiki/Galileo's_ship