Dear Sir,
You are right that "The waves are in a sequence of cause and effect determined by the physics of the circumstance". Everything evolves in that way in a continuing chain of events independent of our observation. But if we look for a particular chain; how to describe it? It has evolved further so that it cannot be described as it was. It is not non-existent, because it still exists in an evolved state unknown to us. The uncertainty is about our knowledge and not its existence. It was perceived at "here-now". It existed before and continues to exist after that in states unknown to us. If we combine its perception over time t' to t'' into one lot, at all other times it existed in an evolving state, but not perceived by us. We cannot differentiate between such states. Hence it has to be described together as a superposition of states. In fact, when it was perceived, it was also in different states, but since these were known, they can be described precisely.
Perception is observation of the observable by the observer. Observation is reporting the state of the observable only. It does not affect the observable. But without observation, the object is meaningless as far as we are concerned. Since perception is comparison of observation to a fixed concept, it has to be time invariant unlike the observable, which is time variant in its temporal evolution. We must note these differences.
The wave does not change the state of the medium; it only passes the momentum to the next position. Hence you are right that it is in a sequence of states.
Regarding your last para, we will quote an anecdote. A famous scientist once directed two of his students to precisely measure the wave-length of sodium light. The students returned with two different results - one resembling the normally accepted value and the other a different value. Upon enquiry, the other student replied that he had also come up with the same result as the accepted value, but since everything including the Earth and the scale on it is moving, for precision measurement he applied length contraction to the scale treating the star Betelgeuse as a reference point. This changed the result. The scientist told him to treat the scale and the object to be measured as moving with the same velocity and recalculate the wave-length of light again without any reference to Betelgeuse. After sometime, both the students returned to tell that the wave-length of sodium light is infinite. To a surprised scientist, they explained that since the scale is moving with light, its length would shrink to zero. Hence it will require an infinite number of scales to measure the wave-length of sodium light!
Some scientists we have come across try to overcome this difficulty by pointing out that length contraction occurs only in the direction of motion. They claim that if we hold the rod in a transverse direction to the direction of motion, then there will be no length contraction. But we fail to understand how the length can be measured by holding the rod in a transverse direction. If the light path is also transverse to the direction of motion, then the terms c+v and c-v vanish from the equation making the entire theory redundant. If the observer moves together with the given measuring-rod and the rod to be measured, and measures the length of the rod directly by superposing the measuring-rod while moving with it, he will not find any difference because the length contraction, if real, will be in the same proportion for both.
The fallacy in the above description is that if one treats "as if all three were at rest", one cannot measure velocity or momentum, as the object will be relatively as rest, which means zero relative velocity. Either Einstein missed this point or he was clever enough to camouflage this, when, in his 1905 paper, he said: "Now to the origin of one of the two systems (k) let a constant velocity v be imparted in the direction of the increasing x of the other stationary system (K), and let this velocity be communicated to the axes of the co-ordinates, the relevant measuring-rod, and the clocks". But is this the velocity of k as measured from k, or is it the velocity as measured from K? This question is extremely crucial. K and k each have their own clocks and measuring rods, which are not treated as equivalent by Einstein. Therefore, according to his theory, the velocity will be measured by each differently. In fact, they will measure the velocity of k differently. But Einstein does not assign the velocity specifically to either system. Everyone missed it and all are misled. His spinning disk example in GR also falls for the same reason.
Regards,
basudeba