I am currently studying special relativity at high school and they do a very poor job of teaching it as they just tell us to apply the formulas and give us no basic intuition. Thus I have many basic, conceptual questions that my teachers can't answer:
1) Light clocks seem to be quite a strange concept, why cant we think about special relativity without a light clock? My current feeling on this is they are purely an illustration which makes instantly clear the properties of SR, is this the correct way to be thinking about them?
2) In the derivation of time dilation with pythagorus' theorem and a light clock (the one where you get (ct)^2 = (cT)^2 + (vt)^2), why must it be time that changes? Couldn't the height of the light clock (and thus the distance for the light to travel in one oscillation inside the light clock) change as an alternative way of keeping the speed of light constant?
2.5) The basic idea I am trying to express in 2) (the question above) is: seeing as time is linked to speed through distance, why can't it be distance that changes rather than time in order to keep speed constant?
3) Consider the classic example for an observer standing on a train platform and the train going past at constant velocity. The usual conclusion is that time passes slower for the person on the train. However, doesn't the person in the train see the platform moving with the same velocity and thus conclude that time passes slower for the person on the platform by the exact same amount as previously concluded (but this time in the opposite frame of reference)? In summary, because there is no preferred frame of reference won't the effects experienced by one observer ALWAYS be experience by the other observer and thus all relativistic effects "cancel out"? (Note: this may just be the twin paradox, I'm not sure)