# Conceptual intuition in special relativity

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)

• What you are looking for, is the absolute foundation of which SR resides within, the very same foundation which creates that array of SR phenomena. Since SR itself excludes many absolutes, a description of SR alone, can not, and does not, reveal an absolute foundation of which SR resides within. – Sean Dec 11 '17 at 10:47
• @Sean Yes I think that is exactly what I'm looking for. Is there a particular name for the absolute foundation which SR resides within? How would I go about leaning about it? – Isaac Greene Dec 11 '17 at 23:38
• As silly as it sounds, the 4 dimensional environment known as Space-Time is the foundation. If all objects are constantly in motion within Space-Time, and just one particular magnitude of motion is being shared by all these objects, and a change in direction of an objects motion within Space-Time also leads to 4D rotation, the outcome of this setting is all of the SR phenomena. Thus absolute motion taking place within an absolute Space-Time environment creates the SR result. – Sean Dec 14 '17 at 16:48
• What should I look for to learn this @Sean – Isaac Greene Dec 16 '17 at 0:11
• @Iso134 You could view my YT videos if you have the time. Total of about 1 hour 37 minutes. youtube.com/… – Sean Dec 18 '17 at 11:41

It is easier to answer your second question first.Let's suppose the height of the clock is measured in the y axis and the width in the x axis in some reference frame $O$. The reason the height of the clock does not change is because we assume our boost does not have a component in the $y'$ axis in the reference frame $O'$ because we stipulate we can only move along the $x'$ axis so there can't be any length contractions measured in the $y'$ axis
For your first question, why do we always talk about clocks. The simple and flippant answer is because we are just following Einstein and that is how he came up with the theory. The more substantive answer is the following: if I have two reference frames $O$ with coordinates $(x, y, z, t)$ and $O'$ with coordinates $(x', y', z', t')$ and I ask my self the following question, "what is the most general form of a transformation between $O$ and $O'$ that is consistent with Galileo transformations?" It turns out that it must be able to change the coordinate $t$ in $O$ i.e I can't assume that $t = t'$ .But this means I need two clocks, one for reference frame $O$ and the other for reference frame $O'$.