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Physics and Special Relativity



The most incomprehensible thing about the world is that it is all comprehensible.  (Albert Einstein)


I thought that quote was obviously something I couldn't wrap my head around.  Yet, I finally think I have some idea as to what he meant.  With reference to special relativity, the length of metre sticks in motion and the period of clocks in motion read differently than if they are at rest.   While learning about special relativity in college, I encountered such weird things as 'length contraction' and 'time dilation.'  As for the former, I was told, but didn't understand, that metre sticks in motion shall measure shorter than those at rest; that is, metre sticks are longest in their own inertial frame of reference. (e.g. a metre stick you are holding in your hand). As for the latter, I was told, but didn't understand that clocks go "tick, tock, tick, tock, etc.." slower  (their period is longer) when in motion relative to our clocks at rest; that is, clocks go fastest in their own inertial frame of reference (e.g a clock on your wrist.).



Perhaps what Einstein meant was understanding the universe, ultimately, despite our fine tools such as telescopes, microscopes, magnetic imaging, x-rays, etc., it ultimately consists of using our sense impressions to make conclusions about reality.  As for a supernova, we see with our eyes its flash and then assume it happened now, when in fact the explosion happened long ago.  This leads to the strange realization that our experiences of reality are of events that happened a few moments ago, in the past, because it took time for the light of something you look at, a chair for example, to reach your eyes and then have your brain process the information to your mind until you see a chair.  So Einstein was interested in knowing the nature of things beyond our appearances of them.  He was very much akin to Parmenides and Democritus of ancient Greece; he also loved reading Spinoza.


What Einstein then did was formalize mathematically these relationships such that when it comes to length, using what is known as the Lorentz Transformation, we can use our measured lengths of metre sticks in motion and then calculate their lengths as if they  were at rest.   Likewise for time, using the measurements of time from clocks in motion and using the Lorentz Transformation, we can calculate its period or durations between 'ticks' and 'tocks', as if the clock were at rest.  (See the Lorentz Transformation page or the lecture below.)


I absolutely love viewing lectures on YouTube as it absolutely prevents me from asking questions.  Below is a great lecture of Professor R. Shankar of Yale University on the subject matter.