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Reference Frames

The grass is always bluer, if you run fast enough.

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In the course of natural events there are some things that are objectively true, e.g.,

  • "the bomb exploded",
  • "the reaction finished", or
  • "I'm dead broke"

but there are other things that are just an artifact of our perspective, e.g.,

  • "the bus is moving at a speed of \(\SI[per-mode=symbol]{30}{\meter\per\second}\)",
  • "the kinetic energy of the missile is \(\SI{1e4}{\joule}\)", and
  • "well maybe I'm not that broke".

It is important to distinguish between universally agreed upon information and things that can change based on the observer.

We start by retracing the work of Galileo who established the basic framework for relativity.

By interrogating the role of the reference frame in our laws and calculations, we'll learn how to translate our equations so that they apply regardless of what frame of reference we happen to be in. In particular, this will allow us to move our calculations into whatever reference frame makes them easiest.

By the end, we'll examine the revolutionary insights of Albert Einstein that forever changed the way we relate measurements in different frames.

In particular, we'll see the effect of relative motion on the nature of things we usually take for granted, such as the length of measuring rods and the flow of time itself.

Master the problem solving skills of Classical Mechanics.

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