The journey ahead
At the end of the 19th century many people thought that physics was pretty much 'in the bag'. Newton had given us a seemingly universal set of laws describing motion and forces, while Maxwell had done the same for electromagnetism. It didn't really seem like there was much left for the apprentice boffins to get their teeth into.
There were some annoying little problems. One was a small incompatibility between the laws of Newton and Maxwell, and in 1905 a young patent clerk proposed a solution to this problem that was to usher in a new era of physics. That clerk was Albert Einstein and the solution was Special Relativity and it changed fundamentally the way we think about time and space.
If you look at any high school or undergraduate physics textbook and you
will find an introduction to Special Relativity based around light
clocks and a presumption that the speed of light is constant. I want to
take a completely different approach which I hope will lead to deeper
understanding while actually making it easier to solve relativity
problems. This approach will be based on Minkowski diagrams,
also called spacetime diagrams, and will hopefully lead you to an
understanding of why the speed of light is constant for all observers,
and why \[ E = mc^2 \]
How Science works
Before we develop the spacetime framework I want to indulge in a few words about how science works. Perhaps one of the most succinct summations of science at work is given by Richard Feynman in a lecture to class at Cornell University in 1964.
In summary, when looking for a solution to a problem we make an educated guess, compute the predictions of that guess, then test those predictions against experiment and observation.
In Einstein's case the problem was the incompatibility between the laws
of Maxwell and Newton. I want to leave the discussion of the nature of
this incompatibility until later. To begin, I just want to introduce
Einstein's solution, which was to suggest that perceptions of time and
space vary according to the relative velocity of the observers. In other
words, if Prof Stick is moving relative to Albert, then they will
measure space and time differently. Our quest in this series is to
develop a framework which combines time and space in such a way that
Prof Stick and Albert can agree on measurements of 'distance' regardless
of their relative velocities. We'll call this framework spacetime.
To develop this framework we are going to make a series of educated and notsoeducated guesses and compute their consequences. This is going to take a fair bit of work but at the end we will have a set of predictions that we can compare observation and experiment.
All aboard!
Before we depart, let's pause, look around and get our bearings. Our starting position has 2 reference points:

Galileo's Principle of Relativity  which states that all motion is relative and that there are no special or absolute frames of reference. This is important because it means that if two observers are moving relative to each other they both agree on their relative velocity.

Einstein's solution to the Newton/Maxwell incompatibility that suggests that observers with relative velocities will measure space and time differently.
OK, so now we know where we are starting from, follow me...and watch your step!
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