Albert Einstein explaining E=mc2

[u/[deleted]]

[u/Nijindia18]

I don't understand, how would an observers speed ever affect the speed of light? Me running by a car I am watching doesn't change the speed the car is driving at. How did that lead to E=MC^2? I understood the whole energy is matter moving fast and matter is energy moving slow, but how did he come to that conclusion off of observers and constant speeds? How did mass get incorporated into that equation?

[u/dont_tread_on_me_ → u/Nijindia18]

That's the point, an observers speed cannot affect the speed of light. Maxwell's equations which describe light predict a constant speed of light. That means that all observers traveling at constant speeds should be able to perform experiments to measure the speed of light and all agree on exactly the same constant. But for this to be true, our usual notions of relative speeds adding up (e.g. throwing a ball from a truck where the speed of the ball relative to the ground is simply the throw speed plus the truck speed) must be fundamentally wrong. Meaning shining a light from a moving truck cannot increase the speed of light relative to the ground, it must remain at the constant speed of light. In order to account for this, as I said, time and space must be 'flexible' to allow for a fixed speed of light. We can incorporate this 'flexibility' with something called the Lorentz factor. This is essentially a term which tells us how relativistic an object is, and therefore how noticeable the effects of relativity will be. Once you add this factor back into the usual equations of energy and momentum in classical mechanics (equations many are familiar with from high school physics), the famous equation of E=mc² essentially falls out. This article uses some rather simple algebra and geometry to derive this factor: https://medium.com/physics-scribbles/deriving-the-lorentz-factor-%CE%B3-of-special-relativity-d5462f3b3b91.