Special Relativity: Overview

Wednesday, October 17, 2018

Special Relativity: Overview

Special Relativity

On this blog we have now gone through the theory of special relativity. The simplicity of this theory is what makes it seem so amazing to me. It only requires skills in algebra and the ability to think through situations logically (the only more complicated part is the calculus needed for relativistic kinetic energy). It starts with the simple assumption that the speed of light does not change between frames of reference. Experiments at the time (such as the Michelson-Morley experiment) were suggesting that this was actually the case and this seemingly contradicted classical mechanics.
Einstein came along and realized that time must be slowing for moving observers for this to work. This also meant that simultaneity is not an absolute idea and that since length relies on simultaneity, lengths must also shrink for moving observers. With this he formed a picture of 4D space-time and used the Lorentz transformations (these had been derived before special relativity by Hendrik Lorentz who was trying to understand the symmetries in electromagnetism) to describe space-time. After seeing implications for space and time we arrived at mass. We discovered that the classical equation for momentum is wrong and the gamma factor in the equation was suggesting that energy and mass were somehow related. We could then directly derive the relativistic version of the kinetic energy formula and from there, reach E=γmc². I think that it is incredible that all this can be directly derived from 2 simple statements.

All this took Einstein just a year to do. His general theory of relativity took 10 years to complete and incorporates gravity into the picture. The mathematics in this is currently beyond my abilities so a full series on the theory will not be happening any time soon. I will however be looking at the conceptual ideas behind it to get a basic understanding of what it is about and so will be sharing that journey on here.

This is not the end of special relativity on this blog.
Things to look out for on special relativity are the relativistic Doppler effect, the twin paradox and the pole in the barn paradox. Make sure you subscribe so you do not miss those.

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