# Science Part 7: The Special Theory of Relativity

This video is part of a series that examines the underlying philosophical framework that underpins the scientific method. Part of that framework is the idea that the tool of mathematics accurately describes the operations of our universe.

Perhaps one of the most amazing formulas to come out applying of our mathematical tool to the data we have obtained from studying our universe, is Einstein’s famous equation E=mc² which states that the energy of matter is equal to its mass times the speed of light squared. This video series will show the viewer exactly where this equation comes from in terms of slowly building the mathematical toolbox required to derive this equation along with the data from our universe on which we build our mathematical model that ultimately spits out the famous energy-mass relationship.

Therefore in this video we consider Einstein’s theory of special relativity because it is this theory that ultimately gives rise to E=mc². The special theory of relativity starts with the experimental finding that the speed of light is always a constant 299,800,000 metres/second no matter what your own speed is relative to another object in the universe. The fact that the propagation of electromagnetic radiation is constant in every reference frame, is a beautiful demonstration of the 4^{th }presupposition of our scientific method which assumes that the laws of the universe are conserved through space time – meaning that they are conserved independent of your relative motion to another object.

In this video we derive the formulas that constitute the Special theory of relativity. While these formulas are not difficult to derive mathematically, their implications are so outside of our normal day to day experience (because none of us ever travel at a speed even remotely close to the speed of light) that often people have a hard time accepting what they are telling us – especially the idea that time can slow down as an object’s speed relative to another object approaches the speed of light.

One particular objection people have with this idea is that given there is no special frame of reference, if a person is in a spaceship travelling near light speed and another person is at rest on earth, both people can claim that they are in the stationary reference frame and it is the other person that is moving. If this is the case then the special theory of relativity predicts that both observers should perceive the other’s clock as running more slowly. This appears to result in an obvious paradox that if one twin travels near light speed to a distant star and then returns again, while the other remains on earth, if both twins’ clocks run slower relative to the other twin’s clock then when they are reunited, both twins can’t possibly be younger than each other. This seems to be the paradox that the Special theory of relativity is predicting.

Yet this paradox is not a paradox at all and in this video I spend quite a bit of time explaining how the paradox is resolved so that it is the twin who actually goes on the journey who is indeed the younger out of the two. For those who want to see my earlier video on the proof of Pythagoras’ theorem which we use to to develop the time dilation equation of special relativity, please use this link Likewise, for those who want more information on the resolution of the twin paradox this Tedx video is excellent and contains space diagrams which really help you account for the various time dilations and contractions that occur during Jill’s stella trip. Finally, this video is useful in terms of demonstrating why acceleration and deceleration are not necessary to explain why those in changing reference frames experience less time.