## Jan 23 Introduction to Special Relativity

It is fair to say that absolutely everybody knows who Albert Einstein is. What many people don't know is why he is regarded as a genius. Einstein's theories of Special and General Relativity have transformed our notion of reality and these theories are central to modern physics. They govern the laws of nature and our understanding of the Universe as a result. In 1905 Einstein published "On The Electrodynamics of Moving Bodies". A complicated title for a reasonably simple concept. In reality there are two reference frames; accelerating or interial, that is moving and and stationary.

First of all, I need everyone to give up their notions of how time and space work. Time and Space do NOT work how you think they work. Space isnt just an empty void between stars and galaxies. Time isn't a universal unit that is exactly the same for everyone everywhere either! At first you will hold on to dear life but don't worry. This is difficult to grasp so I will go as slowly as I can. Ready?

The main message of Special Relativity is that time and space are connected and inseperable. You cant have space without time and time without space. So what is spacetime exactly. Spacetime is the reality that outlines distance between objects and time between events. So why can't space and time just be real? Heres why....

If there are two observers, moving relative to each other and strictly speaking particles can count as observers. If both observers are noting observations between two events in space; neither observer will be able to agree on the distance between the two events. Both observers cant agree on a time between all events. Neither are even able to agree on the order of the events. Both observers will individually measure everything accuately and be completely consistent which means.....neither of them is wrong!

So how can this be? How can two sets of completely different data be different and correct at the same time? The consequences of this can be catastrophic. In theory one observers past can be in another observers future! For nearby events the effect is infinately tiny but who cares? Any disagreement has to be noted. it isn't absolute zero.

So what can the observers agree on if they cant agree on any aspect of the two events they both observed whilst moving away relative to one another? The short answer is CAUSALITY! This is the spacetime interval or sometimes called spacetime separation.

s2=Δx2+Δy2+Δz2(cΔt)2

Einstein concluded that whilst two observers cannot agree on individual aspects of an observation in spacetime, everyone can agree on the spacetime interval between events. The points x, y and z are co-ordinate positions in space, t is time and the c is the speed of light. Special relativity states that the speed of light in a vacuum is the exact same for everyone everywhere regardless. Light is the cosmic speedlimit for anything travelling through spacetime. Nothing is faster, expansion of space doesnt count in this rule. Since the equation involves subtration, the interval can be positive, 0 or negative.

Relativity was hinted at by Galileo but it didnt account for colossal speeds like the speed of light. Einstein perfected relativity and noted that the speed of light is invariant and is extremely well tested. Relativity so far has passed all experimental testing and scrutiny to date.

So why do we think of time and space as seperate? Good question, nobody really knows. This theory also gave birth to gravitational time dilation, the idea that time can vary from person to person. The twin paradox perfectly describes this. If one twin goes on a rocket at the speed of light far from the Earth and another twin stays on the Earth, the twin on the ship would return to find his twin had aged more than him! In the same way if an atomic clock is placed on the International Space Station and one left on the ground, the clock on the Space Station would tick faster than the one on the ground. This is very simplified and generic but it gets the flavour right.

Astrophysicist Gabe Perez Giz summed up Spacetime perfectly to underline our collective existence in Spacetime. Imagine everyone on Earth is reading a flipbook made of graph paper. As we all flip through the graph book, nobody can agree on the positions of the pictures in the book. Nobody can agree on the story. We are all reading the same book. Only there is no graph pages and there is no book! This is a loose introduction to what is called "flat spacetime". Mind blown yet? Wait until we get into Curved Spacetime and General Relativity.

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