'... Problems with electromagnetism
The 19th century was a time of extensive study of the phenomena of electricity, magnetism and light. In 1865 James Clerk Maxwell published a set of equations that combined all these phenomena into a single phenomenon of “electromagnetism”.
Soon after Maxwell’s discovery, people realised that there is something strange when it comes to his equations. Their form changes when we move from one inertial frame to another. So an individual who is not moving can observe distinctively different physical phenomena than a person who is moving.
All the beauty of invariance and irrelevance of observers that we had got used to in Newtonian physics was gone. It now looked like some frames were preferable to others when it came to describing events in nature.
Then, at the turn of the 20th century, a new mathematical transformation was discovered that could preserve the structure of Maxwell’s equations when moving from one frame to another. Although many people contributed to this discovery, we now refer to it as the “Lorentz transformation”.
The Lorentz transformation was different from the standard transformation of inertial frames that had been used in the Newtonian physics. In Newtonian physics, length and time are absolute, so the length of an object in one frame is the same as the length of that object in another frame. Also, time passes in the same way in one frame as in the other frame.
However, if taken literally, the Lorentz transformation implies that time and length do actually change, depending on which frame of reference you are in.
Principle of relativity
This got Einstein wondering whether the transformation that preserved the structure of Maxwell’s equations was merely a mathematical trick or whether there was something fundamental about it. He wondered whether time and space were absolute, or whether the principle of invariance of the laws of physics should be paramount.
In 1905, Einstein decided that it is the invariance of the laws of physics that should have the highest status, and postulated the principle of relativity: that all inertial frames are equivalent, the observer’s motion (with constant velocity) is irrelevant, and that all laws of physics should have the same form in all inertial frames.
When combined with electromagnetism, this principle would require that the transformation from one inertial frame to another must have a structure of the Lorentz transformation, meaning that time and space are no longer absolute and change their properties when changing from one inertial frame to another.
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