Special Relativity is mostly about what are called "inertial reference frames" - dynamic equilibrium near the speed of light (c). Remember, however, it's all relative You might observe an electron traveling past you at 90% the speed of light but that electron sees you doing the same speed in the opposite direction and both perspectives are correct.
Anyway, since light is the speed limit of the universe and you don't just hit a speed wall, acceleration according to Newton's Second Law isn't linear. At least as measured from an external perspective, mass increases with the speed of light acting like an asymptote in this graph:
Relativistic effects noticeable above 10% the speed of light
But remember, you don't notice the mass gain in yourself, you only notice it in somebody else. Kinda like the pot calling the kettle black or pointing out the speck in your neighbor's eye through the log in your own.
Except it's not actually anything like that because all measurements you can do on yourself will always turn out normal. It's the other guy traveling past you at high speed that has the mass gain. He notices the same in you.
Time slows too. If you're on the platform while the train passes, the clock in the train moves slower than yours.
BUT the train rider also sees your clock running just as slow.
Which perspective is correct? Both. Here's another take on it with the Twin Paradox.
Length is contracted. If you're watching a baseball travel past at more than 10% the speed of light, this is what you'll see.
But if you're watching the universe travel past at more than 10% the speed of light, the distance to your destination is shorter.
Remember, both perspectives are real. You always measure everything to be normal in your constant velocity situation but weird for the moving object. The moving object does the same and both are real.
We know it's true because elementary particles live longer near c and particles smash into other particles with much more energy and momentum than we would classically expect.
And just in case you wanted the equations that Einstein used for his theory,
Those are called Lorentz transformations. Hendrik Lorentz developed them but he didn't believe they represented reality. Einstein did. That's how Einstein changed our world - he believed the equations.
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