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The speed of light is constant no matter where the observer is standing. Its been proven where two atomic clocks were flown in opposite directions around the world. When they returned they both showed slightly different times.
The plane flying west to east is flying with the Earth's rotation whereas the plane flying east to west is flying against the Earth's rotation. So time would appear to go slower in the plane travelling towards the east.
If one of a pair of twins travels in a spaceship close to the speed of light, and leaves his brother behind on Earth, and then returns back to his brother then he'l find that his brother on Earth will have aged more than himself.
For the twin travelling in the spaceship time would appear to pass by slower.
Einstein's basis for his theory of relativity was so called because it implies that only relative motion is important.
Einstein theorised that nothing could travel faster than the speed of light. He says that as we use energy to accelerate anything, whether that be a particle or a spaceship, its mass increases,thus making it harder to accelerate further. It would be impossible to accelerate a particle to the speed of light because it'd take an infinite amount of energy. Mass and energy are equivalent, as summed up by Einstein's immortal equation
where "E" is Energy, "m" is mass and "c" is the speed of light.
In Zurich, in 1912 Einstein realized that spacetime was curved and not flat as had previously been the law. He worked this out after discovering the fact that Newton's laws of gravity only applies to a flat Earth.
Einstein's idea was that mass and energy warp spacetime. Objects such as Newton's apples or even planets would appear to be bent by a gravitational field because spacetime is curved.
It was Einstein who related gravity to the curving of spacetime.
The new theory of curved spacetime was called General Relativity and his original theory without gravity is now known as Special Relativity.
In West Africa in 1919, a British expedition observed a slight bending of light from a star passing near to our Sun during a solar eclipse.
Einstein's general theory of relativity explains the expansion of the universe, where galaxies are moving further and further away from each other.
Among Einstein's famous equation's consequences was the realization that if the nucleus of a uranium atom fissions into two nuclei with slightly less total mass, this will release a tremendous amount of energy.

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