How is the acceleration expressed in the general theory of relativity?
Special and general theory of relativity
The older sister - the special theory of relativity
Even in his school days, Einstein dreamed of the nature of light. What would an observer "see" who ran as fast as light next to a ray of light? Could he see anything at all? Wouldn't everything be dark for him? He was quite fascinated by the problem: what you wanted to look at - the light - was exactly what you looked with - the light.
Until the special theory of relativity saw the light of day in 1905, he kept brooding over questions about the light. He had the time at the Bern patent office - despite a 48-hour week. He was still completely unknown as a scientist.
From 1902 to 1909 he sat at his desk on the upper floor of a post office and telegraph office building. His work forced him to think in many ways and "also offered important stimuli for physical thinking," Einstein later said of his job at the time.
After his eight hours of work there was another "eight hours of allotria and one more Sunday", and by allotria - nonsense - he didn't mean going to the bar or feasting. He meant working time for his spiritual children, his ideas for a new building for physics.
Light is always the same speed
The answer to the question from his school days - and with it the basic idea of the special theory of relativity - is said to have come to him, as he himself later communicated, in May 1905. It became official five weeks later, on June 30, 1905.
The basic idea behind his new physics had already been suggested by others, but he was the first to precisely summarize the results of their experiments and research.
The pivotal point is a property of light that seems to contradict our everyday experience: regardless of how the light source moves, light always spreads at exactly the same speed - the speed of light, around 300,000 kilometers per second.
This is not the case with sound, for example. Sound needs air as a carrier in order to propagate - and the speed of sound depends on how the sound source moves. The tone of a train coming towards us sounds higher than that of a train moving away from us.
The nature of light
Light is completely different in nature. It does not need any material support for its expansion. Its carrier is literally nothing: the vacuum. Light has the highest speed with which processes can propagate. There is nothing about that.
One consequence of the fact that nothing can move faster than light is probably the most famous formula in the world - E = mc².
Einstein conjured up this formula with a small rough calculation and a thought experiment: a box in which a single light particle was enclosed. Einstein knew the energy E of the light particle and left the system to itself.
Light travels at the speed of light c. So the light "bumped" - now and then - against the ideal walls of the box. But the light would not lose its impulse to move. From this Einstein was able to conclude how "heavy" the light particle should be: exactly E = mc².
With that, Einstein came up with a formula that also applies to all other bodies and not just to light. The consequences for practical life on a small scale and that of the big world were enormous. After all, this formula indirectly led to nuclear fission and thus to a terrible weapon: the atomic bomb.
The younger sister - the general theory of relativity
Einstein was only 17 and still went to school in Switzerland. At that point he was already busy with a question that bore the seeds of a new theory of gravity.
The question that worried the young student was: What actually happens in an elevator if you cut the cables and everything - the elevator and its occupants - fell freely. It wasn't a bad dream, it was a serious physical question. The pupil Einstein suspected that this picture was the key to discovering the secret of gravity.
In 1907, eight years before the general theory of relativity was actually born, Einstein finally had the decisive answer.
Looking back, he wrote: "I was sitting in an armchair in the Bern patent office when the thought suddenly occurred to me: If a person is in free fall, they will not be able to feel their own weight. A light dawned on me. This simple thought made a lasting impression on me. The enthusiasm that I felt then drove me to the theory of gravity. "
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