Einstein did not know this to begin with. His keen insight was the equivalence principle wherein he made the connection between a gravitational field and an accelerated frame.
Once this was known it was certain that curved trajectories would be involved and it led naturally to Riemannian geometry.
Once this was known it was certain that curved trajectories would be involved and it led naturally to Riemannian geometry.
[PDF]Lecture Notes on General Relativity - Gravity and String ...
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2014年10月17日 - ... General Covariance. 18. 1 From the Einstein Equivalence Principle to Geodesics. 19 ... 2.10 Locally Inertial and Riemann Normal Coordinates . ..... 26.9 First Encounter with Killing Horizons and Surface Gravity . . . . . . . . . . . .How did Einstein know that Riemannian geometry was ...
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The Equivalence principal is an assumption that makes things much simpler. ... was necessary for maintaining the equivalence principle in general relativity? ... "[e-Study Guide for: Classical Mechanics by Herbert ... - Google 圖書結果
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... Homogeneous function Equivalence Equivalence principle General Relativity Geodesic Correspondence principle Coupling Coriolis effect Riemann surface ...general theory of relativity - The Worlds of David Darling
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The starting principle of the general theory, known as the equivalence .... It thus determines whether a surface has elliptic (Riemannian) or hyperbolic geometry.[PDF]General Relativity - damtp
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2013年11月4日 - 5.1 Minimal coupling, equivalence principle . ... 6.4 Symmetries of the Riemann tensor . .... These are lecture notes for the course on General Relativity in Part III of the .... Figure 1.3: Freely falling lab near Earth's surface.general relativity - How (or why) equivalence principle led to ...
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2013年4月21日 - If equivalence principle was origin of general relativity what was the .... and so you know that you have been walking on the curved surface of the Earth. ... the system of concepts of Riemann's general theory of invariants is that ...Controversies Over the Equivalence Principle - MathPages
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In attempting to generalize the (then) restricted theory of relativity in 1907, Einstein ... Einstein gave various statements of the equivalence principle over the years, and .... We could point out the existence of Riemann normal coordinates, give the .... lines of constant latitude on the Earth's surface are generally not geodesics, ...
6 Answers
The equivalence principal is often misunderstood. The Equivalence principal is an assumption that makes things much simpler. Basically, Einstein wanted to treat a freely falling frame as an inertial frame. In a freely falling frame, there is still curvature, as apposed to an inertial frame which is far away from any source of a gravitational field and thus no curvature. The weak equivalency principal basically says that particles will behave the same in both situations. That's what we talking about when we talk about astronauts dropping rocks in accelerating elevators. That's all well and good and fairly intuitive. But it is not enough. What was really needed was that whole systems of particles would also act the same. For example, the laws of thermodynamics would be the same. This is the strong equivalency principal, and it is basically an assumption that there is no curvature coupling - that is, phenomena such as thermodynamics should not depend on curvature, otherwise they would be affected if the curvature vanished. Imagine an elevator that is launched into space by a very large catapult capable of accelerating objects faster than escape velocity. As soon as the elevator is no longer in contact with the catapult it is in freefall - at first, the elevator is still in space that has curvature, but eventually it completely clears the gravitational field and the curvature goes to zero. The strong equivalency principal states that phenomenon like thermodynamics will be the same throughout the journey. If that were not the case, things would be much more complicated. Intuitively, Einstein decided the simpler was the better route.
So to answer the question, Riemannian worked because the equivalency principal allowed it be viable option. Its not the other way around: that any proposed solution had to adhere to the principal.
So to answer the question, Riemannian worked because the equivalency principal allowed it be viable option. Its not the other way around: that any proposed solution had to adhere to the principal.
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"[In 1912] I suddenly realized that Gauss's theory of surfaces holds the key for unlocking this mystery. I realized that Gauss's surface coordinates had a profound significance. However, I did not know at that time that Riemann had studied the foundations of geometry in an even more profound way. I suddenly remembered that Gauss's theory was contained in the geometry course given by Geiser when I was a student... I realized that the foundations of geometry have physical significance. My dear friend the mathematician Grossmann was there when I returned from Prague to Zürich. From him I learned for the first time about Ricci and later about Riemann. So I asked my friend whether my problem could be solved by Riemann's theory [Pais's italics], namely, whether the invariants of the line element could completely determine the quantities I had been looking for."
Albert Einstein, as quoted by Abraham Pais in Subtle is the Lord, Pais's scientific biography of Einstein.
Albert Einstein, as quoted by Abraham Pais in Subtle is the Lord, Pais's scientific biography of Einstein.
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He didn't know. He ignored higher mathematics at university because he didn't believe it would ever be of any use to him. He later admitted that this was one of his biggest mistakes.
Einstein's Special Relativity is a formalisation of some forty years' pondering, ever since Maxwell proposed the etherfer to carry its field.
The resulting theory has a geometry "E3J" (ie euclidean geometry + ict), which permits relativity of inertial observers and the consistancy of light. Minkowski provided the necessary geometry for it.
General relativity is due to in part that E3J, like the newtonian E3T, does not deal with relativity applied to gravity.
As long ago as 1893, Heaviside showed that if gravity had a finite speed, it has a magnetic-like co-force. One can complete the electromagnetic analogy, as Heaviside did, and Jefimenko does, to derive a system similar to relativity, but without Einstein's assumptions (they're derived), or the numerous fixes (dark matter, black holes).
The main implication of GEM that is found unpalatible is that one must suppose that it's a source, rather than a sink, of energy. This is an ideological approach.
The resulting theory has a geometry "E3J" (ie euclidean geometry + ict), which permits relativity of inertial observers and the consistancy of light. Minkowski provided the necessary geometry for it.
General relativity is due to in part that E3J, like the newtonian E3T, does not deal with relativity applied to gravity.
As long ago as 1893, Heaviside showed that if gravity had a finite speed, it has a magnetic-like co-force. One can complete the electromagnetic analogy, as Heaviside did, and Jefimenko does, to derive a system similar to relativity, but without Einstein's assumptions (they're derived), or the numerous fixes (dark matter, black holes).
The main implication of GEM that is found unpalatible is that one must suppose that it's a source, rather than a sink, of energy. This is an ideological approach.
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