Einstein's curvature of spacetime?

Question

I don't understand Einstein's general theory of relativity. How does the sun curve spacetime much like a heavy weight on a rubber sheet? What does it mean when they say this causes planets to follow the straightest possible paths allowed by the curvature or spacetime?

Answer 1

Imagine you stand on the surface of a sphere. It has no water, is perfectly smooth, and no magnetic field. Let's let it rotate like the Earth (for "poles" and "equator"). We'll place you north of the equator, a line we draw on the surface appropriately.



You start walking "due east", and without any course corrections, you will cross the equator twice before ending up back where you started. So the "equator" is like the center-of-mass of the Sun, and you are like Earth. You "orbit" the center of mass of the Sun, without the action of a force (neglecting the one that holds you to the surface of the sphere).



The rubber sheet analogy is supposed to get you thinking about physical mechanisms, and really, does more harm than good. Spacetime is not "stuff".



"Curvature" is supposed to describe the force free path of either light or matter, that deviates from "flat" / Euclidian space. It describes the motions we see around us, without the action-at-a-distance that Newton did not like in his theory of gravitation.



I doubt that this will give you too much more insight, but here goes:

http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/GR/gravity.html



Cross tying to duplicate question:

https://answersrip.com/question/index?qid=20110211193411AAZEk2d

Answer 2

In Euclidean space, a photon has mass and it is attracted to other masses by a force of gravity, and the other masses feel and equal and opposite force of attraction to photons. Gravity acts exactly like you would expect it to in Euclidean space. Consequently, a photon passing near a star or black hole follows a curved path in Euclidean space. However, in Minkowski space-time, the path of light is the definition of a straight line. That is why space-time is warped. The warp is caused by gravity, not the other way around. So don't believe it when you are told that gravity is caused by the warp of space-time.



The rubber sheet (or trampoline) analogy is just an analogy. The rubber sheet represents a 2D slice of 4D space-time. The vertical displacement of the sheet represents gravitational potential. The sheet is warped because gravity pulls the bowling ball down, and the tennis ball curves because the normal force of the sheet is angled toward the bowling ball. This is only a visual aid to help us visualize what really happens in 4 dimensions.



While photons follow straight lines in space-time (by definition), objects obey the principle of least action, which is another sort of straight line. Action is energy times time and has the same units as angular momentum (except the direction of the the force is parallel to motion in action and perpendicular in angular momentum).



Don't expect to understand general relativity until you master tensor analysis (a grad school math study). The whole subject is highly counter-intuitive, but computers love it. Problems that would take days to solve by numerical analysis in Euclidean space (using only the formulas of spacial relativity) can be crunched in seconds in Minkowski space-time with the formulas of general relativity.

Answer 3

Physics and Mathematics are very closely related. In fact, at the university level the title for a full professor is often Professor of Physics and Mathematics. Physicists "mine" the writings of mathematicians looking for equations or systems of mathematics. Mathematicians often find cool calculations that at the time of the discovery of the calculation has no known physical meaning. To the mathematician it is just a cool, very elegant calculation they find especially pleasing. Years later some physicists finds that that "useless calculation" that was just pretty, describes a physical theory. The numbers just fit. So it was with Einstein, the equations of a elastic 4D space, accurately described his vision of space and time. The equations for a curved spacetime fit what we see in the macro universe. If the equations fit, we use them.

Answer 4

GR is the thought that appropriately describes the macro universe (issues too super to persist with the guidelines of quantum mechanics). So it quite is not incorrect. yet, that's incomplete. It would not artwork for issues that are sufficiently small to be coated by capacity of quantum mechanics. yet, then QM is likewise incorrect, it would not artwork for those issues coated by capacity of GR. To make this much greater exciting: Neither GR nor QM artwork for issues that are huge/severe capability and small like the massive Bang and black holes. ===> the two are incomplete.

Answer 5

It's all bout motion and time ... Tangential vector velocity is the path of least energy dissipation and hence the motion described. Read . I can't explain the TOR here .