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Some questions about general relativityby faen
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#1
Nov2712, 07:28 AM

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Hi, I have some questions about general relativity. I'd appreciate if somebody could enlighten me :)
I heard that according to Einstein, objects do not accelerate in a gravitational field, it is just spacetime that is warped around them. So what exactly does this mean? Is it that due to relativistic effects, the speed seems to be faster and faster, but instead it is actually time is going slower and slower? Also if it is true that objects do not accelerate in a gravitational field, how come objects can change speed in the opposite direction. E.g. If i throw a ball up it will change direction and fall down. Then the next question is, how can space be curved? Isn't it a contradiction to say that space is curved within itself? Or does it exist many layers of space curved relative to eachother? Isn't it just easier to say that objects are simply accelerated? Thanks a lot for any reply :) 


#2
Nov2712, 07:45 AM

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#3
Nov2712, 08:59 AM

P: 140

I tried to read it but all I understood is that it just shows a mathematical connection between curved and straight line space? Thanks anyway, but so far I wasn't able to find any answer to my questions.



#4
Nov2712, 09:37 AM

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Some questions about general relativity
However, then we have another phenomenon to explain: tidal gravity. Take two objects dropped from rest at different heights (but with one directly above the other), in vacuum so that there is no air resistance. Both objects are weightless, yet the distance between them increases with time. In special relativity, this is not possible: two objects, both in inertial motion (i.e., weightless), that are at rest at one instant relative to each other, will remain at rest relative to each other forever (so the distance between them will never change). (More generally, objects which are in inertial motion in SR can't change speed relative to each other, so if they are moving at some relative velocity v at one instant, they will move at the same relative velocity v forever.) So special relativity can't be exactly right in the presence of gravity: we need to add something to it. The something that we add is that spacetime, instead of being flat as it is in SR, is curved, and the curvature shows up as tidal gravity. See further comments on that below. It may help in visualizing this to think of a sheet of paper with a coordinate grid on it: one coordinate axis is time, the other is one of the space dimensionsfor this discussion we'll assume it's height above the Earth, or more precisely the radial distance r from the Earth's center. Suppose first that the Earth had no gravity: then we could lay our paper with the grid flat, and draw the path of an inertially moving object, like a ball at some height above the Earth, as a straight line on the grid (because with no gravity the ball just floats at a fixed height). Now imagine that we "turn on" the Earth's gravity: General Relativity says that that corresponds to making the sheet of paper curved, in such a way that the ball's path in spacetime bends towards the Earth (its height decreases with time), while still looking like a straight line relative to the grid on the paper. (I emphasize that this is just a simplified version to help with visualization: the actual spacetime curvature due to the Earth is more complicated than this, because spacetime is fourdimensional, not twodimensional.) The reason this interpretation works is that all objects "fall" with the same "acceleration" due to gravity (where here "acceleration" means coordinate acceleration). Galileo is supposed to have dropped two cannon balls of different weights from the Leaning Tower of Pisa to show that they would hit the ground at the same time; more recently, one of the Apollo missions dropped a feather and a lump of lead in vacuum on the Moon to show that they would hit the ground at the same time. No other force works this way, and this was one of the chief clues that led Einstein to view gravity as a property of spacetime itself instead of as a property of objects. 


#5
Nov2712, 12:28 PM

P: 1,098

Even the term "curved" is misleading imo, sure it's applicable visually in 1d2d, but 3 spacial dimensions? And a temporal? It's measurement (geometry) terminology. And imo is misused when applied to our 4D continuum. I would almost say with out a doubt there are other presentations of GR which use terms such as "pressure/displacement" to describe gravity. GR & curvature are whats popular. In other words I wouldn't get too caught up in the term "curvature" as a physical description of spacetime, not as a layman. 


#6
Nov2712, 12:52 PM

P: 4,035

http://www.physics.ucla.edu/demoweb/...spacetime.html http://www.relativitet.se/spacetime1.html http://www.relativitet.se/Webtheses/lic.pdf (Chapter 2) http://www.adamtoons.de/physics/gravitation.swf 


#7
Nov2712, 01:24 PM

P: 140

I'm still trying to understand how exactly curved spacetime can create motion. No matter how slow time is going, how can it make an object turn and move backwards? 


#8
Nov2712, 01:27 PM

P: 140




#9
Nov2712, 01:28 PM

P: 140




#10
Nov2712, 01:40 PM

P: 1,098

I'd be surprised if his "SR" paper took more than a year & on his own. GR 10 yrs & with much collaboration (specifically math, without doubt the concept was much more easily had...at least for him) 


#11
Nov2712, 02:02 PM

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This is an analogy because it's working with curved twodimensional space instead of curved fourdimensional spacetime. But at least we can visualize it, and we can't visualize our paths through even a flat fourdimensional space time, let alone a curved one. 


#12
Nov2712, 03:20 PM

P: 3,187

https://en.wikisource.org/wiki/Relat...General_Theory In that book he also gives some examples of common warped coordinate spaces. The main criticism that I have against it, is that he is sometimes a bit fuzzy  some things are even less clearly explained than in his "nonpopular" paper (which contains a lot of complex math, but the text around the math is very readable): https://en.wikisource.org/wiki/The_F..._of_Relativity PS this one may also be helpful (and it is, as it promises, rather brief!): https://en.wikisource.org/wiki/A_Bri..._of_Relativity 


#13
Nov2712, 03:22 PM

P: 4,035

http://www.relativitet.se/Webtheses/tes.pdf 


#14
Nov2712, 03:24 PM

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As a matter of fact, I am still searching for a paper in which Einstein discussed the physical interpretation of free fall in a real (nonuniform) gravitational field. 


#15
Nov2712, 03:59 PM

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Let's start with some basics. We can represent spacetime with a spacetime graph. And spacetime curvature can be (loosely) interpreted as saying "we need to draw our spacetime diagrams on a curved surface, rather than a flat one". So, lets take a curved surface, a sphere, and ddraw a spacetime diagram on it, and see what happens. We'll say that on this spacetime diagram, "north" represents the time direction, just as we usually draw time going "up" on the flat spacetime diagram. So, suppose we have two people at the equator, 1 nautical mile apart, and they both go north What happen? Well, what happen is that they get closer and closer together. Not only that, but they appear to accelerate towards one another  initially, the relative rate of change of distance between them, their relative velocity, is zero, but as time goes on they approach each other more and more rapidly, just as if they were accelerating towards one another. It's a bit like they were gravitationally attracting each other  or , perhaps another analogy, being attracted by the tidal gravity of some external source. But neither of them is doing anything more than moving along a straight line on a spacetime diagram. Anyway, the generic name for what I've just described is "geodesic deviation". Geodesics are just the straightest possible lines on a curved surface  if you read about GR, you'll probalby be hearing a lot more aobut them. As far as books go, I' suggest something along the lines of "Exploring black holes" I've heard mixed reviews about Schutz, "Gravity from the ground up", but it's another possibility as it's pretty low level from what reviews I did read. I suspect you'll find the modern treatments more illuminating than Einstein's original work, but  it's hard to predict for sure. If you've got the time, try reading various sources until you find one that you understand. "Exploring black holes" has a few introductory chapters online, some of which cover things like curvature. http://www.eftaylor.com/download.htm...ral_relativity Ben Crowell also has an online book, "Light and Matter". I've only read sections of it. To avoid the appeareance of advertising, I'll let you find "Light an Matter" with a web search, if you're interested. 


#16
Nov2712, 04:19 PM

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#17
Nov3012, 06:34 AM

P: 55

In order to understand how this works, we need to visualize 4dimensional space. This is, of course, extremely hard for the human brain to grasp, so what we do is to compress one of the dimensions to zero length (in other words, flattening the 3dimensional space into a plane) and replace the now "unused" third dimension with the original fourth time dimension. So you have to imagine the entire threedimensional space compressed into a plane. Therefore the Earth is a disc, and the ball is a (much) smaller disc slightly apart from it. Movement in space is now restricted to this plane. What is happening is that this plane (which represents space) is moving along the time axis (which in this visualization would be the third axis, perpendicular to the plane.) So everything moves with the plane: The Earth, the ball, everything. If mass had no effect on the geometry of spacetime, then nothing would change. The ball would simply be where it is and the Earth would be where it is, as both traverse the time axis. However, masses bend spacetime, which means that the time axis does not consist of straight lines, but curved lines. (In reality this is much more complex because the spatial dimensions are also bent, but for the sake of simplicity let's forget about that here.) Because the Earth bends the time axis, it causes the ball to approach the Earth as both move in this time axis. (Basically, the ball is simply moving, due to inertia, along the shortest path that exists in the time axis.) If the ball was "stationary" to begin with, it will not move on the spatial plane at first, but the curvature of the time axis will cause it to make a parabolic path towards the Earth (in other words, making it move in the spatial plane directly towards the center of the Earth disc.) If instead of starting stationary you were to throw the ball parallel to the surface of the Earth, then in this scenario it would have an initial movement on the space plane (parallel to the edge of the Earth disc). As it moves in the time axis, it will follow the curve that bends towards the Earth as well as retaining its horizontal motion, thus following a different path in this threedimensional visualization. (The only question that I do not really grasp yet is why everything moves in the time axis.) 


#18
Nov3012, 09:59 AM

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The fact that we can make the "acceleration due to gravity" disappear by falling freely ourselves is why Einstein wanted a different definition of acceleration, one that wouldn't be dependent on adopting a particular point of view. We see freely falling objects "accelerate" because we're at rest on the surface of the Earth; but our theory of physics shouldn't be dependent on being at rest on the surface of the Earth. Defining acceleration as proper accelerationi.e., as feeling weightis general: it works everywhere, and doesn't depend on adopting a particular point of view. 


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