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What Did Einstein Mean when He Said Space is Curved?
June 5, 2017 at 10:06 am
How does he define the word curved as he used it to describe space?
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RE: What Did Einstein Mean when He Said Space is Curved?
June 5, 2017 at 10:14 am
(This post was last modified: June 5, 2017 at 10:26 am by Alex K.)
The easiest effect of curvature to understand is that parallel rays of light can change their distance, like when two people start at the equator walking north in parallel, they will meet at the pole because the surface of the earh has curvature. The same can happen in space when it is curved. In flat space, parallel lines keep their distance.
The technical definition of curved he uses is that the Riemann curvature tensor is not zero.
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RE: What Did Einstein Mean when He Said Space is Curved?
June 5, 2017 at 10:17 am
there are a couple of ideas to explore
at large distances it is conceivable the circumference of a given large circle may not be related accurately to it's diameter via the factor of pi
additionally, all masses distort space/time such that, for instance, in the case of our sun, we can compare a picture of stars in the vicinity of the sun, and then again months later when the sun has moved away from that patch, and we can notice distortions in the picture that adjust the measured positions of those stars. So space is curved literally everywhere, but it takes a massive object for us with our limited instruments to see the effect. Distant galaxies distort the images of more distant objects we see past them. If the geometry is correct, we can get a magnification effect of those distant objects of a factor of 10 to 20. A 'lens' if you will, in space.
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RE: What Did Einstein Mean when He Said Space is Curved?
June 5, 2017 at 10:20 am
Right over my head.
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RE: What Did Einstein Mean when He Said Space is Curved?
June 5, 2017 at 10:27 am
(This post was last modified: June 5, 2017 at 10:28 am by Alex K.)
One more along vorlon's lines: the angle sum in a triangle in general isn't 180 degrees anymore. How much it deviates from 180 is directly proportional to the amount of curvature enclosed in the triangle.
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RE: What Did Einstein Mean when He Said Space is Curved?
June 5, 2017 at 11:25 am
(This post was last modified: June 5, 2017 at 11:36 am by Anomalocaris.)
(June 5, 2017 at 10:06 am)Rhondazvous Wrote: How does he define the word curved as he used it to describe space?
He meant well known geometric principles known since Euclidean to be true for angles and lines inscribed on a flat plane would not hold true with physical representations of these lines and angles created on sufficiently large scale in space near sufficiently massivee objects. Instead these physical lines and angles would behave as if they were inscribed on a curved surface.
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RE: What Did Einstein Mean when He Said Space is Curved?
June 5, 2017 at 12:39 pm
(This post was last modified: June 5, 2017 at 12:40 pm by Neo-Scholastic.)
I always thought he meant it was curved, like not straight. Guess I was wrong.
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RE: What Did Einstein Mean when He Said Space is Curved?
June 5, 2017 at 1:38 pm
it's puffy in places
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RE: What Did Einstein Mean when He Said Space is Curved?
June 5, 2017 at 6:10 pm
It's only curved relatively.
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RE: What Did Einstein Mean when He Said Space is Curved?
June 5, 2017 at 6:16 pm
(This post was last modified: June 5, 2017 at 6:25 pm by Alex K.)
(June 5, 2017 at 6:10 pm)ignoramus Wrote: It's only curved relatively.
I love spoiling jokes so ...
There is such an idea, namely that curvature can be only an artefact of how somrthing is embedded in space, e.g. a piece of paper can be rolled up in space in a curved fashion, but this curvature is not, as they say, "intrinsic", the paper is still intrinsically flat as parallel lines on a rolled up paper keep their distance. This curvature could be called relative. However, the concept of curvature used in Relativity is largely independent of how a space is embedded, and so is not really relative.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
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