B What does 3-dimensional space deform into, in the presence of gravity?

  • B
  • Thread starter Thread starter jaketodd
  • Start date Start date
  • Tags Tags
    3d Gravity Space
jaketodd
Gold Member
Messages
507
Reaction score
21
I have no expertise in this area, other than rudimentary concepts. The following might apply if the visualization of space, as depicted below, represents actual reality, but I don't know for sure. Please help me understand better, you guys!

2-dimensional space
The curvatures deform into the 3rd dimension, as can be seen in the picture below.

So in 3-dimensional space, what does space deform into? 4th!?
We can't even visualize it! Unless it doesn't deform into the 4th, but instead just stretches space, without a deformation into a 4th. See another picture below.

This is mentioned by Brian Greene, notable for his documentary The Elegant Universe. He's mostly about string theory but poses this question as well.

https://en.wikipedia.org/wiki/Curved_space

1687711776058.png


1687711851246.png
 
Physics news on Phys.org
jaketodd said:
2-dimensional space
The curvatures deform into the 3rd dimension
No, they don't. The third dimension in the picture has no relationship to any dimension in reality. A curved space doesn't deform "into" anything. The curvature is intrinsic.

jaketodd said:
So in 3-dimensional space, what does space deform into?
Nothing. See above.

jaketodd said:
This is mentioned by Brian Greene, notable for his documentary The Elegant Universe.
This is a pop science source and is not a valid reference. In fact, Greene's pop science books and videos are particularly bad because of the number of misunderstandings they create among unsuspecting lay people. We have had many past PF threads on this.
 
  • Like
Likes Dale
@jaketodd, you apparently have failed to take my advice to learn from textbooks and peer-reviewed papers instead of pop science sources. You really, really, really, really need to take it.
 
  • Like
Likes Motore and malawi_glenn
The OP is based on a misconception obtained from an invalid pop science reference. Thread closed.
 
I asked a question here, probably over 15 years ago on entanglement and I appreciated the thoughtful answers I received back then. The intervening years haven't made me any more knowledgeable in physics, so forgive my naïveté ! If a have a piece of paper in an area of high gravity, lets say near a black hole, and I draw a triangle on this paper and 'measure' the angles of the triangle, will they add to 180 degrees? How about if I'm looking at this paper outside of the (reasonable)...
From $$0 = \delta(g^{\alpha\mu}g_{\mu\nu}) = g^{\alpha\mu} \delta g_{\mu\nu} + g_{\mu\nu} \delta g^{\alpha\mu}$$ we have $$g^{\alpha\mu} \delta g_{\mu\nu} = -g_{\mu\nu} \delta g^{\alpha\mu} \,\, . $$ Multiply both sides by ##g_{\alpha\beta}## to get $$\delta g_{\beta\nu} = -g_{\alpha\beta} g_{\mu\nu} \delta g^{\alpha\mu} \qquad(*)$$ (This is Dirac's eq. (26.9) in "GTR".) On the other hand, the variation ##\delta g^{\alpha\mu} = \bar{g}^{\alpha\mu} - g^{\alpha\mu}## should be a tensor...
Back
Top