# Fabric of space time

#### sreekant

hey guys,

i jus got a question regarding space time fabric.....if we take an example of a 2d fabric...it is distorted in the third dimension...now if it is a 3d fabric ( which is what it is supposed to be ) then in which dimension will it get distorted??

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#### bapowell

hey guys,

i jus got a question regarding space time fabric.....if we take an example of a 2d fabric...it is distorted in the third dimension...now if it is a 3d fabric ( which is what it is supposed to be ) then in which dimension will it get distorted??
Good question. You don't actually need to have an 'extra' dimension to accommodate the distortion. In your 2D example, sure, we are accustomed to thinking of a 2D surface embedded in 3D space. However, the surface is still 2D, and we can geometrically encode the bending and warping of the surface by data on the surface, without the need for a higher dimensional ambient space within witch to place our 2D surface. For example, a torus (donut) has a well known form when its 2D surface is embedded in 3D space. However, I can equivalently represent a torus as a 2D sheet, with 'rules' for how to connect opposing edges of the sheet -- specifically, glue together opposite edges. The old Atari game 'Asteroids' is an example of toroidal topology even though the surface (screen) is only 2D!

#### silentbob14

Yeah that's a very good question. In my opinion, it will get distorted in the 4th dimension - time. As well all know from the general theory of relativity, times run slower for objects in a strong gravitational field compared to other objects that are not in such a field.

#### DaveC426913

Gold Member
In my opinion, it will get distorted in the 4th dimension - time.
Also possible - but bapowell's explanation is better because it shows that you don't need to introduce any new elements for its explanation (elements that might or might not get one into trouble later on). It is not necessary to invoke another dimension to have distortions.

#### bapowell

It is not necessary to invoke another dimension to have distortions.
Right. This is key. The Ricci curvature is intrinsic to the surface, and completely independent of the (unnecessary) embedding. Silentbob -- the OP's 2D example helps visualize the problem, but really we have a 4D curved manifold in GR. The question the OP is asking then is...what is the 5th dimension? Time is already included in the 4D.

#### Frame Dragger

Ahh, the 5th dimension is where the String Theorists hide their extra Gravity.

#### bapowell

Ahh, the 5th dimension is where the String Theorists hide their extra Gravity.
Dude, you're not helping

#### Frame Dragger

Dude, you're not helping
Look, it was that or a reference to Buckaroo Bonzai. I think I made the right choice. :rofl: Now, the 6th dimension is where lost ballpoints go... and the 7th is all marmalade.

#### yenchin

I don't think the example works quite well though? Although identifying opposite edges of a square gives a quotient topology of a torus, this torus is flat - it's gaussian curvature is zero.

#### bapowell

I don't think the example works quite well though? Although identifying opposite edges of a square gives a quotient topology of a torus, this torus is flat - it's gaussian curvature is zero.
Right, sorry. I gave a topological example instead a geometric one! However, the point of the example was meant to convey that fact that you don't need to embed a manifold in order for it to have nontrivial properties. Of course, one could just say that the Ricci curvature (or the fundamental form, or whatever) is intrinsic to the surface and is independent of any embedding. But point taken, sorry.

#### DaveC426913

Gold Member
Look, it was that or a reference to Buckaroo Bonzai.
Nicely done John FrameDragger.

#### Frame Dragger

Nicely done John FrameDragger.
You are too kind monsieur! Too kind! Nah... just right. Glad someone got the reference though... classic movie, absolutely classic. Lithgow is an AMAZING actor, and the rest... well.. rofl. just rofl!

EDIT: @bapowell: No need to apologize to anyone. Hell, if we had to say "sorry" every time we're wrong about spacetime... um... have you ever seen a western businessman try to "bow" properly in Japan? I can only describe the resulting series of bows as a kind of "bowing war", or maybe a bit like those rocking-birds that use surface tension as a spring. Anyway, that's what it would look like around here!

#### DaveC426913

Gold Member
You are too kind monsieur! Too kind! Nah... just right. Glad someone got the reference though... classic movie, absolutely classic. Lithgow is an AMAZING actor, and the rest... well.. rofl. just rofl!
It is one of my top ten. And Lithgow was indeed a shining star.

#### Frame Dragger

It is one of my top ten. And Lithgow was indeed a shining star.
You are clearly a man of substance.

Are you a fan of 'Dexter'? Lithgow played the villain this season, and he was TERRIFYING. I'm normally unmoved by simulated violence, but... wow. He has an amazing range.

#### DaveC426913

Gold Member
You are clearly a man of substance.

Are you a fan of 'Dexter'? Lithgow played the villain this season, and he was TERRIFYING.
Huh. Did not know that.

#### Frame Dragger

Huh. Did not know that.
He is amazing, but it is VERY graphic. Frankly he's not the most violent in the show, or on tv/movies, but... well, the opening has him killing a woman and using a mirror to see her die. His acting makes it utterly convincing, and deeply DEEPLY frightning. For this, he won an emmy, I should add.

So... it may not be for everyone (I found it difficult at times... a first for me), but to see a master at his craft, it's worth it.

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