Can anyone tell me what a hell is this "SPACIAL CURVATURE" ?

Who manifested it ?

and Why should we care for it ?

and How was it proved.

Einstein anyone?

http://arxiv.org/PS_cache/hep-ph/pdf/0201/0201172.pdf
http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+K+EXPERIMENTAL++GR&FORMAT=www&SEQUENCE=
http://pdg.lbl.gov/2000/gravrppbook.pdf
http://www.amazon.com/Theory-Experiment-Gravitational-Physics-Clifford/dp/0521439736/ref=pd_ybh_a_1/102-2561788-4956138?pf_rd_m=ATVPDKIKX0DER&pf_rd_s=center-2&pf_rd_r=12WAD2ACMSECB8G8PTQQ&pf_rd_t=1501&pf_rd_p=280124401&pf_rd_i=ybh

Things you'll find:
gravitational radiation from binary pulsars (Nobel Prize 1993)
precession of mercury's perhilion
gravitational time dialation on Earth
gravitational lensing
...

Spacial curvature is the idea that gravity is a consequence of matter. Einstein's equations:
T_{\mu\nu} = R_{\mu\nu}-\mathcal{R}g_{\mu\nu}
The left side is the stress energy tensor, which describes the matter living in your universe (or, more accuratly the type of energy densities you have). The right hand side describes the curvature, or more specifically, the way geometry of the manifold that describes your space-time. Einstein hated the fact that matter=geometry. But this is actually a very beautiful statement:)

So, curvature is caused by the presence of a non-trivial energy density.

Can someone explain it in brief instead of some links, i dont like the PDFs we have to download the whole thing first.

http://en.wikipedia.org/wiki/Special:Search/SPACIAL_CURVATURE

There is no such thing as Spacial Curvature,
wana call me a crack pot ?

There is no such thing as Spacial Curvature,
wana call me a crack pot ?

Tempting.... But not yet.

Spacial curvature is the idea that gravity is a consequence of matter. Einstein's equations:

The left side is the stress energy tensor, which describes the matter living in your universe (or, more accuratly the type of energy densities you have). The right hand side describes the curvature, or more specifically, the way geometry of the manifold that describes your space-time. Einstein hated the fact that matter=geometry. But this is actually a very beautiful statement

So, curvature is caused by the presence of a non-trivial energy density.

Tempting.... But not yet.

I was asking the explanation not the equation, equations are for the experts.

The left side is the stress energy tensor, which describes the matter living in your universe (or, more accuratly the type of energy densities you have). The right hand side describes the curvature, or more specifically, the way geometry of the manifold that describes your space-time. Einstein hated the fact that matter=geometry. But this is actually a very beautiful statement.

Energy density = curvature. Curvature happens because of non-trivial energy density, as per Einstein's equations.

Maybe you could ask a more direct question?

Energy density = curvature. Curvature happens because of non-trivial energy density, as per Einstein's equations.

Maybe you could ask a more direct question?

Ok so what is this non-trivial energy ?

AT first, I had written "matter = curvature". But then this wasn't quite right.

It is true that mass = energy (E=mc^2), but energy can come from other places, the real formula you should know is this:

E^2 = m^2c^4+p^2c^2

so, even if something has no mass (like a photon), it can still have an energy. The energy is what causes the spatial curvature.

AT first, I had written "matter = curvature". But then this wasn't quite right.

It is true that mass = energy (E=mc^2), but energy can come from other places, the real formula you should know is this:

E^2 = m^2c^4+p^2c^2

so, even if something has no mass (like a photon), it can still have an energy. The energy is what causes the spatial curvature.

Hmm, sounds like strong men with lot of energy have good spatial curvature.

PS> U forgot to tell how it curves this space and where; anyways a cup of tea has matter that can be converted into energy enough to blow our planet into pieces.

PS> U forgot to tell how it curves this space and where; anyways a cup of tea has matter that can be converted into energy enough to blow our planet into pieces.

Einstein's equation. That's how.

Einstein's equation. That's how.



Einstein My FOOT, that man with brain mutations was a knuckle head, and u r blindly following him,

i feel sorry for u.

Einstein My FOOT, that man with brain mutations was a knuckle head, and u r blindly following him,

i feel sorry for u.

Well I'm glad this discussion hasn't descended into ignorant name calling...

Ben can maybe correct me on this, if it strays.

A way to approach thinking of space as curved:

pick three points in the universe, that you can travel to. Start at one, sight a straight line to one of the others, and go to it. Then sight a straight line to the third, and

measure carefully the angle between the straight line you just traveled, and the new line you have just sighted.

Then travel along that straight line to the third point. When you get there, sight a straight line to the original point. Measure the angle between the line you jsut traveled and the one you just sighted.

Then travel that line to the original point, and when you get there measure the angle between the line just traveled and the original line that started the trip.

Add the three measured angles. If you get 180 degrees or pi radians, the space you were traveling in was not curved. If you get something else, it was.

You are coming to each point along a curved path, although it is a straight line in your space.

Make sense? Hole in the procedure somewhere?

This is a good explanation, iceaura, and you can see it on a globe.

Singularity is asking, I think, what causes space to bend. I say "non trivial energy density (i.e. mass)" and she (I think it's a she) says "no no no, what causes it to bend". And we go in circles.

The best I can do is say that the presence of energy causes space to bend. The curvature is described by Einstein's equations above. Janus gave a very good explanation in the "Emergence of Crackpots..." thread, in response to this same question, so I assume that Singularity read that.

The question will never be answered, of course, because you can always ask "Why" to any answer that is given, untill the question is answered with the full quantum theory of gravity.

And Singularity never seems to like my answers very much, which is too bad, because I don't think I will ever be inclined to stop giving them:)

Here is the explanation that Janus58 gave
http://sciforums.com/showpost.php?p=1334458&postcount=179