Naked Science Forum

Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: jaiii on 09/03/2014 09:04:26

Title: What is the curvature of spacetime?
Post by: jaiii on 09/03/2014 09:04:26

space time

Postby jaiii Sat Mar 08, 2014 3:47 pm

What is spacetime?
It is a feature of each body having a mass or energy?
How the body distorts spacetime?
One can break like normal fabric?
If breaks which will be in that hole?
If we have a magnetic field north south and then reversed the kurvature space of time different?

Thank you.
Title: Re: What is the curvature of spacetime?
Post by: zunimtn on 08/04/2014 15:47:03
I don't know that much, but since no one else has responded, I will.

"Curvature", the way I see it, means like a gravitation gradient of spacetime.  That's like saying uphill or downhill.  All mass objects can be imagined as being at the bottom of a hill.  That means all masses roll toward each other, or are pulled by each other.  The only way not to roll toward each other is if you're driving by real fast.  Then your speed will carry you forward (at say, a right angle to earth) at the same time that the "downhill" of earth's gravity will pull you toward it.  You will end up circling around earth on the side of the hill.

Reversal of positive and negative charges of a field will not effect gravity because gravity has nothing to do with charge.  Only with mass.  Gravity only attracts.  Electrical charge attracts or repels depending on the charges.

Not much, but I hope it helps.
Title: Re: What is the curvature of spacetime?
Post by: zunimtn on 08/04/2014 15:49:30
Oh, and no, you cannot break a hole into spacetime. 
Title: Re: What is the curvature of spacetime?
Post by: flr on 08/04/2014 22:26:04
My understanding is that certain laws of physics (such as the motion in gravitational field) can be rewritten as a problem of geometry of an "abstract" space.

For example trajectories under gravitational fields can be thought as the geodesics of a space defined by the dimensions (x,y,z,-ict) . No gravity means the space (x,y,z,-ict) is flat and the geodesics are a straight line. Indeed, in absence of any external force we move indefinite along a straight line at constant speed. If we have gravity then the space (x,y,z,-ict)  has intrinsic curvature and in free fall motion we simply follow the geodesic of this (intrinsically) curved 4D-space. 

Note that this 4D-space(x,y,z,ict)  to me is an "abstract" space and not the "real" geometrical space we live in. The "abstract" part came in when the additional dimension "ict" is added. 
Title: Re: What is the curvature of spacetime?
Post by: jeffreyH on 09/04/2014 18:20:50

"Curved space-time
To fully describe the location of an event in our universe, something that occurs at a particular time and place, requires three dimensions of space and one time. In flat spacetime the Cartesian coordinates are often represented in index notation, x=x1, y=x2, z=x3 and Einstein referred to time as a fourth dimension ct=x4, though it is more common today to list the time first as ct=x0. In the early development of relativity it seemed simple to consider time as an imaginary number ict where i is the quadratic root of -1 and c the speed of light. Then the space-time has the following four dimensions: (x,y,z,w=ict), but in modern pedagogy this has been abandoned as it is now understood that the metric tensor is what carries the sign difference in inner product operation yielding a spacetime displacement (line element) between events in flat spacetime of ds2 = dct2 - (dx2 + dy2 + dx2) Calculation of the Riemann tensor for this line element yields all zero elements and so when line elements are frame transformations of this one they also yield a zero Riemann tensor and are said to correspond to flat spacetime. When there is a matter source, the Reimann tensor is not zero and then the line element that yields that Riemann tensor can not be globally transformed into that of the flat spacetime line element of special relativity above, so it is said that spacetime is curved."
Title: Re: What is the curvature of spacetime?
Post by: jeffreyH on 10/04/2014 14:59:30
There is a very good simplified version of relativity and spacetime curvature at this site.