Originally Posted by **ohm** sorry. There is some technical problem in my internet connection. That'r why i am not responding properly.
First of all i thanks for ur response.
1) u thought that it is not possible to visualise four dimensional spacetime. So i think it is useless to try to imagine this.
2) u have disscussed "indefinite metric" and differential geometry . What is this ?
3) i have seen a rubbel sheet model. Does it indicate empty space. If it is then how can empty(nothing) can be curved.
4) i have also seen light cone along with world line. How can straight worldline be path of movement of earth in four dimenssion.
Kindly response this. |

1) I certainly can't visualize it, thought there are probably some topologists that claim to be able to. The best that an otherwise ordinary human could do is to be able to visualize three dimensional "sections" of the 4 dimensional object. Since I can barely manage three dimensional objects, four dimensions are hopelessly out of my league. 8]

2) A metric is, more or less, a way to measure "distances" in a given kind of topological space. For example, in Euclidean three dimensional space the metric is s^2 = x^2 + y^2 + z^2. In Minkowski (aka Lorentzian) space-time the metric is s^2 = x^2 + y^2 + z^2 - (ct)^2. (Some authors use the negative of this.) It is called "indefinite" because s^2 can be a negative number.

3) The rubber sheet model is nice, but really only gives a rough idea of what's going on. Still, like the Bohr model of the atom, it has its uses. The idea is that if we put a mass on a level rubber sheet, it will cause an indentation. This gives us an idea of what how gravity and curved space-time function. Any small ball rolled near the object in the center will no long roll in a straight line, but will have a curved path. This represents the effects of a gravitational field.

4) As I understand it the light cone shows what "events" (basically coordinates) that one can reach when starting out at a different event. It is represented by a cone marked off by straight lines (which represent the places that an object traveling at the speed of light can reach.) Any event outside the light cone cannot be reached.

-Dan