Relativity ?

[1123581321]

Hi, im wondering what the connection is in the dimensions between Einsteins special and general relativity theories..

 

Why did he use the dimensions he did..

 

Is it that the 4th dimension of special relativity accounted for the warping in general relativity..?

[ajb]

Both special and general relativity are both theories of the nature of space and time that rely on four dimensional spaces.

 

The reason for four is hidden in the symmetry of the theory. In special relativity we can pick space and time coordinates. However, this is really a bit of an illusion as we have transformations (changes of coordinates) that mix space and time. This is really why one has to think about four dimensions, rather that 3 space and one time.

 

The situation is very similar in general relativity, though the class of transformations is much wider. In general, there is no canonical way to separate space and time.

 

You can think of special relativity as being "inside" general relativity. Far away from large objects the space-time will be the same as in special relativity. Furthermore, in small enough regions the space-time will also look like that of special relativity even in the presence of the gravitational field of some large object. This is a version of the equivalence principle.

 

It is worth mentioning that you can think about special and general relativity in higher dimensions.

Edited February 8, 2011 by ajb

[IM Egdall]

Hi, im wondering what the connection is in the dimensions between Einsteins special and general relativity theories..

 

Why did he use the dimensions he did..

 

Is it that the 4th dimension of special relativity accounted for the warping in general relativity..?

 

The four-dimensional approach to special relativity (3 space plus one time) did not originally come from Einstein. It came from his math professor, Herman Minkowski. It is based on the so-called spacetime interval; a certain combination of the space and time intervals.

 

In special relativity, both time and space are "relative". That is the space interval (distance) and time interval between two events are affected by motion. But the spacetime interval is not. Inthis sense, it is absolute. It is the same value, no matter what the relative uniform motion of the observer.

 

Einstein later adopted the four-dimensional spacetime to general relativity. Here the spacetime interval represents how the presence of mass (e.g. the Earth) warps both space and time or warps spacetime. This warping of spacetime is what we call gravity. It tells objects in its vicinity how to move.

[DrRocket]

The four-dimensional approach to special relativity (3 space plus one time) did not originally come from Einstein. It came from his math professor, Herman Minkowski. It is based on the so-called spacetime interval; a certain combination of the space and time intervals.

 

 

4-dimensional spacetime has nothing to do with relativity. It is perfectly natural to cast ordinary Newtonian mechanics in a 4-dimensional spacetime.

 

The difference between Newtonian mechanics and special relativity lies in the geometry of spacetime, not the dimension.

 

The geometry of Minkowski spacetime is determined by bthe Minkowski inner product, which determines the Minkowski norm, or what you call the "spacetime interval. The Significance of Lorentz transformations is that they preserve the Minkowski inner product (and preserve the "direction" of time).

 

The Galilean group leaves invariant the Euclidean metrics on each summand of [math] \mathbb R \oplus \mathbb R^3[/math]. It defines the kinematics of Newtonian mechanics.