Wednesday, October 31, 2007
4 D Space and Time Fabric, Twin paradox
What is 4d space and Time fabric?????????
You cant visualize 4D... so first of all you need to stop trying to do that!Geodesics are the entities that nicely describe curvatures in a space (of whatever dimension it may be). If 2 geodesics start parallel to each other, they'll remain parallel all along the space if the space doesn't have any intrinsic curvature. But if they converge/diverge then the space is curved.Geodesics as you know is the shortest distance line joining 2 points, but lying entirely in that space. So first of all you need to have a concept of distance (metric) in the space. Say for example the surface of the earth... it's a two dimensional space and the concept of distance is simple.. the Euclidean distance. Hence the great circles are the geodesics. If you consider two closely lying longitudes lines near the equator, they are parallel. But they gradually converge and meet as u move towards the poles. Hence sphere is an intrinsically curved space.In a 4 dimensional space-time the concept of distance is a bit more involved. It's the 'proper time' there (u need to study SR to know more). It can be shown that the trajectories of free falling bodies follow geodesics in the 4-D space-time. Now we'll see that these geodesics actually converge. Just imagine 2 free falling bodies moving towards the center of the earth and they started off from an infinite distance from the earth say. Thus they started off with their velocities parallel to each other. Eventually since they both are heading towards the center of the earth, their trajectory will not remain parallel any more. In brief, free falling bodies in presence of gravitational field may hit each other even if they started of parallel. This should give you the concept of curvature in 4D space-time.It is even possible to measure curvatures of high dimensional spaces using the concept of Riemann curvature tensor, etc, etc.
What is Twin Paradox/\???????????
In physics, the twin paradox refers to a thought experiment in Special Relativity, in which a person who makes a journey into space in a high-speed rocket will return home to find they have aged less than an identical twin who stayed on Earth. This result appears puzzling, since the situation seems symmetrical, as the latter twin can be considered to have done the travelling with respect to the former. Hence it is called a "paradox". The seeming contradiction is explained within the framework of relativity theory and has been verfied experimentally using precise measurements of clocks flown in airplanes.
Old Models of Cars
Sunday, October 28, 2007
Mechopedia
Mechopedia
It contains the information of all information related to mechanical fields
Images, videos
It contains the information of all information related to mechanical fields
Images, videos
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