Exploring the 4th Dimension: Understanding Time in Spatial Dimensions

[hafiz ns]

Homework Statement

is there a 4th dimension. if yes can anyone explain it ?

Homework Equations

The Attempt at a Solution

4th dimension includes time also am i right ? which is X,Y,Z + time

 

[HallsofIvy]

Do you understand what a "dimension" is? A "dimension", in a given problem, is just a number you use to specify all the conditions of the problem. If I were doing a geometry problem connected with spheres of different radii with centers at different points in space, to identify a specific such sphere, I would have to give the three coordinates of its center and its radius- four numbers so this is a "four dimensional" problem. If I were doing a problem involving points in the plane, I might set up an xy coordinate system and label each point by its x and y coordinates- two dimensions because two numbers. If I were doing a problem involving points in "R³" I would set up a coordinate system with x, y, and z axes and every point would be labeled by (x, y, z)- three numbers so three dimensions.

In physics, we are concerned with "events"- things that happen at a particular point in space at a particular time. We require three numbers (coordinates) to identify the point and one number to identify the time. In that sense we are working with four dimensions. Of course, which is the "first", "second", "third", or "fourth" dimension is purely conventional.

 

[hafiz ns]

thanks hallsofivy ...

 

[The Physics Cat]

Also, you could plot a four dimensional point using a constantly changing graph, say, point A's coordinates are 1 by 2 by 3 by 4, which could mean the x is one, the y is 2, and the z is 3 after 4 seconds have passed. Graphing functions like this also works.