Tensors and Frames of Reference

When describing phenomenon that exist within the spacial frabric of the universe, it is best to use tensors to define the forces relating to the phenomenon in that region of space. This is because tensors used in one region of space for defining something can be used in other regions of space to define the same thing. This is why Albert Einstein used tensors in Special and General Relativity. By using tensors to discribe the force of gravity, as well as other forces, he did not have to concern himself with the curvatures of space. By using tensors, his equations apply equally well in flat space, warped space, stretched space, or any other kind of space. These different types of spaces are each considered a different frame of reference. Each frame of reference has its own coordinate system. Therefore, tensors can describe a phenomenon regardless of the coordinate system. As an example, suppose you are standing at the bottom of a water fall. Your friend is standing at the top of the water fall and is about to jump. You and your friend both have identical thermometers. You use your thermometer and measure a temperature of 15 degrees Celsius for the waterfall. Your friend jumps off the cliff at the top of the water fall, and on the way down, also measures a temperature of 15 degrees Celsius for the waterfall. What this means is that you and your friend both measured the same temperature of 15 degrees celsius, regardless of your frames of reference. This means that temperature can be thought of as a tensor, since it is a phenomenon that does not depend on frame of reference. Now, let us say your friend climbs back up the cliff to the top of the water fall. You continue to stand at the bottom of the water fall and measure the velocity of the falling water at 3 meters per second. Your friend jumps off the cliff again and measures a velocity of 0 meters per second. This is because from your frame of reference, the water and your friend are both falling at the same velocity. From your friends frame of reference it is you and the ground that are ascending and the water that is standing still. Therefore, velocity is not a tensor, since it depends on frame of reference. This is why tensors use vectors to describe phenomenon, because vectors are independent of frame of reference. Coordinates are used to describe vectors and coordinates of a vector are not independent of frame of reference, so even though the coordinates of a vector may change from one frame of reference to another, the vector itself remains unaltered. This means that whatever coordinate system is chosen to discribe the vectors within that space, the relationship between the vectors will remain unaltered no matter what other coordinate system may be chosen to contain the vectors in any space. For example, a vector begins at the origin of a coordinate system and ends at a point in space. Changing a coordinate system is to move or warp the axes that define the vector. Some examples of other coordinate systems are the Cartesian system, elliptic 2-space system, hyperbolic system, triangular system, and so on. No matter which system you choose to use to describe the vectors in that space, the relationships between the vectors will remain unaltered. The axes of the different systems contort around the vectors, but the vectors themselves remain unchanged relative to each other. Tensors are made up of these kind of vectors, and this is why tensors are used to describe phenomenon found in a universe with space that is warped and twisted by gravity.

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