Monday, March 10, 2008

Tangent of the Gravity Wave




What is the tangent of the gravity wave? What can the tangent of the gravity wave reveal about the nature of light and matter? If we assume that the gravity waves oscillates like a sine wave into the 4th dimension, then it is the tangent of the sine wave that will reveal information about the nature of light and matter. The tangent of the sine wave should not be mistaken for the tangent of the angle. The tangent of the sine wave is contained within the radius of a circle, while the tangent of the angle resides on the circumference of the circle. This means that the tangent of the sine wave is confined to the radius of a circle, while the tangent of the angle can extend to infinity. The tangent of the sine wave and the tangent of the angle are equal when the angle is 0 degrees, but as the angle grows larger, the sine of the angle will approach the length of the radius of the circle and the tangent of the angle will approach infinity. At 90 degrees the tangent of the circle is equal the radius of the circle and the tangent of the angle will equal infinity. Therefore, it is important to realize that Aatucagg is concerned about the tangent to the sine of the angle and not the tangent of the angle itself. The tangent to the sine of the angle is the cosine of the angle. The cosine of the angle is equal to the radius of the circle, but is 90 degrees out of phase with the sine of the angle. This means that when sine the angle is minimum, cosine the angle is maximum, and when sine the angle is maximum, cosine the angle is minimum. A tangent to a function is a measure of the rate of change of the function. Therefore, cosine the angle is a measure of the rate of change of sine the angle. In this case, the angle is the gravity wave and cosine the angle is the rate of change of the gravity wave. So, cosine the angle tells us how quickly the gravity wave is changing locations as it oscillates in the 4th dimension. The slope of the tangent to the gravity wave is 0 at the positive and negative peaks of the waveform. A tangent with a value of 0 indicates no change is occuring. In the case of the gravity wave, a tangent with a value of 0 indicates no change in position in the 4th dimension. The tangent of zero occurs at the positive and negative peaks of the gravity wave. Only light exists at the positive and negative peaks of the gravity wave. The slope of the tangent to the gravity wave has a maximum value of the speed of light at the mid-slope of the gravity wave. A tangent with a maximum slope indicates that maximum change is occuring. In the case of the gravity wave, a tangent with a value of the speed of light indicates a maximum change in position in the 4th dimension. The tangent of the speed of light occurs at the mid-slope of the gravity wave. Only matter exists at the mid-slope of the gravity wave. Therefore, Aatucagg believes that at the peaks of the gravity waveform, only light exists with a linear velocity of the speed of light. At the mid-point of the gravity waveform, only matter exists with an angular velocity of the speed of light. At all other points along the gravity wave, light and matter exist together in varying amounts of linear and angular velocities.

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Tangent of the Gravity Wave

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Tangent of the Gravity Wave



Tuesday, March 4, 2008

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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Tensors and Frames of Reference

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Tensors and Frames of Reference