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Understanding Vectors....

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Posted by Mark on September 23, 2001 23:38:46 UTC

The components of a vector are not dependant upon the location of the vector within a givin coordiante system. Since vectors are defined by magnitude and direction only, there is no significance to giving a specific position to these components. Velocity is represented in physics by a vector..... although the value givin to velocity is dependant upon "rate of displacement", it does not incorporate knowledge of the displaced postitions thereof. Therefore, the exact position of a body is irrelevant in describing velocity; velocity is in terms of a ratio, not location.
Getting back to vectors again.... this is why you can translate two vectors to different positions in the coordinate system to perform addition, without changing any intrinsic value that describes the vector. Also two parallel vectors of equal magnitude are said two be "the same vector" if they point in the same direction, no matter their position in the field. So once again, when speaking in terms of velocity, and for that matter vectors in general, position is not an element. All we are concerned with here is the rate of change between two postions... the ratio... not the positions themselves. So I decree that velocity, and more importantly momentum, are in no way dependant upon specific positions. A ratio of displacement and an amount of mass, are the same no matter what location in space you choose to measure them. This is basically a statement of symetry, (the very fundamental concept upon which nature appears to opperate).

I believe the fatal flaw in your argument is the assumption that position plays a role in momentum, when in actuality it does not. Specific location, or position, is a whole other intrisic aspect of a particle. And the wave interpretation simply states that the origin of a particle's influence upon matter, does not lie at a specific location; it is in effect, "smeared" over a broad area. The act of "concentrating" this "smear" to a more specificly defined location, renders any measurement upon this "smear's" momentum innacurate, in proportion to the accuracy gained by confinig its possible position to an ever smaller uncertain location.

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