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Definition Of Dimension

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Posted by Richard D. Stafford, Ph.D. on November 13, 2001 15:59:11 UTC


RE: [ ]

I do not quite understand why you directed me to that particular message to Alex. As I read it I do not see any point where there exists any strong difference between what you are saying and my position. I thought I had made it quite clear that I am in favor of the view that time is parameter of change as seen by Newton and not a dimension. From that perspective, "travel" in time is a rather meaningless concept as "travel" is ordinarily interpreted to be some kind of change in "position". Position is in turn established via some kind of agreed upon coordinate system. The coordinates required to specify that position are generally called the dimensions of the coordinate system.

The term "degrees of freedom" commonly used in physics relates directly to those above dimensions because, under the interpretation of the purpose of the coordinate system and the idea of change in position, travel is not constrained (i.e., it is free) with regard to the coordinates needed to specify that position. If that is not the case, then you apparently have a coordinate system with more dimensions than are necessary to specify the possible changes in position.

Actually, the second case occurs quite often. Consider a bead on a wire. The wire may be bent and you might find it convenient to represent the possible positions along the wire in a three dimensional coordinate system; however, as the bead is "constrained" to be on the wire, its position along the wire is sufficient to specify its position in the three dimensional coordinate system. Thus it is said that the bead has only one "degree of freedom". Likewise, the situation can be represented in a one dimensional coordinate system and all the regular physics relations can be transformed to that "special" coordinate system. Thus it is that the ideas of dimensions and degrees of freedom become intimately entwined. Clearly the source of the ideas in your second reference to "Dimension".

>>> In order to express a singular step of a vector in space-time, we require only one axis.> Hence, armed with that deduction we'd subsequently derive a twofold notion that (1) nothing can simultaneously exist in three dimensions, and (2) three spatial dimensions can only exist in time.>As long as you derive your concepts from the "freedom of movement" definition, you will continue to misunderstand the mutually dependent nature of "space" and "time." >P.S. How do you not travel back and forth in time? Can you instantaneously transport yourself about? Sounds like Star Trek gobbledygook to me!

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