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stingc · 07-31-2003, 08:27 PM

All objects can be considered 4D in a very real sense. A dimension, mathematically, is simply an independent parameter required to describe something. An object is described by its shape in 3D space. Add to that that the shape can change over time. 3 "spatial parameters" and one temporal one are required to describe the object, so it has 4 dimensions.

There is nothing odd or new about this view. Galileo or Newton could easily have stated it, but it wasn't a terribly useful construction/visualization since time was considered universal back then. Special relativity came along to say that time was different to different people. One person's time axis could be rotated with respect to someone else's. This led to the 4D interpretation being a useful way to think about things.

"Higher dimensional matter" does not make any sense. Matter is stuff contained in space(-time). That stuff is represented (sort of) as having some energy/momentum distribution in spacetime: E=E(x,y,z,t), p=p(x,y,z,t). The "dimension" of the matter has to be the dimension of the space, or it makes no sense.

There are some differences in 2D->3D vs. 3D->4D. Physics is not done the way popular books sometimes imply. It is mathematics (logic), not picture drawing. Various types of spaces with arbitrary numbers of dimensions are defined by the mathematicians as abstract things that obey some list of logical rules. There is nothing intrinsically "real" about any of them. What physics has done is to say the universe as we think we know it obeys one of these sets of rules. These are simple things like saying that there exists a well-defined distance between any two points. Everything else is formally derived from these very primitive observations.

07-31-2003, 08:27 PM	#25 (permalink)
stingc Psycho Location: PA	All objects can be considered 4D in a very real sense. A dimension, mathematically, is simply an independent parameter required to describe something. An object is described by its shape in 3D space. Add to that that the shape can change over time. 3 "spatial parameters" and one temporal one are required to describe the object, so it has 4 dimensions. There is nothing odd or new about this view. Galileo or Newton could easily have stated it, but it wasn't a terribly useful construction/visualization since time was considered universal back then. Special relativity came along to say that time was different to different people. One person's time axis could be rotated with respect to someone else's. This led to the 4D interpretation being a useful way to think about things. "Higher dimensional matter" does not make any sense. Matter is stuff contained in space(-time). That stuff is represented (sort of) as having some energy/momentum distribution in spacetime: E=E(x,y,z,t), p=p(x,y,z,t). The "dimension" of the matter has to be the dimension of the space, or it makes no sense. There are some differences in 2D->3D vs. 3D->4D. Physics is not done the way popular books sometimes imply. It is mathematics (logic), not picture drawing. Various types of spaces with arbitrary numbers of dimensions are defined by the mathematicians as abstract things that obey some list of logical rules. There is nothing intrinsically "real" about any of them. What physics has done is to say the universe as we think we know it obeys one of these sets of rules. These are simple things like saying that there exists a well-defined distance between any two points. Everything else is formally derived from these very primitive observations.