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dimensionality of mass part onePosted by rtharbaugh on May 11, 2003 at 07:28:42: Dick and Kx21 You were posting a few days ago about an X partical and a Y partical. I'm not sure I understand what you meant but it occurred to me to ask myself if a partical can be said to occupy a single dimension. In other words, to what extent can a partical be said to be pointlike? Matter is usually said to occupy space and have mass. We usually think of occupying space as meaning to have some greater than zero value in x, y, and z. An infinite open Euclidian plane does not occupy space under this rather restrictive interpretation. Furthermore, the usual definition does not mention time. It seems clear that matter must also occupy some length of time, or it can not be said to exist. So an X partical would have to occupy at least two dimensions, altho I suppose when considering x alone it would be natural to just assume t is inherent in x, as it is when we consider motion in 3-space by displaying time as a displacement along x. However this is just a convenience. We display t along x, y, or z because we do not have a faculty for communicating in the past or the future, but only in the present. Clay tablets, paper pages, and even to some extent computer screens are devices which "collapse" or "hold" past events into the future so that we slow creatures have enough timespace to peruse them. This computer screen is useful in this regard because it takes the time I used to compose this message and collapses it onto the two dimensional image, which I can post now and come back to later, and find it "unchanged", that is, translated in time but not translated in space. My words, here as I compose them, will still be here in the same form later when you or I come back to read them. You have mentioned an X partical and I have assumed you might have meant a partical that exists only in X. I have had to further assume that you meant to include t in X, but is it justified to restrict t to x in this case? We do so when considering "3 space 1 time" systems in three space representations, and get away with the substitution because usually one of the space dimensions in the system doesn't change much. But in this case you seem to be restricting the idea of a partical unecessarily, since two dimensions are easy to display in two dimensions. There is no reason to collapse the t dimension into the x dimension, as there is when displaying four dimensions in two or three dimensional graphics. Now an interesting question in string theory has to do with re-defining our notion of mass. Strings are said to wind around curled up dimensions, thus having less than zero length and less than zero mass. The mass of the string is equated to its length, as would be reasonable in a system of uniform density, uniform or slowly changing x and y, and elongation in z. Unfortunately this analysis is circular reasoning since it attempts to define mass by using a string which is already said to have the quality of mass. I am afraid the question has been evaded. What is mass in string theory? Can strings be used to explain mass by explaining that strings have mass? Winding them around curled up dimensions doesn't help. We need something more. I think that dimensional analysis can help here, if we can ever get beyond the notion that space and time are different things. break.
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