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T-Duality, R vs. !/R, really big really small

  1. Nov 6, 2004 #1
    1. Does R mean "radius of universe"
    2. if so can i assume that an entire universe/multiverse could exist within a (small or microscopic or large(from square km and up) a finite area in our universe, or vice versa(our uni. in anther uni.
    3 or if assumption 1 is wrong, is it better to assume R and !/R are mathematically equivalent, or if not can you explain, the implications of the T-duality(is t duality too broad a term(refe to duality between 2 or more(of the 6 (or is it 5 + 1, i mean should i consider super gravity a sixth string theory, or simply a component of m theory)) string theorys). i think i understood it when i read it, but my copy of elegant universe has been borrowed, so i can not look it up. i just need to know what that means in terms of our reality or any reality for that matter.

    my real question comes if my first two assumptions were correct(i really can't remember the explanaition of R vs 1/R, so the following question may be irrelevent) . so if we assume that "in the beginning"(i asume outside the existance of universes,or nothingness could be infinitely large, old, and producing of universes(i understand that it's hard to talk about infinites, but what i mean is odds are that our universe is one of many and most likely somewhere in the large middle(in terms of "time"(as in "1st" universe to "2nd" to .... to "last")). My reasoning is simple, to speak in percentages we'll say 0 to 99 represents zero universes to infinite-1(joke) uni. (i read in one post that universes could constantly and have always, been popping into existance,with some reaching a critical value to collapse or continue to grow, i know i'm being vague, but even with in this explanation, my reasoning holds true, i presume) and the prob of us being in 0-9 is 11/100 or us being in 90-99. so 22/100 vs 80/100 and obviously with infinities, there is infinite before and after (every reference point is middle,hence problems when dealing with infinities), point is good chance there have been many universes before ours. within these previous universes, there is good reason to believe that their exist a percentage that preduce intelligent life, capable of formulating a unified theory, for simplicity we'll assume it's m-theory. i mean if we have discovered it, others within our universe probably had or will come up with it in our (within our univ.)'s future. in time i would presume that we, and others, will even come to understand our theory on a wide scale, plain common sense for this future society. so if we accept the inevitability of our future understanding of m-t then we almost have to accept the inevitability of some kind of widespread understanding, i mean throughout the multi-verse. what would that mean for our theory, would all these societies be "mature" enough to use the knowledge this kind of theory would bring?? i mean we have developped so much technology that has in turn allowed to greatly increase environmentel destruction and totally through political structures out of balance. so we are naturally ahead of ourselves, we should be learning to be very careful w/ technology very tedious very PATIENT, so i guess my point is we have to stay aware of the world around us and what implications widespread knowledge to this degree, and probably without well defined morals(as products of m-t) we most likely have to develop m-t ethics ourselves. i like to establish some kind of worldview while we develop such theories. i think as capable thinkers it should be mandatory to keep up on world events and ways we can help. like we realize a deep interconectedness between everything in our universe, we understand that if we mess with nature, we can deeply effect our surroundings, what happens when we start messing with new technologies, i mean relitivity: atom bomb, automobile: mass pollution/ozone layer. superbugs. we have to be careful. what about even the implications of destroying peoples belief in God, they are left with this probablistic theory, why do they have to obey laws, we are all just vibrating strings?? it is said that philosopher's can't keep up on science, can't we help out, collaborate, i mean form a chain of understanding, maybe if the leading scientist doesn't have the necessary social rapport, he may need to teach another intellectual, one who relates a little better, this 2nd guy works with a philosopher well versed on the basics of m-t, they can try to incorporate ideas, in constructing some kind of acceptible world view. it would need failsafes of course, we need things to keep goverments in check , the people should run the government as much as they run us. we need to be active. our central goal should be acceptance, we won't change people's ideas, i mean there is gonna be differences of opinions on every intellectual level. i've started ranting, but i don't mean to say my last ideas are right , i just mean we have to be conscious of the implications of understanding, in the short term. people need to slowly learn new ideas. try and excuse my perverse ambiguity and ranting, just think about the responsibilities which will come
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  3. Nov 6, 2004 #2


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    1. R means radius of compacted space, for example a tiny circle. 1/R then becomes a "characteristic dimension" of extended space. I think the term "radius of the universe" brings in too much unwanted baggage (how do you define it? Couldn't the universe still be infinite? and so on).
    2. No this isn't what T duality means. It means that the laws of physics at the R scale map faithfully into the laws of physics at the 1/R scale. The paritcular things that happen at the different scales in obedience to those laws, are different. You don't have "the universe in a grain of sand", at least not with T-duality.
    3. Does the above answer 3?
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