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

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In summary, the conversation discusses the concept of R, which represents the radius of compacted space, and its relationship to the radius of the universe. The speaker also brings up the idea of T duality, which means that the laws of physics at the R scale are equivalent to the laws at the 1/R scale. There is also a discussion about the implications of this theory on our understanding of reality and the responsibility of scientists to consider the consequences of their discoveries.
  • #1
god^2=john
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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 existence 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 existence,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 going to 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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  • #2
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?
 
  • #3
with understanding.

T-Duality is a concept in string theory that shows the equivalence between two different string theories. It states that a string theory in a compactified space with a radius R is equivalent to a string theory in the same space with a radius 1/R. This means that the two theories are mathematically equivalent, but they describe different physical situations.

To answer your first question, R does not necessarily mean the "radius of the universe." It can refer to the radius of a compactified space in string theory. In this context, a compactified space is a space that has been curled up or "compactified" in extra dimensions. This is necessary in string theory to reconcile the differences between general relativity and quantum mechanics.

As for your second question, it is possible to have a universe or multiverse within a finite area in our universe. This is because the concept of space and time is relative in string theory, and it is possible for different universes to exist within the same space.

T-Duality is a broad term that refers to the duality between different string theories. In string theory, there are multiple versions of the theory, known as "string theories." These include Type I, Type IIA, Type IIB, Heterotic SO(32), and Heterotic E8 x E8. It has been suggested that these string theories are actually different limits of a single underlying theory, known as M-theory. So, T-Duality can refer to the duality between any two of these theories.

In terms of implications for our reality, it is difficult to say as string theory is still a theoretical framework and has not yet been fully tested or proven. However, if string theory is correct, it would mean that our universe is just one of many possible universes, and that there could be other universes with different physical laws and properties.

As for your assumptions about the existence of other universes and the inevitability of understanding string theory, this is still a matter of speculation. While some scientists and philosophers believe in the existence of other universes and the possibility of understanding string theory, others may disagree. It is important to keep in mind that these are still theoretical concepts and may never be fully understood or proven.

In terms of the implications of understanding string theory, it is difficult to say as it is still a theoretical framework. However, as with any scientific advancement, it is important to consider the potential consequences and responsibilities that come with
 

1. What is T-Duality?

T-Duality is a mathematical concept in string theory that describes the equivalence between two different types of string theories, known as Type I and Type II. This duality states that the physics of a string theory in a certain spacetime can be equivalent to the physics of a different string theory in a different spacetime.

2. How does T-Duality relate to R vs. /R?

T-Duality is closely related to the concept of R vs. /R, which refers to the compactification of extra dimensions in string theory. In T-Duality, the compactified dimension is said to be in the R state when it is larger than the string length scale, and in the /R state when it is smaller than the string length scale.

3. Can you explain the concept of really big and really small in T-Duality?

In T-Duality, the concept of really big and really small refers to the size of the compactified dimension in relation to the string length scale. When the compactified dimension is much larger than the string length scale, it is considered to be really big. Conversely, when the compactified dimension is much smaller than the string length scale, it is considered to be really small.

4. What is the significance of T-Duality in string theory?

T-Duality is a fundamental concept in string theory that allows for the study of one string theory to be equivalent to the study of another. This duality has important implications for understanding the nature of spacetime and the relationships between different string theories.

5. How is T-Duality tested and confirmed?

T-Duality has been tested and confirmed through various experiments and observations in string theory, such as the behavior of strings in different spacetimes and the consistency of calculations using T-Duality. Additionally, the predictions made by T-Duality have been found to agree with experimental results in particle physics and cosmology.

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