# I am having trouble understanding some details of super string theory.

1. Jan 20, 2007

### orami?

I am having trouble understanding some details of super string theory.
1.) In the documentary I saw describing the theory, the physisists said that there would be an infinite number of other universes apart from ours and it seems that pretty much any theory of how we came to be, at some level, includes an infinity. But I fail to understand how anything that is not, itself, infinity could exist in an infinity. To my understanding, in an infinity, anything that is not an infinity, no matter how large, is not even the tiniest fraction of that infinity, not even 1 x 10 to the -1,000,000,000,000,000,000,000th % of the universe as an example. If there are any simple terms to describe how this works, I would greatly appreciate hearing them. This has been on my mind 24/7.
2.) Also, I noticed that the documentary called super string theory a "theory of everything". However, it only seemed to go back past the big bang to show the theoretical demension that our universe was born of. Does it go on to explain where it came from or is that considered basically satisfactory?
If string theory doesn't do so itself, does anyone plan on finding what did create that demension?

I am sorry, I have had no access to good books about physics and havent started college yet so I haven't taken any good classes on it. I say this because I will most likely have zero understanding of any math and will probably have to be talked to like a small child.

Last edited: Jan 20, 2007
2. Jan 22, 2007

### francesca

just some quik thoughts...

I don't know if I've well understand your questin, but I try to give you some brief issue...
think about 1, the unity, so you can say that, if you consider rational or irrational numbers, you have an infinity in something that is finite.
If you want to know more about this, search for "Cantor" who first pointed out the existence of more degree of infinity.
note: math and theoretical physics at some level would become the same...
this is an open issue in phylosophy of science, but by now you can accept this!
"theory of everything" is a synonym of "theory of great unification", i.e. the theory that can give a unique, unitary, omogeneos theory for all the (four) forces known in nature. In my opinion this would not lead to be able to predict everything, pay attention... And note that non-stringy theories of great unification often don't need to explain why we see only 3+1 dimension if we live in a 11-dim space, because they are 3+1 dim!
The question of why we see just this kind of universe is interesting and told out, but there are a lot of way to debate it...

3. Jan 23, 2007

### orami?

Ok, I looked up cantor. I tried my best to understand it based on the literature I found. My interpretation is that It says that space is made up of cubes (or at least units of spce that are topologically indistinct from cubes) that have no dimensions because they are the smallest unit of space.
Please correct me if I misunderstood.
I assume that in mentioning the irrational and rational numbers, you are referring to the infinate numbers, for example, between 0 and 1, or any two numbers.
Once again, correct me if I am wrong.
So, based on everything in respondence to my question about how there could be existence in infitiy, my understanding of what you are saying is that because every level of infinity could be broken down into their own infinities, something that is not an infinity could still exist in an infinity because it is, at some level, also an infinity.
Before I really concider the implications of that theory, I want to make sure I have it right, so if I need to do more research or am not understanding this correctly, please tell me so.

4. Jan 24, 2007

### paw

Well consider the integers from 1 to 10. There are a finite number of them, 10 to be exact. Now try to divide 10 by 3 using the old longhand operations. You will find that no matter how many times you perform the operation you will never get a complete result. The answer to 10/3 is an infinite string of 3's.

This is a simple demonstration that an 'infinity' can exist within a finite 'space'.

This also has a physical interpertation as well. Imagine that you were given a ruler 10cm long and were asked to cut off exactly one third of it. You know from mathematical analysis that it's impossible so you do the best you can and cut of a piece 3.33cm long. This piece is a finite portion of the 'infinite' piece you were asked for.

Another way to approach this is imagine you have in front of you an infinitely long ruler. You look to the left and right but you can't see the ends, no matter how powerful your vision, because the ruler stretches left and right to infinity.

Now cut the ruler in two directly in front of you. What do you have now? Two infinitely long rulers of course, since, even though you can see one end of each, they both stretch off to infinity.

Now cut a 10 cm section from the end of the left ruler. What do you have now? A finite 10cm ruler and 2 infinitely long rulers. You have created a finite from two infinities. See, finities can exist in infinities which can contain finites etc. etc.

Hope this helps a bit.

5. Jan 24, 2007

### orami?

That is the thing I am saying I dont understand. I don't understand how those rulers could be infinite if they have an end. In fact, it seems to me that they would be non-existant if they had an end because they would be smaller than the tiniest possible fragment of true infinity. And as far as dividing 10 by three, that is only due to our own perception of the number ten and what ten inches really is. You see, those 10 inches could be the same as 9 of something else and then it could be divided by three. And what is to say that any amount of space cannot be divided into x amount of sections?

6. Jan 24, 2007

### mjsd

I don't quite get your original question regarding infinities. you said you don't understand how something which is finite can contain something that is infinite. I mean, if a room is large enough (infinite or not), then surely you can fit in a finite size table in it. A room being "infinite" will ensure that table of any size can be fitted.

Anyway that seems to be too general a statement, you may have to indicate what kind of infinites the finite object contains or vice versa.

7. Jan 25, 2007

### paw

Well, I'm sure you agree that the original ruler is infinitely long, yes? It stretches from -infinity (to the left) to +infinity (to the right). Now when you cut the ruler the left half is also infinitly long, it stretches from 0 (right in front of you to -infinity. Same with the right hand ruler, it stretches from 0 to +infinity.

In mathematical terms infinity-infinity = infinity. This is by definition. You cannot know how 'big' infinity is so this is the only definition that works.

Now when you cut 10cm from the left ruler I'm sure you agree that the cut piece is finite, yes? It is 10cm long, we can see both ends and measure it with another device.

You might think, at this point that the left ruler is shorter than the right ruler because you cut 10cm from it right? Wrong, there is no way to compare the left ruler with the right ruler because they are both infinitly long. Therefore the left ruler is defined as equal to the right ruler.

In mathematical terms infinity-10 (or any real number) = infinity. Again, this is by definition.

Please understand that you are free to define these relationships any way you like but be aware, when you do, large parts of our mathematics will become inconsistant and won't work the way you expect.

8. Jan 25, 2007

### orami?

In reference to the question by mjsd, I meant it the other way around. I meant I do not understand how something finite could exist in something infinate.
In reference to the last post, the thing is, I am not sure I can agree with all those statements.
It seems to me that if you cut that infinately long ruler, it would not be starting from zero, it would be starting from zero-ruler, but the infinity that contains the infinately long ruler would be uneffected.
I don't think it is fair to say that infinity minus infinity = infinity. Why could it not equal zero?
As for the infinity minus 10, that once again brings up my original question. How could that ten exist in a form separate or able to be separated from infinity. It seems to me that for something to be infinately large, it would also need to be infinately small because nothing could be truly subtracted out of infinity. I just don't understand how these infinities could logically exist in levels that are truly separate.
The whole thing about how big infinity is seems like a rediculous point to me. I thought that infinity meant endless. To me, that means no end right, no end left, not back in time or forward, no end anywhere. If that is not what it means, it is still what I meant.

Last edited: Jan 25, 2007
9. Jan 25, 2007

### heusdens

The problem of the (concept) of the infinity are many.
For example, how can an infinite be made up of the finite only?
Yet, we can construct the infinite, from the finite, just by successive addition of a finite quantity to another finite quantity, endlessly, will yield the infinite.

Infinites in the mathematical sense are not the same. We can certainly argue why some infinites are larger then others. For this, please consult set theory and number theory, and Cantor. For instance the set of natural numbers is certainly infinite, but there isn't any way to put the natural numbers in a 1-to-1 correspondence with the real numbers. Therefore the set of real numbers must be a bigger infinite then the set of the natural numbers.
On the other hand, we *can* put the natural numbers in 1-to-1 correspondence with the rational numbers, which means the set of rational numbers is as large as the set of natural numbers.

And to memorize some other problems, like what infinity - infinity or infinity / infinity is or can be, this of course depends on the (mathematical) contect.

Examples:

Let f(x) = x^2 - x

Then, for x -> infinity, we have infinity - infinity, yet f(x) will certainly also yield infinity.

Or f(x) = x / (x^2 + 1)

Then, for x -> infinity, f(x) will yield 0.

Just basic infinitesemal calculations.

Last edited: Jan 25, 2007
10. Jan 25, 2007

### Jimmini

Orami,
If you travel in a circle, your path is infinite. This same idea would apply to potential other universes and our own.
If everything turns back onto itself, then it is not a linear concept. This is a part of superstring theory. Some people use a ball of string as an example where the string is one piece in that it has no beginning and no ending.

11. Jan 25, 2007

### ||spoon||

I also watched the program the elegant universe and found it explained things pretty well for a layman like myself. I watced it about a montyh ago so my accuracy on what he says may not be too exact.

When he was talking about multiple universes, giving examples with the slices of bread and so forth, somewhere he said that these "other universes" could be only milimetres away from us but that we dont know it.

Could someone explain this in some more detail because he lost me on that bit.

Thanks
-Spoon

12. Jan 25, 2007

### mjsd

Reinforcing heusdens post, one really needs to understand the various concepts that related to infinties in order to talk about infinities. The natural vs real numbers issue stems from whether the set is countable. So I guess common sense tells you that (let's keep the discussion in layman terms, since it seems to me that it is the intention of the original poster), we can count each and every natural numbers easily while the same cannot be said for real numbers for we cannot even list them all down.

Now, back to your ruler example. It is like asking is the set $$(0,\infty)$$ smaller than $$(-\infty, \infty)$$? But then you may say they both contains an inifnite amount of elements, how do I know? Think about it...

In the second example, heusdens introduced the concept of a limit. Now, in a sense, one should really talk about infinities IF they understand the concept of a limit.

to ||spoon||: I think Brian Greene was referring to a concept called "braneworlds". You imagine your universe(the 3+1 dimensions) is a "brane" that resides in the bigger space (called "the bulk"), now, outside in the bulk you can have other "branes", these branes can be the "other universes" he is talking about. And these "branes" could be just say a milimeters (in extra dimension coordinates) away from our "brane".

To picture this you imagine our world is a slice of bread (in his example), the longitudinal direction of the loaf is the extra dimension. Now the reason why we don't see these other slices of bread is that (in these models) all forces of nature (with the exception of perhaps gravity) are confined to within each slice, and perhaps only very small leakage of them may propagate away into the extra dimensions. Typically, one needs to have a huge amount of energy to do that. that's the reason why they are building more and more powerful accelerators (eg. LHC) to look for these extra dimensions.

13. Jan 25, 2007

### LukeD

The "density" of the set has nothing to do with it at all. It's nothing but the cardinality. For example, you cannot "list" the rational numbers by simply trying to count them. You will have to count an infinite number of elements from 0 to 1. However, the number of rational numbers is equal to the number of natural (or counting) numbers because one can create a direct 1-1 mapping (technically a bijection) from the natural numbers to the rational numbers (though doing this is quite tricky).

However, an easy way to see something fairly similar is the proof that the number of natural numbers from 1 to infinity is equal to the number of "points" of 2 natural numbers (e.g. (1,1),(1,2), etc) though initially it would seem that there should be infinity of natural numbers, and infinity^2 of "points". To prove that they are equal in number though, simply note that you can number the points like this:

1 - (1,1)
2 - (2,1)
3 - (1,2)
4 - (3,1)
5 - (2,2)
6 - (1,3)
and so on in a diagonal pattern like that. If you extend the mapping to infinity, you will be able to map every point to a natural number. The same technique works for rational numbers. However, it does not work for real numbers, which is why there is not the same amount of real and natural numbers.

14. Jan 27, 2007

### mjsd

Firstly, I am sorry (to those mathematicians out there) if I have been mixing layman language with words that also have technical meaning.... (hey we physicists sometimes don't care about the precise maths def. ) Anyway, my example was nonetheless correct for those who are unaware: the number of real numbers is bigger than any countably infinite set (technical meaning used here). I was just trying to use countability vs incountability as an intuitive example.