# How do strings form a perfect electron?

1. Apr 4, 2005

### eNathan

If everything is made out of strings as described in string theory, or, M - Theory, then how do the strings know how to collect themselves to form an electron of the exact mass of 9.10939 x 10^-31 every time, and also form all the other particles (Proton, Positron, photon)? :uhh:

You would think that if the universe is just a chaos of strings, there would just be strings everywhere and nothing else. :grumpy:

Last edited: Apr 4, 2005
2. Apr 4, 2005

### eNathan

Ok, I am going to assume this is a flaw in String Theory if nobody here has an explination.

3. Apr 4, 2005

### Tron3k

Assume it, then. :rofl:

For god's sake, wait at least a couple of days before whining...

4. Apr 4, 2005

Staff Emeritus
Strings do not combine to form particles in the way you suppose. trings vibrate, and the modes of vibration become particles. In phenomenological models that attempt to reproduce the physics of the standard model, intersecting branes and strings between them play a large role. The branes carry charges, which are rigourously defined by field theory, and the strings have tension, which is also exactly specified and governs the frequency modes of the vibration by known laws. So the interaction of these deterministic physical states produces the same particle every time.

What one would think, having read very little of the theory, is not a reliable guide to thinking about it.

5. Apr 4, 2005

### eNathan

It was more of a joke than a whine.

selfAdjoint, are you saying a single string can vibrate to form an elemtry particle, or it takes several?

6. Apr 4, 2005

### DaveC426913

One string vibrates at a certain frequency in a five dimensional space. This vibration manifests as a certain property such as mass. We see that string with that mass as an electron (or other).

BTW, only certain vibrations are possible in the space, that's why we have a limited set of particles.

Last edited: Apr 4, 2005
7. Apr 4, 2005

### nightcleaner

I think the OP has a legitimate question.

DaveC, can you name the five dimensions? Are three of them space and one of them is time and one for mass? Or should we do two space, one time, one mass and one charge, since we are talking electrons? Or is time already accounted in the idea of frequency, so we can use three space, one mass, one charge?

Just wondering. I would really like to get a better picture of this. Can you, or someone, show the formula that specifies five dimensions?

Thanks,

nc

8. Apr 4, 2005

### eNathan

3 visible dimensions of space, one dimension of time, and all the rest are invisible dimension of space (or atleast, that is my understanding). I did hear of some guy on the NET that said he belives mass has a dimension. This is a very interesting theory...

9. Apr 5, 2005

### codyg1985

A lot of the dimensions are curled up into small shapes only visible at the Planck length, which accounts for why we don't experience them in everyday experiences.

10. Apr 5, 2005

### eNathan

From your description of these dimentions, it seems that each demention exists withing 3D space. How can these dimensions have a shape if they are the very basis of space itself?

11. Apr 5, 2005

### DaveC426913

They are all spatial dimenisons, like the 3 we are familiar with. They are just very, very small and curled up on themselves. I have been trying to work up an image to demonstrate this. Haven't finished it though. Best one I've heard is "the ant on the gardenhose":

An ant spends his entire life living on a one-dimensional gardenhose of arbitrary length. He can freely move to and fro within the confines of his universe, which is one dimensional. We'll call this dimension 'length', and we'll measure it as 'x', just like in our 3D world.

But now we come along with a microscope, and we blow up his universe. We can see that the gardenhose is not of zero width, it actually has a very small diameter, too small for him to detect. His universe actually has 2 dimensions, the second one being the circumference of the hose. We'll meaure this dimension as 'y'.

At all times, he is actually moving through the two dimensions independently, it's just that one of them is very, very tiny and curled up on itself. In fact, the extent of this 2nd dimension (circumference) is so tiny, that for every step forward along the gardenhose, he actually traverses its circumference many, many times, travelling in a spiral all the way along his universe/garden hose. But, the distance it takes to traverse this extra dimension is so tiny that he does not notice any slowing of his speed in direction x.

That microscopic dimension is there, perpendicular to his macroscopic dimension, and he is passing thorugh it just the same, but it is so small that he cannot detect his passage through it, nor does it impede his passage though his other dimension(s).

The other dimensions are right here, you experience them everyday. When you swing your arm, it is passing thorugh these other dimensions, just as surely as it is passing through x, y and z. It's just that the passage through these other dimensions is so tiny as to be undetectable.

Last edited: Apr 5, 2005
12. Apr 5, 2005

### nightcleaner

Hi DaveC426913.

I have read the garden hose thing in Greene. It is a nice picture but as a model it is problematic.

For one thing, it reduces dimensionality to a matter of scale. A garden hose is already in three dimensions, why do we need more dimensions just because the movement around the hose is very small? The small movement is still occuring in xyzt as far as I can tell.

And again, about these Calabi-Yau manifolds. Are they rigid bodies or do they interpenetrate in a fuzzy way? Do they affect each other?

You know, there are any number of dimensions you like, but the better question is, how many dimensions do you need? What is the minimum number of dimensions required to describe a system?

Is a dimension the same thing as a basis line? If we build a physical 3d grid structure, a cubic lattice maybe, we cannot add another line orthagonal to the others. But then there is time. Can we choose another point outside the space of the extended grid lattice by observing that the lattice is a stucture, which has a beginning in spacetime, and so must have an ending in spacetime also? Then the added point is not in the same spacetime as the lattice, so a line can be drawn from the spacetime of the lattice to the point outside the spacetime of the lattice and it will obey all the rules of orthagonality. Voila, the fourth dimension. To be sure, it is an imaginary dimension and one which is very large compared to our usual three, but it should still obey the rules of trigonometry, I think.

Then if that is allright we could go on to draw a new set of orthagonals to the fourth basis.

I have to say that I am a little tired of the answer that they are all spatial dimensions. We have three spatial dimensions. I don't think it is satisfactory to say that there are more but they are curled too small to notice.

And why can't we look at time dimensions? We have spacetime equivalence principle to work with. And there already are multiple time dimensions in our formulations. What is acceleration? L/TT. That is two dimensions of T by my count. No problem with the maths.

I don't see the CPT violations. Causality is preserved in any set limited to one time dimension. So it is broken in higher dimensionalities. This symmetry breaking is a standard feature of many of our models. Just as in perspective drawing, gauge invarience is violated to allow a three dimensional representation on a two dimensional surface.

Time square and time cube represent real physical entities, and are required in our standard models of physics. What argument is there against using time as a space equivalent set of dimensions? Then you can have your five or six or ten dimensions, and make working models without all the little sticks getting bent and broken.

You and many others seem to make a distinction between "dimensions" as in xyzt, and "dimensions" as in Length Time Charge Mass etc. What is this distinction exactly?

Richard

13. Apr 5, 2005

### DaveC426913

Sorry, I was oversimplifying the explanation. The ant's universe really is only 2-dimensional. He can only move on the surface of the garden hose, he has no experience of a third dimension. All light rays in his universe follow the curvature of the surface of the garden hose, so there is no experience of inside or outside the hose.

But none of that is really the point. It's just to allow us to throw away a dimesion so we can wrap our heads around it.

OK, now from there, The ant really thinks his universe only one-dimensional, that is all he experiences. The other dimension is there, it's just very small. The ant is moving thorugh that 2nd dimension, he just cannot detect thae movement.

Now we scale this back to ur 3 dimensional universe. We are passing through these extra dimensions all the time. I am sweeping through them when I wave my arm. But if they are so small that my arm will traverse the entire width of that dimension in, like, one planck-length. I actually traerse the entire dimension many, many, many times over in that one metre sweep. And I will not notice my arm slowing down as it sweeps through this other dimension.

14. Apr 5, 2005

### DaveC426913

"I have read the garden hose thing in Greene. It is a nice picture but as a model it is problematic."

Or look at it the other way. Bear with me.

If our universe is a closed loop, it has to curve through a fourth dimension to do so, right? (Forget about the whole expansion thing, or whether it is closed enough to contract again, I am just asking about its shape at any given instant.)

Now, if we fly a spaceship in one direction long enough (i.e 15 billion light years (or is it x2 = 30Gly)) we will return to our starting point. Correct? Take a moment to satisfy yourself that you agree.

Ok, we can fly our spaceship in *any* direction, and will eventually return to our starting point. We presume the universe is spherical in shape, and thus it is the same distance travelled to return home no matter what direction we choose to fly in.

But that presumes that our current 3 dimensions are equal. What if one is shorter than the others? What if our universe is 15Gly in the X direction, but only 1Gly in the y direction? Picutre it like a cosmic cigar. If we head in direction X (down the length of the cigar), we'd return in 15Gly. But if we headed in direction y (around the circumference of the cigar), we'd have traversed the universe after only 1Gly, right?

Now, what if we head in a direction 45 degrees to both x and y? We would still return to our starting point after a certain length of time. But, while we will have traveresd it only once in the x direction, we will have traversed it 15 times in the y direction. We will travel in a corkscrew - around the cigar AND down its length simultaneously (though we will see our path as straight, just like all the light rays we use to measure).

Now, what if the universe is only 1 centimetre in the y direction? We head off at a 45 degree angle, We effectively traverse the universe in the x direction, and the travel in the y direction is becoming increasingly irrelevant - we corss that space in an instant. If the universe is only a few Planck lengths across, we will never even know we are travelling through it. We will only experience the travel through x.

It would also be meaningless for us to talk about trying to turn and travel in the y direction, since it is too small for us to experience.

But that doesn't mean it's not there!

So, we have 3 macro dimensions, and several extra Planck-scale dimensions that are too small for us to experience.

Whew.

Last edited: Apr 5, 2005
15. Apr 5, 2005

### whozum

I got everything but this. When you described the universe right above as a loop curving through a fourth dimension, is the universe the volume contained in the loop, similar to the image of a sphere in R^3? Or did you mean the universe exists on the actual curve of the sphere in R^3 and it 'exists' in R^4?

If its the first one, I dont understand, if the second then your good to go :bigthumb:

16. Apr 5, 2005

Staff Emeritus
The hose is a stand-in for our space with our 3 or 4 dimensions reduced to 1, the length of the hose. The point is not that it moves - it could as well be a rigid pipe - but that it has circular cross sections at every point along its length. Do the circles interact? No more than the pages in a book interact; each one is separate and they don't intersect. Just so, goes the analogy, in our 3-D space or our 4-D spacetime we have 6-dimensional "cross sections" at every point, they are in some sense parallel to each other and they don't interact, and they are very tiny, halfway to the planck length across, so we can't detect them with our puny teravolt physics.

See above. Strings and branes extend and move through the Calabi-Yaus, along with moving in our 4-D extended dimensions, and the strings can intersect and interact. But the dimensions, no. Does length interact with width? Not as dimensions of a thing but just as directions in space? Orthogonal dimensions are the poster children for non-interaction!

For superstrings the minimum, and also the maximum, is 10. That's the only dimensionality in which the equations work. Did you think they made it all up just to kid us?

Yes this is exactly how it is done. We can't visualize it but we can describe it with math.

In special relativity dimensions are of two kinds: time and space. This is because they have opposite signs in the metric

$$ds^2 = -cdt^2 + dx^2 + dy^2 + dz^2$$

In the special relativity background in superstring theory the metric is:

$$ds^2 = -cdx_0^2 + dx_1^2 + dx_2^2 + ... + dx_9^2$$

So there are 9 dimensions with + and the one time dimension with -. The 9 are called space dimensions by analogy with the 4-d case. Three of the space dimensions happen to be extended, and the other six happen t o be compacted. Physicists are looking for cosmological reasons to expain this fact.

The two time dimensions (this is a DIFFERENT use of the word dimension!) are samplings of the same "timeline", not two new dimensions in the geometrical sense. It's confusing to have two contrdictory meanings for the same word, but not unheard of, consider "fast as light", "tied up fast", and "fast asleep" for example.

Linear time does not guarantee causality; you need to eliminate backward time travel to do that. This is the point of Hawking's "Causality Protection Conjecture", which is basically that nature conspires to make time travel impossible. CPT invariance is not about causality, but about the behavior of the discrete symmetries of charge, parity, and time.

See above, and below.

The dimensions in the sense of dimensional analysis are categories of physical quantities, attached to different physical phenomena. They can all be broken down to rational algebraic combinations of M, L, and T. Algebraic means any one of them can be squared or raised to any other rational power.

Dimensions in the sense of "higher dimensional space" are the independent directions that span the space. Mathematicians would actually think of mutually orthogonal unit vectors (an "orthonormal basis"), each of them one unit long and each perpendicular to all the others, in the sense that their inner product $$e^ie_j = 0, i \ne j$$. If n such vector are sufficient to base any vector in the space, then the space is n-dimensional.

I hope this helps

17. Apr 6, 2005

### nightcleaner

Yes, I can say it helps. Thank you.

You said:

"The dimensions in the sense of dimensional analysis are categories of physical quantities, attached to different physical phenomena"

and

"Dimensions in the sense of "higher dimensional space" are the independent directions that span the space."

I have pulled the two quotes out here to have a close look at them. I trust you to correct me if I have taken them entirely out of context.

My method is to continue to try to make these two into one thing. Perhaps I will find an irresolvable conflict and that will allow me to put my mind at rest in the matter.

Catagories. Directions. Seems to be similar to scalars and vectors.

A catagory is like a box in which you can file all similar objects. Of course there are boundary conditions and resultant conflicts. For any set of catagories, there will likely be some objects that could be counted in either of two, or more, catagories. For example, the tomato. There are still people who argue the question of whether a tomato is more properly classified as a fruit or a vegetable, despite authoritative attempts to quash the squabble.

It may be that all catagory schemes share this problem, and that finally any catagorization of a sufficient number of varied objects will have to make arbitrary, authoritarian decisions. Tomato juice is not a countable object.

A direction, unlike a catagory, seems to be going somewhere. You can put a jar around some tomato juice and make a countable object of it, but how can you contain a direction? It seems to me to be the nature of directions that they penetrate and extend beyond all boundaries. North is still North even if you are in a jar. The jar can contain you or some tomato juice, but it cannot contain North.

Directions only run into trouble when we come to universal boundaries. These boundaries are not arbitrarily defined, so as to fit some collection of objects, but are part of the system of objects in itself. So, North comes eventually to the North Pole, and you can drive a stake in the ice and say that it is, truely, North. Well until the ice shifts anyway, or the orbit precesses, or until some other cosmic accident upsets our sense of balance. But you will see I hope the problem with this approach. Perhaps one could put a catagorical jar around the Earth, and say then that it contains North. But definition is lost. The jar contains South also. We have only contained North by stepping outside the world that defines it.

Anyway universal directions like x, y, and z do not curve around nicely to give us a sphere with related poles. They go out to infinity. Do two parallel lines meet at infinity? The idea of infinity is that there is no boundary in the x, y, or z direction. If there is no boundary, the lines cannot meet there.

Well, you see the universe is like a big jar, but part of the definition of the size of the jar is that the jar cannot exist. This could be a problem to unitarians.

So in general, catagories are sets of definitions that attempt to surround objects in a local space, while directions are sets of definitions that attempt to pinpoint an object by its location, from infinity, in a universal space. Catagories are then local and limited while directions are universal and infinite.

I am going to post this before I lose it in cyberspace. Continue after short break.

18. Apr 6, 2005

### nightcleaner

If a jar cannot contain North, can a jar exclude North? By North of course I only mean, a direction, as North is an example of a direction.

Anyway universal directions like x, y, and z do not curve around nicely to give us a sphere with related poles* such as might be put in a jar.

Can we say catagory and direction are comparable to each other as locality is comparable to universe? Then if locality and universe have a relation to each other, we might expect to find a similar, symmetric relation in catagory and direction.

The jar is local and the direction is universal. The Jar is catagory and the direction is, well, direction. Jar seems pretty clear in definition. We can even put a lid on it. We can give it its own reference marks, front back up down left side right, shape it, call it a sphere with a hole in it if we wish. A jar is designed for the purpose of containing something. Any real object can be contained in a suitable jar. It might have to be an impossibly big jar, but that is only a scalar problem, and falls outside the definition of jar. No matter how large you make the jar, it is still a jar. No matter how small you make the jar, it is still a jar. If it is impossible to make a larger or smaller jar, that only means that it would be possible if we only had more suitable materials.

Space is local. Time is universal? Then what is the time of the universe?

Is there a smallest locality? This is the same as asking, can there be a smaller jar? What if the answer is, there can be, but there isn't? That might be good enough for us. We certainly won't have to build any smaller boxes than that. We can use that tiny jar, that littlest box, as a counting unit. Enough of them together will fill the universe, and fill it exactly, or if there is a tiny remainder, it will be so tiny a percent of the totality as to be negligible.

So if we fix upon the idea of a smallest jar that is necessary to any observation and just depend upon very large numbers to ensure that our universe is effectively infinite in every regard we need to imagine, then we can quantify any universe, in any dimension we can imagine, and have what amounts to a perfect coordinate grid system for any description we need to make of that universe. Our universe is a universe, so that rule includes the universe which we inhabit.

It happens that we are a size in our universe and so our size is necessarily a countable number of smallest units. For this reason SI uses handy sizes of units and can define them with all necessary precision for any common purpose.

I should like you to note that we are still not tied in this logic to any preferred countable background, but only that we have stated that such a background, if it does not already exist, can be reasonably constructed to fit any of our needs. This idea is still background independent, but at all measurable scales it is or can be quantified.

Background independence is a universal viewpoint. Quanta is strictly local.

Directions are universal. Catagories are local.

19. Apr 6, 2005

### nightcleaner

I started with dimensions as catagories versus dimensions as directions. Two different meanings of the word, Dimension, yet related by their standing as a local-universal pair. Catagory and direction. We build up catagories and they result in the expression of directions.

So if we use quanta and the idea of quanta to build up catagories of dimensions we should be able to establish universal dimensional directions from the shape of those catagories. Now our catagories are terms like length, duration, mass, charge, temperature, luminosity, and so on. What are the directions we can establish as universal among these catagories?

Well it would actually be convenient if we could name a catagory and use it as an indicator of the vicinity of the direction we wish to consider universal. If we name a far away long ago very small catagory as the indicator of direction we can be rather precise about determining what the direction will be. Any local members moving in the direction of that indicator should pursue lines that are parallel for the duration of their flight. So what catagories do we have that are suitably very small, very long ago, and very far away?

20. Apr 6, 2005

### DaveC426913

Yeah, this gets a bit tricky.

You can create a virtual dimension every time you categorize something that has a degree of freedom independent of its other properties.

Programmers use multiple dimensions all the time in coding. Length, width, height, colour, price, mass, etc. To represent these six properties properly, you would need a six-dimensional array. The fact that it doesn't exist in real space doesn't mean it isn't otherwise a functional six dimensional space.

But those are not the same as real, spatial dimensions, which is I believe what we're discussing here. (Or have I completely missed nightcleaner's point)