What is string theory?

  • #1
So, what is it?

Math assumes non-dimensional points on a number line are separated.

But assumes the points have no distance between them.

If a point has 0 length on a number line and it is 0 distance from the point beside it, they are the same point. You cannot create a number line with points that have no length and no distance between them.

But string theory assumes points have a length on a number line, or that the centers of the points are separated by a distance. A distance on a number line is 1 / divided by a number.

Math assumes non-dimensional points on a number line are directly beside each other, with no distance between them. The only time that is true is when their size and the distance between them is 1/infinity. Infinities don’t exist in math, so while math incorrectly assumes points with no size can sit directly next to each other, math doesn’t include an exact idea of infinity. And so math has no real input about the exact size and shape of points.

1/9,000,000,000,000,000, or however many zeroes you want to add is included in math, so the closest that math can get to dividing down to zero distance and a zero-sized point on a number line is a very small distance and a very short point, in other words, a string.

That is what string theory could be.

Given that concept for string theory, it’s possible to answer a few interesting questions.

If points are small distances, then the distances can vary, which gives us a space that can stretch, warp, and curve. Now, using that concept of string theory, we can describe a continuum, and it can change shape.

Einstein began to think, in 1936, there cannot be a continuum, maybe because he realized points cannot have 0 size and 0 distance between them, and create the continuum. By 1956, he privately concluded and said to a friend that a continuum is impossible, and said that all of his ideas about gravity are invalid.

But using the definition of string theory that I have just stated, which shows that non-dimensional points have to be strings, a continuum can exist.

So in 1956, when he realized points that are 0 in size and 0 distance apart can’t create any space, therefore, space is just an empty nothing and can’t change shape: therefore there can’t be a continuum. String theory in the 1980's suggests that all points have length. And in math it turns out to be impossible for points not to have length, since 1/infinity does not exist as an actual value.

So let’s create a string theory plane. You take points that have length and connect them together.

It doesn’t matter how long or short the points are as long as they have a length, so let’s use Q-Tips to represent string points and connect them to make a plane.


(Sorry my IMG code is off. I guess I am considered a crazy moron.)

The plane in the photo has two dimensions. You can locate any point (any Q-Tip) with an x and y axis. But to get from any point, to any point on this plane you have to zigzag through an underlying three dimensions because, this plane only contains three directions! That is the strange thing that happens when you use string points, instead of non-dimensional points sitting directly next to each other. But you can’t create any space when you use non-dimensional points with no distance between them. You can only create space when you use string points. But then, you find you are limited to only three directions! These three directions become three dimensions.

If you were to build the plane into a 3D space, you arrange the Q-Tips like this.


Now you have six underlying directions through 3D space. You have the 3 classic dimensions, and you have the dimension of time, for 10 dimensions, exactly how many dimensions string theory predicts.

-John Cauthen

Answers and Replies

  • #2
Staff Emeritus
Science Advisor
Gold Member
Allow me to correct your mathematical mistakes:

Math assumes non-dimensional points on a number line are separated.

First off, the concept of dimension does apply to points, so it's not right to call them non-dimensional. (They're zero-dimensional)

You are correct in that points are separated. In fact, there are varying degrees of what a mathematician means by "separation". One of the fairly weak versions is this:

If you are given any two distinct points P and Q, then there exists a neighborhood of P that does not contain Q.

On the "number line", neighborhoods are open intervals. As an example of separation, suppose you handed me the point P = 0 and Q = 1. Then, I could exhibit the neighborhood (-1/2, 1/2) which contains P and does not contain Q.

But assumes the points have no distance between them.

Incorrect. You are making a very common mistake (aside from the fact you mean "zero distance", not "no distance"): given any two distinct points P and Q, they will indeed have a nonzero distance.

However, we don't only speak about the distance between points... we can also speak about the distance from a point to a collection of points.

For example, I could take P = 0, and T = (0, 1]. Then P is not a member of T, but the distance between P and T is zero.

It is very important to distinguish between working with single points and working with collections of points.

If a point has 0 length on a number line and it is 0 distance from the point beside it, they are the same point.

A point cannot be "beside" another. However, a point can be "beside" a collection of points... take my previous example of P and T.

A distance on a number line is 1 / divided by a number.

No, because a distance can be zero, such as the distance between the points P = 0 and Q = 0, and a zero distance is clearly not 1 divided by a number.

Infinities don’t exist in math ... math doesn’t include an exact idea of infinity.

Patently false.

And so math has no real input about the exact size and shape of points.

The shape of a point is... point-like. A point consists of a single point, no more, no less. The length of a point is zero. The area of a point is zero. The volume of a point is zero. Math has a lot to say about the exact size and shape of points. And this should be obvious, because points are mathematical objects.
  • #3
Thank you for the reply, but if P and Q are distinct points with a "neighborhood" surrounding them, they HAVE a distance between them, even if math doesn't officially recognize the distance. That is why it's such a sticky problem.

If you stack zero sized points, zero distance apart, you get nothing, no space.

If a point is "point-like" or has a neighborhood around it, then you can could call it a little circle or a little sphere with a diameter. That diameter, no matter how small it is (or how unrecognized), is a string.

If you take little circles, or spheres, like marbles or cannon balls, and stack them to make a 3D space. Then, if you travel from "point-like" cannon ball to "point-like" cannon ball in the real stack of marbles or cannon balls, traveling from marble to marble, or point to point you can only travel in six directions. (That's six extra dimensions.)

It would be hard for math to include this idea: 9 dimensions in physical space; so they say a point is "point-like" and that two points which are separate, and are surrounded by a "neighborhood" have no distance between them.

What math assumes works; until you really think about it.

The "neighborhood of P" is a string. A nonzero distance is a string.

If P is at 0, and T is at [0,1], then T is next to P on a straight number line. And the separation between them is a string.

A string is a fine distinction, but makes a lot of difference in certain applications. Strings make up the underlying space of everything, and the physical structure of the strings are triangular loops, just like LQG says.

The current big argument is, can the smallest structures vary in size?

Math doesn't recognize the size of a point, but it doesn't say a point has no size. String theory doesn't contradict math, but says points have size and says they are elastic: they can vary in size.

This supports one side of the big Loop Quantum Gravity argument: can the underlying structure vary in size? Yes, it can. It also implies string theory and LQG are the same theory.
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  • #4
Science Advisor
Gold Member
Einstein's friend must have been quite startled by that 1956 discussion.
  • #5
I found that information here:

Here's what it says.

[1956 from Einstein]
"One can give good reasons why reality cannot at all be represented by a continuous field.

[1936 from Einstein]
In 1936 Einstein wrote that: "To be sure, it has been pointed out that the introduction of a space-time continuum may be considered as contrary to nature in view of the molecular structure of everything which happens on a small scale.

[1940 from Einstein]
Some physicists, among them myself, cannot believe that we must abandon, actually and forever, the idea of direct representation of physical reality in space and time.

And let's underline:

"...among them MYSELF, CANNOT BELIEVE..." In less diplomatic terms he could have written: "There are good reasons to waste time on this red herring, but my superior intuition and philosophical principles prevent me from doing so."

The last thing one writes generally takes precedence over everything else -- and the first quote is the very last thing he ever wrote, which countermands everything said before.

1936: "I'm beginning to have doubts..."
1940: "... but not quite yet"
(15 years later) 1955: "I give up, I was wrong in 1940. There is no continuum."

Written to Michele Besso in 1954:
"I consider it quite possible that physics cannot be based on the field concept, i.e., on continuous structures. In that case, nothing remains of my entire castle in the air, gravitation theory included, [and of] the rest of modern physics."

But Crazy Moron says that fortunately he was wrong to believe he was wrong. He was right when he realized, in the math he was dealing in, there cannot be a continuum, nor one that changes shape. In my concept of what string theory is, there can be a continuum (a continuous succession of points) and it can change shape.
  • #6
Science Advisor
Gold Member
Einstein died april 18, 1955. Factual inaccuracies, like quotes from Einstein, that are alleged to occur after his death, make me think you don't know what you are talking about. Sorry for being critical.
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  • #7
I am very trusting. I simply believe what I hear, rather than being skeptical and waiting till it's proven to me. Some people go through life attempting never to make a mistake. It is possible that some of the dates were stated wrong, or that the 1956 statement was made about Einstein after his death. However, he wrote a letter to Michele Besso in 1954, and it sounds like something someone would say to a woman at the end of his life. The real reason I believe it is because I went through the same thought process and came to the same conclusion.

I said, "How can a solid space (a field) change shape within itself. It can't. It has to be made of individual points. Okay, if it were made of individual points, how would it be constructed?

I came up with a space that can easily be described as 9 dimensional, exactly what string theory predicts. I truly impressed myself.

(Time makes it ten dimensions, but I am talking about space.)

In the basic structure of 3D space made of points, there are only six directions! However, the directions are not always absolute. The three directions in the basic structure of a plane made of points can easily be expanded to six directions by going between points. I have no idea how many ways you can squeeze between points in 3D space, but I have counted over 20, hence 27 dimensions in some versions of string theory. And with that many dimensions and secondary dimensions, it is not surprising all of this didn't jump out at us.

A TV screen is a space made of points (pixels) and it has characteristic rays, three of them, around every bright light as light spills out along the three directions. Then, you look at the stars, which exist in a space that I say has six underlying and basic directions, and you can count six faint rays cutting through every star and every bright light. Some stars have five rays if one direction is pointing straight at you.

The rays coming from bright lights on a TV screen are obvious; and it is obvious what causes them: the alignment of pixels on the TV screen. If stars have the same kind of rays; that must be strong evidence space is made of actual individual points.

My second post, which didn't make sense has been edited. It now makes sense.
  • #8
vaccum filled bubbles of light

if space were only one dimension I would agree about it being made of points but 3 dimensions form a sphere !!!

1 makes a point defining its position
2 a line defining its geometric make up
3 a sphere defining the space it occupies

3 connections make a triangle which is how bubbles connect to form foam

imagine a sphere modelled from triangles in a 3d program then given an iridescent skin

now scale that up or down

and with 3d spheres comes time

time to move around the space or for something to move in that space but movement only takes place within the skin or on either surface like the swirling surface tension as seen on soap bubbles and accounts for mass and gravity
  • #9
another thought

the outer surface is the future, the inner surface the past being dragged along and what is enclosed in between is the present
  • #10
Actually, a point is non dimensional, a line is one dimensional, two dimensions is a plane, and three dimensions is a solid.

All solids must have three dimensions. If it is solid, it has three dimensions.

However....how is it possible for empty space to have three dimensions? How is it possible for an infinite empty space to exist as a given prerequisite for existence?

Physics assumes non-dimensional points make up all the material in a space given to us that has three dimensions. The given space is called Vacuum and it has three dimensions. How can that be? Let’s call the space Nothing, Zip, Zero, Nada. If it’s nothing, how can it have any dimensions?

An even more startling revelation is the concept of nothing is really two concepts, consisting of No and Thing. We can say No and it's meaningless. No is a denial of something. No Thing is a denial of Thing. But we can say Thing alone and it has meaning. So, the most basic form of existence is a thing; and not nothing. Nothing only exists because thing exists. Thing can exist entirely on its own.

In fact, Thing cannot not exist. Thing exists. It is. If it is this thing over here, it is not that thing over there. Therefore, thing has inertia in its concept of existence. It is what it is, therefore, it is not anything else. God called himself “I am what I am”. So the original concept is this: It is what it is. The universe could not have started from nothing because nothing is two concepts, No and Thing.

“Thing”, or “it is what it is”, is one concept, and it has inertia. It is what it is. It has a mass. It is solid. It has volume. It has three dimensions.

Matter has three dimensions. Space is nothing at all. Space has no dimensions.

This is the opposite of what physics teaches and believes. Physics teaches that point particles of matter have no dimension, and that the universe started from a single non dimensional point and exploded into a very handy, very orderly, four-dimensional space time continuum.

That is completely absurd. Instead, it was the primordial matter that had volume and had size, and had three dimensions, and inertia.

I said to myself. “Oh, a point is really a little ball of material, just like we think it is.” “A point has size, volume.” Then I asked, is it like a rock or a piece of metal? Does it have tensile strength? I reasoned, “No. It’s only function is to occupy a place inside of nothing. Therefore it can’t be compressed, but it can easily be pulled apart. It is like liquid.”

This original matter has volume, it occupies a space, it has inertia, and it is liquid. It is surrounded by nothing. The nothing has no space. The matter has space.

Then I remembered the Bible description of the primordial universe. As I remembered it, here was a similar picture to the one I was creating.

“The universe was formless and void and the spirit of God flew over the waves of the abyss.” This describes a huge sea of liquid matter. Most significantly, in a few words the Bible goes to the trouble to say it has abysmal volume. It is not a single non-dimensional point. It is a single point with three dimensions. It's huge.

Now I said, “Divide this sea into two parts, and separate them apart into nothingness that does not contain the concept of three dimensions, or space.”

I did that mentally and had two huge balls of matter. The nothing they were separating into didn’t contain space. So the two seas of matter wanted to come back together, as if they were being sucked back together by a vacuum. If you release the force that is pulling them apart, an amazing thing happens. They crash back together but not immediately. First there is an action, you release the force holding the two gigantic seas of matter apart, then after an interval the two seas crash back together. Time happens.

I reasoned that the two seas would always come back together in the same amount of time, no matter how far apart they are separated. Time, I assumed, is always consistent and is based on a force acting on inertia. The force has to be greater, the further apart they are, in order for them to always come back together in the same time interval. I am a moron. That is when I first learned the Strong Force gets greater the further apart the two points of matter are. That is when I knew I was on the right track.

I said that a string is two points of matter, which have volume, being held apart and being pulled back together by the vacuum. If you exploded the entire sea of matter, you get an uncountable number of droplets, points of space, and they are separated but being pulled back together by the Strong Force. Look at two drops of matter. You have two things, two points of matter, which are two dimensions, and they have volume, and there is a vacuum manifold like a hollow tube sucking them back together. This hollow tube has walls that have no thickness. This is a two dimensional hollow tube that has walls with no thickness. That is the exact physical definition of a string offered by Feynman.
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  • #11
I don't quite see how you can define a point in zero dimensions ?

please explain
  • #12
A point is a place in space. When you describe where a point is, you have to use three dimensions to describe where the point is in space.

But the mathematical point itself doesn't have any volume or size, so it has no dimensions.

When talking about the real structure of space, physics cannot assume an open empty space. An open empty space just can't exist. Space has to be constructured from points. A line has to be constructed from points. The line doesn't already exist so that you can find places or points on that line. The line can't already exist.

So a weird reversal takes place. The space doesn't have size, but the points do. You construct a line with string points that have length. They are like bricks.

When you see it that way, things look different.

For example, when you are studying where a peaking wave is in a pool; and then that wave disappears and another peaking wave appears in another place in the pool; that makes perfect sense to us because we are not looking at the wave but at the water. Yet, if we didn't know the water existed... if we thought the water was a vacuum of nothing, and we saw one wave of real matter appear, then disappear, then reappear somewhere else, that would be a mystery.

If we know about the water, then the actions of the waves are easy to understand.

About space, we don't know that space has a component of matter to it. We think space has three given dimensions and points have no dimension.

Your intiution is right, points do have one dimension, length. But mathmatically, points are said to be zero dimensional.

To edit what you said, slightly...

1 makes a point defining its position
2 a line defining its geometric make up
3 a sphere defining the space it occupies

1 a point has one dimension, length
2 geometry begins to exist when there are two dimensions (squares, triangles, etc)
3 a sphere exists in three dimensions.

Everyone who thinks about something seriously is usually right. You thought a point has one dimension, and it does.

And space really is made of "bubbles". A bubble of space is made of matter and nothing.

The thing to realize is that space has a component of matter. When we begin to see the existence of that matter, we can understand a lot more than we do now.
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  • #13
thanks for that CM

so if everything is made of light and photons have mass couldn't you rearrange einsteins energy equation to suit ?

look at this site and imagine replacing water with light particles in 3d or layered slices of 2d

http://sphericalrobots.universalsuperjet.de/bitfall.php [Broken]
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  • #14
That is a very good model of the way we are told photons fly through space and create images! They fly through space like a lot of little drops. The frequency of the drops, how many drops, or photons, there are in different places gives us images, as they bombard our eyes, or our instruments.

The machine that does the falling drops is a very accurate representation of what we are told is happening. It's real good.

Then physicists say, "Photons aren't really particles, like actual particles, like particles of water. They are just energy waves." They go to a model of empty space, devoid of actual matter. A photon is created at a star. It passes through totally empty space for millions of years, then it manifests itself in your eye or on an instrument. But it was nothing, passing through nothing. And we are supposed to believe that? That is all physics can tell us. Physicists can't really define what they are. They can only say what they do.

Okay, let’s have a different model, but it looks exactly the same. Let's have a line of billiard balls. Hit the ball at the front. It hits the next ball, which hits the next ball. It looks like one ball is passing through the line of balls, so we make statements about it like "It's an energy wave." It manifests itself as a billiard ball at the end of the line, but it’s not really a single billiard ball hurtling through empty space. Instead, it is a chain reaction with a lot of little billiard balls that make up space itself.

Whether it's drop-like particles all hurtling along their individual paths undisturbed by other individual particles, or the idea that space is already full of semi-stationary vibrating points of matter, with actual physical size and mass, it's certainly not empty space.

And when you start to make a model of semi-stationary vibrating points on a billiard table, covering the table with billiard balls, you start to get actual multiple dimensions; because it's easy for the mass of a billiard ball to pass along one line of balls, but when you set up billiard balls covering the table, and try to pass the mass of one ball through that, you find the lines of balls don't always line up the way the energy wants to go.

My first idea is that space is made of many actual particles, but they don't line up neatly. The bottom line is there are six extra dimensions.

My idea of a space filled with actual points of real matter fits with many of the ideas of string theory.
  • #15
I have an idea of 6 spatial dimensions plus one of time

2 sets of 3d + 1 of time

they interchange at superluminal speed essentially switching on and off virtually in the same position and each time they do the universe refreshes to account for movement in it

with your billiard balls

If all of them were exactly the same and connected by black holes through which energy passed but hollow vaccuum filled such that only the outer shell acted as the medium for energy transferrence and all energy was light with mass causing gravity

then you could have non locality given that it is all a connected foam of identical spheres/balls so what one felt in one loacation so to could another

do you get what i mean ?
  • #16

A lot of people try to come up with intellectual ideas about how everything works. I believe it is a lot simpler than that.

My explanation was made after a hard day's work and it was probably hard to understand. I wanted to take a photograph of pennies on the carpet, and show how the pennies on a flat plane only line up in three directions.

The distance from the center of a penny to the center of another penny is a straight line. Here's a photo of how straight lines (Q-Tips) only line up in three directions. Now try to send vibrations through the Q-Tips in a direction other than the three they line up in. The vibrations somehow have to zigzag through the three available directions.


These three limited directions, that vibrations headed in random directions have to zigzag through, become three extra dimensions in this flat plane. It's simple.
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  • #17
Staff Emeritus
Gold Member
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Hevae you tried making squares instead of triangels? That works too. I don't know what deep principle you think you can draw from this.
  • #18
Science Advisor
I foresee a future, a very close one. This thread is headed straight to the theory development forum!
  • #19
that's what pisses me off about this forum !!!

It's like an elitist group who won't help lesser knowing mortals out or submit their own speculations for fear of losing status within the group.

If all the competing quantum gravity/cosmology theories are to be believed there may be only about a couple of hundred people in the world who THINK they know what and how the universe works and within that some aspects of those theories will have to be discarded as BS.

So exactly how does the trickle down process of knowledge infiltrate the masses if not by the sharing of ideas and theories and the asking of questions and where better to do that than than here ?

I see alot of people here looking outside for answers, only capable of explaining that which is explained to them and barely in laymans term.

Whtever happened to original thought, common language and the courage to express those thoughts in a manner that the average person or high school student can understand ? So what if i'm not even right ? I'd still like to know how or where I'm going wrong !

Honestly some of you act like selfish children who take their bat and ball home when you get struck out or won't help others learn the rules of the game preferring instead to mock from the grandstand.

Haelfix, if you don't have anything to contribute just sit back and enjoy the game.

Self adjoint, I don't understand what deep principle a flat plane of connected triangles can provide unless they are made to form a 3d geodesic dome which when connected to others gives us the soccerball patch model.
  • #20
Sam Owen said:
So exactly how does the trickle down process of knowledge infiltrate the masses if not by the sharing of ideas and theories and the asking of questions and where better to do that than than here?

Start with the General Physics forum. If you don't like that maybe the Theory forum. But this forum is just a little bit more specialised.

  • #21
thanks for that Kea sorry for blowing a wee fuse there

I understand the specialised nature of this forum perhaps there should be a specialised olympics for all the regulars

so does CDT, causal sets and Black hole thermodynamics need it's own forum otherwise everything related to those theories is out of place here ?

I 've noticed that each forum have their own set of ususal suspects lurking around and there isn't much cross over and i'm not really interested in the standard physics posters

I like the regulars here I just wish they were a bit more simple with their language and a bit more open with their thoughts, questions and speculations
  • #22
I completely agree with Sam Owen when he was blowing a fuse. He said it all, and said it exactly right. There is only one place to discuss this, and that is here, in the String Theory, LQG, and Brane Forum; because even physicists can't say exactly what string theory, LQG, and branes are, and maybe a discussion between knowlegable people and average people could shed more light on the subject. And this is the only decent Physics Forum on the Internet.

What we may have established is that photons are going in every direction through space. What are photons? What is space? We are told that photons are massless particles and space is absolute nothing. But look at the surface of water. Unlike our idea of space, water is something. It has real mass. And water is given energy from gravity. So every wave is either encroaching on that energy when above the surface; or it is in a negative energy state in a trough.

What water does that is most spectacular is unlike the confusion of a lot of individual particles traveling through space like individual people traveling through a crowded square, the surface of water preserves every wave form that passes through it, no matter how they crisscross or pass through each other. On the surface of water, we have a perfect model of how photons crisscross each other through space. None of them are changed in any way, and they travel at a constant speed.

Okay, suppose space is made of particles of real, actual mass, like little ball bearings, and there is energy like springs between all those ball bearings.

The first question is how do those real bits of mass arrange themselves?

The answer is they organize themselves into the most efficient arrangement: they form triangles, and Loop Quantum Gravity predicts triangles.

Can there be a real matrix of real mass particles? They must have some kind of variable force between them. It’s variable because it changes with distance. A string is defined as mass and elasticity. I don’t think strings vibrate like a violin string back and forth, but they vibrate by getting closer and farther apart.

So we have this matrix that has real mass particles, and some kind of variable energy that makes it work. It is just like the surface of water. But unique to this, the vibrations can only go back and forth from one point to another.

The points in this 3D space line up most efficiently in six directions, which are the only direction the vibrations can travel, which could make for six extra dimensions, plus 3D, plus time, which is ten. Since this model of points, which are actual particles of matter line up in six limited directions, which are like dimensions; since that gives us ten dimensions, precisely as many as string theory predicts, that has to be significant!
  • #23
Crazy Moron said:
And this is the only decent Physics Forum on the Internet.

Was the only ....
  • #24
Science Advisor
Gold Member
Quantify, qualify, give references, repackage and post your theory in the 'Independent Research' forum, Crazy Moron. You are trying to pick a logical argument based on vague generalities, not talking science.
  • #25
Every human activity has its own language. If you want to talk about soccer with people who regularly discuss soccer you have to know the language of soccer. In this case the only differences are a few words, like off-side, goal, corner kick, etc.

Physics has it's own language as well, and a large chunk of it is mathematics. You MUST study mathematics to have meaningful discussions about physics. In particular, if you talk about geometry you need to know about the set of real numbers and the axioms that govern it.

It is really difficult to get a working physicist (not my case) to listen with attention to a theory put forth in a language other than mainstream mathematics. It takes a lot of time to understand a new point of view, or some argument that allegedly contradicts special relativity or whatever.

In my opinion it's easyer, more efficient and more fun to learn the language of you prospective interlocutors to have an audience for your ideas.


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