Why are there exactly 11 dimensions?

[DaveC426913]

But the base is not arbitrary. The base is the number of dimensions of perturbative superstring theory = 10. The number of physical degrees of freedom is 10-2=8, which gives
2 X 8 + 10 = 26, which is the number of dimensions of bosonic string theory.
Everything fits.

Durr. That's where that number came from. I brought this up (a theory with 26 dimensions) in a thread months ago but could not name it or its source. I got trounced.

 

[DaveC426913]

Why three dimensions ?

Because 3 to binary 11. No more minimal and simple symmetry.
Don't forget Jonn Wheeler's "It from bit"

I'm afraid to ask. So I won't.

Sounds like we're back on the numerology train.
All aboard! Woo woooooooo!

 

[azzkika]

there seems to be little agreement of how many extra dimensions exist, even if they do at all from some posts. has anyone actually drew a picture, i mean we have 3d drawing. if 11 dimensions exist, then can we not make an 11d drawing??

 

[arivero]

there seems to be little agreement of how many extra dimensions exist, even if they do at all from some posts. has anyone actually drew a picture, i mean we have 3d drawing. if 11 dimensions exist, then can we not make an 11d drawing??

Hmm. For instance, a TV screen or a computer screen is usually 6+1 dimensional. It sends to the human receiver information of time (so the +1) and information of six different quantities: R,G,B,luminance,xpos,ypos. And we can perceive all of the six.

 

[Mk]

Hmm. For instance, a TV screen or a computer screen is usually 6+1 dimensional. It sends to the human receiver information of time (so the +1) and information of six different quantities: R,G,B,luminance,xpos,ypos. And we can perceive all of the six.

If you say it that way, why wouldn't mass be a dimension, added on to x,y,z, and t, or anything else?

 

[arivero]

If you say it that way, why wouldn't mass be a dimension, added on to x,y,z, and t, or anything else?

Can you see mass? Or do you infer it from all measurements of x,y,z,t, V(x,y,z,t)? It seems more reasonable to think that the extra dimension is the potential energy, and not the mass. In this way you can keep adding dimensions simply by adding new force fields.

But note that Kaluza Klein theories, in origin. were near of this idea of mass coming from extra dimensions. They compared the massless equation for relativistic energy in five dimensions with the massive equation in four dimensions.

 

[trinity_81]

Any one contemplated the idea of infinite dimensions?

History has shown us that we once believed the universe was a finite size only to discover its size is infinite. We once believed there to only be one universe to now believe there, according to m-theory, to be infinite parallel universes. So why stop there. After all 11 does seem to be an arbitrary number as would any defined number. I wonder how the maths would hold up to this idea.

On another point, physicists tend to put a limit to how small the universe is. Hawking did it now string theorist believe it to be in the ball park of 10-34m(the size of a string). Well I say if the universe is infinitely large then by definition the universe should infinitely small. It’s all relative isn't it?

In closing… Infinity on everything.

 

[SimonA]

To go back to the original (and simple) question, the reason it comes down to 11 dimensions in M Theory is this;

Theorists took the formulas that our research into understanding the nature of the universe found, and used the laws of algebra to merge them together. Out of that came 5 different theories suggesting a solution. All of them suggested 10 dimensions. Then some bright spark tried imposing 11 dimensions on the different theories, and suddenly they all appeared to be the same theory seen from different perspectives.

This of course made those who follow Madonna in Kabbalah happy - their mystics proposed 10 dimensions and a hidden eleventh centuries ago.

But to give them credit for that would be to assume that there is an equivalence between spatial calculations and spiritual perception. We must be very careful about that - it may well be that new evidence suggests just 6 dimensions, and then the people in China will say - we told you so.

In the meantime, it seems as if reality is composed of 3 spatial dimensions, 1 temporal dimension, and several other dimensions of which we understand little. And we can be confident that there is more hard evidence for extra dimensions, than there is for extra universes.

 

[arivero]

Well, you should also check that these people of the China or Kabbalah or whatever have actually said it. Most times, it is interpolation. There is a very famous one in Indian poetry, about the speed of the light, in a old poem... that happened to be copied about ten or fifteen years after the actual measurement of the speed of the light, so the copist did the interpolation probably to show that he was a learned men, aware of modern advancement.

About 11 dimensions, it is wrong to say that they come from M Theory because then it seems to date in the mid nineties, while the supergravity papers come from the seventies. Particularly Cremmer Julia Scherk (D=11) is from 1978, and the research linking strings with supergravity in D=10 predates it a couple years, 1976 or so.

Kaluza Klein extra dimensions were ocassionally examined before, but it was impossible to link them to D=11 without the discovery of SU(3) colour and the SU(2)xU(1) electroweak model.

To go back to the original (and simple) question, the reason it comes down to 11 dimensions in M Theory is this;

Theorists took the formulas that our research into understanding the nature of the universe found, and used the laws of algebra to merge them together. Out of that came 5 different theories suggesting a solution. All of them suggested 10 dimensions. Then some bright spark tried imposing 11 dimensions on the different theories, and suddenly they all appeared to be the same theory seen from different perspectives.

This of course made those who follow Madonna in Kabbalah happy - their mystics proposed 10 dimensions and a hidden eleventh centuries ago.

But to give them credit for that would be to assume that there is an equivalence between spatial calculations and spiritual perception. We must be very careful about that - it may well be that new evidence suggests just 6 dimensions, and then the people in China will say - we told you so.

In the meantime, it seems as if reality is composed of 3 spatial dimensions, 1 temporal dimension, and several other dimensions of which we understand little. And we can be confident that there is more hard evidence for extra dimensions, than there is for extra universes.

 

[SimonA]

About 11 dimensions, it is wrong to say that they come from M Theory because then it seems to date in the mid nineties, while the supergravity papers come from the seventies. Particularly Cremmer Julia Scherk (D=11) is from 1978, and the research linking strings with supergravity in D=10 predates it a couple years, 1976

This quote from Madhusree Mukerjee of Scientific American is the contex I was coming from, before then there was little consensus;

"Today's excitement has grown from the finding that if we postulate the existence of a mysterious M-theory in 11 dimensions we can show that the five competing string theories are actually different versions of the same thing. Like a Roman general surveying the battlefield from the third dimension [on top of a hill], physicists today stand on the hilltop of the 11th dimension and see the five superstring theories below, unified into a simple, coherent picture, representing different aspects of the same thing."

 

[tom.stoer]

As far as I know the 11th dimension was hidden in string theory (old 10d version) because this was just a limiting case of the full 11d theory. I do not understand the following:
- how can we be sure about 11d in M-theory if we do know its basic equations (Lagrangian?)
- could it be that M-theory is again an approximation to some deeper theory?

 

[Saul]

What is a “dimension”?

It is possible to create very complicated mathematical models that have no relationship with the physical world, with electrons, protons, and physical space. John Hogan coined the term “Ironic Science” for the creation of very complicated mathematical models that make no predictions that may have no connection with physical science. “Ironic Science” seems scientific. Intelligent people in the last 20 years have written over a 100,000 “scientific papers” concerning “String Theory”, attended conferences, got advanced degrees, however, after 20 years work the string theorists do not have a “theory”, something that can make predictions.

"String Theory" is a methodology. There is no "String Theory".

The "String theory methodology" may be the end of the mathematical theoretical physics methodology as a means to solve practical physical problems, to advance science. Why do we believe that the "String Theory" Methodology will be successful? Why do we believe practicing the "String Theory" methodology is science?

If we met an advanced alien society that had an answer to what is physical space and what is the relationship of physical space to protons and electrons, it would be possible to know whether “String Theory” is science. “String Theory” could be a kin to alchemy. It is obvious now that we have atomic physics and physics chemistry that the alchemists’ methodology would never have produced a viable practical scientific model.

Mathematical theoretical physics started with the creation of the theoretical entity “space-time”. Prior to the coining of the term “space-time”, physical space, electrons, protons, and so on were the only primitives and time was a term that described how the primitives changed. It is the prior success of mathematical theoretical physics over the competing physical methodology that explains the popularity of the "String Theory" methodology. From a practical standpoint, if a 100,000 papers can be written there is no end to the process, as there are more possible "string models" than there are atoms in the universe, there is no reason for the "String Theory" paper writing to cease.

The analysis technique of constraining the model and then trying to develop a model that matches the physical observations is the physical approach of constructing a model. That methodology would be effective if the correct solution is a model that was constrained to 3 dimensions.

The physical approach is misunderstood and incorrectly believed to naïve. The physical approach is simply a different methodology. The model produced by a physical methodology will likely also be mathematically complicated and may have some mathematical similarities to “string models”, however it is the constraint of the set of all possible models by the physical observations that enables the correct model to be found.

From the “Trouble with Physics” by Lee Smolin Introduction page 15.

“David Gross, a Nobel laureate for his work on the standard model, has since become one of the most aggressive and formidable champions of string theory. Yet he closed a recent conference to celebrate the theory’s progress by saying, “We don’t know what we are talking about…The state of physics today is like it was when we were mystified by radioactivity…They were missing something fundamental. We are missing perhaps something as profound as they were back then.”

On the other hand, if string theorists are wrong, they can’t be just a little wrong. If the new dimensions and symmetries do not exist, then we will count string theorists among science’s greatest failures, like those who continued to work on Ptolemaic epicycles while Kepler and Galileo forged ahead. Theirs will be a cautionary tale of how not to do science, how not to let theoretical conjecture get so far beyond the limits of what can be argued that one starts engaging in fantasy.

From "Not Even Wrong" by Peter Woit page 244

"In his recent book, Susskind admits that he has no plausible idea about how one might be able to derive any predictions from string theory. The surprising thing is that he and other prominent theorists don't see this as a reason to give up on the theory (my comment what theory), but instead choose to believe that the theory must be true (my comment again, what theory), even though it can't predict anything.

 

[SimonA]

Yes some good points, and I have read "the trouble with physics". I don't think we can ignore the maths behind string theory, but the trouble is that we are so far away from understanding the most basic elements of space, time and quantum particles at an epistemological level, and so all the maths is hollow.

It's not good enough to say that non-locality and entanglement etc "just are". They are pointing to characteristics - fundamenal properties even - of the nature of the environment in which we exist. We simply don't understand the basics. And all the thousands of papers written about such highly specialised areas of what we think we understand ("almost") hide this reality in an almost fatal way.

Our education system needs to produce more generalists, and less specialists. Without an understanding of the history of science and philosophy, researchers tend to be blind to the way people in any time always think they understand close to everything, with just a few untidy corners to fix/confirm.

The separation of science from philosophy at a fundamental ontalogical level has also done harm to both - accelerated by the drive to empiricism in a way that breaks everything down so far that it becomes something different from what the nature of the whole is. Each cell in a living creature is like a city by itself. It has roads, it has power stations, it has a city wall, it has a system for controlling who goes out and who comes in. It's amazing! But studying a certain persons cells will never be the same as meeting that person. And I'm not taking about the genes versus environment issue. There are things about looking at wholes that are lost when looking at their parts in ever more detail. Once you kill the goose, you may never again get a golden egg.

 

[Saul]

Yes some good points, and I have read "the trouble with physics". I don't think we can ignore the maths behind string theory, but the trouble is that we are so far away from understanding the most basic elements of space, time and quantum particles at an epistemological level, and so all the maths is hollow.

I agree.

One of the last people to make progress using deep fundamental analysis was Faraday. I started researching the origin of modern Field Theory and Relativity starting with Faraday's work. I was quite surprised that Faraday's models do not agree with Maxwell's mathematical representation. Maxwell has aware of the discrepancy and noted that he lacked the mathematical modeling tools to model Faraday's model of matter and space.

Faraday analyzed the physical observations using deep logical parsing, looking at the observations as logical clues as to what was the true/fundamental nature of matter and space. He retained competing models and would come up with new experiments to help reduce the number of fundamental models and to refine the fundamental models he would carrying through the process.

For example. The fact that electrons move at right angles to the "magnetic field" was Faraday's discovery. Ampere and others worked on the problem from a mathematical standpoint and assumed that as electrostatic force and gravity were center based forces that the magnetic force should also be center based.

Why electrons move at right angles to the magnetic field or why electrons move at all is not known. Faraday looked at the complete set of observations as hints as to what is the true nature of matter and space.

Faraday thought of matter as a field of force, rather than an entity that projected force or carried force.

He thought of conservation of force, rather than conservation of matter and energy, as he believe observational evidence indicated that energy and matter where not separate entities. Likewise he believed matter to be part of space rather than separate from space. Curiously the experiments at the beginning of the last century show that to be true but somehow the experiments are incorrectly interpreted that space is empty. Faraday would avoid the fatal mistake (if the objective is to solve a problem that has a unique solution) of picking an incorrect interpretation as he carried all reasonable interpretations (models) through the process, including flawed models.

It seems odd that we will logically accept the "String Theory" methodology that has as many possible models as there are atoms in the universe but decide that it is irrational to consider models where space is full rather than empty and to investigate constrained models.

Faraday experimented with the conversion of one "force" to another which he believed was possible if matter was a collection of force rather than a force center and electricity was movement of the dynamic force (matter). The conversion of matter to energy and energy to matter is consistent with Faraday's model.

Faraday thought matter was dynamic not static which is the essence of the quantum theory and modern atomic theory. The atom cycles through a complex time varying pattern. Depending on where it is in that pattern determines how it reacts which explains why the probabilistic addition is required to correct for an assumed static model of matter. Chemical and atomic bonding are determined by how the time varying entities interact.

Faraday's method is by experiments to come up with a set of possible fundamental models or basis for the new model. The mathematical model would then follow rather than lead. The ultimate mathematical model is likely quite complicate, however, it is fundamentally connected or correct when compared to physical space and matter.

It is interesting to compare Faraday's method to the "String Methodology". The String theorists are approaching the problem from a mathematical standpoint. The addition of extra entities or dimensions would make the problem very, very difficult to solve, if the extra entities and dimensions do not exist physically.

As it is a fact that the "String Theory" methodology has not led to a single theory in 20 years, it seems it would be logical to consider approaching the problem using an alternative methodology.

 

[SimonA]

I agree with the extra entities being unnecesary, certainly in terms of "dark" theories.

However, I don't see any evidence of a desire to understand. Just an aversion to string theory. Is that fair ?

 

[Saul]

I agree with the extra entities being unnecesary, certainly in terms of "dark" theories.

However, I don't see any evidence of a desire to understand. Just an aversion to string theory. Is that fair ?

It is not possible to prove the "String Theory" methodology will not lead to a theory. It has not as of yet, there is no "String Theory". We use the words dimension and string, however, the methodology is the construction of an astronomically large set of mathematical models, that may have absolutely no connection with the physical world.

Is it possible that the development of the "Set of all String models" (there are no string theories, as of yet) is Ironic Science a kin to alchemy, in that the string methodology will never lead to the correct solution? I believe it is possible. My question is there another methodology to approach the problem? And if there is why has it not been applied? Is there a logical barrier or an aversion which is blocking its application?

From the “Trouble with Physics” by Lee Smolin Introduction page 15.

On the other hand, if string theorists are wrong, they can’t be just a little wrong. If the new dimensions and symmetries do not exist, then we will count string theorists among science’s greatest failures, like those who continued to work on Ptolemaic epicycles while Kepler and Galileo forged ahead. Theirs will be a cautionary tale of how not to do science, how not to let theoretical conjecture get so far beyond the limits of what can be argued that one starts engaging in fantasy.

From "Not Even Wrong" by Peter Woit page 244

"In his recent book, Susskind admits that he has no plausible idea about how one might be able to derive any predictions from string theory. The surprising thing is that he and other prominent theorists don't see this as a reason to give up on the theory (my comment what theory), but instead choose to believe that the theory must be true (my comment again, what theory), even though it can't predict anything.

I am criticizing the "String" methodology because its acceptance has stopped the alternative physical approach.

The aversion is to the discussion and the analysis of the observations using constrained models which is the essence of the physical methodology. People incorrectly believe the physical methodology is naive, because of the failures at the turn of the century and the success of the theoretical approach. The word "aversion" is an emotional rather than a logical decision.

In all other fields of science, new models are constructed using a physical methodology. For example, in biology or paleoclimatology one does not change the "laws of physics" when there is new unexplained phenomena. The phenomena must be explained by a constrained model.

The problem situation in physics is there is no fundamental model. There are a set of incompatible very complex curve fitting models and there are phenomena such as the galactic rotational anomaly or the "quantum" anomalies that do not have an explanation. There are place holder theories but they have emerged ad hoc.

 

[SimonA]

It would be great if more people stepped back more like you do. We have too many highly specialised theories in modern physics, often with little rational basis, and often contradictory. Because they are so far away from a rationed basis (as opposed to mathematical speculation around imagined variables), it's impossible to verify one over another. It's not just testability that's missing - it's a lack of fundamental explanatory powers.

Like you mentioned, faraday is a great example of someone who rationalised the basics. The only question I have is whether it's possible to rationalise all the branches of physics that now exist, and all the reams of evidence and pseudo evidence, into something more fundamental ? Or are we now condemed to delve deeper and deeper into string theory and loop gravity etc, until at the far end of one a few pieces fit together and allow us to deconstruct the theory backwards into a coherent rational basis. It seems the wrong way around, but the way peer review etc works nowadays, I suspect it's the only way that has a chance.

 

[arivero]

I am criticizing the "String" methodology because its acceptance has stopped the alternative physical approach.

In your support, it could be argued that most of the important results of string theory were done in the seventies, before the so-called "string revolutions". At that time, string theory still was keeping a physical approach, from its roots in the theory of strong interactions.

 

[Mgt3]

The more you learn about this stuff, the more it appears as though theoretical physicists have been making ad hoc equations and justifications for string theory over the past 20 years without any empirical verification. More frightening is that these bodies of speculation - they cannot be called theories - are presented to the general public as if they are supported by observation.

 

[DaveC426913]

More frightening is that these bodies of speculation - they cannot be called theories - are presented to the general public as if they are supported by observation.

I guess that depends on your idea of "...presented to the general public..."

I am not a scientist; I am merely a science enthusiast. I read layperson books on string theory. I have never gotten the impression that anyone thinks they are truly theories, born out by observation. My reading always talks about how unprovable or unfalsifiable string theory is. Any amount of due diligence into the subject will reveal this, IMO.

I'm not sure it is even meaningful to talk about how string theory is "...presented to the general public..." at any farther arm's-distance than these lay-person's books. Any farther removed (newspaper articles? TV shows?) and you lose any meaningful learning.

 

[Naty1]

ok so maybe "string hypothesis" would have been a better name but even cursory reading reveals string theory is based on perturbative (approximate) math, is incomplete even by string theorists standards themselves, and the basic underlying principles, which we assume are there, remain obscured. So far it has no proven to be the magic bullet once envisioned, er, twice, counting the frist and sec ond "revolutions"...

 

[Naty1]

Post 38 mentions:

... All of them suggested 10 dimensions. Then some bright spark tried imposing 11 dimensions on the different theories, and suddenly they all appeared to be the same theory seen from different perspectives.

The "bright spark" was Ed Witten (Princeton) who was able to go beyond the approximations of the five basic string theory approximations and show that an additional, or tenth, space dimension had been missed in earlier approximations...so what appeared to be five different string theories could be "unified" with an additional space dimension...and to add to the complexity it was discovered that p dimenisonal objects or p-branes were also embedded in the theory and that the tenth space dimension does not have to necessarily be much smaller than the others. Lisa Randall (Harvard) and collaborators have interesting theories on large size dimensions. (described in non mathematical tems in her book WARPED PASSAGES).

 

[twofish-quant]

I think of string theory as something like medieval theologians trying to logically prove the existence of God. Yes it turns out that you can't logically prove the existence of God, but you don't know that until you spend a lot of time and effort trying and not getting anywhere.

 

[DaveC426913]

I think of string theory as something like medieval theologians trying to logically prove the existence of God.

Well, string theory had once been described by some as a piece of 21st century mathematics that fell into the hands of 20th century mathematicians...

 

[Mgt3]

Well, string theory had once been described by some as a piece of 21st century mathematics that fell into the hands of 20th century mathematicians...

My hunch is that physicists are going to continue spinning their wheels as long as they keep trying to find a theory of everything that attempts to explain a finite universe. It's not going to happen. The universe (or multiverse if you prefer) has to be infinite.

 

[twofish-quant]

I can explain why 11 dimensions.

Let's go back to the standard model. You have three matrices that describe the forces in the universe. A one dimensional matrix that describes EM. A two dimensional matrix that describes the weak force. A three dimensional matrix that describes the strong force. Now you are a theorist, and you see that gravity is described by a four dimensional matrix. So the logical thing to do is to lump all of these matrices together and get a 10 dimensional matrix. And you argue that the extra six dimensions that describe all of the forces are just tiny little dimensions so 1+2+3+4 = 10. And you end up with a nice elegant theory that quite nicely seems to describe all of the forces in nature.

Except for one little detail...

You have all of the forces in your 10 dimension matrix, but you don't have any matter... Hmm... it turns out that you can try to fix this problem by adding one more dimension which turns a force into matter and matter into forces. So this is where you get 11. Now the only problem is to then look at the big matrix and then take a sledge hammer to it until you get back the standard model.

Now in 1980, it wasn't obvious that if you think about it long enough you'll come up with neat math trick for getting the standard model out of this 11 dimensional theory. But people have been trying for a lot of years, and no one has getting it to work...

 

[SimonA]

The funny thing is that string theory posits billions of possible realities, and theorists tune it based on the standard model. And then all theorists seem to invent multiple universes to explain the strange fact that goldilocks porridge is perfectly warm.

 

[Mgt3]

The funny thing is that string theory posits billions of possible realities, and theorists tune it based on the standard model. And then all theorists seem to invent multiple universes to explain the strange fact that goldilocks porridge is perfectly warm.

I don't like the term multiple universes, the "multiverse" should be the Universe, and each little "universe" should be considered spatial regions. Let's face it, in an infinite universe an infinite amount of events will occur. Nobody is inventing universes.

 

[SimonA]

I don't like the term multiple universes, the "multiverse" should be the Universe, and each little "universe" should be considered spatial regions. Let's face it, in an infinite universe an infinite amount of events will occur. Nobody is inventing universes.

give me one single piece of evidence that there is more than one universe. "spacial regions" is nonsense in terms of dimensionality.

 

[DaveC426913]

give me one single piece of evidence that there is more than one universe. "spacial regions" is nonsense in terms of dimensionality.

It is a hypothesis. No one is suggesting there is evidence that there is more than one universe. The MWI is another such hypothesis.