String Theory: Why not 3d+1 Dimensional?

My understanding is the formulation of string theory requires n-dimensions for the satisfying degrees of freedom of a string. However, why is typical 3d spacetime insufficient in providing the appropriate degrees of freemdom? Is there any functional model of string theory which doesn't implement extra dimensions?

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Other people could maybe answer this better than I can. But the general idea is that string theory has an "anomaly", an instability, that makes it unusable for describing physical systems. However in universes with special numbers of dimensions-- such as 10 or 26-- the mathematics happen to come together just right such that the anomaly "cancels" and the theory becomes usable. String theory therefore "predicts" that the universe has 10 or 26 or such dimensions, because string theory is not functional in other numbers of dimensions.

String theory with an "incorrect" number of dimensions is called "non-critical" string theory and some people do use it. Because of the anomaly, non-critical string theory cannot be used as a "theory of everything" for the physical universe, which is what people really want to use string theory for. But non-critical strings can still be interesting and useful as mathematical tools. For example ADS/CFT works with non-critical strings.

Sounds like days are numbered for string theory. Adding extra dimensions to make a theory work would seem like a contrivance.

arivero
Gold Member
Sounds like days are numbered for string theory. Adding extra dimensions to make a theory work would seem like a contrivance.
Not so; the problem with string theorists is that they are too literal: they interpreted their objects as being gravitons, Newton coupling, extradimensions and so on... But it is possible for the extra dimensions to be just an artifact.

Not so; the problem with string theorists is that they are too literal: they interpreted their objects as being gravitons, Newton coupling, extradimensions and so on... But it is possible for the extra dimensions to be just an artifact.
But it is possible for the extra dimensions to be just an artifact.

Metasymmetry idea explain why 3:1 is fundamental symmetry of the Universe.Not 3+1 but 3:1.

Metasymmetryis symmetry between discrete and continue symmetry.

Now to Methasymmetry. If we try to represent discrete symmetry and continuous symmetry with minimal means by using at least two symbols, what should we do? We can use signs 0 and 1 . Then the minimal discrete symmetry may be represented as 10 or 01 and minimal continuous symmetry as 11.In this case, to represent continuous symmetry we used some APPROXIMATION without which our reasoning would be impossible. Now, going back to symmetry between the discrete and the continuous we may use representation of one version as 10 & 11.

What can be said about Methasymmetry now? A general conclusion is as follows: the ratio of the total number of zeros (unities) to that of unities (zeros) makes up certain invariant ratio of 3:1 or 1: 3. This is the numerical measure of Methasymmetry.

I call this effect Metasymmetry.

In Nature we often come across the ratio 3:1, or 1:3, the sequence being of no importance:

1. Space is 3-dimensional and Time is 1–dimensional.

2. Only 3 elementary particles are stable with a half-integer spin (proton, electron, neutrino) and 1 is stable with an integer spin (proton),

3. 3 of 4 fundamental interactions (strong, electromagnetic, weak) are relatively closed by their intensity magnitude but are greatly different from gravitational Again the 3:1 ratio.

4. In the Standard Theory of weak electric interaction bosons (W+, W-, Z) have a mass but a proton does not. Again we have the 3:1 ratio.

5. Beta decay where 1 neutron converts into a proton, an electron and a neutrino. Again the 3:1 ratio.

6. Mmin u-quark/Mel+ 1.5Mev/0.51 Mev = 3:1 ratio.

3:1 may be the fundamental symmetry of the Universe?

Metasymmetryis symmetry between discrete and continue symmetry.

Now to Methasymmetry. If we try to represent discrete symmetry and continuous symmetry with minimal means by using at least two symbols, what should we do? We can use signs 0 and 1 . Then the minimal discrete symmetry may be represented as 10 or 01 and minimal continuous symmetry as 11.In this case, to represent continuous symmetry we used some APPROXIMATION without which our reasoning would be impossible. Now, going back to symmetry between the discrete and the continuous we may use representation of one version as 10 & 11.

What can be said about Methasymmetry now? A general conclusion is as follows: the ratio of the total number of zeros (unities) to that of unities (zeros) makes up certain invariant ratio of 3:1 or 1: 3. This is the numerical measure of Methasymmetry.

I call this effect Metasymmetry.

In Nature we often come across the ratio 3:1, or 1:3, the sequence being of no importance:

1. Space is 3-dimensional and Time is 1–dimensional.

2. Only 3 elementary particles are stable with a half-integer spin (proton, electron, neutrino) and 1 is stable with an integer spin (proton),

3. 3 of 4 fundamental interactions (strong, electromagnetic, weak) are relatively closed by their intensity magnitude but are greatly different from gravitational Again the 3:1 ratio.

4. In the Standard Theory of weak electric interaction bosons (W+, W-, Z) have a mass but a proton does not. Again we have the 3:1 ratio.

5. Beta decay where 1 neutron converts into a proton, an electron and a neutrino. Again the 3:1 ratio.

6. Mmin u-quark/Mel+ 1.5Mev/0.51 Mev = 3:1 ratio.

3:1 may be the fundamental symmetry of the Universe?
Unless I am very much mistaken, the number of intelligible, insightful facts contained in this post is approximately zero.

Perhaps someone would wish to delete it?

Unless I am very much mistaken, the number of intelligible, insightful facts contained in this post is approximately zero.

Perhaps someone would wish to delete it?
I would say that approximation is good to at least 3+1 decimal places.

spinning wheel in empty universe

lets think(modern day einstein-yours truly)--If we took every last piece of matter out of the total universe;and out of all other conditions of matter; in the same universe-then- add---one wheel (3 feet dia)--install it in the empty universe-spin it.OK.--is it spinning?-----(no other matter to relate to it--)--is the wheel connected to any kind of time?-what would time have to do with it?--would time exist? does it exist now in this universal soup-really no difference----james green xi

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have to think of gravity as a extremely weak lasor-it is being projected by the gun(4 dimention space) which is reflecting back into our dimention as the weak force(always helps to know how to spell dimention in these cases) which isnt the case here-james green xi -string is for dreamers-

there is no existing universe or anything else existing for us to consider---to describe the world we think we experience-1-there is absoultly nothing-never was -never will be-and 2-in the condition of nothing(which by the way has nothing to do with whats called time) there is no boundrys(why we see no boundrys when we look out for one) we are ca-ught up in a opposite positive-which is a equal opposite of nothing-a flux of sort-which as we see it as existance-our brains try to analize it-naturally-we dont have to try to explain it through some silly mathmatical theory-we do not exist-we feel we exist -feeling is much like the theory of time
(it has no duration) or no instant either-and no past or future either time dosent exist -a feeling dosnt exist(basically when everything may poof back to equal nothing-or not no difference)

Did you do a lot of drugs or something, or do you always make this little sense? Did you really just use the phrase "equal opposite of nothing"?

"Silly mathematical theory"? Are you kidding? Do you know how much our "silly" theories have done for society so far? The fact that you are typing your inane messages is due to a silly theory. Oh wait, I just argued against myself.

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no-not on drugs-hey you got it-equal opposite of nothing- a serious theory-have to be open to get it-some major ideas in phisics-such as big bang where pressure built up from void and exploded into an all universe-and matter came from a hole in the void-is widely accepted-and is basically insane,-equal opposite of nothing-theory could win a peace prise-in fairness are put foward to make us think-IF IM asked to I will quit posting-einstein was thought of as a nut in his day by some-thanks for kindness for posting reply!!

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it may that caculations may not be able to explane the universe even though they are amazeing. in some ways math is an affliction-and one demintional-one sided and a waste of time for absolute solutions-a problem for the human brain

it is possible that a human cant see a (total solution ) it may be there and we may be looking at it-and seeing many variables--look at this symbol----popopop----do you read it pop--o--pop-or do you read it po-pop-op-- or do you read it popo--pop if you dont get this one may not have enough insite-to understand the equal-opposite to nothing theory-officially put out by jamesgreen xi

Hmmm... well, this thread is already in its coffin. Now I just need to find some nails...

I want to see Motl write a 1000-word post on this thread and how it is a perfect example of crack pottery.

kdv
I want to see Motl write a 1000-word post on this thread and how it is a perfect example of crack pottery.
The OP had a very good and legitimate question. The first responder made an effort to provide a good answer. The rest was rubbish.

I still think that the OP deserves to have more explanations and the input of more (serious) people. It's a very interesting fact that a quantum anomaly restricts the number of spacetime dimensions and I would myself love to see more discussion on this from knowledgeable people. The only way I know to get this result (for the bosonic string) is buried under so much maths that the physical interpretation is completely obscure.

Unfortunately, few string theorists visit these pages so it's hard to have good discussion on this topic. The vast majority of the posts are on sociology (the people doing the physics rather than physics itself), not physics and when it's on physics, it's almost exclusively on non-string theory (especially lqg) approaches. Anyone knows of a good forum where string theory is discussed at introductory and intermediate levels?

Demystifier
Gold Member
The OP had a very good and legitimate question. The first responder made an effort to provide a good answer. The rest was rubbish.

I still think that the OP deserves to have more explanations and the input of more (serious) people. It's a very interesting fact that a quantum anomaly restricts the number of spacetime dimensions and I would myself love to see more discussion on this from knowledgeable people. The only way I know to get this result (for the bosonic string) is buried under so much maths that the physical interpretation is completely obscure.

Unfortunately, few string theorists visit these pages so it's hard to have good discussion on this topic. The vast majority of the posts are on sociology (the people doing the physics rather than physics itself), not physics and when it's on physics, it's almost exclusively on non-string theory (especially lqg) approaches. Anyone knows of a good forum where string theory is discussed at introductory and intermediate levels?
I agree with every word you say.

kdv
I agree with every word you say.

Thank you. This means a lot given that you are one of the posters that I have the most respect for. And I have learned a lot from your papers (I still have some questions about things you discussed in some of your papers that I will eventually post when I find the time!)

The OP had a very good and legitimate question. The first responder made an effort to provide a good answer. The rest was rubbish.
Yes I must agree here. To the OP we simply don't know. Given the models used in string theory it appears based on the math the only way for string theory to be physically stable is to assume extra degrees of freedom. String theory must assume extra spacial dimensions, rather than mathematical artifacts, because of the physical status attached to the concept of strings. Perhaps ultimate a good model can be built from it but that does not mean the ontology is correct or even meaningful. String theory is not a part of the standard model. More than a few have serious objections that string theory will only overcome with testable predictions yet not achieved.

In a more general sense we don't nor can we know for sure how many dimensions are required for a complete theory. Even if we had a complete model that described multi-dimensions beyond 3d+1 we can't be sure an equivalent 4d version can't be developed in some cases. The standard model is a 4d theory.

Unfortunately, few string theorists visit these pages so it's hard to have good discussion on this topic. The vast majority of the posts are on sociology (the people doing the physics rather than physics itself), not physics and when it's on physics, it's almost exclusively on non-string theory (especially lqg) approaches. Anyone knows of a good forum where string theory is discussed at introductory and intermediate levels?
Although I personally find lqg much more interesting than string theory (that is why I read this forum ) I too am curious whether there exists any forum or discussion group suitable for asking string theory questions in. There is that sci.physics.strings group but it seems to have been dead for a long time, the one time I attempted to post a question there I got no response.

It's a very interesting fact that a quantum anomaly restricts the number of spacetime dimensions and I would myself love to see more discussion on this from knowledgeable people. The only way I know to get this result (for the bosonic string) is buried under so much maths that the physical interpretation is completely obscure.
So, the math here is well beyond me as well. But! In my generally-futile attempts to understand what string theorists are saying, something I've consistently noticed about string theory is that even fiendishly complicated effects in string theory often turn out to be possible to describe in very simple terms when described in terms of some topological property of the background geometry. (Of course, topology is itself so complicated that this may not give much of a better intuition of what is happening!) As far as I can tell the only reason why these simple topological descriptions of string situations tend to not get mentioned more often is because they are generally not the most useful way of describing things if one wants to do calculations. But, if you catch string theorists off guard they will sometimes leak them .

I bring this up because Urs Shreiber posted an interesting thing in a recent discussion on Not Even Wrong:

...Bosonic 2d CFTs of central charge 26 correspond to effective target spaces which are 26-dimensional manifolds only in a tiny subset of the space of all such CFTs, namely those that are entirely of the naive sigma-model type with large flat dimensions.

Supersymmetric 2d CFTs of central charge 15 correspond to effective target spaces which are 10-dimensional manifolds only in a tiny subset of the space of all such CFTs, namely those that are entirely of the naive sigma-model type with large flat dimensions...

So perturbative string theory does not predict that spacetime is 10-dimensional. What it does predict (essentially as its fundamental hypothesis!) is that spacetime is the effective target geometry of a 2dSCFT of central charge 15. That’s all.

10-dimensional manifolds appear here only in the most simple minded examples. Claiming that string theory predicts 10-dimensional spacetime is exactly like claiming that general relativity predicts flat empty Minkowski spacetime. No, it does not. This just happens to be the most simple solution that comes to mind...
So, why is this interesting? Well, CFT is Conformal Field Theory, which is a tool important for doing calculations in string theory. I am not clear on its exact use but google turns up lots of statements like:

the perturbative expansion of string theory happens to be given by 2D CFT
(Incidentally the wikipedia article on non-critical strings, which you may want to read, kind of makes it sound like when we talk about the "2DCFT" of a string theory, we really just mean the worldsheet.)

Meanwhile, Wikipedia describes "Central Charge" like:

In theoretical physics, a central charge is an operator Z that commutes with all the other symmetry operators... In string theory, in the first quantized formalism, these operators also have the interpretation of winding numbers (topological quantum numbers) of various strings and branes.
So, it sounds like Dr. Shreiber's hinted here at a way of understanding, without having to understand the whole messy anomaly cancellation thing, exactly what property it is that ultimately makes 10 an okay number of dimensions for a string theory background geometry, but not 4: Specifically it sounds like it is required to be using a 2DCFT with a central charge (winding number?) of 15, and ten dimensions is the easy way to do that.

...So, I don't know if this helps or just makes things more confusing! But if I were deadset on understanding why some numbers of geometry are acceptable for string theory and not others, I would maybe focus on trying to understand on exactly what the central charge of a 2DCFT is and why it makes a difference for that central charge to be 15.

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Haelfix