M theory/string theory limits dimensions to 11?

[Almighty]

Do M theory/string theory limits dimensions to 11?

[ajb]

The quantum theory of a single superstring only works properly in 9+1 dimensions.

 

M-theory which is formulated in 10+1 dimensions has as certain low energy limits a supergravity theory in 10+1 dimensions and then superstring theories in 9+1 dimensions.

[koti]

The quantum theory of a single superstring only works properly in 9+1 dimensions.

 

M-theory which is formulated in 10+1 dimensions has as certain low energy limits a supergravity theory in 10+1 dimensions and then superstring theories in 9+1 dimensions.

Dang ajb. I needed to read the above 3 times to grasp it, due to the lack of commas. Have mercy for us non natives

[ajb]

...due to the lack of commas.

I doubt that is the main issue here. Not that I want to write an introduction to string theory, M-theory and string dualities ;-)

[koti]

I'm serious ajb, can you at least put 1 little comma in there somewhere or rephrase this? :

"M-theory which is formulated in 10+1 dimensions has as certain low energy limits a supergravity theory in 10+1 dimensions and then superstring theories in 9+1 dimensions. "

 

It's a mind bender in its present state for me and Witten is my hero btw.

Edited September 21, 2016 by koti

[ajb]

Well, M-theory is a theory of branes (M2 and M5 where the number refers to the dimension) in 10+1 dimensions.

 

Superstring theories can be seen as certain limits of M-theory and these live in 9+1 dimensions. Another limit is a 10+1 dimensional supergravity theory.

Edited September 21, 2016 by ajb

[koti]

Well, M-theory is a theory of branes (M2 and M5 where the number refers to the dimension) in 10+1 dimensions.

 

Superstring theories can be seen as certain limits of M-theory and these live in 9+1 dimensions. Another limit is a 10+1 dimensional supergravity theory.

Yes, yes, this is clear. In laymen terms M theory unified the 5 superstring theories adding an additional dimension on the way. But I want to understand that initial sentence of yours.

Edited September 21, 2016 by koti

[ajb]

"M-theory which is formulated in 10+1 dimensions has as certain low energy limits a supergravity theory in 10+1 dimensions"

 

Okay, so no-one really knows how to formulate the full theory of M-theory, what we do known is that it should be a theory of M2 and M5 branes.It is also known that these branes can be classically viewed as solitons - so special solutions to the theory - in a supergravity theory in 10+1 dimensions.

 

The string theories can basically be seen as coming from this supergravity theory, in a loose sense.

[koti]

M-theory which is formulated in 10+1 dimensions has as certain low energy limits a supergravity theory in 10+1 dimensions and then superstring theories in 9+1 dimensions.

M-theory which is formulated in 10+1 dimensions has (as certain low energy limits) a supergravity theory in 10+1 dimensions, and then superstring theories in 9+1 dimensions

 

It is certainly a lot easier to read for me. Would that be acceptable ?

 

Edited September 21, 2016 by koti

[ajb]

It is certailny a lot easier to read for me. Would that be acceptable ?

So you want to discuss some English and not science?

[koti]

So you want to discuss some English and not science?

I would prefer discussing science ofcourse (or better put learning science) but it is crucial in my opinion to phrase sentences as simple as possible when dealing with complex concepts.

 

As you were saying - no one realy knows...please continue, this is fascinating.

[ajb]

If you have some questions I might be able to help. But for sure M-theory is not my area of speciality.

[Moontanman]

Well I think (big whoop) that we will find out that dimensions are far more complex than just rolled up tubes or extra spatial dimensions. My thoughts go along the lines that both may make up our reality. I wrote a rather long and boring explanation of my idea, it's here on the site someplace but I can't find it...

[geordief]

If you have some questions I might be able to help. But for sure M-theory is not my area of speciality.

Are those putative /posited extra dimensions interchangeable in the way that our 3 spacial dimensions are?

 

So we are talking "simply" about extra spatial dimensions that are interchangeable and orthogonal?

 

And the +1 is the same time dimension as in our everyday 3D+1 spactime ?

[ajb]

Well I think (big whoop) that we will find out that dimensions are far more complex than just rolled up tubes or extra spatial dimensions. My thoughts go along the lines that both may make up our reality. I wrote a rather long and boring explanation of my idea, it's here on the site someplace but I can't find it...

There are several possible ways of compactification in string theory - look up G2-manifolds, orbifolds and Calabi–Yau manifolds.

 

 

So we are talking "simply" about extra spatial dimensions that are interchangeable and orthogonal?

This is poor choice of wording... anyway you should think of these extra dimensions as being 'spacial' rather than 'temporal'.

 

And the +1 is the same time dimension as in our everyday 3D+1 spactime ?

Yes.

[geordief]

This is poor choice of wording... anyway you should think of these extra dimensions as being 'spacial' rather than 'temporal'.

 

 

 

As they say ,I am "shooting the breeze" here but could those spacial dimensions be described in an analogous way to the way the different characters on a chessboard move?

 

You cannot "mix and match" dimensions ,can you? The movement of those pieces could be referred to as "freedom of movement" which is the terminology employed frequently to describe dimensions.

Edited September 22, 2016 by geordief

[ajb]

... but could those spacial dimensions be described in an analogous way to the way the different characters on a chessboard move?

What is the analogy here?

 

 

You cannot "mix and match" dimensions ,can you?

I don't know what you mean by this... we usually allow changes of coordinates and so we do in a sense mix dimensions (or directions).

 

 

The movement of those pieces could be referred to as "freedom of movement" which is the terminology employed frequently to describe dimensions.

Yes, so in this case strings and branes propagate in more that 3+1 dimensions.

 

Anyway, the dimension of space-time is the number of numbers needed to specify any given point - in standard special or general relativity this is 3 spacial coordinates and 1 temporal coordinate: so 4 numbers in total. In superstring theory we need 9+1..

[geordief]

What is the analogy here?

 

 

 

 

 

Well you are very indulgent to even respond to what is no doubt a silly idea. To try and explain what the analogy might be (in my mind) , in Chess the Rook moves (has freedom of movement in one defined way and one move is 2 squares in any direction followed by one square in a diagonal direction.

 

All the other characters have their "units" and direction of movement defined differently.

 

This can be referred to as a "freedom of movement" but ,as you may be suggesting the analogy may (=surely does) begin and end there.

 

I was "fishing" as well as "shooting the breeze" in that I was hoping that my guess bore some resemblance to the actual theory (with which I only have the slightest acquaintance and which i am sure would be outside my ability to learn about in short order)

Edited September 22, 2016 by geordief

[ajb]

Maybe a better analogy is to think of an ant following a line of honey on the floor. A long as the ant just walks along the line the system is effectively 1+1 dimensional. However, the ant could decide to move off this line, the system is then effectively 2+1 dimensional.

[geordief]

Maybe a better analogy is to think of an ant following a line of honey on the floor. A long as the ant just walks along the line the system is effectively 1+1 dimensional. However, the ant could decide to move off this line, the system is then effectively 2+1 dimensional.

Well was my initial attempt quite close then?

 

"So we are talking "simply" about extra spatial dimensions that are interchangeable and orthogonal?" (post#14)

 

You said the wording was bad but was the description more accurate ? (it might not be difficult to be more accurate than my chessboard"analogy"

 

The extra dimensions posited in these 2 theories are similar in character to the 3 spatial dimensions we are used to.?

 

I thought "orthogonal" was a term widely used as a definition for extra dimensions although the precise definition of "orthogonal " is not one that I know.

 

Does "orthogonal" mean symmetrical wrt to a particular axis at any point along that axis in its increasing /decreasing directions?

Edited September 22, 2016 by geordief

[ajb]

Well was my initial attempt quite close then?

I think your analogy is okay - the thing to keep in mind is the number of numbers needed to describe any point of the space in question.

 

 

n

You said the wording was bad but was the description more accurate ? (it might not be difficult to be more accurate than my chessboard"analogy"

Dimensions are not orthogonal as such. Orthogonality is to do with the local coordinates you chose and then you need orthogonality to be with respect to some metric. In Minkowski space-time of any dimension we have a canonical class of coordinates which are rectangular in the obvious sense.

 

The extra dimensions posited in these 2 theories are similar in character to the 3 spatial dimensions we are used to.?

Yes, in the sense that we have a metric of the right signature ie., (1,1,...,1, -1) or the other way round depending on conventions.

 

I thought "orthogonal" was a term widely used as a definition for extra dimensions although the precise definition of "orthogonal " is not one that I know.

The notion of orthogonal requires metric and then refers to vectors or local coordinate systems. You can pick coordinate systems that are not rectangular.

 

Does "orthogonal" mean symmetrical wrt to a particular axis at any point along that axis in its increasing /decreasing directions?

https://en.wikipedia.org/wiki/Orthogonality

 

Generally orthogonal gives us a notion of two vector being 'at right angles' with respect to each other.

[Strange]

Orthogonal is also used (informally) in the more general sense of independent, which could cause some confusion.

[ajb]

Orthogonal is also used (informally) in the more general sense of independent, which could cause some confusion.

Linear independence of vectors (in a metric space) need not imply orthogonality. However, one can always use the GS-procedure to construct an orthogonal basis given any basis.

 

 

In the other direction, as long as we don't include the zero vector, any set of orthogonal vectors constitutes a linearly independent set of vectors.