Where are the missing dimensions?

[LuckyNate]

I've heard that there can be said to exist 11 dimensions of space and time, only 4 of which are perceptible to us directly. My question is this, is it possible that these extra dimensions are just collapsed gravitationally, and if so could this account for the apparently weak force of gravitational attraction that prevents it being unified with the other 3 forces? I know a bit about these topics, but I haven't been lucky enough to study the requisite mathematics to even begin to figure this out mathematically. I'm mainly wondering if this idea has already been broached, or if not can someone attempt to refute it?

I Like Discussion!
LuckyNate

 

[Forestman]

It is believed by people that study string theory that the extra dimensions have been shrunk and compacted into what mathematicians call a Calabi Yau manifold. These manifolds would be very tiny (much, much, smaller than an atom) and exist in each point in space.

In one idea involving string theory our four dimensional universe floats in a higher dimensional space. Anyway, since the strings that make gravitons are closed and form loops these strings would not be bound to our universe, and would be able to just float off. Making gravity very weak. Strings that did not form loops on the other hand would be bound to our universe by their ends.

 

[LuckyNate]

Other 7 is fractal with H_D\approx0 I'm sorry.

ok now if I only knew what H<sub>D stands for, or how a dimension can be 'fractal' this might actually be information instead of random letters and numbers. Again I'm not a mathematician, just an independent scholar by hobby.

As far as the Calabi Yau manifold and string theory go, I am aware of this idea, yet I don't think that this model has ANY experimental or observational data that can confirm or deny this idea in any way. Is this 11 dimensional model ONLY used in string theory and similar models? If so, why? does the standard model NOT HAVE ROOM for all the dimensions, or are the extra dimensions 'needed' to make the string theories work? Why are the curled dimensions preferable to expanded ones we can't feel, or some other configuration? What data points to these 11 dimensions being extant in the first place?</sub>

 

[_PJ_]

I can't comment on the "Hausdorff Dimension", but with regards to the 11 dimensional spacetime of string and "M"Theories:

The concept of folded/compactified (what's wrong with "compact"?) dimensions is based on a boundaryless, finite spacetime. Typically, something like the 2D surface of a 3D torus, but enviosioned in a higher dimensional spacetime.

In considering such geometries, though, particularly within the advent of string theories, the reasoning behind the refinement to exactly 3+1+7 dimensions is born from the need to break symmetry of the E8xE8 group to resolve gluons and electroweak force. Only the E8xE8 group of heterotic strings encompassed gravity in a stable, ten-dimensional spacetime.
To reconcile the neceessary asymetry for the strong and weak forces, required six of these dimensions to be compacted. The reasons for this are closely defined by observed chirality, mass, and topological considerations.
The process is painstaking, and still has many formulae that cannot yet be fully solved, although in a methodical approach, starting with the lowest dimensionality where all elementary objects are bosoinic and chiral symmetry is ratified, there are 4n+2 dimensions. So at n=0, we have 2 extra dimensions. Clearly, this is too few, but the next, when n=1 yields six.
To understand more of thew reasoning behind this, the topology of the dimensions is defined by its 'Euler Characteristic'. The Euler characteristic of the orbifold Calabi-Yau) space determines the generations of fermionic objects, such as neutrinos. Since there are, to the best of our knowledge, three such generations, only certain Euler-characterised Calabi-Yau spaces are valid for describing the observed universe.
String theory in particular contains a much-needed property in defining this description of spacetime wherewby closed-loops can become 'trapped' only by topologies with "holes" (or singularities) and allowing for effects of the curled-up (compact) dimensions manifest effects in our expanded observable spacetime.

Roger Penrose' Twistor space is also based on a ten-dimensional spacetime, and bears many similarities in terms of interaction with string theory, although not based on extended one dimensional objects. Penrose makes use of complex dimensionality in what he terms 'twistor space', where Twistors are complex dimensional objects that can form vast networks which themselves define spacetime geometry and bridge the gap between local and non-local effects.

The 11th Dimension is added only where the development of unified string theories gives rise to brane theories or M-Theory, where the eleventh dimension is a higher, expanded spatial dimension in which separate "brane" universes reside.

 

[Naty1]

My question is this, is it possible that these extra dimensions are just collapsed gravitationally, and if so could this account for the apparently weak force of gravitational attraction that prevents it being unified with the other 3 forces?

unlikey that the collapse is caused by gravitation...it's too weak... it's not the strength of the force that prevents unification...quantum gravity is an approach to combine GR with quantum mechanics...but is still a work in progress...

a good non mathematical discussion is in Lee Smolin's THREE ROADS TO QUANTUM GRAVITY

There is a LOT missing before we can unify all the forces...
The standard model of particle physics is not one model, but rather a hodge podge of different theories and observational facts...for example nobody has any means to predict either the strength of any forces nor the mass of any particles nor the charge strength of such particles...those are all inputs from experimental measurement.

And likewise nobody has a theory of why some dimensions might still be curled up while others are "big"...

 

[_PJ_]

And likewise nobody has a theory of why some dimensions might still be curled up while others are "big"...

There are theories, but they are obviously based on conjecture and assumptions since the concept of compact dimensions and higher dimensions are purely imaginary at present.

 

[reasonmclucus]

The idea of other dimensions is difficult to understand because our brains are programed at an early age to think of dimensions as something like the Euclidean dimensions of length, width and height. We need to look at dimensions in the broader sense as variables. The Euclidean dimensions really can only explain the amount of space an object occupies and the distance from some reference point. These dimensions cannot explain gravity. the moon is smaller than the Earth and has less gravity. The Earth is smaller than the sun and has less gravity, but a black hole smaller than the moon would have the gravity of many suns.

the Euclidean dimensions cannot really explain energy in general so forms of energy may be dimensions. The spin of subatomic particles might also be considered as dimensions.

 

[LuckyNate]

These dimensions cannot explain gravity. the moon is smaller than the Earth and has less gravity. The Earth is smaller than the sun and has less gravity, but a black hole smaller than the moon would have the gravity of many suns.

I don't think anyone was making the claim that the 'size' or 'dimensions' of an object or the lack thereof determines, or describes, or explains the force of gravity, rather the implication is that the unseen higher dimensions may be 'hiding' some of the gravitational force.

It's true that the moon is smaller in size than the earth, and displays a weaker gravitational force, but these 2 facts are totally unrelated, as gravitational attraction is the product of 2 objects' MASSES and not their SIZE. The difference in the SIZE is the result of the objects' DENSITIES and not of their masses. A good example of this is the following, which has more mass, a kilo of LEAD or a kilo of FEATHERS? The correct answer is that they both have the same MASS, yet the kilo of feathers is BIGGER because of the lower DENSITY. The lead exerts an EQUAL gravitational attraction on the feathers that the feathers exert on the lead.

Also a black hole can be as massive as 1.5 suns or more, not that of many suns by necessity, and in the case of so-called 'primordial' black holes the mass can be much lower.

What I am really driving at is this 'WHY IS IT PREFERABLE TO SAY THAT THE DIMENSIONS WE CANT SEE OR FEEL ARE CURLED UP, RATHER THAN JUST NOT SEEN BY US?'

 

[edearl]

Is Occam's razor being applied to hypotheses such as string theory? The idea of 11 dimensions most of which are curled up smaller than an atom, with a multiverse of 10**500 universes having many clones of each person seems a bit far fetched to me.

In elliptic geometry lines curve and eventually intersect, but in the real world parallel lines never intersect--my point being math constructs do not necessarily model the real world.

Why is string theory so popular?

 

[PhanthomJay]

Is Occam's razor being applied to hypotheses such as string theory? The idea of 11 dimensions most of which are curled up smaller than an atom, with a multiverse of 10**500 universes having many clones of each person seems a bit far fetched to me.

In elliptic geometry lines curve and eventually intersect, but in the real world parallel lines never intersect--my point being math constructs do not necessarily model the real world.

Why is string theory so popular?

Ask Hawking et al

"M-theory is the only candidate for a complete theory of the universe".

Now he may be wrong, but nonetheless, M-Theory (an offshoot combination of string theories) is here to stay for awhile.