What are all the Dimensions?

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  • #1
Jeebus
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I'm just curious, and since I'm not having any luck on Google searches; I decided to ask the PF and Mkaku forum.

What are the names for all the 11 Dimensions? Or do they even have given, scientific names? Just wondering.

Oh and one more thing. Does the new hypothesis of the Universe being a dodecahedron have any spin or affect on the 11d theory?

Thanks,
Jeebus
 

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  • #2
selfAdjoint
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The higher dimensions don't have names. In physics the three common names length, width, and height are rarely used since the objects concerned can easily be rotated into any coordinate system without changing the physics. So when you go up to Minkowski space you just have the distinction between time and the three spacelike dimensions. Similarly in string theory, time is distinguished from the 9 or 25 or whatever spacelike dimensions. Sometimes they work in what is called the lightcone gauge, in which time ans one space dimension are singled out, and then the remaining space dimensions are called transverse dimensions.

This is about as far as naming goes. Once you get used to replacing x, y, and z by x1,x2,... the naming thing soon becomes uninteresting.
 
  • #3
Jeebus
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This is about as far as naming goes. Once you get used to replacing x, y, and z by x1,x2,... the naming thing soon becomes uninteresting.

Hehehe. Okay, just making sure. Thanks for the insight.
 
  • #4
hey.like
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The high dimension everywhere

As the mass complex everywhere, the dimension more than 4 is everywhere so. It is not important about dimension number, the important is in a unit and some phys means in the same dimension unit.
 
  • #5
Spaz
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Well, movement in the 5th dimension is sometimes referred to as "ana" and "kata", though I can't remember who coined it.
 
  • #6
cajones
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My understanding is that some of the dimensions were added to the model because of forces. It was suggested that light could be caused by something vibrating in a dimension other than our three, thus creating these energetic "waves" in our three dimensional space. The only puzzling thing about that theory is that, when photons are produced, they don't move in waves such as in water rippling, but more like waves on the beach, only without the returning motion.
I believe that some suggestions have been made on the relationship between gravity and other dimensions that relates to the curavture of space time and the like. I'm not exactly sure what led to the precise numbers of dimensions that have been proposed so for, perhaps someone else can shed some light on this.
 
  • #7
selfAdjoint
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The dimensionality of spacetime is actually a variable in string theory. In the various different kinds of string theory you can solve for the variable. In bosonic string theory (the oldest kind )it comes out 26. In supersymmetric string theory it comes out 10. M-theory builds an extra dimension on superstring theory, for a total of 11. One of these is a time coordinate in each case, and the others are spacelike.
 
  • #8
alkaline
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Originally posted by Spaz
Well, movement in the 5th dimension is sometimes referred to as "ana" and "kata", though I can't remember who coined it.
I believe Charles H. Hinton coined them, and they are the greek prepositions meaning "up" and "down". Some people use the terms "upsilon" and "delta" (favored by Clifford A. Pickover). For directions relative to the orientation of an object (like left & right), i use the words "zant" and "wint" coined by Jonathan Bowers - see my glossary:

Fourth Dimension Glossary
 
  • #9
selfAdjoint
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alkaline, that's a very nice site on the fourth (and higher) dimension.

I notice you say there are two independent kinds of rotation in tetraspace. At least that's what I thought you said. Is this related to the fact that SU(4) = SU(2) X SU(2)?
 
  • #10
alkaline
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thanks :-)

it's possible for an object to have two independent rotations at the same time. There is only one "kind" of rotation in the fourth dimension - everything rotates around a plane. I'm not sure what the SU(n) notation means - i could answer your question if you explained it.
 
  • #11
force5
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I think of the extra dimensions as lower not higher d's. In other words, a sphere represents the three(3) whole dimensions plus time and the sub-dimensions in 10D space includes the following subsets;
= angular momentum =
5 - 60 degrees
6 - 120 degrees
7 - 180 degrees
8 - 240 degrees
9 - 300 degrees
10 - 360 degrees

Each represents a change in direction of angular momentum.
 
  • #12
selfAdjoint
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Why just these multiples of 60? There is a continuum of angles in a circle, so by your idea that's a nondenumerable infinity of new dimensions!
 
  • #13
force5
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Sub-dimensions

hi Self,
I guess I should have stated that this concept refers to the most fundamental state of energy incorperated within the string. If the string turns out to consist of a tubular shape, then the angles refered to would be limited to this confined area. Of course, I'm assuming the string is of a pure energy state.
My research addresses the goal of unification from the bottom up. I'm designing a model of the cosmos based on the assumption that there is only one fundamental force and all of the known forces are secondary. Although my methodology deviates somewhat from tradition, I always follow strict guidelines base on known facts and accepted theories.
Thanks for your response.
 
  • #14
selfAdjoint
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Well, good luck. Many have tried that but with no useful results. If you want to post more details about your theory you should do it on the Theory Development forum.
 
  • #15
kurious
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We may not be able to detect the higher dimensions with our senses but perhaps
our senses exist in them and this is what separates conscious experience from unconscious experience - awareness from sleep.
 
  • #16
sol2
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What is the Metric in Superstringtheory:)

or at least, develope the concept :smile:

http://superstringtheory.com/equations/kkNewton1.gif

So if we added an extra compact space dimension to our three existing noncompact space dimensions, then D=4, but D-2=2, so the force law is still an inverse square law. The Newtonian force law only cares about the number of noncompact dimensions. At distances much larger than R, An extra compact dimension can't be detected gravitationally by an altered force law.

The effect of adding an extra compact dimension is more subtle than that. It causes the effective gravitational constant to change by a factor of the volume 2pR of the compact dimension. If R is very small, then gravity is going to be stronger in the lower dimensional compactified theory than in the full higher-dimensional theory.

So if this were our Universe, the Newton's constant that we measure in our noncompact 3 space dimensions would have a strength equal to the full Newton's constant of the total 4-dimensional space, divided by the volume of the compact dimension.

That's an important detail, because the size of the gravitational coupling constant is what determines the distance scale of quantum gravity. So the distance scale of quantum gravity has to be very carefully defined in theories with compactified extra dimensions.


http://superstringtheory.com/experm/exper5a.html

I am trying to remain consistent with these ideas as well, and it is very hard sometimes to maintain these concepts in light of the theoretical demands new paradigmal models, that are placed before us.
 
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  • #17
force5
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last comment on this subject

Would it not be possible to consider the radius to be the variable and not the degree of angular momentum versus direction?

Sorry for making reference to the source of my comments. I will not comment any further on this subject unless prompted.
Thanks for the advice.
 
  • #18
sol2
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The familiar extended dimensions, therefore, may very well also be in the shape of circles and hence subject to the R and 1/R physical identification of string theory. To put some rough numbers in, if the familiar dimensions are circular then their radii must be about as large as 15 billion light-years, which is about ten trillion trillion trillion trillion trillion (R= 1061) times the Planck length, and growing as the universe explands. If string theory is right, this is physically identical to the familiar dimensions being circular with incredibly tiny radii of about 1/R=1/1061=10-61 times the Planck length! There are our well-known familiar dimensions in an alternate description provided by string theory. [Greene's emphasis]. In fact, in the reciprocal language, these tiny circles are getting ever smaller as time goes by, since as R grows, 1/R shrinks. Now we seem to have really gone off the deep end. How can this possibly be true? How can a six-foot tall human being 'fit' inside such an unbelievably microscopic universe? How can a speck of a universe be physically identical to the great expanse we view in the heavens above? (Greene, The Elegant Universe, pages 248-249)
 
  • #19
Olias
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Bubble of Nothing:But those are not the only new states in the Kaluza-Klein spectrum. The g44 component of the metric propagates as a massless scalar field f(xa) in the noncompact dimensions. This would result in a new long range force not observed in Nature.

I believe Witten addressed this?
 
  • #20
selfAdjoint
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By [tex]G_{44}[/tex] I presume you mean the time-time component, what others call [tex]G_{00}[/tex]. Note that general covariance means that individual components of tensors are not preserved under general coordinate changes, so to tag this as a field (presumably existing prior to coordinate choices) is dubious in the extreme.
 
  • #21
Olias
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selfAdjoint said:
By [tex]G_{44}[/tex] I presume you mean the time-time component, what others call [tex]G_{00}[/tex]. Note that general covariance means that individual components of tensors are not preserved under general coordinate changes, so to tag this as a field (presumably existing prior to coordinate choices) is dubious in the extreme.

The line:
The g44 component of the metric propagates as a massless scalar field f(xa) in the noncompact dimensions.

is from the above link provided by Sol:http://superstringtheory.com/experm/exper5a.html

I presume that the probability of the link statement for transformation from 5-Dimensional Spacetimes, into 4-Dimensional Spacetime is out of the question then?
 
  • #22
selfAdjoint
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Ah. That is in the context of string theory, on the worldsheet of the string against the background of FLAT Minkowski space (of 26 dimensions). So we are not talking about general relativity here.
 
  • #23
sol2
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Olias said:
Bubble of Nothing:But those are not the only new states in the Kaluza-Klein spectrum. The g44 component of the metric propagates as a massless scalar field f(xa) in the noncompact dimensions. This would result in a new long range force not observed in Nature.

I believe Witten addressed this?

So what is this new long range force not observed in nature? A graviton? :smile: The grAviton by its very nature would represent "dimension" from weak to strong?

how does one leave the brane and IS ALLOWED allowed to roam freely in the bulk? There would be a demonstration of this by Witten for sure, I just don't know where that would be.

What other "new states" would exist in the Kaluza-Klein spectrum?

Self Adjoint might know in regards to Witten.
 
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  • #24
sol2
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There are relations between topology and metrics (the simplest example
is that you can't put a flat metric on a 2-sphere), but, in general, you
can always infinitesimally deform your metric. As for topology change,
there are known examples where topology of a compactification manifold
can change by going through a singular transition. One can also think
about tunnelling solutions in quantum gravity that change topology. For
example, Witten showed in the early eighties that there is a
gravitational instanton (a bounce solution to the euclidean equations)
that describes a transition between R^4 x S^1 to a spacetime that
essentially ends in a bubble where the S^1 sort of caps off. It's
sometimes described as an expanding bubble of "nothing". The main point,
however, is that you can wrap a sphere around this bubble, so the
spacetime has changed topology in the tunnelling process. Of course,
lacking a completely understood nonperturbative quantum gravity, this
sort of tunnelling can't be said to be completely understood. There are
decen reasons to believe that it should exist in string theory, but
atleast one paper has argued otherwise.


http://www.lns.cornell.edu/spr/2001-07/msg0034338.html
 
  • #25
catch.yossarian
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Is there a link out there that'll help me "visualize" these higher dimensions, or are they something you can't/aren't supposed to visualize.

Because I can get left-right, up-down, and forward-backward just fine, but after that I run into a bit of trouble, heh. Thanks in advance.
 
  • #26
sol2
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catch.yossarian said:
Is there a link out there that'll help me "visualize" these higher dimensions, or are they something you can't/aren't supposed to visualize.

Because I can get left-right, up-down, and forward-backward just fine, but after that I run into a bit of trouble, heh. Thanks in advance.

http://scholar.uwinnipeg.ca/courses/38/4500.6-001/cosmology/d_corpus.jpg [Broken]


Try visualizing a Tesserack Salvador Dali has a interesting picture as well. Makes you wonder about all these people like Hinton and Abott who were asking the same kinds of questions about the geometry of. :smile:

Imagine trying to describe points on Gaussian Coordinates? All of a sudden you are not thinking in straight lines any more, and Reinmann sphere starts to makes sense from the work of Saccheri in regards to the fifth postulate.

But the Gaussian method can be applied also to a continuum of three, four or more dimensions. If, for instance, a continuum of four dimensions be supposed available, we may represent it in the following way.

http://www.bartleby.com/173/E16.GIF


It a complex issue especially if you move to brane considerations. I mentioned something about Jim Gates the other day that would have help one to visualize what is happening between these two branes.

But how would you visualize complex points, if not in plasmatic association?

How would you visualize a photon interacting with a graviton(dimension)?


We can sum this up as follows: Gauss invented a method for the mathematical treatment of continua in general, in which “size-relations” (“distances” between neighbouring points) are defined. To every point of a continuum are assigned as many numbers (Gaussian co-ordinates) as the continuum has dimensions. This is done in such a way, that only one meaning can be attached to the assignment, and that numbers (Gaussian co-ordinates) which differ by an indefinitely small amount are assigned to adjacent points. The Gaussian co-ordinate system is a logical generalisation of the Cartesian co-ordinate system. It is also applicable to non-Euclidean continua, but only when, with respect to the defined “size” or “distance,” small parts of the continuum under consideration behave more nearly like a Euclidean system, the smaller the part of the continuum under our notice.

http://www.bartleby.com/173/25.html
 
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  • #27
pelastration
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catch.yossarian said:
Is there a link out there that'll help me "visualize" these higher dimensions, or are they something you can't/aren't supposed to visualize.

Catch, after Sol efforts, I will try to feed you some images which may activate that imagination.

Personally I make next distinction in what are dimensions.

1. Dimensions are coordinates in a framework which make it possible to give a position of an event.
That's your: left-right, up-down, and forward-backward. x,y,z axis in a 3D projection.

2. Dimensions can also indicate levels of different properties (ie. the magnitude differences between different 3D levels, the degree of dynamics, ...)

An example: Think of the three forms of water.

1. Water damp (steam).
You start with chaos.
This dimension has no internal structure. (ie. a volume with water-damp).
But you are able to locate particles on certain points of the x,y,z axis in a 3D projection in this steamy dimension.

2. Some spots cool down and condensate: You get water drops which become a sea.
Water has a kind of dynamic bindings and interactions, ruled by a set of physic laws (cfr. Covalence, cohesion forces, Reynolds number, etc).
The internal binding forces are not strong enough to get a large volume at once, you need to do that indirect (ie. a spoon, glas)
You are able to locate water molecules and H+ and OH- ions on certain points of the x,y,z axis in a 3D projection of this water dimension.

3. Some zones of water cool down strongly and you get 'ice'.
Ice has a rigid structure.
The internal dynamics are reduced.
The water molecules are structured strong enough to get a large volume at once.
Of course volumes can be easily projected of the x,y,z axis in a fixed 3D framework.

You can project these three dimension steps also on cosmology.
1. Stream can represent the chaotic pre-geometry. A type of dynamic background with continuos changing positions.
2. Water can represent dynamic geometry/topology. Here is more density. Observable under certain conditions. (Added: Here is a kind of binding or coupling. Indirect measurement: ie. looking how ice goes up and down indicates the water-level/moves)
3. Ice can represent matter-like (more rigid) structures. Higher 'hardness'. Easy observable by other measurement tools of the same level. (ie. different pieces of ice can clash and influence each other position).

These three dimensions (steam, water, ice) have also an balancing dynamic equilibrium against each other. Qua position: Steam above, ice on water. Water waves move ice. Ice pushes water away.

These three dimensions influence each other also on other levels (ie. steam decouples ice back to water, water transforms in steam, etc).

These a just some general basic ideas which may bring back some conceptual thinking.
 
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  • #28
sol2
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Thanks to pelastrian for helping to visualize. Some will feed us bits and pieces to help us in the direction of what they are seeing. What information have they been giving us that would lead one to believe, that there is a way that they are looking at it, that is much different then what we have always known? Even in face of the math's involved. Who is going to tie that math together?

The visualizations are very simple once you have taken in a extreme amount of information, and from this(explosion of insight) fertile ground, new seeds arise, that begin to take shape in the form of images. From this perspective how would you approach this subejct to develope a consistent model of expression if it is not geometrically done? There would be no way to follow such thoughts being expounded upon, without some kind of framework

It becomes much more complex, and in relation to the basis of a consistent model of expression I answer this continued work today here and seek to support this through validation?
 
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  • #29
infinite
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this is my first time on this website and i dont know much about higher dimensions but i would like to have a basis of understanding to the higher dimensions so if anyone could give me some sort of explanation i would appreciate it. thanks
 
  • #30
Netme
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selfAdjoint said:
The dimensionality of spacetime is actually a variable in string theory. In the various different kinds of string theory you can solve for the variable. In bosonic string theory (the oldest kind )it comes out 26. In supersymmetric string theory it comes out 10. M-theory builds an extra dimension on superstring theory, for a total of 11. One of these is a time coordinate in each case, and the others are spacelike.

How do you know it is space like?
 
  • #31
selfAdjoint
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Netme said:
How do you know it is space like?

That's the way the physics comes out. Physicists are not going to assume more than one time dimension until they see some real reason to do so. There hasn't been any so far. So all their theories follow the relativistic model: one time dimension and the rest spacelike.
 
  • #32
Netme
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selfAdjoint said:
That's the way the physics comes out. Physicists are not going to assume more than one time dimension until they see some real reason to do so. There hasn't been any so far. So all their theories follow the relativistic model: one time dimension and the rest spacelike.

I mean how do you know the physics represent space. Could they be representing something that just has the properties of space?
 
  • #33
selfAdjoint
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Doesn't matter if it's "space" or something "just like space". What matters is what the equations say, and they can't tell the difference. You have the same thing in general relativity, with "curved spacetime". Is spacetime a thing? That it can be curved? Or do we just mean that geometry varies from point to point?
 
  • #34
Netme
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Maybe i should refine my question.. What kind of form does this space take and could you compare it to anything in form that can be seen by us.
 

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