What Do Dimensions 5-14 in String Theory Really Mean?

[pallidin]

Well, I quess that my point in all of this, Dimensions are weird. And I do not possesses knowledge of them other than my own thoughts.
Are higher dimensions a combination of the lower ones? Perhaps, but there's a problem with that. Try, for example, to degress the d-4 into d-1, d-2 and d-3 components. Seems rediculous doesn't it? How can pure time be degressed into components of physicality!
Another way to look at that problem is when we use d-2 to represent d-3, such as a line drawing on paper of a cube. Visually it can be very convincing, but it is an illusion without the form or substance of a true d-3 cube!

Now it gets really strange and even contentious... does d-1 really exist?
Think about a point without length or volume, which would be d-1.
How could that even be possible?
My contention is that when a "point" exists it must have volume because it occupies some region of space, however incredibly small.
Similarly, d-2 is non-sensical because it presuposes a d-1 with length and, again, no volume.
How could that be possible! A line, however thin, must occupy space.

So my contention is that everything is d-3 and beyond. The idea that an electron is a "point particle", for example, makes no sense to me with respect to it being d-1.

In other words, d-1 through 3 are considered vector qualities, however, the vectors of d-1 and d-2 have never been truly shown to exist apart from d-3, except mathematically.

So therein lies the problem, and even more so with d-4. How "time" became an acceptable definition of d-4 is beyond me, as I believe it is a trans-dimensional quality simply referencing an aspect of "change"
I do not view time as a dimension at all, rather that it references changes in all dimensions.

My brain is fried, I'll leave this alone for now...

 

[Aftermarth]

haha its a really hard topic hey..

i (on the adivce of other people in this thread) have picked up a copy of Kaku's Hyperspace book, along with his Quantum Field theory.
One thing i can't help but forget is one of the original proofs for a fourth spatial dimension being a modification of pythagoras. In 2D, a^2 + b^2 = c^2 in a triangle.
in 3D (a cube) a^2 + b^2 + c^2 = d^2 where d is the diagonal of the cube.
so 'logically' it can be assumed a^2 + b^2 + c^2 + d^2 = e^2 in what would be a 4D cube.

ok, I am not worried about the numbers here, that would seem to all add up properly, but the issue lies in what a 4D cube would be? I mean, what is the exact definition of a cube in the first place? And couldn't this go on forever, sure, i know its not the only definition of another dimension, but imagine what it could mean.

And reading this sure is helping i must say. But does anyone have some reasoning for why a fourth spatial dimension helps create a grand-unified theory? Kaku mentions waves in the 4th spatial dimension solves lights medium to propogate through, and that it can bond gravity to electromagnetism. And, (not finished yet) that the more dimensions you add, the easier the laws of nature become?
How so!? doesn't nature exist in the 3D we do - or does the math we create exist into more dimensions?

 

[TR345]

I think that dimensions 1-3 depend on each other in that they don't seem to be represented alone, but together they represent the degrees of possible movement. They are spatial dimensions, and the universe is 3d. Time is a little different. Without time the universe is just 3d, but time is actually bonded to the spatial dimensions according to relativity. In relativity, time is dependent on acceleration and gravitation. The more gravitation and or acceleration, the slower the clock will tick relative to a clock ticking under lesser gravitational and or acellerational magnitudes. I guess time is a factor of the interaction of
mass-mass-space which includes 3 space, so the 4 dimensions according to relativity are explicitly bonded and dependent on each other.

If you wanted to get crazy could you not call gravity a dimension, and call momentum a dimension? Could you call electrical charge or lack of a dimension? I guess they are excluded from being classified as dimensions because they are considered forces?(except gravity) I suppose that it may be thought that gravity is a side effect of the 4 dimensions and 4 forces, but attempts to link them have failed right?.

 

[Aftermarth]

well i wouldn't call gravity or momentum a dimension because they do act in the four that we already have. Kaku again seems to think that all of these forces can be combined into a grand theory of everything in five or six dimensions.. now that would be cool

how far could humanity go if we learned how all the forces interact? Could we then manipulate the world around us to be what we want?

i do like the example of the people who live in a 2D world being peeled off it and taken into our 3D world. They would only see everything still in 2D, but things would be appearing and disappearing as it moves past in the 3rd dimension because they can't see depth. So if we were peeled out of our world and taken to the 5th dimension, the effect would be the same. it would be very weird with lots of things we don't understand moving in ways we can't comprehend, but other than that we would see things almost normally... makes you think doesn't it?

 

[TR345]

The only thing is that if these extra dimensions do exist, they are supposed to only apply to very small things that are invisible to us right? The strange things that we see are observations such as gravity inertia etc. So maybe a photon or a quark or something lives in this extra dimensional world. The same way that we don't observe things the way they would, they wouldn't observe things the way we would(if they had eyes that is). Maybe the unexplained things we see are actually the forces and laws of physics which to us are no different than they way a 2d person would view a 3d world? To a photon, from their view if they had one, maybe the forces and gravity are plain as day in how they work?

 

[Aftermarth]

if only we could find all this out. it would be so great to know. i spose this whole thread is built on the desire to know what actually is a fifth dimension and the ones after it.

curious thought:
if a 2d representation of a cube is two squares joined together by lines
then a 3D representation of a hypercube (a 5D variation of our 3D cube) would look like two cubes joined together by lines...
so now try imagining what the actual thing looks like... *brain explodes*

http://www.geocities.com/liviozuc/hyperimages/acolori.gif

wow...

a hypothesis is that gravity is merely waves in the 4th spatial dimension which we can't see... how plausible would that be?

 

[Alex48674]

4d Cube
http://youtube.com/watch?v=Y9KT4M7kiSw

String Theory
http://youtube.com/watch?v=YtdE662eY_M
http://youtube.com/watch?v=L3CnoNdLSao

So who else is writing some nice reputable books on the subject? I was going to order a book by Brian Greene and maybe Kaku.

 

[Aftermarth]

um I am not sure who else writes good books on this... i didnt even know about Kaku until this thread...

ne one with any ideas?

ps... Kaku's Hyperspace is definitely worth a read

 

[aguycalledwil]

Originally, scientists noted that the mathematics of string theory faile when you pass ten dimensions, leaving them to believe that there must be ten dimensions. However, after a while, they realized something (I can't quite remember what) which indicates an eleventh dimension.

 

[Aftermarth]

can we get a bit more detail on that?

i loved reading about how putting einstein's and maxwell's equations together only took the addition of the fifth dimension :)

so one of our greatest discoveries is 15 = 10+4+1 :D

 

[aguycalledwil]

I quote from a book I read by Michio Kaku, "In 1994 another bombshell was droped. Edward Wittan of Princeton's institute for advanced study and Paul Townsend of Cambridge University speculated that all five string theories were in fact the same theory - but only if we add an eleventh dimension. From the vantage point of the eleventh dimension, all five theories collapsed into one! The theory was unique after all, but only if we ascended to the mountaintop of the eleventh dimension.
In the eleventh dimension a new mathematical object can exist, called the membrane (e.g., like the surface of a sphere). Here was the amazing observation: if one dropped from the eleven dimensions down to ten dimensions, all five string theories would emerge, starting from a single membrane. Hence all five string theories were just different ways of moving a membrane down from eleven to ten dimensions."

 

[Dfnoboy]

http: //revver. com/video /99898/i magining -the-tenth-dimension/


I had to make spaces in the URL because I need 15 posts to register...
but I thought I'd share this.

 

[Minkus]

It's all very simple...

...but unfortunately untrue
revver . com/video/99898/imagining-the-tenth-dimension/[/url]

 

[Minkus]

snap!

 

[Aftermarth]

so adding all these dimensions makes the maths becoming increasingly elegant and beautiful. and it sounds all good and fine. just one thing which i was thinking of today bugs me - we add all these dimensions but has anyone actually thought what they mean - like say the 10 dimensions for the 5 string theories.
adding the eleventh collapsed them into one -
but what is the difference from 11 to 10?

 

[aguycalledwil]

I guess that after ten dimensions, the mathematical side of it collapses. Ten is the largest number at which the "maths of the dimensions" will work at.

 

[david s j]

I believe there are only the dimensions we have now in this universe. to say we have more dimensions and more parallel worlds is a little bit foolish and fancy full to say the leased.
The cat in the box experiment when its both alive and dead at the same time
was derived to propell this theory of multipulll worlds.
which ever way you look at it , after the cat has been put in a box with radio active
substance and poisen broken by a hammer triggered radioactive substance
the cat is dead
have you seen monty python scetch my dead parrot
The perpetual thinking in this field of multiple worlds is a compleat waste of time
and would be better spent producing a self producing H2 vehical avoiding
H2 storage and disdrabution problems

atoms can be in two places at once, its only time that tells us where they are
in the one universe.
and its time that puts them in two places not two or more universes.

David Stuart Jones 23/9/51

 

[Shackleford]

I believe there are only the dimensions we have now in this universe. to say we have more dimensions and more parallel worlds is a little bit foolish and fancy full to say the leased.
The cat in the box experiment when its both alive and dead at the same time
was derived to propell this theory of multipulll worlds.
which ever way you look at it , after the cat has been put in a box with radio active
substance and poisen broken by a hammer triggered radioactive substance
the cat is dead
have you seen monty python scetch my dead parrot
The perpetual thinking in this field of multiple worlds is a compleat waste of time
and would be better spent producing a self producing H2 vehical avoiding
H2 storage and disdrabution problems

atoms can be in two places at once, its only time that tells us where they are
in the one universe.
and its time that puts them in two places not two or more universes.

David Stuart Jones 23/9/51

Ditto. There's only one universe.

 

[madmike159]

I believe there are only the dimensions we have now in this universe. to say we have more dimensions and more parallel worlds is a little bit foolish and fancy full to say the leased.
The cat in the box experiment when its both alive and dead at the same time
was derived to propell this theory of multipulll worlds.
which ever way you look at it , after the cat has been put in a box with radio active
substance and poisen broken by a hammer triggered radioactive substance
the cat is dead
have you seen monty python scetch my dead parrot
The perpetual thinking in this field of multiple worlds is a compleat waste of time
and would be better spent producing a self producing H2 vehical avoiding
H2 storage and disdrabution problems

atoms can be in two places at once, its only time that tells us where they are
in the one universe.
and its time that puts them in two places not two or more universes.

David Stuart Jones 23/9/51

The cat experimant is to disprove Bohr's idea of particles existing in every stat until someone looks at them. If Bohr's theory was true the cat would be both dead and alive in the same place at the same time. Which is stupid, there can be other dimensions not sure about other universes.

 

[Alex48674]

Why do you say it is foolish and fanciful to think there might be more then 3 spatial and 1 time dimensions? Many leading physicists think there are more and with good reason.

 

[Gear300]

There is also a proof for 26 dimensions...its somewhat arbitrary. Understanding the right amount seems to be the troublesome part.

 

[humanino]

There is also a proof for 26 dimensions...its somewhat arbitrary. Understanding the right amount seems to be the troublesome part.

26 dimensions applies to the bosonic string theory. If you want to include matter (supersymmetry on the worlsheet) you need fermionic degrees of freedom. This in turn requires 10 dimensions. Exactly, no freedom, the calculation is somewhat elementary (compared to the rest in this field).

Now there are additional developpements starting from those elementary, old, well known considerations. Add one dimension, that gets you to eleven, where an hypothetic M-theory lives, inspired from a unique supergravity theory in 11 dimensions. The 5 popular instances of superstring theory in 10 dimensions would be several limiting case of M-theory, explaining the web of dualities between them.

Even further, you can get more possibilities, but it gets more involved and less developped. Non-commutative geometry allows for several other dimensionalities, based on quaternions and octonions (I am honestly quite unfamiliar with that, even more than the whole thing anyway...). The thing that I am most intrigued with is the possibility to have a 4 dimensional twistor string geometry. Quite an amount of this business has been developped by Witten.

 

[Gear300]

The thing that I am most intrigued with is the possibility to have a 4 dimensional twistor string geometry. Quite an amount of this business has been developped by Witten.

I'm only an amateur (still a student), so I'm just wondering: is what you're referring to the concept of the 4th dimension of time actually being a spatial dimension?

 

[Kopachris]

I'm too lazy to read this entire thread before putting my two cents in, so sorry if this has been explained already.

String theory deals with gravity on a quantum level. I don't know the gory details of how the quantum mechanics is handled, but the gravity part is explained by having all particles be (or have in their centers) tiny vibrating strings. Of course, according to Einstein, moving things warp spacetime, just like what we see as gravity. So the tiny vibrating strings are warping spacetime, and we see it as gravity. The 10-26 dimensions are required to explain why gravity is so much weaker than the other forces: it actually isn't any weaker. Supposedly, gravity is diluted by the extra dimensions, so we only get a fraction of it. M-theory in particular helps illustrate this concept by having fermions be open-ended strings that are attached to membranes that are the dimensions. Gravitons, on the other hand (which have yet to be observed) would be closed-ended strings that would be free to float off of a lower dimensional membrane up to a higher dimension. (Well, some people visualize it as sinking, since they visualize the membranes as a lower dimension floating on top of a higher dimension, but that doesn't really matter.)

In particular, the amount of dimensions is dependent on the amount of potential energy (of something, I don't know what). All I know on that subject is that the discrepancies between the number of dimensions predicted by the various string theories arise from the different theories applying to different things (for instance, M-theory deals mostly with membranes, while there's a string theory that deals exclusively with bosons). Originally, it was thought that there was only one correct string theory, but physicists have started to see dualities between them all.

Or at least, that's how I understand it as the Science Channel and The Elegant Universe explained it.

 

[Dmitry67]

Are these 10,11,26 dimensions real or complex?

 

[Unilinear_Kev]

Are these 10,11,26 dimensions real or complex?

It seems the only thing that has been determined in this thread is that the word "dimension" and exactly how many of them there are seem to be relative to the poster and/or physicist. While we can define the word dimension, it tends to be open ended (which is why you're getting a lot of guesses as to how many there are). This is still really interesting physics and the reason I even registered for this BB.

It's to my understanding that most of these models for the number of dimensions are made from trying to explain 1st hand information that has yet to be explained using the traditional physics "4d". I also get an intense laugh out of "3.5d". Made me think of physics like a version of AOL: "you've got mass!" "you've got movement!".

 

[Dmitry67]

The word 'dimension' is not open ended, it is well defined in mathematics.

If you have 3D space, and each dimension is complex, you need 6 real numbers to define a point, however, still space is 3D and it is different from a 6D real space

 

[Aftermarth]

ok just chucking another idea out there...

in maths I am doing Vector Calculus and Linear Mathematics.
We do simple equations like finding spans and what not

But in the R3 plane, when you find a span of two linerly independant vectors, it is a plane in 3D space.
Given a R4 plane, when you find a span of 3 linerly independant vectors... what does that form? (Visualising things often helps me learn in this maths)

So it would be a complete R3 plane (x,y and z axes) all contained within another plane which we cannot visualise?