What is Compactified Extra Dimensions?

[maani]

Hi, I have a question about extra dimensions. I don't understand what means that a dimension is compactified. Thanks a lot!

Sorry it's the wrong forum. It belongs to Beyond the Standard Model , but I don't know how to remove it!

 

[tom.stoer]

Think about a Universe with one space and one time dimension. It looks like a wire along which one can walk forward and backward. The three dimensions embedding the wire are not necessary mathematically but we need them for visualization.

No - using a magnifying glass - you suddenly discover that the thin wire is not really a wire but a hose! That means instead of walking in one dimension, you are able to move in two dimensions: along the hose and around the hose.

This second dimension is compactified. Only if you are smaller than the radius of the hose you are able to observe the second spatial dimension.

 

[Halcyon-on]

Just consider a string of a guitar. It fills a compact spatial dimension. If you compactify a relativistic wave in an extra dimension you get a discretization of the mass spectrum (KK tower) as the guitar string has a discretization of the frequency spectrum.

 

[wendten]

i know that the compactified additional dimensions is the standart explanation, but the way i have thought of this is the reason we can't see these dimensions, is that light fotons are bound to the 3rd D, and cannot interact with the higher dimensions, just like the mass cannot escape 3D neither.. why is this much simpler theory not a valid explanation?

 

[DaveC426913]

Tom's explanation is how I undertstand it too.

From one hundred yards away, an ant is seen to walk back and forth along a one dimensional string. Zoom in by several orders of magnitude and you see that the 1D string is really a 2D hose, and the ant has a limited amount of freedom in the dimension heretofor imperceivable.

 

[ernestpworrel]

Remember, though, that there are three spatial dimensions that we experience in our daily lives and are free to move about in. The reason that physicists (string theorists, to be exact) suggest more spatial dimensions is that the equations of string theory require nine. When the dimension of time is included, that brings the total number of space-time dimensions to ten. String theorists have suggested that the reason we don't experience these six extra spatial dimensions is that they are compacted within the three so we're just not aware of them.

There is a theory that our universe exists on a three-dimensional brane and so we don't move through these other dimensions but rather they exist outside our universe. I'm really not sure whether this theory has gained acceptance in the mainstream physics community though.

 

[wendten]

I know exactly how this is explained, what I don't know is why these dimensions have to be curled up when a much simpler explanation could be: The reason why we don't experience these additional dimension is that none of our particles can move in these directions, and therefore are stuck on our 3D-brane

and if these dimension are subatomic in size, how can they contain this huge number of other worlds where some atoms are at a different location, or where the physical constant are different than the once in our universe.

how can the multivers exist if it don't have the space

 

[Halcyon-on]

I none of our particles can move in these directions, and therefore are stuck on our 3D-brane

If none of our particles, including the gravitons, can move in the extra dimensions, it doesn't make sense to study extra dimensions. In this case it would be a sector totally disconnected from our physical world (a disconnected world).

The point is that, assuming that particles can propagate in extra dimensions, many conceptual problems of modern high energy physics find answer. Allowing to the gravitons an extra dimension implies the solution of the hierarchy problem between the electroweak scale and the Planck scale. Allowing photons and the others interaction mediator particles as in the Randall Sundrum model, would imply an explanation of the unobserved Higgs particle of the Standard Model, ecc... .

 

[ernestpworrel]

I know exactly how this is explained, what I don't know is why these dimensions have to be curled up when a much simpler explanation could be: The reason why we don't experience these additional dimension is that none of our particles can move in these directions, and therefore are stuck on our 3D-brane

String theorists were following the Kaluza-Klein tradition when they began searching for these additional dimensions. That's how they came to suggest compactified dimensions. Fortunately, the math works. Now M-theory, the theory of branes, was suggested by Witten at a string theory conference as a solution to the problem of five different versions of string theory. The addition of an eleventh dimension to the ten space-time dimensions of string theory unites the five versions. So if there hadn't been more than one version of string theory in the first place, no one would've suggested braneworlds.

and if these dimension are subatomic in size, how can they contain this huge number of other worlds where some atoms are at a different location, or where the physical constant are different than the once in our universe.

Remember, they would only be small in the three spatial dimensions that we experience.

how can the multivers exist if it don't have the space

It may well have the space. We're just not able to experience it.

 

[Bodicea]

Seeing a hose from up close or from far away does not change the state of the hose, its dimensions or how many dimension it has, so if a hose has one, two three four or even ten dimension that won't be altered by the observer being closer or farther away from it...its our perception that is altered...


I don't think a dimension can be compressed either..why would a dimension need to be or be so inclined...its not like it has to fit around us or anyother aspect of space. it either exists or it doesn't and to be able to see it we need to exist within that dimenions. What I mean by this is that: we live in a three dimensional world, we see time as being the forth dimension, we can't feel it see it or touch it but yet we know its there and many would consider it to be conceptual as opposed to being tangible, but so to are the other three dimensions.

If string theorists "need" more dimensions in order for the maths to fit..then their maths are wrong, or there is something wrong with string theory...One day another Einstein or Newton will come along and explain things perfectly...and I would bet my life that it won't be as complicated as some 'theorists' seem to think.

Sorry if above is bit garbled...at work and should be working

 

[marcus]

Seeing a hose from up close or from far away does not change the state of the hose, its dimensions or how many dimension it has, so if a hose has one, two three four or even ten dimension that won't be altered by the observer being closer or farther away from it...its our perception that is altered...I don't think a dimension can be compressed either..why would a dimension need to be or be so inclined...its not like it has to fit around us or anyother aspect of space. it either exists or it doesn't and to be able to see it we need to exist within that dimenions. What I mean by this is that: we live in a three dimensional world, we see time as being the forth dimension, we can't feel it see it or touch it but yet we know its there and many would consider it to be conceptual as opposed to being tangible, but so to are the other three dimensions.

If string theorists "need" more dimensions in order for the maths to fit..then their maths are wrong, or there is something wrong with string theory...One day another Einstein or Newton will come along and explain things perfectly...and I would bet my life that it won't be as complicated as some 'theorists' seem to think.

Sorry if above is bit garbled...at work and should be working

This is an extremely refreshing attitude.
A belated welcome to you, Bodicea. I didn't see your earlier post back in January, when you said hello.

Hi another humble student here, and newbie too, so hello everyone

Hello back.

I believe its the currants in a cake thing. The cake will expand whilst baking, but the currants dont. Its the fabric of space that is being pushed and pulled and the solar system is just being pulled along with it, but yet not affected by it.

I think that's essentially right, about the currants. And if I remember correctly they are quite good in that yellow cake called "pound cake".

The ideas of how to properly represent geometry and matter, so that their interaction can be understood, are at the same time fascinating and unsatisfactory, at least so far. I can imagine your being distracted from work by the thought of this. Please do not let the fundamental nature of geometry and matter, and their interaction, interfere seriously with your job.

Whilst is an excellent word, which we should use more often. For general information, here is background on a famous British head of state, a contemporary of the Roman Emperor Nero: http://en.wikipedia.org/wiki/Boudica

 

[DaveC426913]

Seeing a hose from up close or from far away does not change the state of the hose, its dimensions or how many dimension it has, so if a hose has one, two three four or even ten dimension that won't be altered by the observer being closer or farther away from it...its our perception that is altered...

I had thought that this would have gone without saying, but:

It's only an analogy.


If we described the expanding universe model using the venerable "inflating balloon" analogy, you would be telling us that it must be a spurious analogy because there's no cosmic-scale nipple by which the air is blown in.

Come on.

 

[Bodicea]

I had thought that this would have gone without saying, but:

It's only an analogy.


If we described the expanding universe model using the venerable "inflating balloon" analogy, you would be telling us that it must be a spurious analogy because there's no cosmic-scale nipple by which the air is blown in.

Come on.

Dave, if there was a cosmic scale 'nipple' I think (given most scientists are men) they would have found it by now.

Im amused though... a man that can read a womans mind...what a pity you're wrong though.

I actually think the balloon analogy is good enough for basic explanation of expansion, I think the currant cake one is a bit better, but they are closer analogies (to what they are describing) than the hose one and to be honest the 'hose' doesn't really clarify anything for anyone...cos wether you were stood at location A or location B wrt any dimension, its (the dimension) is not going to change, what will change is ones perspective.

A good analogy is one that will give the abstract an everyday explanation that holds good no matter where one is, cos its not ones perpective one is looking for clarification on, its the subject matter, or more accurately the concept, that needs explaining. E.g I find using the dustbin man as being a good way to explain how we know of the existence of certain particles, even though we can't see them. We don't 'see' the dustbin man collecting the bins, but yet when we get home we know they've been, cos the bin's empty. Trying to think of a way I could fit a nipple in...

Anyway, nobody actually knows how many other dimensions exist, or even if they do, they are just theories. We can barely explain time, never mind a further 10 dimension.

Personally, I don't see dimensions as being physical entities, unless one lives in them. We live in a 3 dimensional world, so we can see dimensions one, two and three as physical manifestations, we can't however see what we consider the 4th dimension (time), nor can we feel it or touch it or give a 100% accurate description of what it is. They are all just theories at this moment in time...and they're all fair game iykwim.

If we were to live in two dimensional world then the third dimension would feel similar to time, we know its there, it does impact us, but we cannot touch or see it and we would have a hard time explaining what it is, what it does and why its there. In short I see dimensions as being more like dutch dolls...the lower ones existing within the next highest one etc etc...


I often wondered though if I were simply energy would I have any concept of any dimension, or would i exist in just one or all of them.

Who thinks I need a life? lol

This is an extremely refreshing attitude.
A belated welcome to you, Bodicea. I didn't see your earlier post back in January, when you said hello.

I think that's essentially right, about the currants. And if I remember correctly they are quite good in that yellow cake called "pound cake".

The ideas of how to properly represent geometry and matter, so that their interaction can be understood, are at the same time fascinating and unsatisfactory, at least so far. I can imagine your being distracted from work by the thought of this. Please do not let the fundamental nature of geometry and matter, and their interaction, interfere seriously with your job.

Whilst is an excellent word, which we should use more often. For general information, here is background on a famous British head of state, a contemporary of the Roman Emperor Nero: http://en.wikipedia.org/wiki/Boudica

Hi Marcus, thanks for the welcome. I agree about the fascinating and unsatisfactory thing...just soo frustrating at times...My god was it january when I last posted...sheez, I need to change jobs

 

[marcus]

...

If string theorists "need" more dimensions in order for the maths to fit..then their maths are wrong, or there is something wrong with string theory...One day another Einstein or Newton will come along and explain things perfectly...and I would bet my life that it won't be as complicated as some 'theorists' seem to think.
...

Let's take that as read, and move on. Is there anything in fundamental physics you are especially curious about?

If you are interested in what geometry might be like at very small scale (where the idea of a fixed dimensionality gets a bit hazy) here is what I would suggest.

It's a well-written and illustrated Scientific American article about some research being done currently in Holland, at the University of Utrecht.
http://www.signallake.com/innovation/SelfOrganizingQuantumJul08.pdf
I keep the link in my signature.
The Utrecht group is led by Renate Loll.

Here is a video talk by Loll, at a July 2009 conference on physics at Planck scale.
http://www.ift.uni.wroc.pl/~rdurka/planckscale/index-video.php?plik=http://panoramix.ift.uni.wroc.pl/~planckscale/video/Day1/1-4.flv&tytul=1.4%20Loll

The Utrecht group is investigating a model of random geometry programmed into computer, which allows small universes to come into existence (in simulation) and to evolve by a process of very many small random fluctuations. This enables the researchert to stop evolution of geometry temporarily and go inside and explore, take random walks, measure whatever the dimensionality is, measure areas volumes ratios etc. They do not fix stuff like the dimensionality ahead of time, they let it happen according to the quantum geometry law they are investigating (which reproduces our kind of world at large scale on average but a quantum geometry at small). So microscopically the dimensionality can vary.

Loll doesn't need any "extra" dimensions. Nothing more than the 4 that we observe. But at very small scale things get a little chaotic and "fractal-like" and there may seem to be less than 4 available, which is curious. Since dimensionality is not controlled or set up by the experimenters, this kind of thing can happen. That's just a taste. Have a look. It is kind of a model of how quantum geometry and quantum cosmology are going these days. There are a number of non-string no-extra-dimensions approaches that have sprung up and are being worked on. What you said about "not as complicated" is right. The new approaches to geometry and matter do tend to be considerably simpler than string. Loll's has a "minimalist" character. Bare bones approach. That's why it can be a good place to start.

But if you are not especially curious about that---about geometry at small enough scale that quantum uncertainty enters---then my suggestion of something to read/watch doesn't apply. It was contingent on your interest being in that direction.