Questions regarding dimensions

[Mike Ockizard]

This is my first post here, and as someone who has always had a pretty big interest in science (particularly physics), I thought this would be a good place to possibly get some answers from those who have some more formal schooling. My first question is; is there a general scientific consensus regarding the number of dimensions that exist? Obviously, there are the the 3 spacial dimensions we exist in, combined with time (the fourth) to create the concept of spacetime. I know that there are few other theories out there such as string theory that have up to 11 dimensions, but anytime I try to get more in depth with those theories, things quickly go over my head.

 

I guess this all comes down to something I was thinking about recently. This will probably sound weird, but I have always felt that there are an infinite number of dimensions that exist within each of us, and we in turn exist within an infinite number of dimensions. These dimensions extend outward and inward in every direction simultaneously. What I mean by this is, is that if you were to "zoom out" infinitely on the entire universe, you would pass through infinite dimensions, and the same would be true if you were to continue to "zoom in" on an atom. Essentially, our universe could just be a quark in an atom in some other beings meatloaf somewhere. The same would be true for that being's stars, and so on, and so on. This doesn't seem to be something that could be proven, since you could never "travel" to the other dimensions being that they extend in every direction at the simultaneously.

 

Does anyone know of any theories that deal with this? Is this completely ridiculous to believe? It just seems like we are putting ourselves at the "center of the universe" so to speak, by believing that everything is relative to our size. Why is it we believe that matter becomes more and more simple the further we get away from our relative size? Is an electron really that much more simple than a star? How do we know that matter does not continue beyond the quark? Just because we cannot observe it? Why can't our entire universe be a small portion of infinite other universes?

 

Sorry for all the questions, but this stuff really interests me. I would appreciate any suggestions for reading material that might delve deeper into this subject matter.

Thanks!

Edited July 2, 2011 by Mike Ockizard

[ajb]

By dimension in physics one is usually referring to the topological dimension of a topological space. For example, every point in the space [math]\mathbb{R}^{3}[/math] can be assigned (non-uniquely) three numbers [math](x,y,z)[/math] say. The assignment of these numbers is a choice of coordinate system and the number of such numbers is the topological dimension.

 

So in superstring theory one needs space-time to be 11 dimensional, that is we need 11 numbers to describe each point.

 

Often in physics on has what is known as a manifold, which is a topological space that locally looks like [math]\mathbb{R}^{n}[/math] for some [math]n \in \mathbb{N}[/math]. I short, one can find local coordinate systems on such spaces.

 

One can have infinite number of dimensions, and these are commonly found in physics. Infinite dimensional vector spaces appear in quantum mechanics and infinite dimensional manifolds appear of configuration spaces of field theories. They are much harder to understand in a rigours way, understanding coordinates is not so easy. To be rigorous one usually take finite dimensional subspaces and then use local coordinates.

 

I have no idea what you are talking about by "infinite number of dimensions that exist inside of us".

[Mike Ockizard]

<br />By dimension in physics one is usually referring to the <a href='http://en.wikipedia.org/wiki/Lebesgue_covering_dimension' class='bbc_url' title='External link' rel='nofollow external'>topological dimension</a> of a <a href='http://en.wikipedia.org/wiki/Topological_space' class='bbc_url' title='External link' rel='nofollow external'>topological space</a>.  For example, every point in the space [math]\mathbb{R}^{3}[/math] can be assigned  (non-uniquely) three numbers [math](x,y,z)[/math] say.  The assignment of these numbers is a choice of coordinate system and the number of such numbers is the topological dimension. <br /><br />So in superstring theory one needs space-time to be 11 dimensional, that is we need 11 numbers to describe each point.<br /><br />Often in physics on has what is known as a manifold, which is a topological space that locally looks like [math]\mathbb{R}^{n}[/math] for some [math]n \in \mathbb{N}[/math].  I short, one can find local coordinate systems on such spaces.<br /><br />One can have infinite number of dimensions, and these are commonly found in physics. Infinite dimensional vector spaces appear in   quantum mechanics and infinite dimensional manifolds appear of configuration spaces of field theories.   They are much harder to understand in a rigours way, understanding coordinates is not so easy. To be rigorous one usually take finite dimensional subspaces  and then use local coordinates.<br /><br />I have no idea what you are talking about by "infinite number of dimensions that exist inside of us".<br />

<br /><br /><br />

 

Thanks for the feedback AJB. What you detailed is what I had always been taught. I'm not sure what I am referring to would actually be considered "dimensions" or not, perhaps dimensional planes of existence may be a better term (but that just sounds weird). I suppose another way I could describe what I theorize, is that everything in the universe seems to be comprised of smaller components, or building block material if you will. Relative to humans, it would go something like: Subatomic particle>atom>element>molecule>cell>organs>systems>organisms>population>ecosystem>planet>planetary system>galaxy>universe. Obviously some of these are specifically human, but you could narrow the hierarchy down to just building block materials.

 

My question is, why stop at universe? Isn't that just an artifact of our limited knowledge? Everything seems to be made up of smaller components, so shouldn't everything also make up something else? It's not like anyone has seen the end of the universe, so why would we think that it would end? Why can't the universe and all of it's components simply be the equivalent of subatomic particles in an atom in an element inside of some giant (again, relative to us)being somewhere? Imagine hypothetically that there is a group of people living on a subatomic particle inside a carbon atom in your spleen. How would they ever be aware of your (and our) existence? I theorize that the same thing continues ad infinitum.

 

On somewhat of a side note, if the universe is expanding outward like most of the scientific community believes, then what is it expanding into? Infinity may be hard to comprehend, but for me, all these things just "ending" somewhere seems much more unlikely...

[niai]

My question is, why stop at universe? Isn't that just an artifact of our limited knowledge? Everything seems to be made up of smaller components, so shouldn't everything also make up something else?

I understand what you mean, I used to have similar thoughts, that the 'secret', if you will, of life is hidden in this infinite going up or down the scale, however... As far as I know, the universe is discrete, meaning that you cannot look closer and closer and see smaller and smaller particles infinitely, the process has an ending. Keep in mind, I can't tell you what goes on on a subatomic level (I didn't find physics interesting, when I had time to study, shame on me), because I fear what I know (or think I know) may be old and incorrect information, but still... I'd say think about this. Do you really have any evidence that everything is made up of smaller particles? Even if it were so, is there any indication that the scaling can go infinitely in the opposite direction?

[michel123456]

(...) Imagine hypothetically that there is a group of people living on a subatomic particle inside a carbon atom in your spleen. How would they ever be aware of your (and our) existence? I theorize that the same thing continues ad infinitum.

(...)

 

You are correct.

But:

from our observation it comes that the universe has a structure. In this structure, from the very small to the outrageous large, we never observe twice the same kind of things. I mean that an atom is not like a solar system, an electron is not like a planet, a quark is not like a flower, etc. So it is unlikely to ever encounter a human inside a quark, or to discover that our galaxy is a tiny element in the brain of some gigantic brontosaur.

Maybe our universe is part of something bigger, but that bigger thing would probably be something different than wathever we have ever observed.

[Mike Ockizard]

You are correct.

But:

from our observation it comes that the universe has a structure. In this structure, from the very small to the outrageous large, we never observe twice the same kind of things. I mean that an atom is not like a solar system, an electron is not like a planet, a quark is not like a flower, etc. So it is unlikely to ever encounter a human inside a quark, or to discover that our galaxy is a tiny element in the brain of some gigantic brontosaur.

Maybe our universe is part of something bigger, but that bigger thing would probably be something different than wathever we have ever observed.

 

I agree. But again, we are looking at things from a perspective relative to human knowledge. Why would the building blocks of matter for the next "plane of existence" if you will, look anything like our own? I wasn't suggesting that everything follow a specific pattern on down the line, just that it could exist. In fact what you stated, is exactly what I believe. Although we could never observe it, it would be unlike anything we could possibly understand.

 

As for the other end of the spectrum, I have always had an interest in the smallest particles as well. Although again, we are always trying to find "the smallest" component of matter that is the basis for everything. Again, I'm not so sure this exists. People used to believe matter consisted of the four elements (fire, water, earth, and air). They then moved on to basic atomic theory. Just over 100 years ago we discovered subatomic particles. Only recently have we come up with the idea of hadrons and quarks, which tend to be the smallest identifiable matter at the moment. Since everything in the universe tends to be infinite (time, space, etc), don't you find it unlikely that we could discover a finite "beginning" of matter? Say an electron or quark is deemed the smallest particle of matter. What would you see if you zoomed in infinitely on that particle? Doesn't everything have to consist of "something"? Or do we get to a point where everything exists as pure energy?

 

[ajb]

I'm not sure what I am referring to would actually be considered "dimensions" or not, perhaps dimensional planes of existence may be a better term (but that just sounds weird). I suppose another way I could describe what I theorize, is that everything in the universe seems to be comprised of smaller components, or building block material if you will. Relative to humans, it would go something like: Subatomic particle>atom>element>molecule>cell>organs>systems>organisms>population>ecosystem>planet>planetary system>galaxy>universe. Obviously some of these are specifically human, but you could narrow the hierarchy down to just building block materials.

 

You mean more like scales? The Universe looks very different at different length or equivalently energy scales. This is fundamental in physics, one can often "cut-off" the details of the smaller scale to get a good description of physics at a larger scale. (Renormalisation group flow methods in QFT are all about this. )

 

A simple example is that one does not need quantum mechanics to describe a ball rolling down a plane, classical mechanics is sufficient.

 

 

My question is, why stop at universe? Isn't that just an artifact of our limited knowledge?

 

This now sounds like the world of mathematics, which a priori has nothing to do with our Universe.

 

Everything seems to be made up of smaller components, so shouldn't everything also make up something else?

 

Maybe, but this is not what we have observed. For example, within experimental limits the electron seems to have no substructure.

 

It's not like anyone has seen the end of the universe, so why would we think that it would end?

 

You make educated predictions based on the models of cosmology at hand. Right mow the Lambda CDM models fits observations well.

 

 

Why can't the universe and all of it's components simply be the equivalent of subatomic particles in an atom in an element inside of some giant (again, relative to us)being somewhere? Imagine hypothetically that there is a group of people living on a subatomic particle inside a carbon atom in your spleen. How would they ever be aware of your (and our) existence? I theorize that the same thing continues ad infinitum.

 

This is a complex idea. You now need to formulate it correctly and make predictions of phenomena that we can test, or at least test in principle. If it is completely unobservable then is it really there?

 

 

On somewhat of a side note, if the universe is expanding outward like most of the scientific community believes, then what is it expanding into?

 

This is a common misunderstanding of the expansion of the Universe. It has been addressed several times on this forum before.

 

 

 

Infinity may be hard to comprehend, but for me, all these things just "ending" somewhere seems much more unlikely...

 

In the words of Steve Harris;

 

Infinite dreams I can't deny them

Infinity is hard to comprehend

I couldn't hear those screams

Even in my wildest dreams

[michel123456]

I agree. But again, we are looking at things from a perspective relative to human knowledge. Why would the building blocks of matter for the next "plane of existence" if you will, look anything like our own? I wasn't suggesting that everything follow a specific pattern on down the line, just that it could exist. In fact what you stated, is exactly what I believe. Although we could never observe it, it would be unlike anything we could possibly understand.

 

As for the other end of the spectrum, I have always had an interest in the smallest particles as well. Although again, we are always trying to find "the smallest" component of matter that is the basis for everything. Again, I'm not so sure this exists. People used to believe matter consisted of the four elements (fire, water, earth, and air). They then moved on to basic atomic theory. Just over 100 years ago we discovered subatomic particles. Only recently have we come up with the idea of hadrons and quarks, which tend to be the smallest identifiable matter at the moment. Since everything in the universe tends to be infinite (time, space, etc), don't you find it unlikely that we could discover a finite "beginning" of matter? Say an electron or quark is deemed the smallest particle of matter. What would you see if you zoomed in infinitely on that particle? Doesn't everything have to consist of "something"? Or do we get to a point where everything exists as pure energy?

 

I have a non standard Point Of Vue.

 

Looking outside at the universe, I believe that we will never be able to see bigger than [insert-here-what-you-think-is-the-biggest-thing]. I think it is admitted by standard cosmology: there is a horizon.

Looking inside I believe the same phenomena occurs. I believe that we have by nature a kind of horizon that will not allow us to see smaller than [insert-here-what-you-think-is-the-smallest-thing].

 

To me the reason is that everything is relative, even the big and the small.

I believe there is no absolute size, and as a matter of consequence, there is no elementary particle. But i cannot prove it, that is the reason why i use the word "believe".