What are Dimensions? A Beginner's Guide

[NanakiXIII]

It might seem like a strange or stupid question, but I really don't know. Of course I know those three basic dimensions, height, length, width, which we all learn in school, but I can't seem to grasp how Time fits into that row.

I also read this theory about a ten-dimensional universe that split into ours and a six-dimensional universe at the big bang. What would those extra dimensions be?

I don't really understand, so I thought I'd start with a basic question, what are dimensions?

Oh, and I'm sorry if this is not the right forum, but I really can't tell where this question would belong.

 

[chroot]

The number of dimensions a space has is the number of independent coordinates that must be specified to denote a unique point in the space.

If you want to meet me at the pizza parlor for dinner, you need to give me four coordinates: the x, y, and z coordinates of the parlor, plus the time you'll meet me there. In that way, our universe has three spatial and one time dimension.

- Warren

 

[pallidin]

Nicely put, chroot. A great example.
Would this suggest that any other dimensions beyond the 4 are mathematically speculated but not acceptably proven as yet?

 

[chroot]

pallidin:

That's correct -- there is no concrete evidence for any more dimensions. According to string theory, any extra dimensions beyond four are "curled up" so small that they are basically undetectable except during very high-energy events. We haven't been able to do experiments at the necessary energies yet.

- Warren

 

[NanakiXIII]

Thanks. That explains it quite well.

 

[protonman]

pallidin:

That's correct -- there is no concrete evidence for any more dimensions. According to string theory, any extra dimensions beyond four are "curled up" so small that they are basically undetectable except during very high-energy events. We haven't been able to do experiments at the necessary energies yet.

- Warren

If they are curled up then when they curl they must curl to the north, south, east, west or some combination. Therefore they must move through at least one of the existing three spatial dimentions.

 

[Gokul43201]

There are other dimensions, but let's say that they are not important now, because of their nature. This is a very complex subject to talk about, but a bad analogy may be given. Consider a really long and thin rod. It looks like this rod has only one dimension, length, but if you look very closely, you see that it has thickness too. The extra dimensions of space are kind of like the thickness of the rod - they are coiled up so tightly, that they are hard to notice at normal scales.

 

[Gokul43201]

No, they don't move through the existing spatial dimensions - if they did, they would not be dimensions themselves. Using the rod analogy, the radius has no component along the length.

Don't try to picture the curling from a 3D point of view when you are talking about dimension other than the 3.

 

[protonman]

There are other dimensions, but let's say that they are not important now, because of their nature. This is a very complex subject to talk about, but a bad analogy may be given. Consider a really long and thin rod. It looks like this rod has only one dimension, length, but if you look very closely, you see that it has thickness too. The extra dimensions of space are kind of like the thickness of the rod - they are coiled up so tightly, that they are hard to notice at normal scales.

This is a terrible analogy used by scientists who want to explain their ideas to popular audiences. There is no such thing as a 1-D rod. Any rod that exists must exist in 3-D. Everyone [except some physicists] know this.

 

[protonman]

No, they don't move through the existing spatial dimensions - if they did, they would not be dimensions themselves. Using the rod analogy, the radius has no component along the length.

Don't try to picture the curling from a 3D point of view when you are talking about dimension other than the 3.

Take a sheet of paper. If you curl it in any way you are moving through [at least] on of the three spatial dimentions.

 

[chroot]

protonman,

This is not the place to attack theories you don't understand.

- Warren

 

[protonman]

protonman,

This is not the place to attack theories you don't understand.

- Warren

Is there any place you won't hide from views that challenge your understanding?

 

[chroot]

protonman:

Please respect our policies, or you will be unable to post here anymore.

- Warren

 

[protonman]

protonman:

Please respect our policies, or you will be unable to post here anymore.

- Warren

The policy to avoid any question that you can't answer?

 

[chroot]

protonman:

This is your last warning.

- Warren

 

[Gokul43201]

Chroot,

you haven't seen the fun over at the "non-conservation of KE in an inelastic collision" post.

 

[HallsofIvy]

If they are curled up then when they curl they must curl to the north, south, east, west or some combination. Therefore they must move through at least one of the existing three spatial dimentions.

No, that's not true- at least not in string theory where additional dimensions are necessary.

Take a sheet of paper. If you curl it in any way you are moving through [at least] on of the three spatial dimentions.

If you ASSUME that there are only three dimensions, that's true, however, the original question was about additional dimensions. Chroot was answering in that spirit.

This is a terrible analogy used by scientists who want to explain their ideas to popular audiences. There is no such thing as a 1-D rod. Any rod that exists must exist in 3-D. Everyone [except some physicists] know this.

Even physicists know that (it's just some mathematicians who really deal with 1-d rods)- if such things did exist, then this wouldn't be an analogy, would it?

Is there any place you won't hide from views that challenge your understanding?

Where did you "challenge" anyone's understanding? You just said "no, it's not true" without any sort of explanation.

The policy to avoid any question that you can't answer?

Perhaps you should read the policies before you post. In any case, you are correct that this is a question we can't answer- we can't answer questions that assume things that are not true (in this case, that there was any "challenge".). IF you have something to say about dimensions that is different from what everyone else believes, then you may post that under "Theory Development".

 

[electronman]

No, that's not true- at least not in string theory where additional dimensions are necessary.

Then you must explain why it is not true.

If you ASSUME that there are only three dimensions, that's true, however, the original question was about additional dimensions. Chroot was answering in that spirit.

You don't understand my question. Regardless of whether there are 3 dimentions or more the question still stands. If you accept 10 or 11 dimentions you need to resolve my objection.

Even physicists know that (it's just some mathematicians who really deal with 1-d rods)- if such things did exist, then this wouldn't be an analogy, would it?

This is not true. Physicists accept point particles in QFT.

Where did you "challenge" anyone's understanding? You just said "no, it's not true" without any sort of explanation.

Maybe you are not that intelligent so I will give you the benefit of the doubt. All my attacks are supported by reason. The example of how folding a sheet of paper.

Perhaps you should read the policies before you post. In any case, you are correct that this is a question we can't answer- we can't answer questions that assume things that are not true (in this case, that there was any "challenge".). IF you have something to say about dimensions that is different from what everyone else believes, then you may post that under "Theory Development".

Not everyone else believe what you people say. There are many people out there who question these ideas.

This site is extremely anti-scientific and anti-intellectual. Your contempt for views that challenge your accepted dogma parallels totalitarian dictatorships. You are not mainstream. You are frindge bunch of little men who have no capacity for a challenge. You behavior is an insult to all people like Newton and Einstein who you claim to hold in esteem.

 

[MiGUi]

'Dimension' is a math concept, the dimension of a vectorial space is the number of elements in a base. We take this concept to a system of coordinates and we say that the space has at least, three coordinates. Three values to put a point in the space without ambiguity.

But since dimension is a math concept, we can not say that "dimensions over four are not proved" because maths are abstract, not real. It turns real with physics :)

I think that say we live in a 4D world is false, since special relativity (with minkowsky's perception of space) is only a model, a way to tell us why the universe is as it is ... but it's only a model (hey, imagine a 4th dimension of imaginary time takes a lot of headache :) ).

Moreover, the 3D are only a geometric? way to explain our world.

 

[electronman]

'Dimension' is a math concept, the dimension of a vectorial space is the number of elements in a base. We take this concept to a system of coordinates and we say that the space has at least, three coordinates. Three values to put a point in the space without ambiguity.

But since dimension is a math concept, we can not say that "dimensions over four are not proved" because maths are abstract, not real. It turns real with physics :)

I think that say we live in a 4D world is false, since special relativity (with minkowsky's perception of space) is only a model, a way to tell us why the universe is as it is ... but it's only a model (hey, imagine a 4th dimension of imaginary time takes a lot of headache :) ).

Moreover, the 3D are only a geometric? way to explain our world.

You are right. We can not move through time in the same way we move through space. But, for an event to be described the same by all observers in all reference frames time and space must be united [mathematically]. If we apply the same logic to string theory it is not that the six [or five] extra dimentions are "space" dimentions in the same sense as the three existing spatial dimentions.

Physics comes down to making measurements of physical events. In order to make certain measurements, phenomena such as time and space must be mathematically unified. Just like in some Kaluza-Klein theories E&M is seen as a fifth dimension without any matter. This may be just a useful way to develop a model and make measurements. It most likely is necessary to enforce conservation of energy.

 

[ahrkron]

The example of the folded piece of paper is not properly built. The "bending" of the paper can indeed fall into the regular three dimensions even if there are more, much in the same way as a line can bend in two dimensions even when three are available; however, it can easily be shown that in a multidim'l space, such need not be the case.

After you work for some time with the math of more than three dimensions, it is not so hard to realize how the behavior would be of those objects. It is quite logical; and, although counter-intuitive, it is a nice door to cross (especially because it allows you to realize how misguided your intuition can be sometimes).

 

[JasonRox]

This is more of a rookie, amateur, odd physics kind of forum.

This isn't the place to go into details. Personally, it would be a big waste of chroot's time if he had to "prove" everyone wrong everytime someone posted a question about something.

The best way to go about this is to go in a forum that is appropriate. Chances are it has been discussed. Remember, most people might be reluctant to start a new thread, so you will have to spend quite some time going through the 30 pages of discussion. No sense posting the same question that was answered on page 12, or 21.

The sad part is, sometimes it may take an entire book or hundred of pages to explain/prove something.

What makes you think chroot or any physicists can do it in ONE post?