What are all the Dimensions

[Raider5678]

I have heard alot about the different dimensions, I understand 1D, 2D, 3D, but 4D and 5D are a little confusing to me. Time is supposedly a dimension because you CAN travel through it given the right conditions(I.e gravity anomaly) But the 5th dimension is completely out of my understanding. I have read that there are 10 dimensions (http://www.universetoday.com/48619/a-universe-of-10-dimensions/) but I think that may be just a little bit leaning towards a theory rather then fact. If someone can explain what the dimensions are and how they work that would be nice.

Thanks!

 

P.S. I know I am going to take some heat about the gravity anomaly but if I do take heat for it at least I'll learn what the proper reference to it is.

[Strange]

Dimensions are the number of pieces of information you need to uniquely locate a point. For example, if you want to meet someone, then you will need to specify three spatial dimensions (e.g. latitude, longitude and altitude) plus the time = 4 dimensions.

 

Dimensions above these (as far as we know) only exist as mathematical abstractions. The mathematics of string theory requires 10 (or more?) dimensions and there are various reasons (excuses ) why we can't see them: the most common being that they are wound up really small.

[Phi for All]

I have heard alot about the different dimensions, I understand 1D, 2D, 3D, but 4D and 5D are a little confusing to me. Time is supposedly a dimension because you CAN travel through it given the right conditions(I.e gravity anomaly) But the 5th dimension is completely out of my understanding. I have read that there are 10 dimensions (http://www.universetoday.com/48619/a-universe-of-10-dimensions/) but I think that may be just a little bit leaning towards a theory rather then fact. If someone can explain what the dimensions are and how they work that would be nice.

Thanks!

 

P.S. I know I am going to take some heat about the gravity anomaly but if I do take heat for it at least I'll learn what the proper reference to it is.

 

It's a coordinate system for determining any spot, both physically and temporally (x, y, & z coordinates to pinpoint the spot in space, and t to let you know when to be there).

 

I had it explained this way. 1D is a line, and if you take every point on that line and move 90 degrees, you have 2D, length and width, in this case in a flat square. Now take every point on that square and move 90 degrees from that, and you'll have a 3D cube. NOW, take every point on that cube and move 90 degrees, and you'll have a 4D hypercube. That's the one that's difficult to grasp. How do you move 90 degrees from every side of a cube?!

 

The rest (including the 4th spatial dimension) are part of different theories, which is the way all science works. When you say something is theoretical rather than fact, you're misusing the term "theory". Theory is the best you can get in science. Theoretical doesn't mean "unsupported guess". Science doesn't try to "prove facts". It's all about the evidence that supports a concept, and a theory is a model of how we're explaining reality.

[EdEarl]

I'm not a scientist, but will share my opinion about all the dimensions, specifically how they came to be a hot topic. Einstein worked on a unified field theory to mathematically link all of physics. Since then theorists continue that effort with string theory. To make string theory math model the subatomic particles, more than three dimensions and time are needed. It is a workable hypothesis, and the LHC at Cern may be able to find evidence. But, no one knows for sure.

[ajb]

To make string theory math model the subatomic particles, more than three dimensions and time are needed.

A little more carefully, the quantum theory of a superstring is only consistent in 9+1 dimensions. In other dimensions the superstring has what we call an anomaly, which means that the methods of producing a quantum theory from the classical theory break down.

[Raider5678]

Dimensions are the number of pieces of information you need to uniquely locate a point. For example, if you want to meet someone, then you will need to specify three spatial dimensions (e.g. latitude, longitude and altitude) plus the time = 4 dimensions.

 

Dimensions above these (as far as we know) only exist as mathematical abstractions. The mathematics of string theory requires 10 (or more?) dimensions and there are various reasons (excuses ) why we can't see them: the most common being that they are wound up really small.

I'm thinking this is the reason your title above your name is Genius. Anyway, thanks for the reply!

 

 

It's a coordinate system for determining any spot, both physically and temporally (x, y, & z coordinates to pinpoint the spot in space, and t to let you know when to be there).

 

I had it explained this way. 1D is a line, and if you take every point on that line and move 90 degrees, you have 2D, length and width, in this case in a flat square. Now take every point on that square and move 90 degrees from that, and you'll have a 3D cube. NOW, take every point on that cube and move 90 degrees, and you'll have a 4D hypercube. That's the one that's difficult to grasp. How do you move 90 degrees from every side of a cube?!

 

The rest (including the 4th spatial dimension) are part of different theories, which is the way all science works. When you say something is theoretical rather than fact, you're misusing the term "theory". Theory is the best you can get in science. Theoretical doesn't mean "unsupported guess". Science doesn't try to "prove facts". It's all about the evidence that supports a concept, and a theory is a model of how we're explaining reality.

The hypercube is something I don't understand how moving 90 degrees will get to, it looks more like a 135 degree angle to me. But then its also related to time because its moving, placing it into the 4th dimension. Nice explanation!

A little more carefully, the quantum theory of a superstring is only consistent in 9+1 dimensions. In other dimensions the superstring has what we call an anomaly, which means that the methods of producing a quantum theory from the classical theory break down.

Hence a new theory that works like the old one and doesn't break down when you reach the anomaly is wanted. To anyone working on a new theory make sure it tackles this!

[StringJunky]

Hence a new theory that works like the old one and doesn't break down when you reach the anomaly is wanted. To anyone working on a new theory make sure it tackles this!

Nah... string theory will be pimped and modded until it fits; square pegs will go into round holes.

Edited March 11, 2016 by StringJunky

[ajb]

Hence a new theory that works like the old one and doesn't break down when you reach the anomaly is wanted. To anyone working on a new theory make sure it tackles this!

 

In string theory you are forced to consider certain gauge groups and a fixed dimension so that the theory is anomaly free. By anomaly, I mean in the context of quantum field theory. An anomaly is a classical symmetry that does not pass to the quantum theory. These can be phenomenologically helpful, if the symmetries are global, but if they are local then they mess up the whole theory. It is an amazing fact that superstring theory predicts the dimension of space-time and it gets it right to an order of magnitude ;-)

[Raider5678]

In string theory you are forced to consider certain gauge groups and a fixed dimension so that the theory is anomaly free. By anomaly, I mean in the context of quantum field theory. An anomaly is a classical symmetry that does not pass to the quantum theory. These can be phenomenologically helpful, if the symmetries are global, but if they are local then they mess up the whole theory. It is an amazing fact that superstring theory predicts the dimension of space-time and it gets it right to an order of magnitude ;-)

Phenomenologically. That's a word that would impress people if you casually dropped it into a conversation. But it's about the study of conscious structures from the first person point of view so that might be a little difficult. As for string theory, that is probably the most complicated theory I have ever read about. But it makes sense once you know what it is, but either way if we could find a way to "cut" one of the strings, what do you think would happen? Not that they are a physical thing that could be cut though.

[dimreepr]

Phenomenologically. That's a word that would impress people if you casually dropped it into a conversation. But it's about the study of conscious structures from the first person point of view so that might be a little difficult. As for string theory, that is probably the most complicated theory I have ever read about. But it makes sense once you know what it is, but either way if we could find a way to "cut" one of the strings, what do you think would happen? Not that they are a physical thing that could be cut though.

 

 

The only people it would, properly, impress are those that fully understood his post; I don’t claim that but I do understand that you don’t.

[Phi for All]

The hypercube is something I don't understand how moving 90 degrees will get to, it looks more like a 135 degree angle to me. But then its also related to time because its moving, placing it into the 4th dimension. Nice explanation!

 

The hypercube doesn't have to be moving. It's not related to time until you assign that coordinate (a place on a map only needs 3 dimensions to tell you where; time will tell you when something happens at that place). And you don't really "place" something into any dimension. Dimensions aren't places, they're part of the information you need in order to know where and when anything is.

 

Weird, I know. Here's something to think about. Living in 3 dimensions (even though we only see in 2D), we're able to look at a 2D object and see anything inside it (imagine a square, with 3 circles inside it). So technically, if someone could see in 4D, they could look at us 3Ders and see our insides!

[Raider5678]

 

 

The only people it would, properly, impress are those that fully understood his post; I don’t claim that but I do understand that you don’t.

I probably don't understand exactly what he said to the depth that he understands it, but I understand enough of it that I can apply it to what I'm thinking. Kind of like drawing a stick figure to represent a human. Not exactly the same, but gives you the basic concept of what we look like. By basic I mean really basic.

 

 

The hypercube doesn't have to be moving. It's not related to time until you assign that coordinate (a place on a map only needs 3 dimensions to tell you where; time will tell you when something happens at that place). And you don't really "place" something into any dimension. Dimensions aren't places, they're part of the information you need in order to know where and when anything is.

 

Weird, I know. Here's something to think about. Living in 3 dimensions (even though we only see in 2D), we're able to look at a 2D object and see anything inside it (imagine a square, with 3 circles inside it). So technically, if someone could see in 4D, they could look at us 3Ders and see our insides!

So the 4th dimension is seeing in 3D, which makes me think of every part of my body put into a pixel "cube" and then all the cubes spread out, allowing the person seeing in 3D to see what is inside me. That's the way I visualise a 4D person would be seeing, although I'm fairly certain nobody does. Additionally, a machine that could see in 3D would be a huge impact for many things. Imagine a medical machine that could see if the heart's pumping or not, where theres internal bleeding, see a collapsed lung. That would be a huge scientific improvement too.

[studiot]

Dimensions?

 

The word is almost completely meaningless without the rest of the sentence.

 

Dimensions of what?

 

There are no such things as the first, second, third, fourth or fifth etc dimensions by themselves.

Edited March 11, 2016 by studiot

[dimreepr]

By basic I mean really basic.

 

 

I realise that; but AJB’s post is far from basic.

 

 

Kind of like drawing a stick figure to represent a human.

 

 

 

That is the difference between a child like drawing and a masterpiece.

[Raider5678]

Dimensions?

 

The word is almost completely meaningless without the rest of the sentence.

 

Dimensions of what?

 

There are no such things as the first, second, third, fourth or fifth etc dimensions by themselves.

My Bad, I understand that now, in fact I understood that before this post. Thanks for the input!

[StringJunky]

 

That is the difference between a child like drawing and a masterpiece.

What?! Lowry's matchstick men pictures, not masterpieces?! Besides, that's not the essence of what he meant.

[ajb]

Phenomenologically. That's a word that would impress people if you casually dropped it into a conversation. But it's about the study of conscious structures from the first person point of view so that might be a little difficult.

It means relating to phenomenology, which in this context is the bridge between theory and experiment.

 

 

... but either way if we could find a way to "cut" one of the strings, what do you think would happen? Not that they are a physical thing that could be cut though.

You can study interacting strings and there you do have a cutting when they pass through each other. People model gases of such things on the computer.

 

 

Anyway, I think that the notion of dimension, in the common context, has been explained. It is the number of numbers needed to specify a point on 'nice' spaces. That is the number of coordinates needed so (t,x,y,z) etc. But what one should realise is that although the number of coordinates needed is fixed, how you chose these coordinates is far from fixed and you have a lot of freedom.

 

Informally, I think of a choice of coordinates as 'picking directions' (locally at least). So we have the direction x and y (say), but again this is tied to our choice of coordinates and has no deep meaning.

 

And just because, I will say that I work with spaces for which these coordinates are not real numbers but elements of a much more complicated algebra

Edited March 12, 2016 by ajb

[studiot]

Raider, thank you for the polite reply and being interested.

It is a pleasure to help someone with this attitude. +1

 

Basically we are interested in some quantity or property, (for example volume, position, energy ) that depends upon other quantities or properties. (for example volume depends upon length x width x height).

 

We call these other properties ‘dimensions’ or sometimes generalised ‘dimensions’.

In popular parlance the word dimension refers particularly spatial dimensions as with the volume example.

Generalised dimensions are more used in the energy where a body may have mechanical energy, thermal energy, electrical energy , magnetic energy, chemical energy and so on.

 

Returning to the volume example, another term of importance is

‘The number of degrees of freedom.’

This is the number of ‘dimensions’ that can be independently varied.

For a general volume that is 3

Considering the volume of baking tins that are 2 inches high, the height is fixed so there are only 2 degrees of freedom.

The fixed height is known as a constraint.

Sometimes the constraint comes in another form. For instance if we talk of the volume of baking tins with a perimeter of 40 inches if we know the length, we can calculate the width, so both cannot vary independently.

 

Finally it has been discovered that some properties appear frequently and work has been done to find the minimum and best minimum list of ‘dimensions’ that we can use throughout Science.

 

Since there are many possible candidates, international standards have settled on half a dozen on this list.

 

There are Mass, Length, Time, Temperature, Electric Current, Illumination.

 

They are given symbols M, L, T, [math]\theta [/math], I and C.

 

Remember these can all vary (they are variables) so Physics constants (such as the speed of light) do not appear here.

 

In our volume example Length appears three times and we write this as L³.

No other dimension is needed.

 

Kinetic Energy is given by one half mass times the speed squared.

 

Now the constant half is not represented, and speed is distance divided by time which we write LT^-1

 

So energy is M(LT^-1)² = ML²T^-2

 

The interesting thing is that all forms of energy can be reduced to this.

 

Does this help?

[Raider5678]

Raider, thank you for the polite reply and being interested.

 

It is a pleasure to help someone with this attitude. +1

 

Does this help?

Yes this helps a lot, thanks! I had to read it a few times, and work out the logic behind the meaning, but I eventually understood most of it. I learned what the degrees of freedom is, what generalized dimensions are, what constraints are, and that I have been forgetting to divided the mass in half before multiplying the speed when calculating kinetic energy. The only thing I didn't understand fully is what properties are, can you explain that a little bit better? Not that you didn't explain it very well the first time, but I'm sadly not scientifically minded enough to understand it. Or smart enough to understand it if it doesn't have to do with science. Thanks!

 

P.S. I removed most of his post if you can't figure out what the quote means.

[ajb]

You may find an old blog post of mine useful

 

http://blogs.scienceforums.net/ajb/2013/08/30/what-is-a-manifold/

 

In that post I describe how we can understand manifolds as spaces that locally look like R^n for some n. I do this quite informally with the intention of just giving some 'feeling' without the details.

 

I also discuss, again very informally the notion of a topological space here

 

http://blogs.scienceforums.net/ajb/2013/08/31/what-is-a-topological-space/

 

Informally a topological space is a collection of point for which we have a notion of points being 'close to each other', but we do not nessisarily have a notion of distance.

[michel123456]

You may find an old blog post of mine useful

 

http://blogs.scienceforums.net/ajb/2013/08/30/what-is-a-manifold/

 

In that post I describe how we can understand manifolds as spaces that locally look like R^n for some n. I do this quite informally with the intention of just giving some 'feeling' without the details.

 

I also discuss, again very informally the notion of a topological space here

 

http://blogs.scienceforums.net/ajb/2013/08/31/what-is-a-topological-space/

 

Informally a topological space is a collection of point for which we have a notion of points being 'close to each other', but we do not nessisarily have a notion of distance.

This "close to each other" notion, isn't it related with time?

[ajb]

This "close to each other" notion, isn't it related with time?

Time is not involved in the definition of a topological space (or manifold) at all.

 

We have a topology, which is a way of breaking up the space in to collections of point that are close to each other. What I have said here is very non-technical.

[michel123456]

I have the impression that after 100 years of Spacetime mathematicians should examine the possibility that time is indispensable before even thinking about a manifold.

[ajb]

The points on the manifold maybe interpreted as points on space-time if the manifold comes with a Lorentzian signature metric. You can use this metric to define a topology known as the Alexandrov topology which is related to the causal structure of the space-time.

 

But generally, a topological manifold or a smooth manifold has nothing to do with space or time (which is why I found your question strange).

[Robittybob1]

"TEDxBoulder - Thad Roberts - Visualizing Eleven Dimensions" was a help to me understanding the other dimensions. It was just a talk though. But there were terms in there that would help with other searches.