Dimensions

[g2006]

I was reading the thread on the 2 dimensions of time in this forum, and i just thought of somethin but please correct me if i am talking rubbish. theirs are 4 dimensions up down left right back wards forwards and time right. but time is only one dimension so would it not just account for one of the other 3 dimensions or is it in someway layer on all the dimensions. sorry if it sounds stupid somebody please explain this time thing.

Thanks

[Daecon]

I'm not entirely sure I understand what you mean, but as the dimension of time isn't a two-way direction, it can (and does) exist in the same place as the 3 spacial dimensions, all at once.

 

Does that help any?

[g2006]

yeah it helps alot but can you or someone explain how this happens as i thought that it would just apply for one dimension or have another 2 simension of time making it three dimensions , 1 for each of the specail dimensions.

thanks

[brad89]

I have started wondering why time is a dimension. Dimensions are spacial, and that is why time shouldn't operate in spacial dimensions. Why is it considered it's own dimension?

[J.C.MacSwell]

yeah it helps alot but can you or someone explain how this happens as i thought that it would just apply for one dimension or have another 2 simension of time making it three dimensions ' date=' 1 for each of the specail dimensions.

thanks[/quote']

 

You can be at a certain height at the corner of x street and y street today at 12 noon. The 12 noon applies to all 3 spatial dimensions.

[g2006]

thanks but i shoudl ahve made it more clear,how is the one dimension of time applied to all of the three other dimensions.

Whilst im on this thread can i please ask what the 11 dimensions are in what i think is called m theory.

Thanks

[Phi for All]

theirs are 4 dimensions up down left right back wards forwards and time right.

Wrong. There are 3 spatial dimensions we are able to sense. They are length, width and height (up/down, left/right, backwards/forwards are specific to a frame of reference). Each is dependent on the one before it. You can't have width without length and you can't have height without length and width.

 

There is one temporal dimension, time, and it is like a layer on the spatial dimensions. Various other theories offer mathematical possibilities for higher, smaller, curled up spatial dimensions.

[Phi for All]

Whilst im on this thread can i please ask what the 11 dimensions are in what i think is called m theory.

Please use the Search function and type M-theory. There are a few threads already started.

[J.C.MacSwell]

Wrong. There are 3 spatial dimensions we are able to sense. They are length' date=' width and height (up/down, left/right, backwards/forwards are specific to a frame of reference). [b']Each is dependent on the one before it. You can't have width without length and you can't have height without length and width.[/b]

There is one temporal dimension, time, and it is like a layer on the spatial dimensions. Various other theories offer mathematical possibilities for higher, smaller, curled up spatial dimensions.

 

I'm sure you are correct, but where is this from?

[Phi for All]

I'm sure you are correct, but where is this from?

I will search. It was either from here at SFN, Physics Forum, one of Michio Kaku's books or Brian Greene's The Elegant Universe. It might have been from Flatland, which I find referenced here.

 

The idea is that width without length is just length again. You can say you are measuring an object's height but without the length and width you are still just measuring length along one axis.

[EL]

There are two Latin words of related concepts.

1- dimano = (to flow in all directions).

 

2- dimensio = (measuring)

The second word is obviously closer to the English one and dimension is then related to measuring or making a measurement or even better (measurable).

 

In Physics (the discipline of studying natural phenomena) there are seven arbitrated dimensions (measurable phenomena). Each of the seven dimensions has been given a name and a standard base-unit of measure in the SI system:

 

Length is measured in meters.

Mass is measured in kilograms.

Time is measured in seconds.

electric current is measured in amperes.

Thermodynamic temperature is measured in kelvins.

Amount of substance is measured in moles.

Luminous intensity is measured in candela.

****

Unfortunately, the word "Dimensions" has been overloaded to include a common usage, where the physical length dimension is measured out in three orthogonal directions to indicate the volume of the minimal box that can contain an object, hence the width, length and height.

Notice that the word "length" also is overloaded to mean "how long" and not the Length Physical Dimension.

Therefore, Time is second to Length as a physical dimension but it is fourth to the 3D of an Euclidian Space.

When a body moves with a constant velocity for a finite interval of time it covers a distance, which Minkowski considered to be the 4th spatial dimension, which when generalised using the speed of light with the arbitrated base unit of time, represents a fourth dimension of all time at light speed.

This 4D-space is capable of graphing all space for all time, which is perfect for representing anything within the whole universe since ever to whenever as long as now is a zero.

[DQW]

Unfortunately' date=' the word "Dimensions" has been overloaded to include a common usage, where the physical length dimension is measured out in three orthogonal directions to indicate the volume of the minimal box that can contain an object, hence the width, length and height.

 

 

When a body moves with a constant velocity for a finite interval of time it covers a distance, which Minkowski considered to be the 4th spatial dimension, which when generalised using the speed of light with the arbitrated base unit of time, represents a fourth dimension of all time at light speed.

This 4D-space is capable of graphing all space for all time, which is perfect for representing anything within the whole universe since ever to whenever as long as now is a zero.[/quote']I don't understand 3 things here :

 

1. What exactly is "the volume of the minimal box that can contain an object" ?

 

2. Does 4 dimensional space-time become invalid if the body is not traveling at constant velocity ?

 

3. What does "since ever to whenever as long as now is a zero" mean ? And is 4D space perfect for representing what makes me confused ?

[EL]

1. What exactly is "the volume of the minimal box that can contain an object" ?

When you express the width, height and length of an irregular solid figure or even a sphere, is it not the minimal box dimensions that can contain such an object!

 

2. Does 4 dimensional space-time become invalid if the body is not traveling at constant velocity ?

No, and also bodies do not move in 4D space because it does not contain "now-time" as it must be a static zero or at the point of origin. The positive 4D spacetime is the future light-cone (in which all predictable motion will happen), and the negative one is the past light-cone (in which all histories of motion are recorded).

 

3. What does "since ever to whenever as long as now is a zero" mean ? And is 4D space perfect for representing what makes me confused ?

 

Since ever is the infinite past, and "to whenever" is the infinite future.

"Now" is the zero-point Origin of the 4D Spacetime manifold.

And, yes, 4D space is a perfect way of representing very confusing concepts and paradoxes.

My perfect understanding of 4D Spacetime manifold does not necessarily mean that I like it or think that it is useful or that it is easy to understand.

[DQW]

By the last question, I meant something like "is 4D space perfect for representing the taste of my apple", but nevermind.

 

And thanks for the replies.

[g2006]

Thanks for all the replys just going to search m theory now.

thanks

again

[□h=-16πT]

I have started wondering why time is a dimension. Dimensions are spacial, and that is why time shouldn't operate in spacial dimensions. Why is it considered it's own dimension?

 

Dimensions aren't just spacial. A dimension is an independant parameter, it could be momentum and velocity (as in phase space), the Euler angles representing orientation or anything that some function on a manifold may have as an independant variable.

[brad89]

But I did plenty of searching, and we now have found and visually represented 4D shapes. It means that the 3D parts are represented as the sides. 5D shapes must use 4D shapes to represent the sides. So, we could have infinite dimensions when looked at from the spacial point of view. But why is time able to be represented as a dimension? Time can't make room to fit into infinity!

[brad89]

I think I just have a hard time defining a dimension. What really is a dimension in the first place. I understand them because I have always just accepted them, and just moved on without asking questions. But now I have to, to understand this early before it moves on and gets even more complicated.

 

Thing is, why are dimensions involved at the same time with motion?

 

Here is another good question. Picture a 1D atom. Maybe a 2D atom. 3D atoms are what we already get. But a 4D atom? A hyper atom? How could that happen? Wouldn't that be what would make up a 4D shape?

[□h=-16πT]

In reference to the shapes in higher dimensions, they only involve spacial dimensions. Dimensions aren't necessarilly spacial.

[brad89]

So dimensions can be both spacial and mobile. Are there more mobile dimensions included, rather than just time?

 

I still have to wonder about the atom question, and that is why I wonder about the 11 dimensions of string theory.

[DQW]

Here is another good question. Picture a 1D atom. Maybe a 2D atom. 3D atoms are what we already get. But a 4D atom? A hyper atom? How could that happen? Wouldn't that be what would make up a 4D shape?

What is the difficulty with a 4D atom. If you can be content with 4D space, you should have no problem with a 4D atom (or for that matter, an n-dimensional atom, for any n)

[DQW]

So dimensions can be both spacial and mobile. Are there more mobile dimensions included, rather than just time?

I hope you did not infer this from Dave's posts - because he never said anything about "mobile dimensions". He was talking about the mathematical concept of dimensions as the basis vectors of a vector space. This is an algebraic concept.

 

It appears though, that you are interested in spatial dimensions, which is a topological (or geometric) concept. Simply put, the dimensionality of an object (or space) is simply the number of co-ordinates (or scalars) that need to be specified to identify every point in that object.

 

For instance :

 

A line, (or a circle or a parabola) is a 1-d object because every point on it is uniquely identified by a single co-ordinate. For a line (or a parabola of the form y=ax^2), specifying the x-coordinate of a point on the line (or parabola) completely specifies the location of the point. On a circle, specifying the angle (theta, from some fixed direction) completely identifies the point.

 

A plane, or the surface of a sphere (the surface of the earth, say) is a 2-d object. Any point on this object can be specified using 2 co-ordinates. On a plane, the x and y co-ordinates will do, and on a spherical surface the [imath]\theta,\phi [/imath] co-ordinates.

 

A sphere itself is a 3-d object as you need also specify the radial position to determine the location of a point in a sphere.

 

Keep in mind that these are all mathematical objects. Physically though, all objects have the same (not lower) dimensionality as the space they inhabit. In our universe, this is (to an excellent approximation, at the very least) 3. It is also important, to specify an additional dimension (in the framework of classical physics) that is important to fully describing the location of an event. This dimension is time. It is simply a useful dimension to have in your metric if you want to describe dynamics. Note, however, that some physical frameworks (such as Quantum Mechanics) do not treat time as a dimension, but still do a great job of describing dynamics.

[brad89]

What is the difficulty with a 4D atom. If you can be content with 4D space, you should have no problem with a 4D atom (or for that matter, an n-dimensional atom, for any n)

 

No, what I meant was that shouldn't a 4D atom be what would make a physical 4D shape?

[brad89]

I hope you did not infer this from Dave's posts - because he never said anything about "mobile dimensions". He was talking about the mathematical concept of dimensions as the basis vectors of a vector space. This is an algebraic concept.

 

It appears though' date=' that you are interested in spatial dimensions, which is a topological (or geometric) concept. Simply put, the dimensionality of an object (or space) is simply the number of co-ordinates (or scalars) that need to be specified to identify every point in that object.

 

For instance :

 

A line, (or a circle or a parabola) is a 1-d object because every point on it is uniquely identified by a single co-ordinate. For a line (or a parabola of the form y=ax^2), specifying the x-coordinate of a point on the line (or parabola) completely specifies the location of the point. On a circle, specifying the angle (theta, from some fixed direction) completely identifies the point.

 

A plane, or the surface of a sphere (the surface of the earth, say) is a 2-d object. Any point on this object can be specified using 2 co-ordinates. On a plane, the x and y co-ordinates will do, and on a spherical surface the [imath']\theta,\phi [/imath] co-ordinates.

 

A sphere itself is a 3-d object as you need also specify the radial position to determine the location of a point in a sphere.

 

Keep in mind that these are all mathematical objects. Physically though, all objects have the same (not lower) dimensionality as the space they inhabit. In our universe, this is (to an excellent approximation, at the very least) 3. It is also important, to specify an additional dimension (in the framework of classical physics) that is important to fully describing the location of an event. This dimension is time. It is simply a useful dimension to have in your metric if you want to describe dynamics. Note, however, that some physical frameworks (such as Quantum Mechanics) do not treat time as a dimension, but still do a great job of describing dynamics.

 

Thanks, that sums it up pretty well. The universe in approximation is made up of at least 3 dimensions. Yet, for the modern backbone of physics, an additional dimension must be included, so for that matter, it is time.

[DQW]

Yes, it would take 4-d atoms.

 

But my question is this : If you can concieve of a 4-dimensional object, why should you have trouble conceiving of a 4-dimensional atom (which itself, is nothing but an object) ?

 

All (non-fundamental) physical objects (from atoms to elephants) exhibit the same dimensionality as the space they live in.