What is Spatial dimensions: Definition and 26 Discussions
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces.
In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions (4D) of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. Minkowski space first approximates the universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. 10 dimensions are used to describe superstring theory (6D hyperspace + 4D), 11 dimensions can describe supergravity and M-theory (7D hyperspace + 4D), and the state-space of quantum mechanics is an infinite-dimensional function space.
The concept of dimension is not restricted to physical objects. High-dimensional spaces frequently occur in mathematics and the sciences. They may be parameter spaces or configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space we live in.
A 4D planet has no axis of rotation. Nothing special about planets, all freely rotating 4D bodies have two perpendicular planes of rigid rotation. (Clifford proved this in the 19th century.)
Now there is nothing stopping us from thinking of planes of rotation here in 3D Universe. It's the...
Hi,
although there is a lot of discussion here in PF, I'd like to ask for a clarification about the definition of 'spatial x direction' in the context of flat or curved spacetime.
Consider a set of free-falling gyroscopes (zero proper acceleration) passing through an event A with different...
So I had a topic which I would like to fact check from an informed scientific source.
Basically there is an argument about whether or not an object that naturally exists in a fourth dimensional space, would by default have more than countably infinite times the energy of a 3 dimensional Object...
I need to know what is the typical extention of the (spatial) wavefunction of an atomic nucleus in a crystal, in particular I am interested to the case of a Germanium cristal.
Please together with the actual number of the size of the nuclei wavefunctions, let me know the references (articles or...
A recent post asked "why does physical space need to be 3-dimensional?"
However, the thread became infected with personal insults and was (properly) closed.
I felt sorry that PeterDonis, whose posts I respect, was subjected to this abuse !
I have read several posts which start by assuming that...
Dear Physics enthusiasts,
I'm just a curious guy, I don't have any fancy credential, and in fact I don't have formal education at all (for 'legal' purposes I'm just "literate"). I'm being honest about that right away so if that's a problem (what seems to be the case for a lot of...
I know modern physics theories make use of really high number of spatial dimensions, I wonder how relevant these high dimensions are for physics. I am only a guy from High school interested in physics, but I would like if possible a formal answer
A 2-dimensional creature living on the surface of a 3-dimensional sphere could conclude he lives in a finite, unbounded universe. Is it necessary for a 3-dimensional creature to assume there is a 4th spatial dimension in order to conclude the universe is finite and unbounded?
I have seen a...
According to general relativity, time is a dimension, one of four dimensions that form 4D spacetime - a structure which is mathematically symmetrical and homogeneous.
Should not all four dimensions, therefore, be mathematically interchangeable? Assuming that we are 3-dimensional bodies...
Homework Statement
Two objects, Red and Blue, are in inertial motion with respect to each other and are graphed on the attached Minkowski diagram (representing a third inertial frame). Red and Blue are in relative motion along the x axis, and offset slightly on the z axis such that they...
On the page 17 of this article by Max Tegmark http://arxiv.org/pdf/gr-qc/9704009v2.pdf, in figure 7, it has been argued that why spatial dimensions other than 3, is not possible for our universe. But in string theory, people are talking about 10, 11 or 26 spatial dimensions (even if these...
Basically, I'm writing a story that involves beings of 5 spatial dimensions visiting Earth. And when I say "writing" I mean "putting thoughts down on paper as they come to me" or almost that, i.e. not much thought has gone into world-building. Mostly 5-dimensionality manifests in crazy...
hello all
I am so glad to have found this forum. I've always had an interest in astrophysics, cosmology, SR/GR, etc, and no place to ask questions. I'm an engineer and was once a member of Mensa (I only left the organization because I thought other members were crazy. Sorry). So although I'm...
Hi Everyone,
I have not understood or even studied string theory.
However I was wondering whether the extra dimensions demanded by M-theory (10 spatial dimensions in that case), other string theories or even any other field theories necessarily demand the dimensions higher than four...
I have just a quick question I was wondering about and I was wondering could someone answer it here.
Is it true that for example the third dimension is composed of an infinite number of 2 dimensional planes on top of each other which give rise to width, the third dimension? If this is true...
I have just a quick question I was wondering about and I was wondering could someone answer it here.
Is it true that for example the third dimension is composed of an infinite number of 2 dimensional planes on top of each other which give rise to width, the third dimension? If this is true...
Hi everybody,
I've a started a little a game, it is based on the nokia game snake, where you have to guide the snake and eat the food.
I wrote a little script in python, and a C++ version of the game but in 4 spatial dimension. The snake moves through a euclidean 4 space.
what do you...
So I'm sure everyone here knows of the basic spatial dimensions. 1D is a line, 2D a plane and 3D a cube. There is even a 4th dimension (theoretical), the tesseract. And an infinite number of dimensions beyond, represented by various hypercubes. Finding the space taken up by one of these objects...
String theory requires 9 spatial dimensions, M-theory 10.
One followup to Verlinde's paper is this:
http://arxiv.org/abs/1002.0488
Hidden symmetries for thermodynamics and emergence of relativity
Liu Zhao
(Submitted on 2 Feb 2010)
Verlinde recently proposed an idea about the thermodynamic...
do all of the equations and postulates of the general theory of relativity apply in a universe with only 2 spatial and one time instead of 3 spatial and one time.
Why only three "non curled up" spatial dimensions?
Is there a reason (inherent in the theory) that string theory describes 10 spatial dimensions with 7 of them curled up rather than having 8 or 3 curled up? In other words, is this curling up a consequence of other parts of string theory, or is...
what do spatial dimensions higher than the third dimension mean? what do they represent. any object can be described in 3 dimensions, how are higher dimensions possible? how can you even comprehend them?
Spatial dimensions are dependent on...
...the existence of a temporal demension. According to the Elegant Universe by Brian Green, the geometry of a sphere is similar to that of a flat (2D) circle in spinning on its axis at a high speed. After reading this passage, I concieved the idea...