Dimensions Definition and 40 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.

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  1. NODARman

    B How to describe complicated dimensions?

    Hi, just wondering if the dimension of velocity is m/s that can be described as what distance is passed in a specific time, then how can I describe volt which is kg•m²÷s³÷A? Mass in the area that moved... I can't even imagine. Thanks.
  2. H

    A quite verbal proof that if V is finite dimensional then S is also....

    If a linear space ##V## is finite dimensional then ##S##, a subspace of ##V##, is also finite-dimensional and ##dim ~S \leq dim~V##. Proof: Let's assume that ##A = \{u_1, u_2, \cdots u_n\}## be a basis for ##V##. Well, then any element ##x## of ##V## can be represented as $$ x =...
  3. S

    A Branes with any number "n" of dimensions and laws of physics?

    I had a few questions about this paper by Nima Arkani-Hamed, Georgi Dvali and Savas Dimopoulos (https://arxiv.org/abs/hep-th/9907209) which is closely related to the concept of branes (https://en.wikipedia.org/wiki/Brane) 1. The authors of the paper mention that the branes in the model could...
  4. TheHeraclitus

    I String theory in 4 dimensions?

    Non-critical string theory, on Wikipedia it says: Has it been experimentally disproven or are other reasons for its apparent obscurity?
  5. S

    I Brane cosmology without string theory?

    There are several models of brane cosmology (https://en.wikipedia.org/wiki/Brane_cosmology) and several physicists working in this field (e.g Lisa Randall and Raman Sundrum), but as you will notice, apparently they are all directly related to string theory. This has several consequences, for...
  6. S

    A String Theory in N dimensions?

    String Theory and related theories like M Theory have strong constraints in the number of dimensions where they can be formulated (for example, in the case of M theory, it is only allowed in 11D or in the case of bosonic string theory is only allowed in 26D. Since string theory and related...
  7. Lars1408

    I Does a 2-dimensional world really exist?

    When we try to explain different dimensions we say that higher dimension beings have control over lower dimension beings. If a sphere moves trough a 2D world, the 2D beings will see a dot appear followed by a line which is increasing in size. Thereafter, the line decreases in size and becomes a...
  8. N

    I Dimensions and dark matter

    Is it correct that dimensions more than the three (4th being time) that we perceive can be mathematically modeled but as yet remain unobserved? If so, is it possible that dark matter/energy are "elements" which exist in those higher dimensions, and as such remain invisible to those constrained...
  9. M

    I Why does quantum mechanics believe that gravity is a field?

    According to general relativity, gravity is simply the side-effect of bending the geometry of space-time. As a thought experiment imagine a 3D image being projected from a 2D hologram - the distance between the actual 2D pixels in the 2D plane always remains constant, yet depending on the shape...
  10. S

    A Do Holographic Screens eliminate holographic dualities?

    Do Holographic Screens eliminate the need of finding holographic dualities? There are various models in physics based on the famous holographic principle (https://en.wikipedia.org/wiki/Holographic_principle) This does not always work since in these models we must find a correlation between two...
  11. A

    B Extra dimensions

    Why do physicist presenting extra dimensions with 2d creature experiencing 3d space with object falling through 2d dimension. And that, that 2d creature can see only a slice of the 3d dimension. If time == space that means that 2d creature also experiences time because objects are moving...
  12. Ginosko

    B Does dimensions have the same meaning in the Quantum world?

    Does dimensions and time have the same meaning in the Quantum world? Maybe that explain weird things as the spooky action at distance. What evidence are about the real existence of a 3 geometry dimensions world at quantum level? Maybe even time have a different meaning in the quantum world.
  13. pairofstrings

    I Please help me understand Complex Numbers

    Hi. If you have seen the above image which shows a parabola then you can also see that there is a colored portion of the parabola that have solution in "another dimension" - the "another dimension" can give me new numbers to form a solution of a function like f(x) = x2 + 1. 1. Is this "another...
  14. A

    Uncertainty/error of a volume is greater than the normal volume

    Homework Statement I have an empty cylinder with an external diameter of (23.0 ± 0.5) mm, an internal diameter of (22.5 ± 0.5) mm and a height of (60.0 ± 0.5) mm. I need to calculate its volume with its uncertainty/error. Homework Equations The Attempt at a Solution I do it like this...
  15. Gabriele99

    I Spacetime Of Flatland

    I started this post on physics.stackexchange but it's too vague for that site, so here I am! :) I'm trying to really get the intuition of spacetime. This video explains how Minkoswki was the first to think that maybe our universe does not consist of a 3d space which evolves in time, but rather...
  16. V

    I Hidden dimensions and quadratic term of a free field

    Consider a free real scalar field. The quadratic term in field of spacetime implies that a universe of these free particles is created, annihilated, recreated, and so on moment by moment. In this video Susskind explains the quadratic term in the Lagrangian youtu.be/D7yXoNAg3J8 (At minute...
  17. scottdave

    Insights Make Units Work for You - Comments

    Greg Bernhardt submitted a new PF Insights post Make Units Work for You Continue reading the Original PF Insights Post.
  18. J

    I Are dimensions real?

    I wonder if dimensions of space are real things, or just a way that humans describe space, rather like 'good' and 'evil' are just ways that humans describe behaviour, but good and evil are not themselves real. So just as good and evil are not real, perhaps dimensions are not real, and space...
  19. T

    B Why does physics consider only 3 of 6 dimensions

    This may seem a very elementary question, but I don't believe it is; so I put it in the advanced section. I'm mathematically experienced, and this question has stumped Ph Ds. I haven't figured out why space is usually described in terms of only 3 spatial dimensions rather than six: x,y,z, Tx...
  20. B

    I Hamiltonian for spin-1/2 particle in B-field: units issue

    Take a spin-1/2 particle of mass ##m## and charge ##e## and place it in a magnetic field in the ##z## direction so that ##\mathbf B=B\mathbf e_z##. The corresponding Hamiltonian is $$\hat H=\frac{eB}{mc}\hat S_z.$$ This must have units of joules overall, and since the eigenvalues of ##\hat S_z##...
  21. Kaura

    Higher Dimension and Randomness

    I often here claims that higher dimensions such as the 5th and 6th dimensions deal with different possible realities, be it branching off or from different start conditions. I find this confusing and would like to have it cleared up how it is possible for different so called realities to occur...
  22. haruspex

    Insights Can Angles be Assigned a Dimension? - Comments

    haruspex submitted a new PF Insights post Can Angles be Assigned a Dimension? Continue reading the Original PF Insights Post.
  23. Nader AbdlGhani

    I Why Planck's Constant Has Dimensions and a Unit?

    Despite being a constant, It has both dimensions and a unit, can someone kindly explain why ?
  24. C

    Mathematics of The Multi Dimensional Universe

    What are the mathematics behind multiple dimensions? Does mathematics allow for the existence of more than four dimensions? What allows the ability to possesses more that four dimensions, if there is already proof? I looked around, but I didn't find much by way of the answer I was looking for.
  25. Ryan Reed

    B How would you calculate RF cavity dimensions?

    In a linear accelerator that use cavities and microwaves or radio waves to accelerate particles, how would one find dimensions such as cavity openings, cavity size, length between cavities, etc.
  26. P

    B Division for kids

    I am following up my 8 years old daughter's homework, and want to show her how division and multiplication work together , such as in division by a fraction : am I right if I say " we divide chocolates by boxes and 6 chocolates divided by half a box means 6 x 2 half boxes = 12 in one box ? " or...
  27. R

    I Transformations in higher dimensions

    Is there an alternative set of equations similar to Lorentz Transformations that transforms vectors from one dimension to a higher or lower dimension?
  28. S

    Volume in n dimensions

    Hello, Surfing across the internet, I learned that the volume of a sphere in n dimensions can be expressed by V(n) = (Π^(n/2)) / Γ((n/2)+1), where n is the number of dimensions we are considering But if we consider n=0, then we get 1. So, how do we interpret this? I mean what does volume in zero...
  29. P

    Are 10 dimensions related to the tensor of 3d

    I think I've read the the tensor in three dimensions has 10 elements in its matrix(?). Is this related to the 10 dimensions in some forms of string theory?
  30. joneall

    Units if conversion between covariant/contravariant tensors

    I am still at the stage of trying to assimilate contravariant and covariant tensors, so my question probably has a simpler answer than I realize. A covariant tensor is like a gradient, as its units increase when the coordinate units do. A contravariant tensor's components decrease when the...
  31. E

    How do physicists approach dimensions higher than 3rd?

    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
  32. R

    Are spatial and temporal dimensions interchangeable?

    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...
  33. Dimitri655

    What exactly is a dimension?

    Hey guys! After watching another awesome video of minutephysics: I couldn't help but wonder, what is a dimension? Thanks for your replies in advance,
  34. I

    Do dimensions of a piezoelectric material affect voltage?

    Consider a block of a piezoelectric material sandwiched between two parallel plate conductors, sort of like a parallel plate capacitor with a piezoelectric material as its "dielectric." If applying the same pressure to two of these configurations, does the thickness of the piezoelectric block...
  35. Ien Cleary

    Why does imaginary time behave like space?

    I know what imaginary numbers are, but I'm struggling to understand why the Lorentz transformation makes a time-like dimension space-like. I suppose what I'm really asking is what is the difference between time-like and space-like. I've read that it has something to do with special relativity...
  36. Saffat Rafsan

    How to imagine higher dimensions?

    In the links below Carl Sagan and TED-Ed described about higher dimension: and here's a description of Brian Greene: Carl Sagan and TED-Ed explained, we can not see the higher dimensions because we are limited to perceive only three dimensions. They didn't say a dimension can be small or...
  37. Einstein Devotee

    Time dilation why or how, Special Relativity causes

    I understand the theory of special relativity and the mathematics which support it. I even understand that the time dilation has been proven. Therefore I am going to ask a question which on first blush may appear that I disagree with it but that is not the case. The question I can not seem to...
  38. T

    Can time have more than one dimension?

    hi guys, i am new here, not even sure this is right place to put this questions, I always understood time as a 4 dimension, just a diferent reference when compared with x,y and z. but is it possible that we r trying to see it in a different way? is it possible that time itself have its own x y...
  39. S

    Wrapping a 3D space wihtin a 4D space

    Let’s imagine a moving point bound to a 2D plane. If we wrap this plane on a sphere within a 3D space the point would now eventually end up at the same position while moving in a seemingly fixed direction (it is actually not fixed in the 3D space). I am now wondering: Can a 3D hyperplane be...
  40. M

    Imaging a Parallel Dimension

    Assuming that the double slit experiment creates interference patterns when electrons interact with themselves (or 'other' selves) from a parallel 'space' - one wonders if one can 'image', or at least gain more information about that other 'space' (dare I use the word 'dimension'?) in which the...