What is Dimension: Definition and 897 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.

View More On Wikipedia.org
Recent contents Top users
  1. S

    Collisions in Two Dimension

    There is a collision between two pucks on an air hockey table. Puck A has a mass of 0.031 kg and is moving along the x-axis with a velocity of +5.5 m/s. It makes a collision with puck B, which has a mass of 0.066 kg and is initially at rest. The collision is not head-on...
  2. F

    Velocity/acceleratio in one dimension question

    Man, this is another embarrasing question. A 1000kg weather rocket is launched straight up. The rocket motor provides a constant acceleration for 16 s, then the motor stops. The rocket altitude 20 s after launch is 5100 m. You can ignore any effects of air resistance. First this question...
  3. R

    What are the implications of time being a fourth dimension?

    Spacetime raises many questions. Three-dimensional space is easy to visualise. We live in it. We can denote orthogonal axes as x, y and z and have oodles of fun with three-dimensional geometry. One wonders, is there really a fourth dimension and is that dimension time? Newtonian...
  4. F

    Acceleration In One Dimension

    ~~~acceleration In One Dimension~~~ I didn't get any replies :cry: , this is due monday, i still dun understand the concepts and all the new concepts are built on the previous ones! :frown: I was wondering if an object can have a negative acceleration and be speeding up? If so, can you...
  5. S

    Kinematics one dimension. help

    kinematics one dimension. help! hi I've had a lot of trouble with this problem and i hope someone can help me. Car B starts from rest and accelerates at 2.00m/s^2 along a straight road. Car A starts from rest at the same instant 20.0 m behind car B and accelerates 3.00 m/s^2. How far must...
  6. S

    Kinematics one dimension. help

    kinematics one dimension. help! hi I've had a lot of trouble with this problem and i hope someone can help me. Car B starts from rest and accelerates at 2.00m/s^2 along a straight road. Car A starts from rest at the same instant 20.0 m behind car B and accelerates 3.00 m/s^2. How far...
  7. E

    Quantum gravity in 4-e dimension

    let be e>0 but small so quantum gravity is renormalizable then what would be the calculation of mass and charge of it depending on e,now let,s take the limit e--->0 what would we have?...
  8. A

    How to Solve a 2 Body 1 Dimension Problem with a Dropped Ball and a Thrown Ball?

    Hello, I'm having a bit of trouble starting this problem: A ball is dropped from a height of 30 m. At the same instant another ball is thrown straight up from the ground with aspeed of 30 m/s. How long are the balls in the air before they reach the same height? I'm not sure what equation...
  9. N

    0th dimension and other dimensions

    hi :D after reading up on 10 dimensions (and how more can be added any time we need them even though they might not exist) i found it interesting how it stated that 5-10 dimensions where located in the well known 3 dimensions we see every day (with the 4th dimension being time). what i don't...
  10. P

    Difference between R^2 and R: What distinguishes them in terms of topology?

    What makes R^2 different from R? Unless I'm mistaken (which is unfortunately quite possible), R^2 has the "same number" of points as R. I'm thinking that what makes R^2 different from R is the topology, which is why I picked this forum. But what sort of conditions do we really need to...
  11. bayan

    The 4th Dimension: Learn About It Here

    HI. I was wondering if anyone can tell me a bit about the forth dimension? Any comment is welcome
  12. A

    What is the relationship between time and the 4th dimension?

    Hello, this is my first time posting, I do hope I've found the right place. I have relatively no knowledge of physics but am about to minor in it in college. The questions and ideas I am about to set down concern time, an issue of which I again know very little. While sitting idle one day...
  13. Physicsfreek

    Three Dimensional Space in the Forth Dimension

    The Lorentz Transformations on a Block of Space Reference system V, RSV, is a block of three-dimensional space that has a velocity, v, reference to a block of space that is at rest, RSR. The Lorentz transformations express the measurement of length, mass and time in RSV, as measured by RSR...
  14. N

    Is Time a Mobius Dimension in Relativity Theory?

    Is it possible for time to be a "Mobius dimension," with its non-linear topology and simultaneous one-way linear direction, as described by relativity theory?
  15. Antonio Lao

    Can Quantum Jumps Same as Dimension Jumps ?

    Can Quantum Jumps Same as Dimension Jumps ? By going back to Bohr's stationary orbits of electrons, The idea of quantum jumps was born. We can hypothesize that matter such as electrons are 4D objects and photons are 3D objects and the continuous space between orbits is a 2D continuum. So...
  16. T

    Can someone explain what the 4th Dimension is?

    Can someone explain what the 4th Dimension is?
  17. S

    Gaussian Discription of Dimension

    Nigel was polite enough to offer some discriptive views for extending awareness that I thought I too would indulge. To raise the issue, to include the GR perspective, one has to retain some comprehension and viewing of the hyperdimensional realities when it comes to the geometries? This...
  18. M

    Each dimension is perpendicular at all another

    Does this concept is connected with a pure geometry (of space)?. Thus each dimension is perpendicular at all another. It is simple for presenting graphically up to three dimensions: point, line, square, cube and ….. Further it is much more difficult. What a physical sense of...
  19. B

    4th DIMENSION EQUATIONS CALCULUS HELP

    4th DIMENSION EQUATIONS! CALCULUS HELP I have to explain the 4th dimension and hyper-space using for my High School calculus AP final project. IF someone can give me some insight or some equations to help me see and learn more about the 4th dimension it will be greatly appreciated. Some...
  20. N

    0 & 1 Dimension; question comment

    Ok, how can we see a point (0 dimensions) or a line (1 dimension) without it being 2 dimensional as well, and how can something exist within a 2 dimensional plain if dimensionality doesn’t explain something to exist. How can 3 dimensions exist if dimensionality must be infinite at any point in...
  21. A

    Motion in one dimension of a swimmer

    Hi, i need help with the following: One swimmer in a relay race has a 0.50-s lead and is swimming at a constant speed of 4.0 m/s. He has 50 m to swim before reaching the end of the pool. A second swimmer moves in the same direction as the leader. What constant speed must the second swimmer...
  22. F

    Time a Velocity not a Dimension?

    A New Theory of Time -------------------------------------------------------------------------------- My Theory is based on the notation that the reason we experince time in a smooth motion is because we are also traveling in a smooth motion. if we took the centre of our galaxy as the...
  23. N

    Is Time Travel Possible Through Mental Projection?

    Time is just a way of measuring the velocity of the motion of an object through the 3 real dimensions. In order to go into the future you would have to stop your particles for the desired amount of time (basically cryogenics). Your particles weren't present to have their effect on the future so...
  24. U

    Dimension of the electric charge

    could someone told me an experiment that ı can find the dimensions of the electric charge in therms of m, kg, sec the answer is kg^(1/2)*m^(3/2)/sn it can be found by assuming the epsilon zero is dimensionless please say me an experiment that i can check it :confused: :confused:
  25. D

    Linear Algebra - Dimension, Basis

    Linear Algebra -- Dimension, Basis Had a horrible lecture this morning and the following was presented at a lightning quick pace. I'm not sure whether I messed up my notes in my haste to get them all down or if I'm completely not understanding something. I have two sets of vectors: W =...
  26. C

    Einstein's Space-Time Continuum: Is Time a 4th Dimension?

    Did Einstein meant by space-time continuous that time is just another dimension, like the other 3? If so, why are we experiencing this one that differently? (Should this have gone in the phylosophy section?)
  27. M

    Hausdorff topological space M of dimension m

    I have printed a notes about differential geometry, and it says: -A Coo differentiable structure on a locally Euclidean, Hausdorff topological space M of dimension m is a collection of coordinate systems F Then it specifies the conditions that F must satisfy, but I'm a little lazy and won't...
  28. U

    Q: non-local effects & 4th spatial dimension

    i've been reading Brian Greene's latest book and have enjoyed his excellent analogies and metaphors for understanding quantum mechanics (among other things). IANAP, but one thing that comes to mind as a theory is that the concept of particles that are non-local having an effect on each other...
  29. S

    Gravitons in the 5th Dimension

    Can someone please explain to me or direct me to a website about the theory that there are 4 spatial dimensions, and that gravitons exist in the 4th one. I am now aware of this theory, and that this could explain why gravity is so weak. I find this really interesting, and would appreciate any...
  30. Antonio Lao

    How Does Dimension Influence Direction and Freedom in Physics?

    All Theorists, I have been searching for the complete understanding of "dimension" since the time when I fell down the stairs as a baby. There never was any difficulty when I walk or crawl around in two dimensions but for three dimensions, there were a lot of pains (I found out the hard way)...
  31. I

    What is a Dimension? Exploring the 4th Dimension & Beyond

    Hello all- This is something that has been on my mind ever since I first learned about the fourth dimension and beyond, sometime back in fifth grade. This is simply one of those things that I never really 'got'. What is a dimension? How does an n-th dimension (where n>3) exist? What...
  32. Antonio Lao

    How Does Dimensional Analysis Apply to Fermat's Last Theorem and Beyond?

    What is done in the following might be considered as “not mathematical.” Nevertheless we must be allowed to use crazy ideas if only for the sake of exploring the uncharted domains of human mathematical logic. This is not to prove again the famous math problem called Fermat’s Last Theorem. The...
  33. Mk

    Proof there is TIME as a dimension

    I want some proof there is TIME as a dimension or anything having to do with science. Time is something we humans invented to organize society and ourselves.
  34. A

    Exploring the 4th Dimension: Properties & Links

    has anybody done any thinking on the properties of a universe with four "normal" spatial dimensions? I've done a bit and some interesting properties have surfaced. I've discovered that rivers don't need bridges, sponges and screens can pass through each other, and there are several types of...
  35. S

    How Dimension is Arrived At?

    IN a Flash it Can all be explained? Currently we see unification only in supersymmetry? If this is the case how would dimension speak to this? I have been thinking about Gravity a lot, and the strength and weakness seem to me, to be only a matter of dimensional significance? What is the...
  36. G

    How can a dimension be small ?

    how can a dimension be "small" ? Sorry, I'm not much of a physicist. I have read that extra dimensions may be "small" and curled up. Since height, width, and depth appear to be limitless, I am having a hard time understanding what small means when applied to dimensions. I suspect it has...
  37. T

    Exploring the 4th Dimension: What Is It?

    hey, anyone out there care to offer their thoughts on the fourth dimension? as in what would it be, all I have is that a fourth dimensional object would seem like a 3 dimensional object moving down and then disapearing?
  38. H

    Schrodingers Equation in 3 space Dimension

    i read a book on quantium theory, it states that a vector of x = x,y,z. When i think about 3 dimensional space, we cannot see that, is that correct?
  39. M

    Tesseract or time which is the fourth dimension

    I am hoping someone can help me to develop a working definition for the term "dimension". In the past I was taught that there is the first dimension which is a single point, the second dimension is defined as this single point being extended in such a way that a second dimensional object would...
  40. A

    Fourth Dimension: Visited by Aliens?

    So my question is (and this is aimed at cmdrsponge so please reply after he has thank you) What is the fourth dimension? Where is the Fourth dimension? Are the Fourth dimensional aliens going to hunt me down and kill me for asking to many questions?
  41. D

    A theory for a FIFTH dimension .

    a theory for a FIFTH dimension... All this talk about dimensions I am sure has bored a number of you, although here is another theory! (If it has been thought of before, I apologise!) Bearing in mind 'time' is established as the 4th dimension, it occurred to me that there must in turn be a...
  42. D

    Why the 4th dimension was created

    So we start with the singularity having lots and lots of mass in it. Now this is too much mass so it pops open into the 1st dimension so just a lot of mass covering a line. Since there is no concept of time that means all this mass covering the line exists over and over again making and...
  43. Loren Booda

    Fractals of rational dimension and fractals of integral powers

    What generalizations can be made concerning fractals of nonzero rational dimensions M/N (where M and N are nonzero integers)? How does a fractal of non-integral dimension F compare geometrically to a fractal of dimension GF, where G is a nonzero integer?
  44. S

    Mass in 2D: Understanding the Concept

    I was wondering what mass means in a 2 dimensional world...
  45. Ploegman

    What would life be like in the fourth dimension?

    I would like to start off by introducing myself, my name is Jonathan Ploegman from Long Island, New York. I am 18 years old and I am new to the physics world, however I am very interested and eager to learn all that I can. I was wondering what life in the "fourth" dimension would be life. I...
  46. F

    Time as a Spatial Dimension: Is It Possible?

    I came up with an idea more than a year ago, but I've yet to take a physics course, still in high school, but please bear with me. Take the Kaluza-Klein approach that light originates from the 5th spatial dimension, at the nearly unreachable Planck length. Now, light is supposedly a vibration...
  47. A

    How Can a Hyper-Tesseract Explain High-Energy Particle Tunneling?

    I have been able to visuallize what a tesseract and its propperties look like. I then applied the same principal to a tesseract and came up with a hyper-tesseract with phase properties (the ability to access other planes of existence). Is this a possible model for mathematical explanation of...
Back
Top