# Tag Info

## New answers tagged dimensions

0

We do physics in a space of some number of dimensions. We think space exists and, as confirmed by our eyes and hands, is a big place that needs coordinates to specify its many locations. Your question is based on that assumption. Then maybe there is some smallest pixel in this space. Instead of specifying n=4 coordinate values for the pixel, perhaps we ...

1

It seems the keyword OP is searching for is AdS/CFT correspondence. The holographic principle in string theory is realized between a gravity theory in an $n$ dimensional AdS bulk manifold $M$ and a gauge CFT on an $n\!-\!1$ dimensional boundary $\partial M$. In the most famous example, the 10 dimensional target space of superstring theory is a product of a ...

0

In Electrostatics you can write $F=qQ/(4\pi\epsilon_0 r^2)$ in 3D, or as $\vec\nabla \cdot \vec E = \rho/\epsilon_0$ and $\vec F=q\vec E.$ And the later generalize to 2d as a $1/r$ force. In Newtonian Gravity you can write $F=mMG/r^2$ in 3D, or as $\vec\nabla \cdot \vec C = \rho 4\pi$ and $\vec F=m\vec C.$ And the later generalize to 2d as a $1/r$ force. ...

0

They are three dimensional! Two of the dimensions tell us where to locate a point on the surface, and the third tells us how high the wave is above the surface. Or to put it another way, the value of the wave is the "vertical disturbance".

0

The waves are of 1D,2D,3D and if their nature is described within those dimensions of space. 1D Waves : The direction of propagation of wave and the oscillation of the particles of wave are in same direction.(Spring Waves) 2D Waves : The direction of propagation of wave and the oscillation of the particles of wave are perpendicular to each other in the same ...

0

We (humans) exist in and so perceive our world as one of 3 dimensions in space. Although some physical phenomena we observe may appear to be 2 dimensional in nature, if observed more closely we will see that behavior poking its way into the third dimension somewhere. Strictly speaking 2 dimensional behavior cannot exist in a three dimensional world. While ...

3

There are two different kinds of wave here. The ones that you see on the surface are the (IMO) badly named Gravity Wave (not to be confused with a Gravitational Wave), which is the familiar phenomenon of waves on the ocean surface and arise at the interfaces between dissimilar fluids. Their phase velocity is $\sqrt{\frac{g}{k}}$ and the group velocity ...

1

Do physicists have idea about medium that would be required to perceive other dimensions? No, I'm afraid not. For example, to sense the existence of any object, we have eyes as receiver and photons as the medium. Similarly we have ear and sound-waves to hear, nose and air to smell and skin to receive the touch etc. And probably all these mediums ...

5

If our universe has extra dimensions, they exist at each point of space, even in the vacuum. These extra dimensions have a certain universal shape and size. The size is almost certainly a tiny one – most like comparable to the Planck length $10^{-35}$ meters but possible to be up to 0.1 microns in some unlikely "large extra dimensions" models. The shape of ...

2

General relativity in just one dimension will always be flat, as all 1D manifolds are diffeomorphic to flat space : $$ds^2 = -f(t) dt^2$$ As you can perform the variable change $$\frac{dt'}{dt} = \frac{1}{\sqrt{f(t)}} \rightarrow t' = \int \sqrt{f(t)} dt$$ Giving you ds^2 = - ...

3

The question asks simultaneously about both Newton gravity (NG) and Einstein gravity/general relativity (GR), which are two different theories. For Newton gravity (NG) in 2+1D, the gravitational force is inversely proportional with distance. More generally, in $n$ spatial dimensions, then the gravitational force $F\propto r^{1-n}$. This is due to Gauss' ...

1

Technically speaking, manifolds are by definition topological spaces, which resemble locally an inner-product space. Since there are vector spaces (with a dot product) of infinite dimension, then there shall be infinately-dimensional manifolds as well. The infinity of the dimension is not a problem for the tensors as well - each multi-linear function over a ...

Top 50 recent answers are included