# Tag Info

## New answers tagged dimensions

0

Yes, a particle can have potential energy in one dimension as potential energy depends upon the configuration of the body. We can have configuration in one dimension as in hook's law and hence potential energy.

2

Sure, a particle can have potential energy in one dimension. Just look at Hooke's Law or the gravitational force. Both of those are conservative forces in one dimension ($x$ and $r$, respectively) that have a corresponding potential energy. In higher dimensions, nothing has to change, but it is possible to have potential energies which depend on the value ...

0

I'd like to point out that there is a big difference between the physical reality and the mathematical model describing it. Science has developed various mathematical models to describe the physical reality: the universe of Newton is $T\times E_3$ where $T$ is the time-axis (geometrically speaking, a copy of the real line) and $E_3$ is the euclidean ...

2

We could easily prove that more than four dimensions exist simply by observing a fifth dimension, but proving that only four dimensions exist is much harder and probably impossible. This is an example of the general case that proving something doesn't exist is usually impossible outside the halls of Mathematics. I wouldn't stake my life on no proof being ...

6

The dimension of the string is a special case of the concept of dimension for a much more general class of objects called manifolds. Manifolds are a mathematical abstraction and generalization of the concept of a surface (like the surface of a sphere). The dimension of a (real) manifold is, roughly speaking, the number of coordinates (real numbers) ...

0

We can perceive more than three dimensions; in physics the world in which we live is modeled as space-time, a four-dimensional place. I don't know about you, but I'm pretty sure I have the ability to perceive the passage of time. One might also reasonably argue that we can perceive more than three dimensions in other physical contexts as well; it comes ...

1

Modern mathematicians would use a very rigorous approach to your question but i'll retain the old approach(Euclid's approach) which might be technically wrong but it is how i understand the word one dimensional. i'll mention the informal definition of point and line from the work of Euclid :Euclid's Elements. A point is that of which there is no ...

0

You can definitely represent a 3d QHO wavefunction as a composition of radial components and angular components (spherical harmonics).

2

You can derive the desired expression in the following way: \begin{align}\delta(R_{ab}R^{ab}) &=\delta R_{ab} R^{ab}+R_{ab}\delta R^{ab}\\ &=\delta R_{ab}R^{ab}+R_{ab}\delta R_{cd}g^{ca}g^{db}\\ &=\delta R_{ab}R^{ab}+R^{cd}\delta R_{cd}\\ &=2R^{ab}\delta R_{ab}\\ &=2R^{ab}\delta(R_{cadb}g^{cd})\\ ...

5

the article in wikipedia says that in string theory the particles at lower level are broken down into one dimensional strings, but I understand that only a straight line can be one dimensional, how are these loop like strings still said to be one dimensional ? Maybe this will help: In mathematics, the dimension of an object is an intrinsic property ...

1

A plane charge would be an infinite 2-dimensional sheet with constant charge density. Already in a line charge you have neglected edge effects, because the $1/r$ dependence holds true only near the line provided you are far away from the end-points. Similarly, for a plane, the constant electric field holds true provided that you are much closer to the plane ...

3

While keeping the array page $9$ in ref1, already given, in mind, we add a new ref2, especially fig $1$ page $7$, paragraph $2.2.3$. $D = 6$, page $11$, table $5$ page $13$, and discussion page $12$ From fig $1$, page $7$, we see, that in $D=6$, the $N=2$ supersymmetry corresponds to a $(N_+, N_-) = (1,0)$ supersymmetry Looking at the discussion page $12$, ...

1

Ok, this question requires a more careful answer than what was presented here. First, extra-dimensions appear in string theories or M-theory (which is in fact not a well defined or well known theory, if any). Considering only the bosonic string we have the Weyl invariance. If you calculate the energy momentum tensor then the Weyl invariance implies that its ...

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