Dimensions Definition and 1000 Threads

I have been trying to imagine extra dimensions for a long time now. I came across this article and it is certainly the most vivid pictures I have ever seen painted of the extra dimensions: https://phys.org/news/2014-12-universe-dimensions.html For example, it describes "In the sixth, we would...

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...

Hello. Questions: How can special relativity describe four dimensions when we only see three spatial dimensions and we experience time?Why time is the fourth dimension and not another physical quantity? Is this only a generalisation that was needed to describe more physical phenomena and the...

Wich The Program (Software) Using To Draw Statics And Dynamics Mechanichal Same This 100% When Create This below Which Program Using ? And set Dimensions Thanks For All

When drawing a tesseract in 3D how large should the inner cube be compared to the outer one?

When solving the Schrodinger equation by separation of variables to atom with one electron and in the spherical coordinates, we get $$\Psi = \Theta(\theta)\phi(\varphi)R(r)$$ Specifically, $$\phi = e^{im\rho }$$ The question is, why we adopt this particular solution, in general, we have this...

Assuming there are higher spatial dimensions are there things that exist in 3D that actually cannot exist in higher dimensions? Maybe even dimensions?

I'm trying to 3D model a specific sofa but I can't figure out the exact dimensions of each segment. I'm reasonably certain all four segments are the same size. Is there enough information here to work it out? It's the Bowie sofa from Wewood if you're curious. (Also not sure if this is the right...

Suppose I have a R^3 manifold that goes into R^3 charts, if that is possible. The manifold has curvature and is Riemannian and has a metric. I want to eliminate all curvature in R^3 charts, so I want to add another dimension to the manifold, I would extract all the curvature information from the...

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...

For a single particle, $$Z=\frac{1}{h^2}\int_{-\infty}^{\infty} e^{-\beta \frac{P^2}{2m}}d^2p \int e^{-U(r)}drd\theta= \frac{1}{h^2}(\frac{2\pi m}{\beta}) 2\pi [\int_{0}^{r_0}e^{U_0}dr+\int_{r_0}^{R}dr]$$ $$ =\frac{1}{h^2}(\frac{2\pi m}{\beta}) 2\pi [e^{U_0}(r_0)+(R-r_0)]=\frac{\pi...

As of 2020 is there any proof of tiny extra dimensions or observations of them?

If it were supposed that time were a 4th non-spatial dimension how would it influence the gravitational movement ? The problem I have when trying to solve this invented problem is that Newtonian physics works in coordinates and that there are a lot of ways to find 4d 3+1 hyperbolic-spherical...

I'm watching Sean Carroll's video on symmetry [relevant section at around 8:05] He talks about 120 degree rotations of triangles that leave them invariant. Then he proceeds to talk about flipping them with an interesting (at least to me) remark - "there's nothing that says I'm confined to...

I understand how to get the dimensions that equal 8436m^3. What I don't understand is how to find the range of all possible dimensions. I solved the inequality to get ##6w^{3}-13w^{2}-5w-8436## Using systematic guessing I found the root is x=4, so the factor is x-4. Dividing (x-4) into...

Since a phone is an object which can show three dimensions on a two dimensional screen, I wondered what a two dimensional being would see when they look at a smart phone or any other screen. So:What would a two dimensional being see, when they look at a smartphone?

Since we don't know how far does it move in y-axis, I assumed that only x-component does work. a) W=Fx*Δx = 50N*(-6m) = -300 J b) Θ = arctan(12/50) = 13.5° But, I'm not sure that did I do this in right way...h

I don't know how to combine the x,y components with the equation of work.

(pw is person to water, pf is person to ferry, fw is ferry to water) I get Vpw = Vpf + Vfw. Therefore Vfw = Vpw + Vpf, which is Vfw = -Vwp + Vpf. I also have that the x component of Vpw is negative. I think I'm getting confused with either the order of the formula or the negative negatives (or...

The problem is as above, My attempt is as below but there is lot of effort in terms of imagining and not very confident, Required the magnetic field on the y-axis let us say point P. The magnetic field due to the x-axis wire is out of the paper at P with the values as R=2.0m, i =30A. B1 =...

i am able to understand problems and solve electromagnetism problems, if the currents are given to be flowing in wires and circle loops in the xy axis. But if they provide similar problems in z axis i am finding it difficult to imagine and do the calculations. My question is any simple concepts...

Neural networks have come a long way since I first took a course, 25 years ago. Now that I'm in the Online Masters in Analytics program at Georgia Tech, I see these topics come up often. I found the following article an interesting read...

Hi everyone, I am looking at a paper on compact dimensions. Equation 65 makes sense except for the term of 4*pi*n*R in the denominator. Why is it 4*pi and not 2*pi? I cannot rationalize this. Please help. Thank you. https://arxiv.org/ftp/hep-ph/papers/0609/0609260.pdf

Hi everyone, I have a question about sizing a bolted joint. How to calculate the size of the screw? Knowing that the bolt material is 316 stainless steel and the thread material where the bolt will be bolted is 6061 aluminum. This screw will be pulled at 2000N. Thanks!

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.2 Differentials ... ... I need some further help in order to fully understand the proof of Theorem 8.15 ...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.2 Differentials ... ... I need some help in order to fully understand the proof of Theorem 8.15 ... Theorem 8.15...

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...

Hi, this is probably a stupid question, but, does rotational invariance in ##d=2+1## mean to only rotate the spatial coordinates and not the time. I mean bascially I want to show that ## \int d^3 x \epsilon^{\mu\nu\rho}A_{\mu}\partial_{\nu}A_{\rho} ##, yes epsilon the antisymmetric tensor, is...

I want to know why an else solution can not get the right answer. And want to know the way to correct this solution.Supposed that a frame S'' is moving in the lab frame at ##\beta_x## in the x-direction, ##\beta_y## in the y-direction, now I want to find out the Lorentz transformation between...

I take 2 points given by the vectors of coordinates ##\vec{p}_i,\vec{p}_j## and a plane spanned by ##\vec{e}_k,k=1,2##. All the vectors are in dimension n. I want to find the intersection of the segment described by the extremities given by the ##\vec{p}_k## with the plane, if any. Is it...

Is it saying is the plane in the xy or xz or yz plane?

In 3D the most general motion of a rigid body consists of a displacement and a rotation. In higher dimensions is this still the most general motion? Or are there unexpected ways of moving with more freedom? One subtlety, for example, is that we would have to allow for multiple rotations...

Hi, So I have a uni project and were required to design a jockey wheel and corresponding power screw. We're given a maximum load and have to do the relevant calculations, moment of torque, efficiency etc. My question is I don't understand how to take the given maximum load and find the relevant...

I'm trying to get a handle on how general a space in R_n can be. Part of my motivation is the curled up dimensions physicists talk about. How does one dimension work differently than another dimension? Can one part of the dimensional structure follow one metric and another part follow a...

Hello! I know this is a very general question (and I am really a very beginner in the field) so I am sorry if it is dumb, but here it goes. In Schwarz book on QFT, at the end of Section 14.4 (path integrals chapter) he says: "We do not know if QED exists, or if scalar ##\phi^4## exists, or even...

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...

I am creating a two-dimensional model of an ideal gas, and I was wondering how I should determine initial velocity. Ideally, I would like for the simulation to reach a point where the velocity distribution resembles that of the maxwell-boltzmann curve — will this be achieved if I, say, assign...

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...

I’ve seen posts similar to this one, but I’m still struggling to understand this concept. Huygen’s principle is only valid with an odd number of spatial dimensions, yet it is often taught with the visual aid of 2 dimensional water waves. So why doesn’t Huygen’s principle apply in 2...

Sorry for my speculative question, i just wondered, is there any sensible theory that thinks strong nuclei force is so weak in the distance, because it isn't three dimensional? Again i don't intend to say my speculations are facts, but i think the above question needs a bit explanation. I would...

Hi! I am trying to change the hydrogen ground state wave funcion from position to momentum space, so i solved the integral Ψ(p)=(2πħ)^(-3/2) (πa^3)^(-1/2)∫∫∫e^(prcosθ/ħ) e^(-r/a) senθ r^2 dΦdθdr and got 4πħ(2πħ)^(-3/2) p^(-1) (πa^3)^(-1/2) I am [(ip/ħ-1/a)^(-2)], which according to the...

So imagine there are now two dimensions of time, instead of the one dimension which we're used to. The laws of physics which we're used to won't make anymore sense unless they're adapted for the two dimensions of time. How would you adapt them?

A point is taken as an example of a 1D, a plane 2D and a sphere is 3D. If a point is viewed say at 1000x enlarged the point appears as a plane similarly if we a view a large sphere from very far it does appear as a dot. So can we say that dimension are relative to the observer ? Had our sights...

If I have a Lagrangian of the form \mathcal{L}=-\frac{1}{2} (\partial \phi)^2 - \frac{1}{2} m^2 \phi^2 - \frac{\lambda}{3!} \phi^6, in 3 dimensions, what is the one-loop correction to the 4-point function? Am I correct in thinking that the following Feynman diagram is the representation of the...

I would assume that it has some area even if it is really really small. But I guess a line implies that the left and right boundaries are going to the middle an infinite amount, so it has area =0? does anyone get what I mean?

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...

Hello everyone. I am dealing with a stochastic optimization problem with three sources of uncertainty and I am using generalized polynomial chaos to solve this problem. The level with I am working is 1 (l=1). There are 3^3=27 realizations to make. I want to use instead a Smolyak reduced grid...

It seems to me that for a set of loci of cardinality M having dimensions Di in a space of dimension N, aside from degenerate intersections (e.g., a pair of spheres that touch at a single point), the dimension of the net intersection locus L is: L = N - ∑ ( N - Di ) = ( ∑ Di ) - N ( M - 1 )...

What are the dimensions of kilo Watt hours? Is is M L2T-2?? If yes, why is that? If no, please teach me about what the right dimensions are and please be kind enough to provide a good explanation. Thank you in advance. P.S. I am wondering why it doesn't have the dimensions ML2T-3...

Homework Statement Examine if the function is differentiable in (0,0)##\in \mathbb{R}^2##? If yes, calculate the differential Df(0,0). ##f(x,y) = x + y## if x > 0 and ##f(x,y) =x+e^{-x^2}*y## if ##x \leq 0 ## (it's one function) Homework Equations ##lim_{h \rightarrow 0}...