Dimensions Definition and 1000 Threads

Hi all, I am not a physicist. Some engineer friends of mine and I have a question about special relativity in two dimensions. To set it up, there are 2 lights floating in space parallel to the x-axis and a spaceship is traveling at .8c flying parallel to the y-axis towards the midpoint of...

Ok, I often hear that things become more easily understood in higher dimensions. I also hear that it is easier to express them in math than with words. But what does equations that express higher dimensions look like? Is it something as simple as (x,y,z,w)? I might be over thinking this far...

I'm working on a visualizer of sorts for a system: x_{n+1} = sin(a y_n) - cos(b x_n) y_{n+1} = sin(c x_n) - cos(d y_n) with a,b,c,d \in [-2.5, 2.5] So for whatever initial (x_0,y_0) I give the system, I know the next iteration will have both x and y between -2 and 2, and that will be...

I'm hoping someone is willing to help me with this question. Time is well explained when observed at point between absolute rest and c. The faster an object travels through the dimension of space, the slower that object travels through the dimension of time. Fair enough. Does this...

What experiment could determine whether our universe is fractal?

Homework Statement Object 1: m1=1.9x10^4 kg v1'= 972 m/s [E5.1*N] Object 2: m2=1.7x10^4 kg v2'=944 m/s [E5.9*S] Determine their original speed when they were linked together. Homework Equations Pti = Ptf m1v1 + m2v2 = m1v1' + m2v2'

So, I've got a problem understanding the "algorithm" for changing variables in a more-than-one-dimensional integral. For the two-dimensional case, I've got a specific problem that I'm looking at: \int^{a}_{0}\left(\int^{2a-x}_{x}\frac{y-x}{4a^2+(y+x)^2}dy\right)dx which I assume is an...

Homework Statement Dimensions: These derivations are not correct ( as stated by the book) I'm just reading my textbook at the moment and I saw this example ( So I don't have work for it myself by the book shows all the steps). ***√[L]/[L/T^2] =√[T^2] Homework Equations The...

Well, it's more of a general inquiry than a specific question, but this looked like as good a place as any to bring it up. Can a quantity have dimensions NOT of the form: [L]^{x}[M]^{y}[T]^{z}, where x, y and z are real numbers? This includes two primary cases as far as I can see. One is...

I'm beginning to study multiple dimensions, and I guess the first step after the x, y, z coordinate system is to study how the TESSERACT is formed. How is this weird 4 dimensional cube formed? I've seen videos and pictures of it, but I cannot imagine the 4th dimension. any advice?

Hey Everyone, So I've been working on some very basic QM mathematics. Basically I've worked out the wave equation for a particle in one dimension (briefly) like so: -\frac{\hbar 2}{2m}\psi"(x) + V(x)\psi(x) = E\psi(x) V = 0 for 0 < x < L ; (L = "Length" of the Boundary) =>...

waht caused compactification of the extra dimensions in the early universe?

It is my understanding that physicists hope to use conservation of energy in the LHC to determine if there are multiple dimensions AND if there is dark matter. Let's suppose that through conservation of momentum, we detect a particle that apparently only reacts through gravity, and there is some...

Homework Statement A piece of machinery of weight W is temporarily supported by cables AB, AC, and ADE. Cable ADE is attached to the ring at A, passes over the pulley at D and back through the ring, and is attached to the support at E. Knowing that the tension in cable AB is 300 N, determine...

I have an equation for a curve that lies along the surface of a truncated cone. In polar coordinates: theta(r) = K * [ U + arctan(1/U) - (Pi/2) ] where: U = SQRT[ ((r/r1)^2) - 1 ] K = SQRT[ 1 + (H/(r2-r1))^2 ] r = r1 + (r2-r1)(z/H) r1 = minor radius of the truncated cone r2 =...

I have a bunch of data x1, x2, x3, ... x49, z. I need a function f(x1, x2,... x49)=z. Does anyone have suggestions for a method that they have used before or key words to google?

Homework Statement Puck A has a mass of 0.0320 kg and is moving along the x-axis with a velocity of +7.65 m/s. It makes a collision with puck B, which has a mass of 0.0640 kg and is initially at rest. The collision is not head-on. After the collision, the two pucks fly apart with the angles 65...

Hidden dimensions of string theory "hiding" in 4D spacetime? Could the hidden dimensions of string theory be "hiding" in 4D spacetime? Thank you for any thoughts.

I'm searching for an online text on units, units systems, dimensions, dimensional analysis and so forth. A nice overview or summary, or an introduction not geared to the complete beginner. Has anybody a good link? thank you

Hello everyone. This is my first post here, though I've stumbled upon the site on several occasions while investigating various physics concepts over the years. I've decided to post now because of a maddening dearth of information regarding the definition of each of the additional dimensions...

in 2d, "curl"(grad(f)) = 0 "curl" is the operation that green's tehorem talks about. In 3D, curl(grad(f)) = 0 and div(curl(F)) = 0. We may consider vector calculus in 4 spatial dimensions, for vector fields F:R^4 -> R^4. what is "curl" like in 4D, since curl is actually only difined in 3D...

Why do they say there can there be no gravity in 2 spatial dimensions (and 1 temporal dimension)? wouldn't the gravitational law be an inverse-law instead of an inverse-square law?

I always here talk of there being multiple universes or there being higher dimensions. When people use these terms are they referring to the same thing? If not, what's the difference?

Homework Statement Evaluate: \int _C{xydx - yzdy + xzdz} C: \vec{r}(t) = t\vec{i} + t^2\vec{j} + t^4\vec{k} o <= t <= 1 Homework Equations The Attempt at a Solution I understand that you cannot use Green's Theorem in 3 dimensions. How else can I go about solving this?

Homework Statement A quarterback claims that he can throw the football a horizontal distance of 171 m. Furthermore, he claims that he can do this by launching the ball at the relatively low angle of 26.2 ° above the horizontal. To evaluate this claim, determine the speed with which this...

Homework Statement A box of mass M=10 kg is at rest on a frictionless level surface (like an ideally smooth ice rink). A rope tied to the box is pulled horizontally, such that the tension in the rope is T = 75 ˆx + 25 ˆz N, where both the x-axis and the z-axis are parallel to the floor. What...

Hi. It asks to calculate the focal length range of a projector of square pixel SXGA is from 4 to 12 m from the screen. It gives the diagonal size of the display (in mm) as well as the horizontal size (in m). The thing that am not sure about is how the focal length would be calculated with the...

I know that string theory tells us that 10 space-time dimensions have a rather special property, namely that a certain central charge vanishes. This allows for an anomaly-free quantization of s.t. Two questions: - are there other statements (not necessarily from s.t.) that something special...

Homework Statement If I have a rectangle rotated at a known angle with respect to a rectangle of known dimensions that inscribes it, how can I find the dimensions of the inscribed/inner rectangle...

I have a question about the dimensions of quantum fields. In natural units, the dimensions of bosonic fields (both scalar and vector) is 1. The dimension of spin=1/2 fermion fields is 3/2. This is all very good, but I have never read any explanation anywhere why we cannot have other types of...

Hi, I need to find the dimensions for O ring grooves for different size o rings, for static, dynamic and face sealing. Does anyone have a web link for these for BS and/or ISO metric dimensions. All the ones i can find are subscription ones. Many thanks Ed

I understand calculus, I just don't understand how it is applied to solve these sorts of problems. Homework Statement What is the smallest perimeter for a rectangle with an area of 16, and what are its dimensions?Homework Equations A=L*W P=2W+2L The Attempt at a Solution I managed to get the...

Does string theory use multiple dimensions to explain why certain particles don't interact with others? If so, why wouldn't shape be used; as it is when explaining why certain proteins don't interact with cells?

Hello! I'm in a search for information on the topic to devise a strategy of solving H. equation in N dimensions with Dirichlet - von Neumann type of boundary conditions. I'm assured that problem can be solved in closed form. As far as I can see, boundary conditions in any number of...

Kaluza Klein in 8 dimensions with the 4 dimensional compact space being the homogeneous space H=SU(3)/SU(2)xU(1), so that the resulting KK bosons are those of SU(3). Similarly, KK in 10 dimensions with H x T^2 as compactified space will produce a SU(3)xU(1)^2 gauge theory. For energies smaller...

I am quite familiar with 11-dimensional string theory and with the concept that the other seven dimensions outside of the four we can perceive are, in theory, curled too tightly (meaning too small) for us to see. However, is it possible that instead of being too small, they are too large...

Homework Statement In a road test,a car was uniformly accelerated from rest over a distance of 400m in 18.5s. The driver then applied the brakes, stopping the car in 4.9 s with constant deceleration. a) calculate the acceleration of the car for the first 400m. b)Calculate the average...

Hello, I have some trouble seeing why the solution of the wave equation in 2 dimensions exist at all later times once it passes an initial disturbance... For example, take a simple case where the initial position is zero, and the initial velocity equals some function inside some circle domain...

Is it possible?

Would the Gravitational force be applied equally across multiple dimensions or exponentially? Could you measure the Gravitational force across 3 dimensions and the take that value divide by 3 and get the value of the gravitational force across 1 dimension?

A 3+1-dimensional Lorentz transformation can be written as \Lambda=\gamma\begin{pmatrix}1 & -v^T\beta \\ -v & \beta\end{pmatrix} where v is a 3×1 matrix representing the velocity difference, \gamma=1/\sqrt{1-v^2}, and \beta is a 3×3 matrix that's orthogonal when v=0. When \beta=I, \Lambda is...

Hi everyone, I know that in P=nRT/v R = 8.314 m3*Pa/mol*k Now, when you are trying to calculate P, if you have volumn in m3 on the bottom, everything cancels out and you are left with Pa. I've just developed a simulator which simulates particle motion over time and calculates...

Why does string theory need so many dimensions? i know in our 3 it would break special relativity but i don't know why

Hi all, I'm a biologist with a mathematical and statistical question. I have a dataset of measurements of the maximal cross-sectional width of icosahedral bodies inside bacteria. Since they are icosahedral, the cross-sectional width (if precisely through the middle of the object) is a measure...

do all of the equations and postulates of the general theory of relativity apply in a universe with only 2 spatial and one time instead of 3 spatial and one time.

Homework Statement An airplane with a speed of 59.6 m/s is climbing upward at an angle of 40° counterclockwise from the positive x axis. When the plane's altitude is 600 m the pilot releases a package. (a) Calculate the distance along the ground, measured from a point directly beneath the...

This is perhaps a stupid question but: When we use natural units and set h=c=1, do we choose appropriate units so that their value is one but these constants still have dimensions, or are we somehow choosing h=c=1 to be a pure number with no dimensions?

Homework Statement The ends of two identical springs are connected. Their unstretched lengths l are negligibly small and each has spring constant k. After being connected, both springs are stretched an amount L and their free ends are anchored at y=0 and x= (plus minus)L as shown (Intro 1...

Homework Statement A brick is thrown upward from the top of a building at an angle of 25 degrees to the horizontal. It's initial speed is 15 m / s. If the brick is in flight for 3 seconds, how tall is the building? Thanks for the help. Homework Equations The Attempt at a Solution i thought i...

I have a question about Witten's original 1998 paper on AdS/CFT http://arxiv.org/abs/hep-th/9802150 Since the AdS metric diverges at the boundary, the boundary metric is only defined up to a conformal class Eq. (2.2), ds^2 \to d\widetilde{s}^2 = f^2 ds^2 Similarly, the solution for...