Dimension Definition and 909 Threads

How is a dimension defined in quantum mechanics?

Homework Statement \lim _{ (x,y)\rightarrow (0^{ + },0^{ + }) }{ \frac { { e }^{ \sqrt { x+y } } }{ 4x+2y-5 } } Homework Equations eh. SO I did the problem. I usually sub 1/n for 0+ in most of these, but clearly the top goes to 1 from +inf, and the bottom goes to -5... Hence...

I recently watched a series of Youtube videos based on a book titled "Imagining the Tenth Dimension" by Rob Bryanton, but I noticed a few inconsistencies so I haven't bought the book yet. Does this book accurately represent what is known about the higher dimensions? If not, could you suggest...

If it does, is there a way to calculate what the force of a single photon would be if it were acting in 3 dimensions?

"Picture" of electro-magnetic vector potential in 1+1 dimension spacetime? I'm trying to model the electro-magnetic vector potential, does the following come close for 1 + 1 dimension spacetime? See sketches below. Consider an elastic string, under tension, between two fixed points A and B...

Hi everybody! I would kindly ask you if somebody know some method to solve analitically the following equation (written in cylindrical coordinates): \Big[\frac{\partial^2}{\partial\rho^2}+ \frac{1}{\rho}\frac{\partial}{\partial\rho}+\frac{\partial^2}{\partial...

Hi, Suppose you have a collection of fields \phi^i (t,x) depending on time and on 1 space variable, for i=1,...,N. Its dynamics is defined by the Lagrangian L=\frac{1}{2} g_{ij}(\phi) (\dot{\phi}^i \dot{\phi}^j - \phi ' ^i \phi ' ^j ) + b_{ij}(\phi) \dot{\phi}^i \phi ' ^j where...

the speed v of sound waves in a gas can be express in terms of the pressure p and the density q (mass per unit volume) of the gas, as v=ap^bq^c, where a, b, and c are dimensionless constants. The dimensions of pressure are m/((LT)^2). What must be the values of b and c. I am confused on...

Homework Statement At t=0, a particle leaves the origin with a velocity of 9.0 m/s in the positive y direction and moves in the xy plane with a constant acceleration of (2.0i - 4.0j)m/s^2. At the instant the x coordinate of the partice is 15 m, what is the speed of the particle? Homework...

Homework Statement Assume V = \mathbb{R}^n where n \geq 3. Suppose that U,W,X are three distinct subspaces of dimension n-1; is it true then that dim(U \cap W \cap X) = n-3? Either give a proof, or find a counterexample.The Attempt at a Solution The question previous to this was showing that...

I have a quick question. On a typical cartesian coordinate system you have the x-axis and y-axis for two dimensions and the z-axis for the third. What would you label the axis representing the fourth dimension? I know this is a bit of a silly and unimportant question, but I was thinking...

In http://arxiv.org/abs/0912.3272 , figure 1.2 says that the 2D and 3D Ising universality classes are related by a renormalization flow. How can the RG flow change dimension? Is there anything I could read that does the calculation in more detail?

Since spin is a separate variable in a wave function, independent from its location in spacetime, why isn't it considered a dimension beyond the 3+1 of spacetime?

Is it true that strings can vibrate in certain manners in which they cause a "ripple effect" in spacetime, affecting the topology of the higher dimensions, causing these different timelines to occur in which you have changes so minor as to electrons a plank's unit to the right, or so drastic as...

How do you calculate an object in 4 dimensions? Like the 4 dimensional cube. I understand that a point is the beginning of a line and a line is the beginning of a plane. From there a plane translates into a 3 dimensional object. A 3 dimensional object translates into a 4 dimensional thing... I...

The Word "Dimension" I have some difficulty understanding the exact connotation of the word "dimension" as used in string theories re "extra dimentions". Are these extra dimensions really meant to be dimensions of space or are they simply extra parameters that need to be integrated...

Hey guys, who can tell me briefly about the 10+1 dimensions in the string theory? I am going to deliver a short presentation on string theory ,but i am not very clear about the reason that we have to introduce 11dimendion to string theory ...

Hello guys, I'm trying to understand bosonic condensation and i would really need your help. The actual question, before getting into the details is: "Why Bose-Einstein Condensation doesn't take place in a one-dimensional (1D) space?" In what follows i'll give you my own (mis)understanding so...

according to M-theory, there should be 7 ekstra spatial dimensions curled up at the plank lenght, but why do they need to be curled up? if light and matter is bound to the 3rd dimension like waves of the ocean is bound to the 2D surface of the water that wouldn't that be sufficient for us not to...

Linear transformation f:C^∞(R) -> C^∞(R) f(x(t)) = x'(t) a) I have to set up the eigenvalue-problem and solve it : My solution : ke^λtb) Now I have to find the dimension of the single eigen spaces when λ is -5 and 0. My solution : Eigenspaces : E-5 = ke^-5t E0=k (because ke^0t = k)...

Homework Statement I am doing an experiment to determine the fractal dimension of hand compressed aluminium spheres. I cut a square of foil of some length ##L## and known thickness, ##t##. I do this a few times, varying ##L##. The radius of the hand compressed spheres, $$r =...

Hello all . We know Planck length is and universe was in that density at big bang . Is that mean there was dimension at that time ? I mean , can we move in Planck length ? like up , down, right, left, forward, backward ؟

Homework Statement When a ball was thrown and caught at the same height from which it was thrown, it was measured to have traveled 12 meters in 1.3 seconds. What was the launch velocity? The answer on the key says 11.2 meters per second. Homework Equations Yfinal = Yinit + Vt + 1/2...

What dimension is the vector [0,0,0] in? For example, I know that vector [o] is in dimension zero, but would [0,0,0] be in that too? Or, is it classified as being in R3 since there are three components?

Homework Statement An object moves along the x-axis according to the equation x = 3.00t2 - 2.00t + 3.00 , where x is in meters and t is in seconds. Determine : (a) the average speed between t = 2.00 s and t = 3.00 s. (b) the instantaneous speed at t = 2.00 (c) the average acceleration...

So I'm given a matrix A that is already in RREF and I'm supposed to find the null space of its transpose. So I transpose it. Do I RREF the transpose of it? Because if I transpose a matrix that's already in RREF, it's no longer in RREF. But if I RREF the transpose, it gives me a matrix with 2...

Homework Statement An empty (charge-free) slab shaped region with walls parallel to the yz-plane extends from x=a to x=b; the (constant) potential on the two walls is given as Va and Vb , respectively. Starting with LaPlace's equation in one dimension, derive a formula for the potential at...

Hello I have this problem, I find it difficult, any hints will be appreciated... Two subspaces are given (W1 and W2) from the vector space of matrices from order 2x2. W1 is the subspace of upper triangular matrices W2 is the subspace spanned by...

Hi All PF Members... I'm New to this website.. Also new to physics... nd I'm very exited about this aweSome website...where I can post my problems... Experts I want list of All physical quantities and their Dimension... I've been searching and cannot find any thing good enough... Sorry for my...

A ball is released from the height 3 meters and after it hits the floor it reaches the height 2 meter. A) Whats the speed of the ball in the moment when it meets the ground? My answer : V^2-V0^2=2gs and here we find V=sqrt60. What is the speed of the ball in the moment it leaves the ground...

An automobile which travels with the constant speed 20 m/s passes in a section in the moment t=0s and 5 seconds later in the same section passes another automobile which travles with the speed of 30 m/s in the same direction.a) Find when the second car meets the first one. My solution : x1=x2...

Homework Statement The set K of 2 × 2 real matrices of the form [a b, -b a] form a field with the usual operations. It should be clear to you that M22(R) is a vector space over K. What is the dimension of M22(R) over K? Justify your answer by displaying a basis and proving that the set...

Homework Statement X-axis t1= 3 min t2= 2 min (Since it's west, it is -2) t3= 1 min (Since it's northwest, it is -1) Y-axis V1y= 20 m/s (Since it's south, it is -20) V2y= 25 m/s (It's -25) V3y= 30 m/s (Stays positive since it's in the northwest)Homework Equations A) Total Vector Displacement...

Homework Statement A beam (note: part of a truss, I chose to use the beam in the truss with the most force and length for my calculations, which I assume is the correct thing to do) of length 6m with a force of 9N is being constructed out of a material with a Young's Modulus of E = 70 \times...

Homework Statement How to find the work done by a variable force in (two dimension) When F = ax^2 i + b y^3 j If a subject move from (x1,y1) to (x2, y2) Homework Equations F = dW/dr The Attempt at a Solution I tried to solve them separately by x-direction and y-direction, and then I added...

Hey all, I'm reading Chaikin's Principles of Condensed matter, and he's talking about the effect fluctuations have in various systems. He says: So I get why order is destroyed in 1D, and not in 2D. But I don't see why they destroy the phase transitions. Can anyone tell me? Thanks!

Generally, Gamma matrices with one lower and one upper indices could be constructed based on the Clifford algebra. \begin{equation} \gamma^{i}\gamma^{j}+\gamma^{j}\gamma^{i}=2h^{ij}, \end{equation} My question is how to generally construct gamma matrices with two lower indices. There...

I started recently to study physics for motions, it is interesting so far but sadly I need some basic knowledge in calculus, I can get the Instantaneous velocity if the question gave me a function of time, but I don't know how to get it from a graph. I used the equation of calculating average...

I am really confused about something. I know that if I have a vector space, then the dimension of that vector space is the number of elements in a basis for it. But this brings up some confusing issues for me. For example, if we are looking at the null space of a non-singular, square matrix...

1. Let V={(X^2+X+1)p(x) : p(x) \in P2(x)} Show that V is a subspace of P4(x). Display a basis, with a proof. What is the dimension of V? 2. 3. I started to try to figure out how to prove that V is a subspace of P4, but I'm not sure how. To show that it is closed under addition: p(x)=x^2 is in...

Help please! simple Physics motion in one dimension problem! Urgent!? A rock is shot vertically upward from the edge of the top of a tall building. The rock reaches its maximum height above the top of the building 1.60 s after being shot. Then, after barely missing the edge of the building as...

is the time the fourth dimenson ? http://www.youtube.com/watch?v=qKJ6-WJoW1U

Homework Statement During a car accident, a vehicle with an intial velocity of 100km/h hits a concrete wall. The "crumple zone" in the front of the vehicle is a space that makes up the engine compartment that is designed to allow the passenger compartment to continue forward a distance of...

Homework Statement Is it correct to say that the dimension of a given vector space is equal to the number of vectors of the canonic solution? For example: Vector space |R3 Canonic solution = {[1 0 0],[0 1 0],[0 0 1]} Therefore its dimension is 3. Homework Equations The Attempt...

It's hard to convince people that they should hear and/or learn about the 4th dimension, string theory, and all of the like without giving them real world examples as to why these are all important. I've been trying to find a way to incorporate the 4th dimension in particular into a short...

Homework Statement In my general relativity class my professor mentioned that in dimension 4 there are only six statements in the Einstein equations and that this is exactly the number needed. Homework Equations G_{\alpha\beta}+\Lambdag_{\alpha\beta}=8{\pi}T_{\alpha\beta} The...

So, in Nu=\frac{hD}{k} h is the heat transfer coefficient, and D is the diameter of the pipe in which heat transfer takes place... ..but what are the dimensions of k in terms of mass (M), length (L), time (T) and temperature (\theta)? So far, I've worked out that the units for h...

How do i go about this? Find a basis for the subspace W of R^5 given by... W = {x E R^5 : x . a = x . b = x . c = 0}, where a = (1, 0, 2, -1, -1), b = (2, 1, 1, 1, 0) and c = (4, 3, -1, 5, 2). Determine the dimension of W. (as usual, "x . a" denotes the dot (inner) product of the...

Hi, I was reading the definition of dimension from the book: "Topology", Munkres, 2nd ed. Surely I don't understand, but I wonder how ℝ2 can have dimension 2. Take the open sets U_n=\{(x,y)\mid -\infty < x <\infty, n-1<y<n+1\} for every integer n. It covers the plane but its order is...

Homework Statement A particle of mass m is subjected to a net force F(t) given by F(t)=F0(1-t/T)i; that is F(t) equals F0 at t=0 and decreases linearly to zero in time T. The particle passes the origin x=0 with velocity v0i. Show that at the instant t=T and F(t) vanishes, the speed v and...