Dimension Definition and 909 Threads

How is it like to travel at the speed of light in the 4th dimension? and according to general relativity, the 4th dimension is time, what does that mean ?...and why? :rolleyes:

Hello all, Special relativity tells that space and time should be seen as a single four dimensional space time. Even the metric for SR has four components, x1, x2, x3, and x4 = ict. The Lorentz transform tells us how to convert these coordinates from this to another providing that we are...

Homework Statement Let V be the vector space of n × m matrices with entried in a field F . What is the dimension of V ? Give an explicit basis for V over F . The Attempt at a Solution The question is a little vague, but if I understand correctly, wouldn't the dimension of V simply be...

in the book of quantum mechanics concept and application by Zettili, chapter 4 write a theorem, that is: in one dimensional problem the energy level of a bound state system are discrete and not degenerate. i can not prove this theorem. can you help me to do this!

I think I may have asked this question a few years ago, but I forget the responses. We know that gravity is the curvature of spacetime in the presence of mass and energy.. The curvature of spacetime was proved by experiment during a solar eclipse, whereby light from a star behind the sun was...

A question about the average velocity of bodies undergoing one-dimensional motion and a constant acceleration (gravity in this case). A case scenario. Suppose that initially, I throw a stone into the air at a height h. For the sake of argument, let's suppose that even though I threw the...

Homework Statement given two matrices A, B of 5x5 order: \rho(A)<\rho(B) the nullspace for A is Sp{(0, 3, -1, 2, 1),(4, -2, 1, 4, 0)} prove that AB\neq 0Homework Equations \rho(A)=n- \rho(P_a)The Attempt at a Solution so I now that the nullity is 2 and so \rho(A)=3 and because of that 4\leq...

Alright, I have a kind of dumb question: Why do I distinguish between dq and dqi when considering the propagation from qi to q to qf? For example, if we want the wave function at some qf and tf given qi and ti, we may write: ψ(qf,tf)=∫K(qftf;qiti)ψ(qi,ti)dqi Why do we distinguish between dqi...

Well? Is there? And if there is what kind of experiment could I perform to prove that there is? Or prove that there isn't?

I made a code in assembly 8086. I load matrix (array) in memory with dimension 3x3. but this code works just for this dimension of matrix 3x3. Could someone give me an idea how could i make it to work with dimension m x n? the array is loaded in memory and at the end just print the result...

A projectile is shot horizontally at 220 m/s from the top of a 620 m high cliff. A) How long till the projectile hits the ground? B) How far from the base of the cliff does the projectile land? I am going to be honest. I have no idea how to do any of my Physics homework. ): I still...

Homework Statement V is a vector space with dimension n, U and W are two subspaces with dimension k and l. prove that if k+l > n then U \cap W has dimension > 0 Homework Equations Grassmann's formula dim(U+W) = dim(U) + dim(W) - dim(U \cap W)The Attempt at a Solution Suppose k+l >n. Suppose...

Greetings This is my first post in this section of PF. As the title says, I just want to know the typical dimensions of the two-slit experiment, intended for electron interference. That is, what are the slits made of, what is their spacing from the screen,source and from each other. Is...

Homework Statement A ball is thrown straight up. At the top of its path its instantaneous speed is a) 5m/s b) 20m/s c) 50m/s d) 10m/sHomework Equations The Attempt at a Solution

For what value of x, y, and z, will the equation P^x v^y T^z = constant, become Boyles law?

Is it to possible to use the special case of elastic collisions in one dimension with bodies that posses different mass. Ordinarily I know that if the body has same mass the velocity of the bodies will simply be exchanged but is the fact also hold for body with different masses? v_1 - v_2 =...

Hi there, does anyone knows the overall dimension for 2.5' hard disk drive?including all the components inside. who has the complete dimension? tq =)

Problem of the day: Trying to find the formula to use for my 15 year old daughter. A 20,000N car is parked on an incline that makes an angle of 30 degrees with the horizontal. If the maximum force the brakes can withstand is 12,000N, will the car remain at rest? She is just learning how to...

Let A be an n*n matrix. Consider the space span \{ I, A, A^2, A^3, ... \} . How would one show that the dimension of the space never exceeds n? I feel like the answer lies somewhere near the Cayley-Hamilton theorem, but I can't quite grasp it.

According to Nobel Prizer Steve Weinberg, there may a second dimension of time in the quantum realm. Instead of a particle being “spread out” occupying no address in space until the wave function is collapsed, it rather does have an address but not necessarily in our time. Is this possible? Can...

Hi, this is my first post, and I'm not an expert of any kind or do not believe I am. I have always been fascinated by science, but I some time ask myself some questions, here's one I don't seam to find much info. I found a lot of treads that mentioned the subject but nothing that actually...

Halo everyone, I am trying to consider a dice game using MATLAB. I used 'r=randi(6,a,b)' to get random number from MATLAB.Also run it for 200times.(a=a:1:x,b=b:1:y) Then used '[a,b]=mode(r)' to get the highest frequency value and add them together then put them in the table. For x=1 with y=1,2...

I was flipping through a physics text and some of the units seemed pretty 'crazy'. Just wanted to know if they can always be understood intuitively, like you can visualize what's going on e.g. force, mass x acceleration, if I look at it as kg*m/s^2 then it doesn't really make sense to me...

Homework Statement I have a problem trying to code these two programs, one is related to the obtain the fractal dimension of the Koch curve by using the method of the box counting dimension and also using the Grassberger-Procaccia algorithm Homework Equations For the box counting...

Homework Statement If we have ker(T)={0}, why is the dim(ker(T)) = 0? Does the 0 vector not count when determining the dimension? I thought the answer would be 1.

Homework Statement A stone is thrown downward with a speed of 18 m/s from a height of 11 m. (acceleration due to gravity: 9.81 m/s2) Your answers must be accurate to at least 1%. Give your answers to at least three significant figures. a) What is the speed (in m/s) of the stone just before...

Homework Statement A model rocket accelerates upward from the ground with a constant acceleration, reaching a height of 76 m in 7.2 s. What is the acceleration (in m/s 2)? What is the speed (in m/s) at a height of 76 m? Homework Equations V=Vo+at X=Xo+Vot+1/2at^2 V^2=Vo^2+2at(X-Xo)...

1. A pitcher throws a baseball at 60mph. How much time does it take the ball to reach the batter 50 ft away? 2.t = x/v 3. t = 50/60 t = 0.83

Homework Statement If VΩW contains only the zero vector, then dim(V+W)+dim(VΩW) = dim(v) + dim(W) becomes dim(V+W) = dim(v) + dim(W). Check this when V is the row space of A, W is the nullspace of A, and the matrix A is mxn of rank r. What are the dimensions? Homework Equations...

Homework Statement A 10.0g bullet is fired into a stationary block of wood (m=5.00 kg). The bullet imbeds into the block. The speed of the bullet-plus-wood combination immediately after the collision is 0.600 m/s. What was the original speed of the bullet? ball m=10.0g=0.01kg wood m=...

Prove that the space of 2×2 real matrices forms a vector space of dimension 4 over R. [12] Im unsure, anyone any idea?

Homework Statement 10. In reaching her destination, a backpacker walks with an average velocity of 1.34 m/s, due west. This average velocity results because she hikes for 6.44 km with an average velocity of 2.68 m/s, due west, turns around, and hikes with an average velocity of 0.447 m/s, due...

Been stuck on this question for days and any help would be greatly appreciated A baseball going horizontally at 32.0 m/s [E] with a mass of 0.152 kg is hit by a bat for 0.002 seconds. the velocity after the ball after contact is 52.0 m/s [W 20 N] Find the impulse experienced by the ball...

a car starts from rest travels for 5.0s with a uniform acceleration of + 1.5m/s^2. The driver then applies the brakes, causing uniform acceleration of -2.0m/s^2. If the brakes are applies for 3.0s (a) how fast is the car going atthe end of the braking period and b how far has it gone I have...

A race driver has made a pit stop to refuel. After refueling, he starts from rest and leaves the pit area with an acceleration whose magnitude is 5.5 m/s^2; after 4.1 seconds he enters the main speedway. At the same instant, another car on the speedway and traveling at a constant velocity of...

Homework Statement \mathfrak{g} is the Lie algebra with basis vectors E,F,G such that the following relations for Lie brackets are satisfied: [E,F]=G,\;\;[E,G]=0,\;\;[F,G]=0. \mathfrak{h} is the Lie algebra consisting of 3x3 matrices of the form \begin{bmatrix} 0 & a & c \\ 0 & 0...

i know that line is a one dimension but i cannot understand then why do sometime need two spatial variable to specify the st line for example x+y=c is a straight line but we require two coordinates to define it then how it is one dimensional?

The lecturer said that a way to find the determinant of a matrix is to do the following det(A) = xdet(B) (1) where A is the original matrix, B is an arbirtray matrix and x is a scalar multiplier The lecturer also said that a simple way to find the determinant of a high...

Alright, I have wondered this for a very long time and probably thought about it for longer than I should have but the more I think about it, the more I seem to be correct and the more frustrating it is to talk to people about it... Anyways, I'm sure everyone has heard of the saying "lefty...

I'm moving on to my next section of work and i come across this example: Consider the homogeneous system x + 2y − z + u + 2v = 0 x + y + 2z − 3u + v = 0 It asks for a basis to be found for the solution space S of this system. And also what is the dimension of S. I know this might be...

Homework Statement A ball is thrown by Jed in the street and caught 2 seconds later by Jelo on the balcony of the house 15m away and 5.0m above the street level. What was the speed of the ball and the angle above the horizontal at which it was thrown? Homework Equations The Attempt...

Hello All, It's rather a simple question for advanced people. Consider a 3D Euclidean space: if one is given 2 points, a line can be build that goes through the points; for 3 points -- there is a plane. For 4D space: a line goes through 2 points and a hyperplane through 4 points...

Is it true that in 1+1 dimensional Minkowski spacetime scalar quantum filed theory defined by the lagrangian (in the interaction picture, so that the normal ordering makes sense): \mathcal{L} = : \frac{1}{2} (\partial_\mu \phi) (\partial^\mu \phi) - \frac{1}{2} m^2 \phi^2 -...

Please teach me this: Why in two dimension space many QTF theories become renormalizable.By the way,are there any relation between this and the world-sheet in string theory? Thank you very much in advance

Homework Statement Let F be a field. Prove that the set of polynomials having coefficients from F and degree less than n is a vector space over F of dimension n. Homework Equations The Attempt at a Solution Since the coefficients are from the field F, the are nonzero. So, if...

General relativity states that our universe is four dimensional curved space so time dimension is not separated from space dimensions .Why then is the time dimension different from the 3 space dimensions ? and why there must be 3 space dimensions and not 4 for example ?

Hi. In the book I'm reading I've come to a question regarding degenerate states in one dimension. It says that in one dimension there are no degenerate bound states. But say I have a stationary state with some energy E, and assume that it is normalizable. You can easily show that the complex...

error 542, J appears in the dimension of a variable,yet is not a dummy argument,a variable available through USE or CONTAINS association,a COMMON variable,a PARAMETER,or a PURE FUNCTION the same error about I i am using i,j in order to point the temperature in length and time T(i,j) it is a...

What are the conditions for which it can be concluded that a system has discrete energy levels? For example a system in one dimension with the potential V(x)=b|x| has only a discrete spectrum. How I can prove it? My book says moreover that the energy eigenvalues have to satisfy the...

Hi, I was listening to Susskind's lecture on statistical mechanics (lecture 8). He mentioned in relation to Ising model of magnetized spin systems that there could not be any phase transitions in one dimensions. He mentioned that it has to do with the stability of the system. Can anybody...