Dimension Definition and 881 Threads

Can someone tell what are dimensions and what does the line "Three diemsion space and one dimension time means". please. :confused:

This is probably a simple question, but just to be sure: if the kernel of linear transformation is {0}, then the set is linearly dependent since 0-vector is LD, right? So dimension is 0, right? Then what's the basis of kernel? No basis? thanks in advance.

Here's my problem: Car A (mass 970 kg) is stopped at a traffic light when it is rear-ended by car B (mass 1600 kg). Both cars then slide with locked wheels until the frictional force from the slick road (with a low mk of 0.23) stops them, at distances dA = 5.8 m and dB = 3.6 m. What are the...

I'm reading this book (Hartshorne), and it uses a funny definition of topological dimension, which I'm having a hard time convincing myself is the usual one. The definition is as follows: dim X is the supremum of natural numbers such that there exists a chain Z_0\subset Z_1\subset \dotsb...

Dimension, what does this mean?! and Has anyone heared about 2-d matter?

Has the Dimension a mathematical defination?

I'm having trouble with some matrices questions, can someone please help me? A = \left[ {\begin{array}{*{20}c} 1 & 2 & 3 & 1 \\ 2 & 4 & 8 & { - 2} \\ { - 5} & { - 10} & { - 19} & 3 \\ \end{array}} \right] B = \left[ {\begin{array}{*{20}c} 1 & 2 & 0 & 7 \\ 0 &...

ok I've just cracked the ****s, for this question: A car rolls gentley(Vo=0 m/s) off a vertical cliff. How long does it take for it to reach 100km/hr. why can't i use V = Vo + at where: V= 100 Vo = 0 a = 9.8(gravity) t = ? the only equations I've been given to do this are: V...

Hi everyone--I'm curious why terms in the Lagrangian with mass dimension greater than four are "nonrenormalizable." I understand that the action must be dimensionless, hence the Lagrangian [density] has mass dimension 4. However, in effective field theories, we can end up with terms of...

Hi, I'm just learning for my linear algebra exam and I wonder if somebody could give me an example of a nontrivial subspace which has as many dimensions as the original space. Thanks a lot

Hi, I'm just learning for my linear algebra exam and I wonder if somebody could give me an example of a nontrivial subspace which has as many dimensions as the original space. Thanks a lot

I mean is it somewhat science or is it purely sci-fi?

What is the dimension of soln space of the heat equation: \frac{\partial U }{\partial t}=a^2\frac{\partial^2 U}{\partial x^2} U(0,t) = U(L,t) = 0 U(x,0)= f(x) Is it infinite , if so why?

we are familiar with the "running" of coupling constants, as for instance in QCD or even in QED where alpha (the electrodynamic coupling) is about 1/137 at long distances and low energies but increases to about 1/128 as energies increase and distances diminish. Who would have imagined that...

Im new to this and i know this must be a very simple problem. I can't seem to find any formulas for distance or a way of doing this problem. Most of the help sites give you the distance and want you to find something else. Could someone help me understand what i need to do to solve this. Thank...

Recently I was thinking about these statement: 1. Dimension is as if a 3-D graph, which every coordinate is the smallest unit for dimension. 2. Volume of an object is a whole number multiply the volume of the dimension unit. 3. Distance is a whole number multiply the length of the dimension...

I would be interested to hear what others think of the general concept of relativistic velocity in the time dimension, analogous to spatial velocity. To get going, consider the Minkowski velocity 4-vector: \gamma(c,v_1, v_2, v_3) The time component of this 4-velocity is \gamma c. With...

If there is a black hole in the 4th dimension, how will it looks like in the observer in 3rd dimension?

While we're in a 3-D world, we can only see two dimensions at a time. By seeing all three dimensions, we would be able to see every face of every object in our world. But a lot of people, when I explain that to them, don't accept it and say it's false. Can anyone come up with a good explenation...

Just an idea: It occurred to me that people can't see the fourth dimension because, in reality, we can't even see the third. Think about it. When you're looking at something, each of your eyes registers a 2D image, and the sense of depth (the third dimension) is inferred from the two 2D...

Hi all, I have a homework problem that I would like someone to check: this relates to the eigenvectors: in the problem we are given characteristic polynomial, where I put x instead of lambda: p(x) = x^2*(x+5)^3*(x -7)^5 Also given A is a square matrix, and then these questions (my answers)...

If we exclude time as the fourth dimension, is it possible that over many years of trial and study, that our thee-dimensional brains can comprehend a higher dimension? :bugeye:

Can Dimension and Time be quantized? For example, distance and time is a whole number multiple a smallest unit. p/s: I don't have any facts to support my question, so this is possibly one of my illogical thought :smile:

let suppose we have an hypercube in R^4 then m y question is how many 3-dimensional cubes could we put inside our hypercube?...

How would you calculate the volume of a 4-dimensional object? Like a hypercube, hypersphere, etc...

Does this mean there are 8 Dimension creatures roaming the universe?

I am told time is a dimension, indeed the 4th dimension but then I am also told time is effected by other things such as gravity These two seem to be at odds with each other. the three classical dimensions are length breadth and width. yet no one I know of argues that gravity or any...

I have a Homework here I'm trying to solve like the last 3-4 hours but somehow I'm stuck so I ask you guys for help: They gave me the Green Function like this: http://idefix.physik.uni-freiburg.de/~aufgabe/THEO204/theo9/img50.png with...

Is universal "time" the 4th or 5th Dimension? Do we live in a 4 or 5 Dimensional Universe? If Einstein had been told before writing SG and GR, that we live in a 5 Dimensional Universe, in which we can only see or detect the properties of the 4th Dimension, at speeds approaching the light...

Quote: "Because gravity also spreads outside spacetime, only a fraction of its strength is available inside spacetime, and this is given as the explanation of why gravitation is so much weaker than the other forces." If this statement is true, is it still possible that there are infinite...

Time is not the 4th dimension. Well... depends on perspective. Why do people say time is the 4th dimension? I know you can say it's a dimension and there are already 3. But why not say mass is a dimension? Each point in space has a certain mass. What's the difference? Einstein said it and it...

On a frictionless horizontal air table, puck A (with mass 0.366 kg) is moving toward puck B (with mass 0.254 kg ), which is initially at rest. After the collision, puck A has velocity 0.119 m/s to the left, and puck B has velocity 0.655 m/s to the right. What was the speed of puck A...

Do black holes actually have dimension (I mean size)? Thanks.

1.Is it possible that different dimensions co-exist?For example:3 dimension space and four dimension space 2.Is it possible that the same type of dimension exist separately in another dimension?(For example:Two 3-dimension space exist together in a higer dimension) 3.Will force in a dimension...

Collision in One Dimension? Problem: A 45kg girl is standing on a plank that has a mass of 150kg. The plant, originally at rest, is free to slide on a frozen, lake (flat, frictionless surface). The girl begins to walk along the plank at a constant speed of 1.5 m/s relative to the plank...

Hi everyone, I was hoping someone could help me with something. Could someone explain to me exactly what this expression means: H = {(a+b) + (a - 2b)t + bt^2 | a E R, b E R} the purpose is to find the dimension of the given subspace, which I know how to do, I have just...

There is a collision between two pucks on an air hockey table. Puck A has a mass of 0.031 kg and is moving along the x-axis with a velocity of +5.5 m/s. It makes a collision with puck B, which has a mass of 0.066 kg and is initially at rest. The collision is not head-on...

Man, this is another embarrasing question. A 1000kg weather rocket is launched straight up. The rocket motor provides a constant acceleration for 16 s, then the motor stops. The rocket altitude 20 s after launch is 5100 m. You can ignore any effects of air resistance. First this question...

Spacetime raises many questions. Three-dimensional space is easy to visualise. We live in it. We can denote orthogonal axes as x, y and z and have oodles of fun with three-dimensional geometry. One wonders, is there really a fourth dimension and is that dimension time? Newtonian...

~~~acceleration In One Dimension~~~ I didn't get any replies :cry: , this is due monday, i still dun understand the concepts and all the new concepts are built on the previous ones! :frown: I was wondering if an object can have a negative acceleration and be speeding up? If so, can you...

kinematics one dimension. help! hi I've had a lot of trouble with this problem and i hope someone can help me. Car B starts from rest and accelerates at 2.00m/s^2 along a straight road. Car A starts from rest at the same instant 20.0 m behind car B and accelerates 3.00 m/s^2. How far must...

kinematics one dimension. help! hi I've had a lot of trouble with this problem and i hope someone can help me. Car B starts from rest and accelerates at 2.00m/s^2 along a straight road. Car A starts from rest at the same instant 20.0 m behind car B and accelerates 3.00 m/s^2. How far...

Hello, I'm having a bit of trouble starting this problem: A ball is dropped from a height of 30 m. At the same instant another ball is thrown straight up from the ground with aspeed of 30 m/s. How long are the balls in the air before they reach the same height? I'm not sure what equation...

hi :D after reading up on 10 dimensions (and how more can be added any time we need them even though they might not exist) i found it interesting how it stated that 5-10 dimensions where located in the well known 3 dimensions we see every day (with the 4th dimension being time). what i don't...

What makes R^2 different from R? Unless I'm mistaken (which is unfortunately quite possible), R^2 has the "same number" of points as R. I'm thinking that what makes R^2 different from R is the topology, which is why I picked this forum. But what sort of conditions do we really need to...

HI. I was wondering if anyone can tell me a bit about the forth dimension? Any comment is welcome

Hello, this is my first time posting, I do hope I've found the right place. I have relatively no knowledge of physics but am about to minor in it in college. The questions and ideas I am about to set down concern time, an issue of which I again know very little. While sitting idle one day...

The Lorentz Transformations on a Block of Space Reference system V, RSV, is a block of three-dimensional space that has a velocity, v, reference to a block of space that is at rest, RSR. The Lorentz transformations express the measurement of length, mass and time in RSV, as measured by RSR...

Is it possible for time to be a "Mobius dimension," with its non-linear topology and simultaneous one-way linear direction, as described by relativity theory?

Can Quantum Jumps Same as Dimension Jumps ? By going back to Bohr's stationary orbits of electrons, The idea of quantum jumps was born. We can hypothesize that matter such as electrons are 4D objects and photons are 3D objects and the continuous space between orbits is a 2D continuum. So...