Dimensions Definition and 1000 Threads

Hello, I am an amateur physics enthusiast and would like to pose a question to you. It is my understanding that for string theory to make sense there should be 11 dimensions. Three extended spatial dimensions and one time dimension that we perceive, as well as seven hidden dimensions which...

Homework Statement Homework Equations From my notes I'm aware of the following equation: dim(A + B) = dimA + dimB − dim(A ∩ B).The Attempt at a Solution I'm assuming part of the solution involves the equation above and rearranging it but I'm not sure how I would determine dim(A + B). I also...

My Professor frequently uses the term higher dimensions. Could someone tell me exactly what is a dimension. I think of it as some parameter which can vary. Also, I only know of 4 dimensions: time, length, width and height. Could someone give me more examples of dimensions? And lastly could...

I am seeking to understand reflection groups and am reading Grove and Benson: Finite Reflection Groups On page 6 (see attachment - pages 5 -6 Grove and Benson) we find the following statement: "It is easy to verify (Exercise 2.1) that the vector x_1 = (cos \ \theta /2, sin \ \theta /2 )...

I don't know how to frame my question but i will try - Is it a rule / property / characteristic of (our) universe that we have three dimensions and all are independant of each other? I am not sure about my doubt but i think what confuses me is the independance of the three dimensions

I seem to have read something once that suggested that gravity may be leaking into other dimensions/branes, this could explain why this force is so weak. I've been left thinking that it makes sense as a possibility. If it turns out to be the case, could Dark Energy then be leaked gravitational...

Homework Statement A light passenger vehicle weighing 1470 N collides with a train engine weighing 1.23 x 10^5 N, which was being moved from one rail siding to another. The train engine and the vehicle were entangled after the accident and from your measurements you have been able to...

A light passenger vehicle weighing 1470 N collides with a train engine weighing 1.23 x 105 N, which was being moved from one rail siding to another. The train engine and the vehicle were entangled after the accident and from your measurements you have been able to determine they skidded 15 m...

Homework Statement A neutron (mass 1.7x10-27 kg) traveling at 2.7 km/s hits a stationary lithium nucleus (mass 1.2x10-26 kg). Afterwards, the velocity of the lithium nucleus is 0.40 km/s at 54° to the original direction of the motion of the neutron. If the speed of the neutron after the...

"Find the most economical dimensions of a closed rectangular box [. . .]" Homework Statement Find the most economical dimensions of a closed rectangular box of volume 8 cubic units if the cost of the material per square unit for (i) the top and bottom is 5, (ii) the front and back is 2 and...

Homework Statement a wire carrying a current of 3.2A has a radius of 1.2mm. the material of the wire has 2.5x10^25 free electrons per cubic metre. the elementary charge is 1.6x10^-19 Homework Equations I=Anev cross section = pi*r^2 The Attempt at a Solution pi*0.0012^2 =...

There might be 11 dimensions like some physicists say, but why can't we see them? Is it because we are too small or too big to see them? what if dimensions were something relative? the bigger/smaller you become in comparison with something else, the less/more dimensions you can experience from it?

Maria designed a rectangular storage unit with dimensions 1m by 2m by 4m. By what should he increase each dimension to produce an actual storage that is 9 times the volume of his scale model? v= (1) (2) (4) v= 8 v has to be 9 times larger v= (x+1) (x+2) (x+4) How do i find the value of x?

If you search electric charge on the German Wikipedia (search electric charge on Wikipedia and click on the "Deutsch" blue link on the left side) its dimension is defined as "M^(1/2)*L^(3/2)*T^(-1)". I always thought of electric charge as fundamental property that by definition has its own...

Hi, I was wondering whether it's possible to define a rotation in 3 dimensions about the origin. Is it necessary to define an axis of rotation or would it be legal to say that you rotate abput the origin (like a phasor in 3 dimensions.) Thanks!

Hi Everyone, I have not understood or even studied string theory. However I was wondering whether the extra dimensions demanded by M-theory (10 spatial dimensions in that case), other string theories or even any other field theories necessarily demand the dimensions higher than four...

[SOLVED] Elastic collision in 2 dimensions Homework Statement A ball with mass m and initial velocity v1i collides elastically with a second ball of the same mass that is initially at rest. After the collision, the first ball moves away at an angle of θ1 with respect to the initial...

I am participating in science project on behalf of my school. I am a 12th grade student and very much interested in Maths,Physics and Computer Science. My teacher has assigned me to do project on Multi Dimension i.e Fourth Dimension. I need some good stuff of resource and information on Fourth...

Supposed reality was described by String Theory and there were 6 compactified dimensions. Could it describe quantum non-locality or does it still take light speed to travel in the compactified dimension? For example. You live in New York, I live in California. If we can send signal in one of the...

I read this article: http://www.sciencenews.org/view/generic/id/338500/title/Crystals_may_be_possible_in_time_as_well_as_space What dimensions is the article talking about? Doesn't everything have a fourth dimension, time?

I'm not sure if I'm posting this in the right place, but either way I was doing some research earlier and I came across a theory that I hadn't heard of before, and it came out in the early 2000's. And that's Moving Dimensions Theory, and from what I read it unified relativity and quantum...

I'm worried about the process of solving this problem, can anyone help me? We are to make a rectangular box, including the top, that has a volume of 144 cubic inches and for which the base is twice as wide as it is deep. The bottom, which must be strong, is made of a material that is three...

In 3 space dimensions consider a 1D string under tension between two fixed points. Let the string lie at rest on the z axis between z = 0 and z = ∞. We can produce linearly polarized and circularly polarized waves if I move the end of the string properly? Now if we add an extra space dimension...

This isn't really a 'problem', I'm just trying to follow Feynman's reasoning in section 18-2 of Volume 1 The Feynman Lectures on Physics. I've attached a png of the paragraph in question. I have 2 issues with this: 1. If the length OQ = OP, how can there be a right angle at P(x,y)? 2. I...

Reading the February edition of the New Scientist (about space-time being possiblly quantized in its own right) I read that the event horizon of a black hole is a 2-dimensional entity that may possibly encode all the information to describe the 3- 0r ->3 dimensional universe inside. That is...

The universe appears to have three space dimensions because of our size. The smaller an object is the less dimensions it has. If we where 4th dimensional beings we would probably be millions of miles in height looking into the known solar system with a microscope as if it was a marble. Time is...

1. Say you have a linear transform from A to B, and where A has a higher dimension than B. How do you show that the kernel of the transform has more than one element (i.e. 0)? Also, if B has a higher dimension than A, then how to show that the transform isn't surjective? 2. The attempt at a...

Homework Statement A heat-seeking missile is located at (2,-3) on a plane. The temperature function is given by T(x; y) = 20-4x^2-y^2. Find the equation of the curve along which the missile travels, if it continuously moves in the direction of maximum temperature increase. Express your...

Homework Statement Hey guys, so here's the problem I'm given: You are watching an archery tournament when you start wondering how fast an arrow is shot from the bow. Remembering your physics, you ask one of the archers to shoot an arrow parallel to the ground. You find the arrow stuck in the...

Homework Statement A metal can which holds 450 cm^3 is to be manufactured in cylindrical shape. The top and bottom will be cut from two squares and the corner scrap discarded (but paid for). The metal for the sides costs 0.1 cents/cm^2, while the cost for the top and bottom is 0.15cents/cm^2...

Can dimensions exist that are neither spatial nor temporal?

Homework Statement A watercraft with an initial velocity of 6.4 m/s [E] undergoes an average acceleration of 2.0 m/s2 [S] for 2.5 s. What is the final velocity of the watercraft?Homework Equations vf = vi + a * t a = v / t v = v2 + (-v1) pythagoras and cosine law? The Attempt at a Solution I...

On the arbitrary idea of some String Theorists that some dimensions are "small". [Disclaimer: I'm not an expert; a genuine question on basic notion of the theory follows, pardon the excitement:] I don't get the arbitrary idea of some String Theorists that beyond the 3rd/4th dimensions the...

I've heard there's no up and down in space due to the absense of gravity. So does the mean that outer space just has two spatial dimensions?

First post! I'm investigating chaos in non linear coupled spring oscillators. After generating a poincare' map of said system i wanted to see if the map was fractal. i proceeded to use a box counting method in order to calculate a fractal dimension. I generated a plot of log(number of...

Homework Statement First of all, sorry if this isn't the right place to post this. Four points A, B,C and D have coordinates (0, 1, -2), (1, 3, 2), (4, 3, 4) and (5, -1, -2) respectively. Find the position vectors of a. The mid-point E of AC b. The point F on BC such that BF/FD = 1/3 Use...

Hi, I don't think my textbook gives much information on vectors in 3 dimensions. The first chapter is on vectors, but only uses 2 and 1/2 pages to explain vectors in 3 dimensions. I have found a wealth of information on vectors in 2 dimensions (there are literally hundreds of detailed videos...

I don't really know much about GR, but I was just wondering about this theoretical question. I am asking this, because I think Special Relativity is a theory of four dimensions, and wasn't sure how many dimensions GR involved.

Homework Statement See attachment Homework Equations The Attempt at a Solution I'm not sure how to determine which points are co linear or which point lies in between the two. My book doesn't discuss how to do this at all. but PQ→ = <1,-1,2>, PR→ = <3,-3,6> I believe I found...

Homework Statement a baseball with a mass of 0.152 kg is moving horizontally at 32.0 m/s [E] when it is struck by a bat for 0.00200 seconds. The velocity of the ball just after the collision is 52.0 m/s [W 20 N] a) Find the impulse experienced by the ball b) find the average net force of...

I've just been thinking about moments of inertia in n dimensions and I just want to establish if this makes any sense: I'm considering doing a Monte Carlo evaluation of the moment of inertia of any n-ball - a solid sphere in n dimensions. Now I think you can say that the moment of inertia of a...

Hello, I have a question, please let me have your answer, if possible: In a space with an extra spatial dimension , where the extra coordinate is compact: 0 \le y \le 2\pi \alpha And the metric of the space is: {G_M}_N = \left( {\begin{array}{*{20}{c}} {{g_\mu }_\nu (x)} & {{A_\mu }(x)}...

Hi, Calculate the dimensions of a solid rectangular beam using the information below: Max Bending Moment= 8280Nm Ze = 36cm^3 Allowable Stress = 230MPa d = 2b Stress = moment/section modulus

Homework Statement Find the centroid of the region D, lying above the sphere x2+y2+z2 and below the paraboloid z=4-x2-y2. Homework Equations The Attempt at a Solution I decided it might be easier to change it to polar coordinates soo I did M=∫∫∫ dzrdrdθ where z goes from...

Hi everyone Homework Statement At first I want to find the langrangian function and the equation of motion for a system which exists of 2 masses(m) coupled by a spring(k). It's moving in 3 dimensions.We shall use cylindrical coordinatesHomework Equations LangrangianThe Attempt at a Solution...

Homework Statement find the components of the velocity of a car that is moving 10.0 km/h in a direction of 35degrees north of east Homework Equations The Attempt at a Solution

Hi! I'm a bit stuck with this special relativity assignment, here's is the problem: So the problem here is that not only does the hole shrink in S', as stated in the problem description, the pole should also be wider by a factor of 3 in this frame. So we have an 18 ft wide pole that has to...

What Higher Dimensions "Feel" Like nevermind.

Curl is easy to compute in 3 dimensions and if you let the third component be 0, its also easy in 2 dimensions. If you let the second and third components be 0, it is also easy in 1 dimension. My question is, is there a generalisation for curl to n dimensions and if there is, what is it and is...

My teacher said e2 c x ħ/R Where e is the electric charge, c is speed of light and h is reduced constant and R is radius. My teacher said this has dimenions of energy, is this right?