Dimensions Definition and 1000 Threads

Must two quantities have the same dimensions if you are using one quantity as an exponent in raising other to a power? What is the dimension ( or dimensionless) of '2' in mv2/r ?( v is raised to the second power)

Homework Statement A ball of mass m hits the floor with a speed v making an angle of incidence theta with the normal. The coefficient of restitution is e. Find the speed of the reflected ball and the angle of reflection of the ball. The Attempt at a Solution I know that momentum is conserved...

Hello! I hope I'm in the right place for this questions. In short, I'm a musical instrument builder. I'm looking at placing a piece of wood above a closed resonator box. The box (also made out of wood) will have a hole in the top that is centered under the piece of wood. I know the material that...

Homework Statement Sorry for another question so soon, I am not sure if there is a limit on how many I can ask. I try to keep it to a minimum but sometimes I can't figure it out on my own. Question: In a physics lab, 0.30 kg puck A, moving at 5.0 m/s [W], undergoes a collision with 0.40 kg...

Here is an animation I created in R. I built this Markov chain of order 50 by correlating the information in one of the coordinates while randomly varying the rest. Is there an explanation for the clustering and flattening out over increasing dimensions of the vector space? Is it due to the...

If light is one dimensional, yet has gravity, and gravity is the warpage of spacetime, and spacetime has four dimensions, then how does a one dimensional wave/particle warp multiple dimensions?

String theory and M-theory and Kaluza Klein theories predicts additional extra dimensions at least 2 recent papers proposed tests these predictions of extra dimensions String theory phenomenology and quantum many body systems Sergio Gutiérrez, Abel Camacho, Héctor Hernández (Submitted on 24...

I'm not a math machine, but I dabble in dimensional stuff. I think this falls under knot theory. I have built several prototypes of a tesseract. Each of them sits in a little case in my office. One of them is made from truncated cubes, held together with elastic cord: In theory, the...

Homework Statement Consider gamma matrices ##\gamma^0, \gamma^1, \gamma^2, \gamma^3## in 4-dimension. These gamma matrices satisfy the anti-commutation relation $$ \{ \gamma^\mu , \gamma^\nu \}=2\eta^{\mu \nu}.~~~(\eta^{\mu\nu}=diag(+1,-1,-1,-1)) $$ Define ##\Gamma^{0\pm}, \Gamma^{1\pm}## as...

Hi there. It is well known from the theory of differential equation the Sturm-Liouville theory, concerning with the eigenvalue problem: ##\displaystyle \frac{d}{dx} \left ( p(x) \frac{dy_n}{dx} \right ) - q(x) y_n(x)=\lambda_n w(x) y_n(x)## with prescribed boundary condtitions for ##a\leq x...

A recent post asked "why does physical space need to be 3-dimensional?" However, the thread became infected with personal insults and was (properly) closed. I felt sorry that PeterDonis, whose posts I respect, was subjected to this abuse ! I have read several posts which start by assuming that...

We often hear about string theory requiring extra dimensions over and above our 4D spacetime. Does this shed any light on the singularity which is supposed to exist at the centre of a black hole? Does our normal spacetime simply join the other dimensions in their hidden (curled-up) form? This...

Signatures of extra dimensions in gravitational waves David Andriot, Gustavo Lucena Gómez (Submitted on 24 Apr 2017) Considering gravitational waves propagating on the most general 4+N-dimensional space-time, we investigate the effects due to the N extra dimensions on the four-dimensional waves...

Homework Statement i am showing the invariance of the Levi-Civita symbol in 4 dimensions The Attempt at a Solution $$\varepsilon_{ijkl}'=R_{im}R_{jn}R_{kp}R_{lt}\varepsilon_{mnpt}$$...

Take a spin-1/2 particle of mass ##m## and charge ##e## and place it in a magnetic field in the ##z## direction so that ##\mathbf B=B\mathbf e_z##. The corresponding Hamiltonian is $$\hat H=\frac{eB}{mc}\hat S_z.$$ This must have units of joules overall, and since the eigenvalues of ##\hat S_z##...

first of all english is not my mother tongue sorry. I want to ask if you can help me with some of the properties of the levi-civita symbol. I am showing that $$\epsilon_{ijkl}\epsilon_{ijmn}=2!(\delta_{km}\delta_{ln}-\delta_{kn}\delta_{lm})$$ so i have this...

first of all english is not my mother tongue sorry. I want to ask if you can help me with some of the properties of the levi-civita symbol. I am showing that $$\epsilon_{ijkl}\epsilon_{ijmn}=2!(\delta_{km}\delta_{ln}-\delta_{kn}\delta_{lm})$$ so i have this...

What's so special about higher dimensions? I did some youtube research and didn't find a lot of information. All I found is that beyond 5 dimensions all dimensions have only 3 platonic solids. I've got this simulation I'm working on. I don't want to go into detail for obvious reasons but so...

Hi folks, This is the Lorentz transformation in 1D, x axis: I want to get the second term of the time t equation, I mean vx/c2, in two dimensions, I mean for a point in the XY plane. I know this term arises because if we want to syncronize a point B with the origin what we do is sending a...

I don't have a degree in Physics but studied it in secondary school and I was wondering , Can each point on a sphere be classed as another dimension in relative comparison to like a 1 dimension plane ,two dimension plane ect. ?

I often here claims that higher dimensions such as the 5th and 6th dimensions deal with different possible realities, be it branching off or from different start conditions. I find this confusing and would like to have it cleared up how it is possible for different so called realities to occur...

The ##{\bf su}(2)## Lie algebra in a representation ##\bf R## is defined by ##[T^{a}_{\bf R},T^{b}_{\bf R}]=i\epsilon^{abc}T^{c}_{\bf R},## where ##T^{a}_{\bf R}## are the ##3## generators of the algebra. In ##2## dimensions, these generators are the Pauli matrices ##T^{1}_{\bf 1} =...

Homework Statement [/B]A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball as shown (The first ball is traveling to the right). If the first ball moves away with angle 30° to the original path, determine the speed of the first ball after the collision...

Has anyone performed the double slit experiment in three dimensions? By this I mean, having double slits and a detection screen on three sides? This would imply there are 6 slits and 3 detection screens. What would we observe? Would we see the electron exhibiting wave like behavior (ie...

If strings are one dimensional objects and they make up every particle that we know of then there is no second or third dimension. There are only one dimensional objects that seem like they are three dimensional objects because they spin as they move through space.

The angle between two ℝ2 or ℝ3 vectors makes sense. I have a vector like [0 0.707 1 0.707 0 -.707 -1 -.707]T (Actually my vector is A/D conversions of a sine wave from the wall power outlet. The sample rate is 4800 so there are 80 samples, separated by 1/Fs for a 60Hz sine wave. If I...

I want to model atoms of the periodic table using OpenGL (API for 3D graphics). I was told by a physics teacher one time that this cannot be done because it's not solvable. Can you guys confirm? Apparently only the shells of the hydrogen atom has been solved meaning that I can only model the...

So the Holographic Principle says that our 3 dimensonal world is encoded in the 2d surface of the cosmological horizon. What about the remaining dimensions? Are they there in the regular 3space or are they also encoded?

will there be any effect on the speed of light ,when it travels from higher dimensions to three dimensions of space ?

Why can't we perceive higher dimensions?

I've been given that in an electromagnetic calorimeter the radiation length of a material consisting of a single nucleus is: ##X_0 = \frac{716.4A}{Z(Z+1)\ln(287/\sqrt{74}}## Where ##X_0## is in g ##cm^{-2}##. How can it be in those units when everything in that expression is dimensionless? It's...

The pion decay constant f_{\pi} is defined by <0|\overline{d}\gamma^{0}\gamma^{5}u|\pi^{+}>=f_{\pi}m_{\pi} where I have set the momentum \boldsymbol{p}=0 (and used the temporal component of the axial vector). Now, at the right-hand-side the dimension is two (the decay constant and the mass are...

Hi, I have a system with a lever arm that's attached to a vertical support at its pivot point. The lever is pushed up by hand and is supported by a stay lid like in the image. I need to calculate the area and thickness of the arm and the column but the only numbers I have is the load attached...

Homework Statement Three charges, q1, q2, and q3, lie in a plane, as shown below. Find the net force on charge q2 (please refer to attachment for diagram) Homework Equations F= k x q1q2/R^2, knowledge of trig functions and separating x and y components The Attempt at a Solution So I found the...

I am trying to evaluate the following integral. ##\displaystyle{\int_{-\infty}^{\infty}f(x,y)\ \exp(-(x^{2}+y^{2})/2\alpha)}\ dx\ dy=1## How do you do the integral above?

haruspex submitted a new PF Insights post Can Angles be Assigned a Dimension? Continue reading the Original PF Insights Post.

Homework Statement A cylindrical metal can is to be manufactured from a fixed amount of sheet metal. Use the method of Lagrange multipliers to determine the ratio between the dimensions of the can with the largest capacity. Homework EquationsThe Attempt at a Solution $$V(r,h)=\pi r^2h$$ $$2...

Homework Statement Homework Equations xf = x0 + v0cos(θ)t + (1/2)axt2 yf = y0 + v0sinθt - (1/2)gt2 F = ma The Attempt at a Solution [/B] I first tried to find the acceleration in the x direction so I could solve for the force xf = x0 + v0cos(θ)t + (1/2)axt2 In order to find the time I used...

The Dirac equation describes the behaviour of non-interacting spin-##1/2## fermions in a quantum-field-theoretic framework and is given by ##i\gamma^{\mu}\partial_{\mu}\psi=-m\psi,## where ##\gamma^{\mu}## are the so-called gamma matrices which obey the Clifford algebra...

I have a question to anyone experienced with graphs and topology. The question is relevant for this topic: https://www.physicsforums.com/threads/a-graph-based-model-of-physics-without-dimensions.887694/ Is it possible to construct an arbitrarily large graph (a set of vertices, a set of edges)...

Despite being a constant, It has both dimensions and a unit, can someone kindly explain why ?

We live in a world with 3 space dimension and 1 time dimension, and i saw a video how a universe would look like is their where n-space dimension but what would happen if their where 2 time dimensions?

Im not sure where to find a good place to learn kinematics in one and two dimensions. Using calculus

I've tried to imagine and draw the effect of a large object would have on space time in 3d but it just doesn't seem right. Would I be right to assume that maybe spacetime has more than 3 dimensions?

I am looking to use Gauss's law to find the electric field in ##1+1## dimensional spacetime: ##\int \vec{E}\cdot d\vec{A}=\frac{Q}{\epsilon_{0}}## Now, for a point charge in ##1+1## dimensional spacetime, the Gaussian surface is the two endpoints (a distance ##r## away from the point charge)...

I know photon is considered a point particle, so it means it has no physical dimensions, if I'm not wrong. Plus, it has a probability wave function associated to it. It also interacts as a wave which consists of an electrical and magnetic field perpendicular to each other and delayed by a...

Dear Physics enthusiasts, I'm just a curious guy, I don't have any fancy credential, and in fact I don't have formal education at all (for 'legal' purposes I'm just "literate"). I'm being honest about that right away so if that's a problem (what seems to be the case for a lot of...

The first equation of the left hand side is the Schrodinger Equation of the Harmonic Oscillator.The second equation of the left hand side is the new equation doing by the Dimensions Analysts. But I don't understand how the new equation come from according with Dimension Analysts of the right...

I.e. x,y,z

Hello, i have here some identities for gamma matrices in n dimensions to prove and don't know how to do this. My problem is that I am not very familiar with the ⊗ in the equations. I think it should be the Kronecker-product. If someone could give me a explanation of how to work with this stuff...