Relation Definition and 1000 Threads

Let us suppose we have a covariant derivative of a contravariant vector such as $$\nabla_{\mu}V^{\nu}=\partial_{\mu}V^{\nu} + \Gamma^{\nu}_{\mu \lambda}V^{\lambda}$$ If ##\Delta_{\mu}V^{\nu}## is a (1,1) Tensor, it must be transformed as $$\nabla_{\bar{\mu}}V^{\bar{\nu}} = \frac{ \partial...

hi guys i would like to know what is the physical significance of the dispersion relation , i know that it relates the energy and momentum vector and correspondingly the energy and momentum with each other , but what does this tell me about the system , and why should i care that the dispersion...

In Principles of Lasers by Svelto, while deriving the Planck radiation formula, equation 2.2.3 says $$I_{\nu} = \frac {c_0} {4n} \rho_\nu$$ where ##I_\nu## is the spectral intensity at some hole in the cavity wall (energy per time per area per frequency), ##c_0## is the speed of light in...

I'm wondering what the relationship between blackbody radiation and spontaneous emission is. As far as I know, there are three sources of EM radiation - thermal radiation, oscillating dipole (multipole?), and LASER. And it seems like light emission from an atom can be separated into two...

I was recommended a paper: <https://digital.library.adelaide.edu.au/dspace/bitstream/2440/101285/3/hdl_101285.pdf>. And in the opening sentence read: "The Einstein equivalence principle (EEP) is at the heart of special relativity." To me this didn't make sense. Firstly because Einstein...

Here we are talking about non-relativistic quantum physics. So we all know kinetic energy T = E - V = \frac{1}{2}mv^2 in classical physics. Here V is the potential energy of the particle and E is the total energy. Now what I am seeing is that this exact same relation is being used in quantum...

How do you prove Heisenberg uncertainty relations for mixed states (density matrix), only from knowing the relation is true for pure states?

A golfer hits a tee shot into the rough and the ball stops approximately 120 yds from the green. There is a tree located 40 yds from the ball, directly in the path of the shot. The golfer decides to try to hit the ball over the tree. The path of the shot can be modeled by the equation h =...

Homework Statement:: time step must be greater than stability criterion Relevant Equations:: stability criterion= h^2/4 x alpha Hello. I have had to do 2 MATLAB codes based on the 2D Heat diffusion equation using the Explicit Finite Method. In those codes, the time step must be greater or...

Hi, I would like to prove the following congruence relation: Let p be a prime number and let ##n## be a natural such that ##p < n < p^2##. Then $$ {n-1 \choose p-1} {n \choose p-1} \equiv 0 (\mbox{mod p}) .$$ I am expecting it to have a rather trivial proof. Thanks in advance for any...

If (u,v) = 1, prove that (u+v,u-v) is either 1 or 2. Where (,) means: $$ux_1 + vx_2 = 1$$ $$u + v(x_2/x_1) = 1/x_1, u(x_1/x_2) + v = 1/x_2$$ $$u + v = 1/x_1 + 1/x_2 - v x_2/x_1 - u x_1/x_2$$ $$u - v = 1/x_1 - 1/x_2 + u x_1/x_2 - v x_2/x_1$$ Now we can express (u+v,u-v). But i am not sure if...

##(\frac {∂p} {∂ρ})_s=ϒ(\frac {∂p} {∂ρ})_T## The variables are p for pressure, ρ for specific mass density and γ is ratio of specific heats. I am able to show that the relation is valid for a perfect gas but cannot show its validity in general. The closest I get is ##dp=(\frac {∂p} {∂ρ})_s...

Hey! :unsure: At the cash register of a store we want to give change of worth $V$ cents of euro. Create and analyze a greedy algorithm that gives the change using the minimum number of coins. Assume that the available coins are the euro subdivisions, i.e. $\{1, 2, 5, 10, 20, 50\}$ and that we...

Which of the following implies that S∘S=S? There are 5 options, select all that are right. S is reflexive S is symmetric S is transitive S is reflexive and symmetric S is reflexive and transitive I assume that S acts on a set A. So let a,b,c be elements of A. For S to be reflexive, for all a...

I am trying to develop a relation between scale factor (a(t)) and ##\Omega##. The relation came out to be evolve as ##\Omega_i=\Omega_io * a^{-n}## but my graph isn't right it's giving values of ##a(t)## to higher extent. I consulted my instructor he only added that I should include ##H_o##...

In the following proof: I didn't understand the following part: Isn't it supposed to be : ## a > s_A - \epsilon >0 ## and ## b > s_B - \epsilon >0 ## Because to prove that ## s ## is a supremum, we need to prove the following: For every ## \epsilon > 0 ## there exists ## m \in M ## such...

I get that the impulse is I=FΔt, but why is it even equal to change in momentum caused by the force under consideration?

Hello, everyone. Need I understand Dirac equation if I plan to learn QED?

I am solving some GR problems. In one problem, some relation between a second covariant derivative and the Riemann tensor is to be proven. In the solution, the relation is first proven in a local flat coordinate system, followed by a statement that, since this relation is covariant it is true...

[Moderator's note: Spun off from previous thread due to new question.] I have read here: http://backreaction.blogspot.com/2016/02/everything-you-need-to-know-about.html?m=1 That there is a proportionality between the size of LIGO arms and the wavelength of gravitational waves that it can...

Why is it generally accepted that black skin is only caused by melanin, due to the intensity of UV radiation, in order to protect the body from skin cancer to develop? Because melanin is also, together with adrenaline, linked to the precursor: dopamine, thus both chemicals share the same pathway...

I don't understand why sometime for paper : Kramers-Kronig relations and sum rules of negative refractive index media for paper : A Differential Form of the Kramers-Kronig Relation for Determining a Lorentz-Type of Refractive Index* for paper : Comparison Among Several Numerical...

Good afternoon guys, I was making some researches about building my own EV and its' specifications but I have a few no direct answered questions and some of them I humbly ask the help for you guys, based on the configuration example below. Considering that I hypothetically have an electric DC...

I was thinking to myself, how come are particles coming from the sun gets deflected the way they do due to Earth's magnetic field? They are getting pulled toward the poles, but if we think in terms of classical Lorentz force, they should not just follow the magnetic field lines, but rather start...

I can’t understand it.

I was having a discussion with someone, regarding whether Time Travel was possible. The opposing individual argued that people are composed of matter that is simply woven into the fabric of space-time, therefore, rendering us unable to travel through time. I wasn't sure if he was right because I...

Hello! (Wave) Suppose that we have the recurrence relation $a_k=3^k-a_{k-1}, a_0=1$. By replacing the terms of the sequence we get that it is equal to $a_k=3^k-3^{k+1}+3^{k+2}-a_{k-3}$. How do we get that it is equal to $a_k=3^{k}-3^{k-1}+3^{k-2}- \dots+ (-1)^k$ ? :unsure: Also, why is the...

I know that this is the general case of the Einstein and Debye Model.

After computind dirac 1D equation time dependant for a free particle particle I get 2 matrixs. From both,them I extract: 1) the probablity matrix P =ps1 * ps1 + psi2 *psi2 2) the current matrix J = np.conj(psi1)*psi2+np.conj(psi2)*psi1 I think that current is related to electricity, and...

My friend gave me some statements which are wrong, but I could not tell why they are wrong. He wrote, Since ##\omega = \frac E \hbar = \frac {\hbar k^2} {2m} = k v##, then##p=\hbar k =2mv##. I guess that ##E =\hbar \omega## may only appied to photons, not matter waves. Is that correct?

Let me define the letters before because they will be confusing: ##x##: 3-vector ##v##: 3-velocity ##a##: 3-acceleration ##X##: 4-vector ##U##: 4-velocity ##A##: 4-acceleration ##\alpha##: proper acceleration ##u##: proper velocity One can define the proper time as, $$d\tau = \sqrt{1 -...

If i have a thermal shock in a thermo-elastic material with crack mode I propagated ? what are the stress-strain relations in this case? or what is the factor K relation? "sorry if the question is not true, but i hope you understood what i mean"

I'm following this video on how to establish an equivalence relation to define the tensor product space of Hilbert spaces: ##\mathcal{H1} \otimes\mathcal{H2}={T}\big/{\sim}## The definition for the equivalence relation is given in the lecture vidoe as ##(\sum_{j=1}^{J}c_j\psi_j...

So, I was reading through this thread: https://www.physicsforums.com/threads/would-a-portable-railgun-make-a-lot-of-noise.985309/#post-6309691 and I managed to make one of my usual questions which need more specific knowledge on the subject than I can find on the web. I (think I) understand...

I would like to demonstrate the equation (1) below in the general form of the Log-likelihood : ##E\Big[\frac{\partial \mathcal{L}}{\partial \theta} \frac{\partial \mathcal{L}^{\prime}}{\partial \theta}\Big]=E\Big[\frac{-\partial^{2} \mathcal{L}}{\partial \theta \partial...

According to https://plato.stanford.edu/entries/zermelo-set-theory/ , Zermelo (translated) said: I don't know if that quote is part of his formal presentation. It does raise the question of whether set theory must formally assume that there exists an equivalence relation on "elements" of...

Now, with the given set of natural numbers, we can deduce the relation ##R## to be as following $$ R = \big \{ (1,6), (2,7), (3,8) \big \} $$ Now, obviously this is not a reflexive and symmetric. And I can also see that this is transitive relation. We never have ##(a,b) \in R## and ##(b,c) \in...

I need to find the properties such as specific heat capacity, thermal conductivity, density and others.

After noting w=vk and differentiating with respect to k, and lots of simplifying, I get: Vg = c/n +(2*pi*0.6)/(k*n) This doesn't correspond to any numerical value though...

If anyone is familiar with the calculation of scattering amplitudes using momentum twistors. I am working through the book "Scattering Amplitudes in Gauge Theory and Gravity" by Elvang and Huang. I am completely stumped by one step that should be simple. My question is about Eq. (5.45). My...

Hi equivalent class is a Cartesian product of A*A. Then shouldn't it's union be a partition of A*A, instead being a partition of A

I have some questions about this video. I have watched other videos in this series. Otherwise very nice series, but I think there may be mistake. Isn't the video flawed because it forgot forgot 0'th component of 4-fector ##A## aka ##\varphi## in 3-vector representation, I think it because...

I'd like to point to the following paper: C. Rovelli, Physics needs philosophy. Philosophy needs physics. Foundations of Physics 48 (2018), 481-491. From the abstract:

Can anyone explain while calculating $$\left \{ \Psi, \Psi^\dagger \right \} $$, set of equation 5.4 in david tong notes lead us to $$Σ_s Σ_r [b_p^s u^s(p)e^{ipx} b_q^r†u^r†(q)e^{-iqy}+ b_q^r †u^r†(q)e^{-iqy} b_p^s u^s(p)e^{ipx}].$$ My question is how the above mentioned terms can be written as...

Hey! :o Let $M:=\{1, 2, \ldots, 10\}$ and $\mathcal{P}:=\{\{1,3,4\}, \{2,8\}, \{7\}, \{5, 6, 9, 10\}\}$. For $x \in M$ let $[x]$ be the unique set of $\mathcal{P}$ that contains $x$. We define the relation on $M$ as $x\sim y:\iff [x]=[y]$. Show that $\sim$ is an equivalence relation. For...

Hey! :o I am looking at the following: There are the terms reflexive, symmetric, antisymmetric and transitive. Give for each combination of the properties (if possible) a set $M$ and a relation $R$ on $M$, such that $R$ satisfies these properties. What is meant exactly? Every possible...

What is the relation of the arrow of time and entropy according to thermodynamics?

What part of double slit mystery remains considering single slit can produce interference pattern as well? Does holography not fully explain those patterns behind any number of slits as a sort of "encoded image" of the slit(s)? Does the word "focus" have any meaning in these kinds of experiments?

I have some doubts about whether Planck's relation (E=hf) applies to radio waves. This has been bugging me because trying to apply Planck's relation to radio frequency results in some inconsistencies that I've been unable to resolve. BTW, I have no physics training, so please go easy on me...

NO TEMPLATE, MISPLACED HOMEWORK Summary: What are the values of constants in power-law fluid relation when the fluid behaves as an ideal fluid, a Newtonian fluid and a non-Newtonian fluid? τ = A(du/dy)^n +B Where A, B and n are constants that depend upon the type of fluid and conditions...