General Definition and 1000 Threads

Hi, as follow-up to this thread I've a question about general representation of a two-port network. Basically it is ad hoc built four-terminal linear network (using controlled sources + nullator-norator pair): for it I found a general representation ##AV + BI = 0## as in the picture above. If...

I don't know how to solve this

I don't know how to calculate this. Pls help

I am doing a project where the final scope is to find an extra operator to include in the proca lagrangian. When finding the new version of this lagrangian i'll be able to use the Euler-Lagrange equation to find the laws of motion for a photon accounting for that particular extra operator. I...

How does general relativity shows the conservation of energy. Because I was reading and listening to something today that touched on this subject. It almost seems as though if you scale GR to larger sizes it stops working and turns into an incomplete law of nature like Newton's laws of gravitation.

I am in the second year of my Physics B.Sc and will soon have to make the decision how to continue from there. My grades are generally good, and I certainly want to continue my education, specifically a Masters. My goal is to be employed in industry, where I would strongly prefer actually...

$\tiny{307w.3.2.5.3}$ https://mathhelpboards.com/{http%3A//faculty.sfasu.edu/judsontw/ode/html-snapshot/linear02.html Find the general solution of each of the linear system \begin{align*} x' & = -3 x + 4y\\ y' & = 3x - 2y \end{align*} $A=\begin{pmatrix}-3&4\\ 3&-2\end{pmatrix}...

What I've done is using the TOV equations and I what I found at the end is: ##e^{[\frac{-8}{3}\pi G\rho]r^2+[\frac{16}{9}(G\pi\rho)^{2}]r^4}-\rho=P(r)## so I am sure that this is not right, if someone can help me knowing it I really apricate it :)

Moderator's Note: Thread spun off from previous thread due to topic change. I see. Basically you are worried by stuff a mathematical physicist would study with fancy schmancy functional analysis. I'm not worried too much by such stuff because I don't think that actual infinities (actually...

I think increasing the damping would decrease the amplitude and increase the Period (T). But, what I'm really unsure about is the frequency, wavelength and wave speed. Would it be no effect on those three? Because if dampening acts like friction, wouldn't it slow down the wave/ increase speed?

Suppose you have a tensor quantity called "B" referenced in a certain locally inertial frame (with four Minkowski components for instance). As far as I know, a parallel transportation of this quantity from a certain point "p" to another point "q" consists in expressing it in terms of the...

I know the basics of GR, but I'm far from an expert. I'm interested in the general formula for the angle shift experienced by a light ray in presence of a gravitational field. Light bending is topic covered in many books, of course, however the usual treatments would just not do for my purposes...

if the Work done by friction is -4.73 for object #1 but the work done by friction for object #2 is -4.63, in which scenario is the Work greater - the signs are throwing me off. Also, let's say the initial elastic energy of a ball is 5 and its final energy is 0.27 (scenario #1) vs its final...

In classical Hamiltonian mechanics, because of Liouville's theorem about the volume of phase space being preserved by time evolution, there are no attractors. Naively, I think of the Raychaudhuri equation in GR as showing a shrinking volume. However, I guess Raychaudhri's equation does not...

Recently, when reading an entry about Mercury's perihelion shift, someone mentioned a "hand-wavy" explanation as to why GR predicts the orbit so precisely. I was wondering if there was some elementary way to expound on what he was saying. Fundamentally, the comment said something to the effect...

I really would like to know the process of your preparation... Like how and when you started preparing, what growth you saw in your problem solving capacity and so on. Kindly share about the beautiful journey. If possible, give me some tips/resources as I'm also an aspiring olympian.

Hi, I was trying to do the following problem. My attempt. Finding the reduced row echelon form for the system above. I do not see any way to proceed any further. The following is the solution presented in solution manual. How do I proceed to get the following answer?

(1) I remember reading somewhere that in general relativity, "space" and "time" lose their metrical meanings. Is that true? And yet, we continue talking of space and time in general relativity as spacetime. (2) Moreover, as someone mentioned in this thread, what happens to the speed of light? In...

On the first attached page ##\mu_z## is associated with orbital angular momentum (Eq. 41.34). On the following pages (Eq. 41.38) it is associated with spin angular momentum? Are these both part of the same thing? I tried to read further but the book does not address this. In example 41.6 it...

The International Bureau of Weights and Measures combines the readings of 450 atomic clocks around the world to obtain a time standard with sub-nanosecond accuracy. These clocks run at different rates - a clock at 1 km of altitude gains about 7 ns a day compared to one at sea level due to the...

Hi everybody I saw quite a nice Youtube vid about general relativity and how gravity bends spacetime and therefor redirects angular momentum into the center of gravity. I thought the first time I begun to understand the concept but immediatly the questions poped up. The video basically says...

In the test of General Relativity by perihelion motion of mercury, the stress-energy tensor is set to 0 in Schwarzschild solution. Then, is the curvature caused by solar mass, or by the 0 stress-energy? Or, do we consider solar mass as the gravitating mass? Or the 0 stress-energy the gravitating...

Hello, I am looking for a worked out solution to diagonalize a general 4x4 Hermitian matrix. Is there any book or course where the calculation is performed? If not, does this exist for the particular case of a traceless matrix? Thank you!

This video explains gravity in a way I haven't encountered before (regardless of how irritating the presenter may be). Nevertheless, I find it hard to believe that a squirrel falls from a tree to the ground due to gravitational time dilation between its head and its feet. The amount is so...

We are discussing the introduction to Einstein field equation, so he start talk about the linearity in Newtonian gravity and the non linearity in GR. But there is somethings I am missing: > " (...) in GR the gravitational field couples to itself (...) A nice way to think about this is provided...

How do I simplify the expression...

The first two parts I think were fine, I expressed the tensors in coordinate basis and wrote for the first part$$ \begin{align*} \mathcal{L}_X \omega = \mathcal{L}_X(\omega_{\nu} dx^{\nu} ) &= (\mathcal{L}_X \omega_{\nu}) dx^{\nu} + \omega_{\nu} (\mathcal{L}_X dx^{\nu}) \\ &= X^{\sigma}...

I know that general relativity fails in singularities like the center of a black hole or the big bang. GR also fails at fundamental particle levels like electrons, protons and neutrons etc. I.e. GR cannot explain interactions of various fundamental particles?? (Am I correct?) But these does...

I was going over the Einstein-Hilbert action derivation of the Einstein field equations and came across a term that does not seem to be explicitly defined. That term is the Langragian for the matter fields. What exactly is matter in General relativity in the context of the Lagrangian? Here is...

Is it possible to have some kind of General Relativistic Quantum Theory without passing through the stage of Quantum Field Theory (where Quantum Theory is married to Special Relativity)? Einstein attached primary significance to the concept of general covariance as shown in this letter in 1954...

I had some questions about Archimedes' Principle. This image shows an object being gradually submerged into fluid: As far as I'm aware, when the object is floating, weight of fluid displaced by object = upthrust acting upwards on the object. When the object is fully submerged, volume of the...

Hello. I have a question about the law of energy conservation in GR. As time is inhmogeneous, we don't have energy-momentum 4-vector which would be preserved during system's dynamical change. It is only possible to define 4-vector locally. And next, the problem regarding how to sum this vectors...

Summary:: I am looking for a good introductory book about general relativity at undergraduate level. I am looking for a good introductory book about general relativity at undergraduate level.

I just finished multivariate calculus (without any linear algebra experience yet) and I am seeking out a path to understanding General Relativity. I am wondering what are the mathematical fields after multivariate calculus that I need to master before beginning to understand GR, and what...

I am trying to understand a thought experiment I just posed, which is: if an observer is traveling near the speed of light, and sends out two photons; one in the direction of travel and one in the opposite direction, how does general relativity account for time dilation? The photon "in front"...

https://www.cnn.com/2020/12/07/us/chuck-yeager-death/index.html What an amazing life. I'm glad we had him all the way to 97!

Trying to understand how Einstein predicted the appearance of stars during the solar eclipse around the turn of the 20th century (the first experimental confirmation of General Relativity, I believe). My impression, which is not physically correct, is that the sun attracts the photons as they...

General relativity. Curvature of spacetime: ok. time dilation: ok. What about space? Curvature is intrinsic and given by complex equations. But could we definitely say is there more space between 2 points along curved space through the star than would be through flat space (no star there) or...

I am trying to calculate the power calculation of a general circuit with voltage leading the current by a phase difference of ##\theta##. The instantaneous voltage is given by ##v = V_m\sin(\omega t +\theta) ; i = I_m\sin(\omega t) ##. The instantaneous power is then ##p = V_m I_m \sin(\omega t...

Summary:: Covid 19: How effective would a two week worldwide lockdown be? How effective would a two week worldwide lockdown be against Covid 19? In March when the news first hit, the US went swiftly into a hard lockdown. But things have mostly let up since then with mostly just masks, and...

I'm looking for a source that fully derives the complete formula for the surface area of a general (triaxial) ellipsoid. I'd prefer a source that has more than just a full derivation, but also has a fair amount of prose discussion on this topic. Some historical context would be nice, as well...

Is there a relationship between the Lagrangian ‘hill diagram’ and the spacetime curvature embedment graphs? The Lagrangian map shows effective potential, which deals with centrifugal force. As centrifugal force is a fictitious force (and gravity is as well), I would assume the underlying...

Einstein's theory describes gravity as a curvature of spacetime. As such, everything is affected by it. This includes light, which has no mass, as was made clear for the first time during the famous 1919 solar eclipse. In the standard model, the cause of gravity is supposed to be gravitons...

hi guys i was trying to derive the general formula of two orthogonal waves $$x^{2}-2xycos(δ)+y^{2} = A^{2} sin(δ)^{2}$$ where the two waves are given by : $$x = Acos(ωt)$$ $$y = Acos(ωt+δ)$$ where ##δ## is the different in phase , i know it seems trivial but i am stuck on where should i begin...

$\tiny{27.1}$ 623 Find a general solution to the system of differential equations $\begin{array}{llrr}\displaystyle \textit{given} &y'_1=\ \ y_1+2y_2\\ &y'_2=3y_1+2y_2\\ \textit{solving } &A=\begin{pmatrix}1 &2\\3 &2\end{pmatrix}\\...

In the Hamiltonian formalism, the space-time transformation are realized via canonical transformation, and the transformations are generated by Poisson brackets of certain functions of phase-space variables. In Newtonian mechanics, Galilean boosts are generated by the sometimes called dynamic...

I haven't gone to movie theaters in 6 months. So I have to be content with online movies, and reading sci fi models, and maybe writing a short story or two. If a flying ship could travel thousands of miles per second, it can't suddenly turn 90 degrees because of inertia, the occupants would be...

Hey there.Have you read about the alternative theories proposed by other scientists to General Relativity?So far General Relativity still stays the most accurate.But if we could generalise it?Perhaps try with some new maths like complex differentiable manifolds or Lie groups or another...

Actually I know there would be some permutations used here. I know how to calculate the symbols but estimating is quite a new thing to me