General Definition and 1000 Threads

Hello, Newton's second law, when the mass is constant, tells us that the acceleration ##a=\frac {F}{m}## which produces a simple ODE. The acceleration is a function that can be constant ##a= constant##, time-dependent ##a(t)##, velocity-dependent ##a(v)##, position dependent ##a(x)##, etc...

Hello forumites, I've been working with the following expression for the change in internal energy in an isentropic scenario. $$dU = n*c_v *dT = -pdV$$ However, I'm a bit stumped here, the left hand side of the expression (or middle rather), states the change in internal energy is the...

Summary: At this point, I am thorough with single variable, multivariable calculus, differential equations, linear algebra and basic concepts of point-set topology and tensor analysis. To learn General Relativity along-with its mathematical rigor, what are the topics I should first be thorough...

I would like to apply a General Lorentz Boost to some Multi-partite Quantum State. I have read several papers (like this) on the theory of boosting quantum states, but I have a hard time applying this theory to concrete examples. Let us take a ##|\Phi^+\rangle## Bell State as an example, and...

I've only recently started my journey into physics. While on this journey I realized quite a bit of the dumb down scientific information given to the public may not have been completely accurate or presented in a way that resulted in an inaccurate understanding. Lately I've been spending most of...

This thread is supposed to be about finding flaws in General Relativity, but the way these people talk they sound like they have no real knowledge of GR. I was just curious if any of you guys could explain further.

Is it appropriate to say that within classical physics the general form of Newton II is the Cauchy momentum equation? This equation applies to an arbitrary continuum body. Therefore it is more general than the common form of Newton II which applies basically to point masses and centers of mass...

Find a general solution to the system of differential equations \begin{align*}\displaystyle y'_1&=2y_1+3y_2+5x\\ y'_2&=y_1+4y_2+10 \end{align*} rewrite as $$Y'=\left[\begin{array}{c}2 & 3 \\ 1 & 4 \end{array}\right]Y +\left[\begin{array}{c}5x\\...

Publication: Rafael G. González-Acuña and Héctor A. Chaparro-Romo, "General formula for bi-aspheric singlet lens design free of spherical aberration," Appl. Opt. 57, 9341-9345 (2018) Open access preprint: arXiv Given one surface of a lens, how does the other surface has to look like to avoid...

Have there been any recent developments in the attempt to unify the standard model of quantum theory with General Relativity? It appears the no progress has been made recently in string theory or loop quantum gravity.

I am studying a beginner's book on QFT. In a chapter on electromagnetic form factors, the authors have written, using normalized states, $$\begin{eqnarray} \langle \vec{p'}, s'| j_\mu (x) |\vec{p}, s \rangle \ = \ \exp(-i \ q \cdot x) \langle \vec{p'}, s'| j_\mu (0) |\vec{p}, s \rangle...

I recently found the centre of mass of a semicircle using polar coordinates, by first finding the centre of mass of a sector, and then summing all the sectors from 0 to pi to get the centre of mass of the semicircle. However, being a beginner at integrals, I struggled for a long time getting the...

If Earth's motion about the sun is described by General Relativity why was Eddington's experiment with the bending of starlight needed to confirm the theory? In other words, don't we see enough common phenomena in our every day experiences to confirm GR without verifying subtle phenomena such as...

I have personally always had an interest in "how things work" from an early age. It seems to me to be our responsibility as such to have a basic understanding on how the world around us functions, came to be, and what causes things to be the way they are. I struggle to truly comprehend how so...

Hi guys, I'm reading a book 'the theoretical minimum: special relativity and classical field theory'. In chapter 1.3, author explains the general Lorentz transformation. He said "Suppose you have two frames in relative motion along some oblique direction, not along any of the coordinate axes...

I know that it would vary depending on the type of research a specific astronomer would be doing ( Astrophysics/Cosmology research versus an Astronomer researching exoplanets ) ; but in your opinion, “how much” or “how well” should an Astronomer with a graduate degree in Astronomy know General...

An electromagnetic wave has a phase speed and a group speed. Or velocities, for that matter. In a medium, the phase speed of a wave is generally determined by the medium's permeability μ and permittivity ε. What are the general parameters that determine the group speed of a wave in a medium?

i am far from an expert in Special and General Relativity, however, my attempts to learn from this forum are hampered by the large volume of posts involving common misconceptions and lack of understanding of the material. while the members of the forums patiently [usually] help our novice and...

Hi everyone, I am honestly pretty confused as to where to start with this. Can anyone give any pointers as to where I could possibly go, for (a) and (b)? Thanks!

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So in my previous math class I spotted on my book an exercise that I couldn't solve. We had to find the general solution for the differential equation. This was the exercise: 4y'' - 4y' + y = ex/2√(1-x2) Can anyone tell me how to solve this step by step?

$\tiny{28.1}$ 2000 Find the general solution to the system of differential equations \begin{align*}\displaystyle y'_1&=y_1+5y_2\\ y'_2&=-2y_1+-y_2 \end{align*} why is there a $+-y_2$ in the given ok going to take this a step at a time...

Hi, I'd like to be clarified regarding the general natural/Neumann boundary condition for a PDE. 1. The natural boundary condition is generally defined as: (1) and can be expressed as, according to this resource: (2) But apparently, according to...

1. I am rather confused about the usage of Cp0 and Cv0 in the solutions to the question below: In the solution to the depicted question, the solution involves setting up the equation as follows: Q-W=me*he-mi*hi+m2*ue-m1*u1 -W=-mi*Cp*Ti+m2CvT2-m1CvT1 I don't follow for the second step. How can...

I am interested, from a lay man's perspective mainly, in the incompleteness theorem but not sure I understand even on a general level what is being said. From what I recall, it states something like the following: in all formal mathematical systems there are certain statements that can't be...

I was trying to follow the solution for this problem and got stuck in the last portion of the solution. I encircled the part that I did not understand. I can't figure out how the solver was able to come up with tangent terms. Please enlighten me. TIA

Hello, I'm trying to find the general solution of this homog. system w/ constant coefficients. I can't even get past the first step, which is to find the eigenvalues. As far as I know, there are a few approaches: 1) solve det(A-λI) = 0 2) solve the trace determinant plane equation (which is...

We all heard about the "photo of black hole". My question is: did this image show any hints of physics beyond general relativity? I read once (not sure where) that the apparent size of black hole shadow is very sensitive to corrections to general relativity. Add some minor correction and the...

I'm an MS student in Aeronautics & Astronautics who wants to work in industry after I graduate. My undergraduate background is in physics and EE. I wasted a lot of time as an undergrad to health issues and maturing in general and I view myself as lucky to even have a chance to continue my...

Find the general solution to the system of differential equations $\begin{cases} y'_1&=2y_1+y_2-y_3 \\ y'_2&=3y_2+y_3\\ y'_3&=3y_3 \end{cases}$ let $y(t)=\begin{bmatrix}{y_1(t)\\y_2(t)\\y_3(t)}\end{bmatrix} ,\quad A=\begin{bmatrix} 2 & 1 & -1 \\ 0 & 3 & 1 \\...

The general interpretation of flux as I understand it (and please correct me if I'm wrong) is that it represents how much something is going through another (surface or volume (and perhaps lines?)), I'll quote Khanacademy : Considering that magnetism is a force, I very well understand that we...

I am a student of physics at a local Junior College in Mendham NJ and am planning on transferring to a 4 year program at the University of Alabama in a year. Iam having a bit of a difficult time understanding general relativity. Why does a photon bend twice as much under a gravitational field...

Has anyone formulated a general solution to the time-independent Schrödinger equation in terms of the potential function V(r), and if so, what is it? For any type of V(r). So, instead of a differential equation, a direct relationship between the wavefunction and the potential.

Homework Statement Prove that for all a, b, c ∈ ℤ, if a|c and b|c and (a,b)=1 then ab|c. Prove result does not hold in general when (a,b)≠1. Homework EquationsThe Attempt at a Solution This is not my formal proof it's just the scratch work, for the first part, I have there are integers x and...

I'm searching, but so far I have not found a derivation of the coordinates shown by wikipedia in the very beggining of https://en.wikipedia.org/wiki/Rindler_coordinates#Characteristics_of_the_Rindler_frame. It seems obvious from the relation ##X^2 - T^2 = 1 / a^2##, (##c = 1##), that ##X =...

Hello. I have some questions about general relativity that (I hope) will be permitted in this forum. Not long ago I discovered that there is more than one interpretation of GR. Now, I believe that the issue of interpretation is considered to be philosophy and therefore off topic. If that's...

$\tiny{2.1.9}$ 2000 Find the general solution of the given differential equation, and use it to determine how solutions behave as $t\to\infty$. $2y'+y=3t$ divide by 2 $y'+\frac{1}{2}y=\frac{3}{2}t$ find integrating factor, $\displaystyle\exp\left(\int \frac{1}{2}...

Hey my fellow physics-students/physicists. I'd like to ask if you guys could suggest me a textbook/s that sufficient for integrated course of "special" and "general relativity". More precisely, That contain about: Introduction about the birth of relativity and principle, and the transformation...

This week I am at "General Relativity as a Challenge for Physics Education" 690. WE-Heraeus-Seminar https://www.we-heraeus-stiftung.de/veranstaltungen/seminare/2019/general-relativity-as-a-challenge-for-physics-education/ (...

How do you know what fields can be coupled with the gravitational field? Is there a general procedure for knowing it or we have to try out and see whether it makes sense or not?

Dear Everyone, I am having some troubles with the problem. The problem states: Let $(G,\star)$ be a group with ${a}_{1},{a}_{2},\dots, {a}_{n}$ in $G$. Prove using induction that the value of ${a}_{1}\star {a}_{2} \star \dots \star {a}_{n}$ is independent of how the expression is bracketed...

A while back I posted a black hole horizon puzzle. This is another puzzle in the same general spirit. It is based on the scenario described in this old PF thread: https://www.physicsforums.com/threads/a-flaw-of-general-relativity.115418/ Needless to say, as was the case with my previous...

Does General Relativity allow for transformations which are not isometries of the metric?

We have all seen Lorentz transformations being written like this ##\Lambda ^\mu\;_\nu##, but why are they never written as ##\Lambda _\nu\;^\mu##?

Hello. The book "General Relativity, Astrophysics, and Cosmology", by Raychaudhuri, et al., looks like a good compact exposition of GR, astrophysics and cosmology, which is exactly the kind of book I'm looking for. What do you think of this book? Thank you in advance.

2000 find the general solution for $y' + 2y = 2 - {{\bf{e}}^{ - 4t}} \hspace{0.25in}y\left( 0 \right) = 1$ find $\displaystyle u(x)=\exp \left(\int 2 \, dt\right) =e^{2t}$ $e^{2t}y' + 2\frac{e^{2t}}{2}y =2 e^{2t} - {{\bf{e}}^{ - 4t}}e^{2t}$ $(e^{2t}y)'=2e^{2t}-e^{-2t}$ i continued but didn't...

Greetings: I can understand that an object's trajectory curves about a greater mass (e. g., satellite in Earth's orbit). The spacetime is curved via the great mass and the moving object simply follows the curvature. My problem is this: Why does a stationary object at a short distance from...

Suppose we have to deal with the question : $$\frac{\partial}{\partial x}\frac{\partial}{\partial y}=?\frac{\partial}{\partial y}\frac{\partial}{\partial x}$$ This seems true for independent variables. But if at the end x and y are linked in some way like $$x=f(t),y=g(t)$$ this is no more the...

Is it possible to calculate with precision the orbits of the Earth, Moon and Sun with general relativity instead of Newtonian Physics? How would this work? Would the software have to record past positions of each body and have the Earth be attracted to the old sun's position 8 minutes ago...

After making a couple of comments on this StackExchange question, and pointing yet again to this article, a thought occurred to me. I have been working on an Automatic Differentiation based ODE solver and equation analyzer, mentioned in this thread. Why not use it to solve equation (7) in the...