General Definition and 1000 Threads

Special and General relativity --Basic findings Hello All, Kindly note that it is not a home work. The Special Relativity (SR) and the General Relativity (GR) has some basic findings. I mean to say that say, SR:has some findings like: (a) The speed of light c is constant. (b) The...

What are theorems (lemmas, axioms, etc) exactly? I know what a theorem is, and I know how theorems are motivated; I also know what lemmas and axioms are. My question concerns something a little deeper. Are these theorems and mathematical tools we have merely a consequence of the way...

Homework Statement I am studying enthalpy and heat transfer and I have a question that has been bugging me. It is said the that the enthalpy change is the enthalpy of the products minus the enthalpy of the reactants. However, I understand that it is not possible to measure the total...

Recently (or a few weeks ago), I've started to take interest in the idea of relativity but after watching many videos and reading a couple of websites, I still don't think that I really understand it. I'm probably not suppose to understand it (or at least not yet) considering that I'm still...

There are several possible topologies for an electrical circuit. However, if we limit our circuit to be a two terminal device, how will this limit the options for the different topologies? I am a beginner in this field, but as far as I can tell by drawing the circuits, the only possible...

Homework Statement Let ##\displaystyle a_n=\frac 1 2+\frac 1 3+...+\frac 1 n##. Then A)##a_n## is less than ##\displaystyle \int_2^n\frac{dx}{x}##. B)##a_n## is greater than ##\displaystyle \int_1^n\frac{dx}{x}##. C)##\displaystyle \lim_{n\rightarrow \infty} \frac{a_n}{\ln n}=1##...

Wikipedia says it a collection of culturally valued knowledge. What exactly is culturally valued? These are the types of questions generally asked: - 1) Name of the nth U.S. president 2) Location of some river or place 3) Birthdate of some famous person etc. Why are these questions...

Say I have a simple series like \Sigma^{∞}_{n=0} X^{n} When I differentiate this series the first term goes to 0 because it's a constant. Does that mean that I have to adjust the index of the series from n=0 to n=1? If I don't do it, the first term still goes to zero as n(x^(n-1)) when n=0...

The invariant mass of special relativity: m_0{^2} = E^2 – p^2 There doesn't seem to be any quantity with units of mass that is invariant in general relativity. Invariant mass loses significance, as other than an approximation where space-time is sufficient flat. But at the same time, mass is...

General relativity -- Conceptual question Hello, I have a conceptual question. May be I am sounding a little bit idiotic, so apologize for that. I believe, there is no harming in knowing that I am wrong. Einstein's general theory of relativity describes gravity as a geometry of space...

This is a more general question: is it always true for a mixture that if we define M(average) such that m(total) = n(total) * M(average), where n(total) is the total number of moles of species in the mixture (summed over all species) and m(total) is the total mass of the mixture, then M(average)...

Hello - I asked a similar question before, but it was not resolved for me, and the person who answered was rude, so I did not continue the conversation. I read this here: http://tutorial.math.lamar.edu/Classes/DE/SecondOrderConcepts.aspx "If y_1(t) and y_2(t)are two solutions to a...

So I've encountered many "what is the projection of the space curve C onto the xy-plane?" type of problems, but I recently came across a "what is the project of the space curve C onto this specific plane P?" type of question and wasn't sure how to proceed. The internet didn't yield me answers so...

I don't know much about the two ideas but I'm confused because the two theories seem to contradict each other, if all matter (with mass) bends space, then there is no such thing as "gravity", or maybe gravity is just the actual bending of space, so should we refute the idea of "gravity"? or just...

Well, here's the scenario I am particularly curious about: A riffle barrel and a laser point directly towards a target some distance away. Now, General relativity says that the bullet and the light experience the same downward acceleration during horizontal travel, yet the bullet hits...

I have a question regarding the qualitative difference between General Relativity and classical Newtonian gravity. I understand this difference in theory (warped space-time as opposed to a force operating in flat space). However, I read an article (taken with a grain of salt) which claimed...

Non-maths general question on history of space time :) Hello, I'm doing a Bsc project on space-time and was hoping to receive some advice on how others would structure the history of the topic. I know this is a broad question but what I'm struggling with is how to narrow down the relevant...

In grocery stores I often see the scales. It's basically a frame connected to a vertical spring, with the spring compressed at amount x. Next, I drop an apple on it from a certain distance above the bottom of the frame. I want to calculate how far the spring will extend. So for this...

Homework Statement Prove that F(k•r -ωt) is a solution of the Helmholtz equation, provided that ω/k = 1/(µε)1/2, where k = (kx, ky, kz) is the wave-vector and r is the position vector. In F(k•r -ωt), “k•r –ωt” is the argument and F is any vector function. Homework Equations Helmholtz...

Hi everyone, I've been reading posts here occasionally, and have been impressed with the amount and quality of knowledge that is being shared. I've just registered, and as my first thread I thought I would post some questions / thoughts that have puzzled me for a long time, related to...

I am studying field theory. A general question I have is the following: Let E \supseteq F be fields and let u \in E . Now, if I determine an irreducible polynomial f in F[x] such that f(u) = 0 in E, can I conclude that I have found the minimal polynomial of u over F. Can someone...

Hello, I am a physics major who is going to graduate soon, and am taking the general and physics GREs. I am looking at both physics and engineering graduate schools. I believe that the physics GRE is pretty much irrelevant to engineering schools, but I have had difficulty with the...

Just started multivariate course, can't figure out this simple question. If f(u,v,w) is a function of 3 variables. And u, v and w are themselves function of t. Then does f(u,v,w)=0 implies df/dt=0 or df/du=0. or both.

What is the least restrictive set of conditions needed to utilize the formula ##\int\limits_{\Omega}\mathrm{d}\alpha=\int\limits_{\partial\Omega} \alpha##?

term “scattering” more of a general process Is the term “scattering” more of a general process which incorporates the linear effects of reflection, refraction and diffraction?

I would like to know if there is a general formula, and if so, what it is, for finding the $limsup$ and $liminf$ of a sequence of sets $A_n$ as $n\rightarrow \infty$. I know the following examples: **(1)** for $A_n=(0,a_n], (a_1,a_2)=(10,200)$, $a_n=1+1/n$ for $n$ odd and $a_n=5-1/n$ for $n$...

In addition to the Global Guidelines, these rules also apply to posts in the lounge. Overly Speculative Posts It is against our Posting Guidelines to discuss new or non-mainstream theories or ideas that have not been published in professional peer-reviewed journals or are not part of current...

So I have been asked to prove a result that is supposedly valid for any norm on any vector space. The statement to prove is: | ||x|| - ||y|| | <= ||x - y|| The problem is, I have no idea where to start with this proof. Maybe I'm missing some fundamental property of norms, but it seems that...

I was wondering if there is any way to know in general how many real solutions $x^n=n^x$ may have with n being a positive integer. Thanks! Using IVT one can see that if n is even there must be at least three solutions, and if n is odd there exists at least two. But are these the "sharpest" bounds?

Hi, I'm interested in doing small projects for curiosity. I'm designing an optical structure as shown below. Please tell me what kind of lenses (concave, convex, plano concave etc.. ) to be used at different points of the structure.

Hi. So, currently I'm a senior in high school taking classes at the community college (my high school is paying for them) and I am having trouble deciding between these two courses. I learned that General Physics w/ Calculus doesn't actually have that much calculus, and I already learned a...

Homework Statement I am trying to understand when the positive or negative of a specific value in an equation (work-energy and momentum-impulse) is to be evaluated based off the motion diagram and when it is not? Homework Equations The ones in particular I am unsure about is...

I've been watching leonard susskind's lectures on general relativity on youtube, I'm now at the fifth of them. It is my first exposure to general relativity and so far the lectures are pretty easy to follow. So my question is this, to anyone who has had more exposure to the subject: Do you...

Hey, sorry for not using the exact template; I just have a general question about how to calculate the moment of inertia that I will have to apply to a number of instances. In this particular case, I need to calculate the moment of inertia for a rod pendulum. Of course, I could just use...

This is a general question, so I hope you don't mind the lack of specificity. How do you guys approach or think through any given problem? It's my first semester in undergrad physics and I find that, while I'm capable of doing the math, I'm bogged down or get side tracked in the process of A...

Find the general solution of x'=(2, 3, -1, -2)x+(e^t, t). (this is 2x2 matrix, 2 and 3 on the left, -1 and -2 on the right. and e^t on top, t on bottom. I know that the answer for 2x2 matrix is c1*(1, 1)e^t+c2*(1, 3)e^-t but I don't know how to get the other part.)

How much do you memorize to do general derivatives/integrals? While it is possible to do everything by going back to first principles, I imagine it gets exhausting to do so every time. So which derivatives/integrals do you memorize? Are the ones that I have attached to this post good enough to...

Express the general solution of x'=(1, 2, 3, 0, 1, 2, 0, -2, 1)x in terms of real-valued functions. (this is 3x3 matrix, 1, 2, 3 on the left, 0, 1, 2 in the middle, 0, -2 and 1 on the right. I found that the roots are 1, 1+2i, 1-2i. And a=2, b=-3, c=2 for the first root. a=0, b=1, c=i for the...

Express the general solution of x'=(2, 9/5, -5/2, -1)x in terms of real-valued functions. (this is 2x2 matrix, 2 and 9/5 on the left, -5/2 and -1 on the right. The complex roots are (1/2)+(3/2)i and (1/2)-(3/2)i and a=1, b=(3/5)+(3/5)i for the first root. And a=1, b=(3/5)-(3/5)i for the...

Express the general solution of x'=(3, 4, -2, -1)x in terms of real-valued functions. This is 2x2 matrix, 3 and 4 on the left, -2 and -1 on the right. I know that the eigenvalues are 1+2i, 1-2i. And a=1, b=1+i for the first eigenvalue. a=1, b=1-i for the second eigenvalue. But how do I get...

Homework Statement I have been trying to understand the actual applications and mathematics behind Einstein's Field Equations. I have watched a two hour long lecture on how they were derived and have pretty much understood it, however I still don't know how to actually "use" Einstein's Field...

The CMB used to be gamma rays, right? And now it's microwaves - more redder energy: so where did the rest of the energy go?

I'll begin by admitting that I did not scroll through the entire list of threads to see if there was already a post similar to the one I am beginning. I do apologize if I've broken any rules but I gave up searching after 6 pages and noticed there were at least a hundred more. My question...

Hi, everybody. I have some problem with Wald's statement shown in the picture. This is from the last paragraph in Page 178. He claimed that there are only solutions with two of the p_{\alpha} positive and one negative. But it's easy to find out that if two of the p_{\alpha} are negative while...

For particles with non zero mass m we know that: E = mc2γ (1) P = mvγ (2) with the usual meaning of the symbols. From those two equations is easy to prove the equation: E2 = (cp)2 + (mc2)2 (3) which doesn't contain the factor γ any longer and so it can even be used for...

I know that (1-x)/(1+x) is equivalent to (2/(x+1)) - 1 via 'hand waving' in my textbook but i cannot figure out the steps to arrive at this result. Suggestions??

So i love astronomy, physics, maths and cosmology. I want to bring this all together so i found a degree 'AstroPhysics", and it is something which i can do well in and enjoy. I'm wounding if i should go for this degree or go for an Advanced Science Degree major in Physics? So it is more of a...

I am wondering as to how many metrics have been discovered that obey all the laws of General Relativity? I am posting the ones that I have briefly studied, please post more if you have knowledge of them. Schwarzschild metric: c^2 {d \tau}^{2} =\left(1 - \frac{r_s}{r} \right) c^2 dt^2 -...

hi i read an article by S.carlip about quantum gravity, arXiv:gr-qc/0108040v1 , in this article carlip stated: why we need quantum gravity what's problems of quantum gravity and two ways of quantization of GR. I couldn't realize some clues in section of "the problems of quantum gravity"...

What can it be about? How do we ascertain the novelty of the intended paper? How should it be structured? Where should it be submitted and how? What can it be written in and what format should it be forwarded in? Any advice is appreciated. Thank you.