General Definition and 1000 Threads

Is it true than general relativity can be deduced from a maximum mass density for matter?

On the website http://www.real-world-physics-problems.com/physics-of-billiards.html they take this equation ∑Mg = IG∝ where ∝ = -agx/r for the rotation of a rigid body where there is no slipping They then change the equation to F⋅(h-r) = IG(-agx/r) why is ∑MG = F⋅(h-r) when ∝= -agx/r?

I am having trouble connecting some of the differential geometry in gr to what is actually measurable in the real world. As far as i understand we can measure physical quantities in terms of coordinates x^\mu on the tangent space of a 4-dim Pseudo-Riemannian manifold M. So let's say we are...

I am currently learning general relativity and I kind of understand what the symbols in einstein field equationd represent. But I need example like those that involves actual numerical values. I have been trying to search for it online but I cant. So does anyone mind showing me how you apply...

I was looking relative velocities and I saw General case in Relativity part.That part means every direction isn't it. http://en.wikipedia.org/wiki/Relative_velocity and in there B is the observer or A is the observer Thanks

I hope this is the appropriate thread (I am a new user)--I figured any thread may be full of people who attend the APS meetings. I did a summer REU program, and my advisors want me to submit an abstract to the APS April meeting. I just found out there is an undergraduate session, but that...

How can it be deduced general relativity from Planck length?

While fiddling around with some very simple linear ODEs, I "discovered" a formula that gives a solution to ODEs of the form: ##y'+y=ax^n ##. here it is: i'm sure that this was discovered before, but i was just wondering if it had any official name or something.

The Hamiltonian operator in the equation i×h/2π×∂/∂t×ψ=H×ψ(where 'i' is the imaginary no.,'h/2π' is just expanded form of the reduced Planck constant,'∂/∂t' is the partial derivative with respect to time 't' and ψ is the wave function) is,as I recall,H=I+V(i don't know how to get those carets...

Ok, so I was just in physics class today and we were talking about special relativity... anyways, the instructor referred to how the universe is expanding, and so much so that there are places we could never ever get to because it's expanding fasterling than the speed of light. Anyways, this...

Does the discriminant have any specific definition? I've come across two discriminant definitions that don't seem to be very relevant to each other, and I was wondering if there is any particular property that discriminants convey. In finding roots and using the quadratic equation, I've seen ##...

I'm planning on taking a second semester general chemistry course in the spring, and I'm wondering what I should study before hand. Based on RateMyProfessor, my teacher is going to be super hard. I took the first semester general chemistry course and I got an A in it, but that was last fall...

Let's assume the Earth was perfect sphere with radios of 6,750,000 meters. There are 3 clocks , one will not move one will move west in velocity V and the other will move east in the same velocity. The Earth is still rotating. So one clock is going with the Earth rotation and the outher is going...

Hello all, I have a quick question regarding the relation of the space-time metric and the curvature. I have determined the space-time metric, g_(alpha beta), but I am unsure as how to go from the line element ds^2 = [ 1 + (dz/dr)^2] dr^2 + r^2 dtheta^2 and the space-time metric g to the...

So I want to go into applied mathematics, I can either get a general math degree or an "applied and computational" degree. Does the degree title make a difference? The general math degree I can graduate a term sooner with, the main differences in the courses is that for the applied and...

Decades have passed since the first idea of General Relativity arose in the mind of Einstien. Surely development of the GR must have taken place during these years. May anyone one update me about these development that took place since the late past.oo):w

Hi, I was trying to form a summation for ##y_1## and have provided a solution but do not quite understand how it was formulated. I was trying to look for general patters and besides a ##(-1)^{n+1}x^2n## in the numerator, I'm a little lost on how to find a general term for the denominator. Also...

I was solving this problem and I didn't want to do it the really long way by finding the equation of B(t) by first finding T(t) and N(t). So i took the cross product of r' and r'' so that they would be in the direction of B. Found the parametric equation of the plane but the book answer was in...

Hi, there is a result that every closed, oriented 3-manifold is the boundary of a 4-manifold that has only 0- and 2- handles. Anyone know other of these "boundary results" for some higher-dimensional manifolds, e.g., every closed, oriented k-manifold is the boundary of a (k+1)- dimensional...

why not the 2nd order linear homogeneous ODEs have three Linearly independent solutions or more? I know for the characteristic equation, we can only find 2 answers but.. just wondering if that is the only case to solve the question and if it is, then why it has to be. so my question is,1. 2nd...

In the derivation of the generalized uncertainty principle (as pgs 1-2 of here), there is an anticommutator term that is dropped at the end, leaving just the commutator part...this is said to "strengthen" the relation, as both terms are positive. I don't understand this. So we basically have...

I know it follows a geodesic in space-time, but is it not being able to bend space-time itself, part of the definition? When I google i just find 'follows a geodesic in space-time'. I thought that it also should not bend space-time itself - but this isn't included in the definitions I've...

Hi, I'm trying to understand the process of finding the elements of a given group, such as SE(2). What I do understand is limited to finding elements of very simple symmetry groups, such as those corresponding to rotations/reflections of shapes. My overall knowledge of groups is also pretty...

Hello, This spring, I will have the opportunity to do a one-on-one independent study in math or physics. I've narrowed down my choices to differential geometry and general relativity. I'm thinking about the future here- will studying general relativity this spring better prepare me for...

the question statement is2. In a course, a student's final exam is weighted twice as heavily as his midterm exam. If a student receives a score of 84 on his final exam , 90 on his midterm, what is the average for his courses? now i am pretty confused should I have to know the total marks for...

Ok, I went through a video to understand it more simply. But there is one point I just don't understand. Which is this: How does Adam think others' clock is SLOW? Shouldn't it be FAST? Here's my breakdown of the video: Adam is in- Space Sarah is on - Ground Beam of light shone from the...

is there a general formula/algorithm to parameterize an equation? for example if i have a function f(x,y)=0 then can i always change it to the form x(t),y(t)? or if i had g(x,y,z)=0 then can i change it to something like x(u,v),y(u,v),z(u,v) i know of examples, like if i have x^2+y^2=1 then...

Hello! I am an undergraduate student currently pursuing my Bachelor's before I attain my PhD in Particle Physics. I do however have an exciting concept I would like to have to my name before I disclose it to the world; therefore, I was wondering how this would happen, and if it is possible...

Hello, I've always been interested in space and space flights and have often wondered how rockets are lunched into space, how their trajectories are defined, how they are sped up (like gravity assist), how they are slowed down (like the complicated trajectory of the Rosetta mission etc . . . I...

I can fairly understand the concept of gravity as a curvature in space time in general relativity, but so far I could not understand completely the tidal forces explained by the curvature of spacetime. When the moon is on one side of the earth, the oceans on this side come closer to the moon...

I have created a macro file that should produce a Gaussian (Normal) distribution of gamma particles ranging in energy from 0 to 250 keV as follows: /control/verbose 0 /run/verbose 0 /tracking/verbose 0 /gps/particle gamma /gps/ene/type Gauss /gps/ene/min 0 keV /gps/ene/max 250 keV /run/beamOn...

I'm trying to derive a general work function (provided force and displacement vector-valued functions). Below are my best guesses. Can someone let me know whether these are valid? Rigid-System: ## \sum W = \int \left ( \sum \vec{F}(t)\cdot \vec{r}\,'(t) \right ) dt ## Deformable-system...

Homework Statement Hello, I'm a bit confused about the calculation of the expectation values. Normally, when I have a wave function of sort and I want to calculate the expectation value of some operator, I just insert it into the braket <ψ|A|ψ>, where ψ for example is a wave function composed...

If you look at Newtonian gravity, there is no major deal with coordinate systems. I am guessing we use coordinate systems because in general relativity we think of coordinate systems as different frames of references and that all frame of references must have the same laws of physics. Is that why?

I am thinking of taking a course on General Theory of Relativity in the next semester of college. My major is in aerospace engineering. I have already completed courses on Calculus, Differential equations, Linear Algebra, and also have a fair bit of idea about tensor calculus. What other prior...

Hello, $f(x)$ and $g(x)$ have the following property: for all $\epsilon > 0$ and all $x$, $$ \text{if} \space 0 < |x - 2| < \sin^2(\epsilon^2/9) + \epsilon \space \text{then} \space |f(x) - 2| < \epsilon$$ $$ \text{if} \space 0 < |x - 2| < \epsilon^2 \space \text{then} \space |g(x) - 4| <...

hello, I would like to learn general relativity. To understand general relativity, do I need to understand the math on a rigorous level? (the way mathematicians understand the math) . What math do I need? Can you suggest me some math/general relativity books? Thanks and sorry if my english...

I haven't studied much physics or mathematics in a few years, and I was wondering if someone could recommend me a few good books to get started? I don't want to miss anything important. I've been taking some free courses online, but I would love some reading materials to supplement.

As some may know, I have been studying the Morris-Thorne wormhole metric for quite some time now. ds2= -c2dt2 + dl2 + (b2 + l2)(dθ2 + sin2(θ)d∅2) Now, from this space-time interval, it is easy to see how I would deduce the following metric tensor: g00= -1 g11 = 1 g22= (b2 + l2) g33= (b2 +...

Hey there, i need some help please :) As an assignment from my course, they asked us to bring some mechanical solutions for electric problems, and I don't mean in a specific area, i mean generally... i looked over the internet for it and found nothing.. If someone can please help with that would...

Suppose that we have the four-vector potential of the electromagnetic field, [texA^i[/tex] The wave equation is given by $$(\frac {1}{c^2} \frac {\partial^2}{\partial t^2}-\nabla^2) A^i=0$$ Now the solution, for a purely spatial potential vector, is given by $$\mathbf{A}(t...

Just a quick question. I've recently thought about the various equations I'm learning about calculating velocity or vertical motion and have wondered that sense these equations are using Gravity as a constant force (9.8m/s^2) Is it not true that Einsteins' theory would denounce this idea and...

Hey PF! I have a quick question. When I was solving a PDE via separation of variables, I was able to come up with a same format solution for ##n \geq 1## but when ##n=0## I had a different "type" of solution. This doesn't really bother me since I am dealing with a linear PDE. However, I matched...

Hi, Problem: Given the DE: y^(6) + y = 0, find the general solution. Solution. I found the roots to be: (sqrt3 - i)/2, (sqrt3 + i)/2, i, -i, (-sqrt3 + i)/2, (-sqrt3 - i)/2 Thus, my general solution led to: y = c1cost + c2sint + c3exp(t/2*(sqrt3))*cos(t/2) + c4exp(t/2*(sqrt3))*sin(t/2) +...

Hi! I'm a student reading a book given to me by my teacher about relativity and spacetime. It says that the separation between events in spacetime is measured in "intervals," and I can understand that part. What I don't understand is why you subtract the squares of the distance in space instead...

From Abel–Ruffini theorem, we know that, there is no general algebraic solution to polynomial equations of degree five or higher. So there are general solutions for degrees n={1,2,3,4}. Does degree have to be an integer? What about the fractional degrees? Are there general solutions for example...

I am 72 and my background is in the humanities (I read classic authors in Latin and Greek, which I learned in high school in Italy, I love history and I have a more recent M.A. in Philosophy from a Canadian University). Over the last few years, though, I developed a strong (and totally...

Tell me if the following is correct. For a simple infinite square well potential, the solutions to the Schrodinger equation are \Psi_n(x)=\sqrt{\frac{2}{a}}sin(\frac{n\pi x}{a}), then you plug in the appropriate value for n and operate on the function accordingly to get your observables. Then...

It is often stated and proved in textbooks that the momentum density is also the energy flux. The explanation is often done using the dust model. However, it is possible that in a real fluid, there is heat conduction via particle collision. There is energy flux, but since no molecules are ever...

If a rocket takes off from upper part of Earth then it will have to pass the curvature(known as gravity) experiencing gravity which we also experience in reality.But if a rocket takes off from lower part (say antarctica) and moves straight downwards then it would not have to pass the curvature...