Einstein Definition and 811 Threads

Could someone explain to me what specifically distinguishes Einsteins more advanced treatment of gravity over Newtons? Here’s what I (think I) know. Newton described gravity as a “force” of attraction between two bodies or masses. That force was given by the G constant times the two masses...

http://www.stuff.co.nz/science/8101704/Einstein-Medal-for-NZ-professor

Hello, I was hoping someone might be able to give a approachable explination of the Gross-Pitaevskii equation. All the sources I've been able to find seem to concentrate on the derivation, and I don't have the physics background to follow. From what I understand, however, is that the GP...

They say ZPE is the energy of the system at 0 K due to vibrations and even though the Schroedinger equation gives us the ground state minimum energy of the system (lets say by DFT/HF/QMC whatever), this energy is a little higher than that. My first question is, because I have learned that...

I can fairly well grasp the trace relationship between the Einstein tensor and the Ricci tensor, and see that Ricci tensor is a multiple of the metric. If the cosmological constant is included I don't get why the Einstein tensor shouldn't become a multiple of the metric (leaving out physical...

Hi, I am using Hartle to study GR and at one point, there is a leap that I don't understand. He finds the result for the geodesic deviation equation and introduces the Riemann curvature tensor. Then, we are told that there is an object called the Ricci curvature tensor which is a...

During one of the Einstein-Bohr debates, Einstein proposed a thought experiment that would prove that one could measure time and energy simultaneously. It's known as the Einstein box: http://en.wikipedia.org/wiki/Bohr%E2%80%93Einstein_debates#Einstein.27s_second_criticism Then Bohr came up...

Sorry if I am asking a too trivial question! I am having a confusion regarding the following-The solution to Einstein equation in vacuum is given by the Schwarzschild metric. However, what does the mass represent in the metric in Schwarzschild coordinate? Whose mass is it and how does it enter...

Hello, Please excuse me if the following questions are very mundane: (1) The Einstein tensor in indices form: Guv=Ruv-1/2guvR Does uv means the indices i.e. just as we define row column in a matrix.? (2) The Einstein tensor is symmetric. Does that mean in matrix as we mean aij=aji...

Greetings, This is just an opinion question about notations. Having learned the basics of bra-ket notation and using the ESC, as far as I can tell, ESC is just plain better, at least when dealing with finite bases. Using bras and kets, you can represent and manipulate states using...

While taking notes in class, I was trying to write the moment of inertia tensor in Einstein notation as Iij instead of a 3x3 matrix, but when we diagonalized the matrix with diagonal elements Ii, I was confused on how to write it. Ii doesn't work because that means that treats it as a vector...

This is quoted from "The Elegant Universe" "the velovity of light is a kind of cosmic speed limit, a speed that nothing in the universe can exceed." - The Elegant Universe, On Einsteins Discovery My Question is, How did einstein test/know this? How could he have possibly known what the...

Good day! I am quite blur with the Space-time concept proposed by Einstein. Can anyone explain briefly on what he meant by that term(Space-time)? 3-D space+1-D time? :confused:

Determining the commutation relation of operators -- Einstein summation notation Homework Statement Determine the commutator [L_i, C_j] . Homework Equations L_i = \epsilon_{ijk}r_j p_k C_i = \epsilon_{ijk}A_j B_k [L_i, A_j] = i \hbar \epsilon_{ijk} A_k [L_i, B_j] = i \hbar...

I am aware of the motives of finding a modification of Newtonian mechanics, but the effects of relativity are so subtle and negligible. How in the world was he able to even find it? Even at speeds of the Earth orbiting the Sun, the effects are almost negligible. I know he started out with a...

In reviewing some basic GR (just to keep my old brain sharp), i was looking at the Einstein notation cinvention and was a bit confused. I see how you do the dot product of say: ei.ej = δij (i.e. 1 or 0) But then the book I'm reading talks about ei.ej or ei.ej. Isn't that just the...

So, I realize the basic theory behind Einstein Summation Convention is that any repeated set of indices implicitly indicates a sum over those indices. However, what if an index is repeated three times? For example, my mathematics professor posted this problem: εijkajaj = ? As you can...

Hi everyone, Say that one can separate the metric of a space time in a background metric and a small perturbation such that g_{\alpha \beta}=g'_{\alpha \beta}+h_{\alpha \beta}, where g'_{\alpha \beta} is the background metric and h_{\alpha \beta} the perturbation. Computing the christoffel...

Homework Statement This is from lecture, not a homework problem per se. But I need assistance. The problem was to write this form of a flow equation in Einstein's notation: Homework Equations \frac{\partial }{ \partial x_1}(K_1 \frac{\partial h}{\partial x_1}) + \frac{\partial }{...

In the paper http://arxiv.org/pdf/hep-th/9301028.pdf pages 8-9 Pullin shows how to write the Einstein action in terms of tetrads e^a_I. Part of the proof is: "...the last term yields e_M^{[a} e_N^{b]} \delta^M_{[I} \delta^K_{J]} C_{bK}^{\;\;\; N}. It is easy to check that the prefactor in this...

In Gravitation by MTW in section 17.3, they state (I assume it was a typo putting the cosmological constant in the center portion) Changing the symbol of the Einstein tensor and the cosmological constant to L and Ω so as not to confuse myself, I can see how with...

London theory, Landau theory... and Lorentz Einstein law I am trying to learn all I can about superconductivity and discovered an interesting document in Internet. Does the Lorentz Einstein law hold true for the supercurrent : 1) of the London approach? js = ... ∂θ/∂r - A where θ is the...

The weak force was not discovered until 1953 or thereabouts so that pretty much made Einstein's attempt to unify all forces an impossible task. Does anyone know how much time he wasted on trying to find a unified field theory? Other than write a paper on gravitational lensing and the EPR paradox...

\vec{v} = v^i\vec{e}_i = g(\vec{v},\vec{e}_i)\vec{e}_i The last bit is a sum over i but will need a Ʃ because the Einstein rule only applies to matched superscripts and subscripts and here bot the i are subscripts. Even if I write out the metric in the basis it doesn't work...

I have seen and read a few different versions of the Einstein field equations (EFE). For example; R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R = - 8\piGT_{\mu\nu} , R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R + g_{\mu\nu}\Lambda = \frac{8 \pi G}{c^4}T_{\mu\nu} , and 8\piT_{\mu\nu} = G_{\mu\nu} So which one is...

Hi all, I've been looking around at formulae for determinants (using them for tensor densities) and I just want to clarify that the expression below is correct (i.e. formulae are correct): |M| = \sum^n_{a_1,a_2, \ldots ,a_n = 1} \epsilon_{a_1a_2 \ldots a_n} M_{1a_1}M_{2a_2} \ldots M_{na_n}...

Homework Statement Calculate the Einstein coefficient of spontaneous emission for nitrogen transitioning from Ei: 32P1/2 to Ek: 32S1/2. Total duration τ = 16ns, emission wavelength λ = 589.593 nm. Homework Equations The Attempt at a Solution I want to use A_{ik} =...

Hi all, I have been trying to solve the Einstein Field Equations for its (0,0) component. So I have got that (c=1) Einstein Tensor (upper,0,0)=8*pi*G*T(upper,0,0) Now, let's see what T (0,0) really is. It is energy density, right? So According to famous E=mc^2 the energy density is the same...

Einstein postulated that the speed of light in vacuum is constant and is the same for all observers. It this related to the fact that in Maxwell's equations for electromagnetic waves in a vacuum, c = \frac {1} {\sqrt{\mu_0 \epsilon_0}} ? The electric and magnetic constants, which are...

I was reading through a book on statistical physics when i came across this sentence: "An Einstein solid has two degrees of freedom for every oscillator." How is this possible? I picture an oscillator (ex. mass on spring) to move only in one dimension, thus one degree of freedom. Where does...

Hi, So I have taken a math course dealing with the mathematics behind GR. In it I learnd how to calculate many of the objects that GR deals with such as curvature tensors, geodesics and so on. However, not much physical explination into how these object tie into gravity was discussed (due...

I got some trouble from this question: For a given metric: ds2 =t-2(dx2-dt2), derive the energy-momentum tensor which satisfies the Einstein equation: Rαβ- 1/2Rgαβ=8\piGTαβ. I got the Ricci scalar R=2, but Tαβ=0 for all α,β. Does this means a curved spacetime without any source(energy-momentum...

So, I've recently come across the following quote: "I am thankful to all those who said NO to me. It's because of them I did it myself." -A. Einstein I've tried googling to see if there's any proof he actually said that, but my search yielded little to no result. So, now I'm here and I need...

Einstein thought the cosmological constant was the biggest blunder of his life. however, I think his biggest blunder was refusing uncertainty. dou you agree?

I'm sure many of you are familiar with the "Pole-Barn" paradox. It demonstrates the concept (or lack of) simultaneity from two different inertial reference frames. (basically whether 2 events happen at the same time depends on the relative speed of the observer) My paradox concerns a...

If Eisenstein taught us the space time is one and the same thing, then how did he mathematicaly prove that. How did he put dimentions into his E=mc2 formula. The first 3 dimensions are strictly positions, positions in 3D require 3 numbers, and time is linear movement in one direction, the...

I have been reading Lieber's book "The Einstein Theory of Relativity" which describes the derivation of the Lorentz Transformations: archive.org/details/einsteintheoryof032414mbp -- see pages 39-56 bartleby.com/173/a1.html The entire derivation makes no sense, whatsoever. Why is it...

I want to prove that Euler Lagrange equation and Einstein Field equation (and Geodesic equation) are the same thing so I made this calculation. First, I modified Energy-momentum Tensor (talking about 2 dimension; space+time) : T_{\mu\nu}=\begin{pmatrix} \nabla E& \dot{E}\\ \nabla p &...

Homework Statement Show that Gij = Gji using the Riemann tensor identity (below) Homework Equations Gij = Rij - 1/2(gijR) Rabcd + Rbcad + Rcabd = 0 R = gmrRmr Rmr = Rmnrn The Attempt at a Solution I have tried to put the Ricci tensor and Ricci scalar (from the Gij...

This is not homework but a problem I would like to learn to solve before my exam. Homework Statement https://dl.dropbox.com/u/23889576/Screenshots/01.png Homework Equations Series Formulae The Attempt at a Solution I went about trying to determine a sum formula for the fly's...

I want to show that ∇2ϕ=ρ/2, which governs gravity in Newtonian physics? I found solution of this question in [General Relativity for Mathematicians, R.K.Sachs and H.Wu, 1997, page 112&271]. Solution refer to optional exercise as follows: Let R^ be the (0, 4) –tensor field physically...

Okay, I am not sure if this is the right subforum, but here goes: An einstein solid is a solid composed of N quantum harmonic oscillators, which can store evenly spaced energy units q. Now suppose we have an einstein solid of N oscillators with q energy units, where q>>N. My book wants to...

Dear, I am reading a paper on Bose Einstein condensate and an atom laser. I have two questions which are bothering me for a time. - When you are going to make do all the atoms start with the same the Broglie wavelenghts or do they start with different wavelenghts due to different...

For Dalespam: The difference between Lorentz and Einstein is that the transformation is only applicable to one frame and must be fully inverse for the moving frame. Lorentz transform into the moving frame but invert the calculation to arrive back at the stationary one. The transformation is...

no gut? well, from GR or LQG as well, gravity is not force but geometry right? When einstein knew gravity is geometry and not force, why did he try to unify them? Will we have 3 fundamental forces. Is gut ruled out?

Does anyone know if Einstein equation predicts the existence of particle jets fired by massive black holes observed by NASA from active galaxies? If yes, what would be the predicted relation between the black hole mass and rotation speed to the flux of matter ejected, how long these jets...

Lorents and Einstein both made equations to describe time dialation. One of these equations was used in quantum mechanics, the other equation was then used in cosomology. These equations then made two new areas in physics. One describes one area of physics and the other describes an area of...

Dear Professors and learned readers, The book Relativity: The General and Special Theory by Albert Einstein is, in my opinion worthy of discussion in this forum. My particular questions concerning this book are: 1. Why do you think it not used in high schools since the author recommends this...

Hi, someone posted the following quote on facebook this morning, attributed to Albert Einstein: "Everything is energy and that’s all there is to it. Match the frequency of the reality you want and you cannot help but get that reality. It can be no other way. This is not philosophy. This is...

Hi all, Einstein definitely had to learn tensors from someone else <via correspondence>. But he did not need tensors to intuitively get idea of curvature. So, Can some one share in that simple language, How he got the intuition that space time should be curved in accelerated/...