Einstein Definition and 788 Threads

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}...

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 [FONT="Comic Sans MS"]"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...

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/...

The lifetime of the 32P1/2 to 32S1/2 transition of the Na atom at 5896 angstrom (one of the Na D lines) is measured to be 16.4 ns. What are the einstein a and b coeff? What is the transition moment in debye? What is the peak absorption cross section for the transition in angstrom2, assuming...

Start with \nabla^{\mu}R_{\mu\nu}=\nabla^{\mu}R_{\mu\nu} Insert \nabla^{\mu}R_{\mu\nu}=\nabla^{\mu}\frac{g_{\mu\nu}g^{\mu\nu}}{4}R_{\mu\nu} Contract the Ricci Tensor \nabla^{\mu}R_{\mu\nu} = \nabla^{\mu}\frac{g_{\mu\nu}}{4}R Thus...

Reading about einstein's model of a solid as being made up by quantum harmonic oscillators. Now while the idea is VERY interesting, I think my book's explanation of the multiplicity of an energy state is quite flawed. One can easily derive a simple formula using the binomial coefficient...

Einstein inoculated general relativity with the help of equivalence principle and space elevator as shown in the following link http://www.astronomynotes.com/relativity/s3.htm QUESTIONS 1- What is the direction of weight [force] of a person standing on the floor of aforementioned...

Start with \nabla_{μ}R^{\mu\nu}=\nabla_{μ}R^{\mu\nu} insert the multiplicative identity, expressed as the product of the covariant and contravariant metric \nabla_{μ}R^{\mu\nu}=\nabla_{μ}(g^{\mu \nu}g_{\mu\nu})R^{\mu\nu} contract the indices of the Ricci Tensor, to get...

One person on the ground and the other traveling in a train. Two light detector X and Y are placed in the train at equal distance from the observer in the train. If only one is hit first by the light, only that detector will display its name else if both detector are hit simultaneously...

http://arxiv.org/PS_cache/gr-qc/pdf/0310/0310002v3.pdf Can someone explain the following statement on page 2 of the paper regarding "our limited understanding of the space of Einstein metrics"... I'm just asking in general, not specifically related to the paper...Is this general...

What would be the total contribution from Einstein's theory of relativity?

I have developed a theory that shows that the more massive an object, the faster time seems to move, thus proving that time dilation is wrong. You see, as I get older, I've noticed I've been gaining more weight, but it seems I have less time to do the stuff I want now rather than more time...

Hi. Just read this article regarding test with neutrinos that suggest they travel faster than light. [PLAIN]www.theprovince.com/technology/test+suggests+Einstein+relativity+theory+wrong/5733221/story.html[/URL] I'm wondering if this apparent breaking of the speed limit might be due to...