Einstein Definition and 809 Threads

Sometimes as I am reading about the history of physics I run across this phrase. Ponderomotive force. I have tried looking it up several times but can never find an answer that explains what is meant by this phrase. Can someone tell me in laymens terms what is a Ponderomotive Force? Sometimes...

##2+1##-dimensional Einstein gravity has no local degrees of freedom. This can be proved in two different ways: 1. In ##D##-dimensional spacetime, a symmetric metric tensor appears to have ##\frac{D(D+1)}{2}## degrees of freedom satisfying ##\frac{D(D+1)}{2}## apparently independent Einstein...

General relativity passes test at Milky Way’s central black hole by Ken Croswell For the first time, astronomers use stars orbiting a supermassive black hole to test Einstein's general theory of relativity, finding no sign of a fifth fundamental force. Links: John Batchelor Show...

On page 30 of the notes (https://arxiv.org/abs/1501.00007) by Veronika Hubeny on The AdS/CFT correspondence, we find the following: So far, we have been describing just one particular case of the AdS/CFT duality, namely (3.3). There are however many ways in which the correspondence can be...

The original thread was closed << Mentor's Note -- the previous thread was closed because of age, not a rules issue >>, but I am really interested in hearing your opinions on a couple of theories I had. I am baffled at the idea that someone, with the ability to understand the math language to...

Hi, I am reading the biography "Einstein's greatest mistake" from David Bodanis. On page 39 the author explains some of the consequences of relativity by referring to (although he doesn't mention it by name) the twin paradox. He explains that someone accelerating at high speed away from Earth...

This past semester, I just took an introductory course on G.R., which translates to a lot of differential geometry and then concluding with Schwarzschild's solution. We really didn't do any cosmology. However, one of the themes that kept creeping up again and again is that in 4-dimensions...

Hello everyone. Below are two problems I have been thinking about lately. Let’s consider two cases: we have a spaceship surronded by an utter void - nothing outside which the spaceship’s pilot could refer to. The pilot (in his robotic body, allowing him to withstand enormous G-forces) turns on...

Hello, Einstein evaluated the size of an atom by analysing a brownian motion, assuming the size of the molecules is a a factor. In order to demonstrate this concept, I want to put some powders with different sizes of grains on a vibrator and watch how a ball moves. What is the expected result...

For those of you interested in the racier side of Albert Einstein National Geographic Channel has started a series on it: https://www.theguardian.com/tv-and-radio/2017/apr/24/genius-review-geoffrey-rush-impresses-as-an-unexpectedly-racy-Albert-einstein I've yet to see it but would be...

Homework Statement I'm dealing with some pretty complex derivatives of a kernel function; long story short, there's a lot of summations going on, so I'm trying to write it down using the Einstein notation, for shortness and hopefully reduction of errors (also for the sake of a paper in which I...

Hello everyone. I was reading Einsteins 1916 original paper on GR, the "The foundation of the general theory of relativity". There are some derivation that he did but I didn't quite understand. It would be nice if someone can give me some direction or some guidance on it. Here is the link to...

I met with a little conflict between Pauli and Einstein? Can you please help. Its a thought experiment. Consider a single crystal which is 1km long. During its formation, due to Pauli’s exclusion principle, no two electron will have same quantum state. Now consider two electron, one with E and...

I don't know much about general relativity, but I'm curious if Zeno somehow foresaw the reallty of the universe many many years before Einstein did(without any rigour ofc, but still the idea holds?). Understanding the Zeno's arrow paradox, stating that an arrow is motionless at a certain moment...

I've been doing some research into Einstein's equation E2=(mc2)2 +(pc)2 but apart from in nuclear reactions, where you can use the simpler E=mc2 as momentum=0, I have been unable to find any applications. Thank you in advance

If you could ask Einstein one question what would it be?

Hi, Need your help to unravel the claims made by a poster in my local forum, if it has any merits. I do not have the expertise to evaluate his claims but am hoping if you can give me a few points on his line of reasoning, if it is faulty or not. I have a general background in undergraduate...

Homework Statement Can someone please check my working, as I am new to Einstein notation: Calculate $$\partial^\mu x^2.$$ Homework Equations 3. The Attempt at a Solution [/B] \begin{align*} \partial^\mu x^2 &= \partial^\mu(x_\nu x^\nu) \\ &= x^a\partial^\mu x_a + x_b\partial^\mu x^b \ \...

Has anyone heard of "Bauer's Paradox" in Einstein's working out his equations for General Relativity? The description I came across was extremely fuzzy (something about an expression for a certain tensor adding up to be zero when it shouldn't, or vice-versa), so I am looking for a better...

Special relativity states that according to an observer at rest, a measuring stick on a moving platform will appear shorter. Would this observer still see the measuring stick as comprising of the same amount of atoms as the observer who is at rest with respect to the measuring stick? If this is...

The D'Alembert equation for the mechanical waves was written in 1750. It is not invariant under a Galilean transformation. Why nobody was shocked about this at the time? Why we had to wait more than a hundred years (Maxwell's equations) to discover that Galilean transformations are wrong...

This paper; https://arxiv.org/abs/1701.07261, Einstein's 1917 Static Model of the Universe: A Centennial Review, offers an informative insight into the mind of Einstein and, to large extent, his motivation for adding the cosmological constant to his field equations. Interestingly, both the...

Hi forum, I followed through Feynamn's derivation to show the different times taken for light by the parallel and perpendicular paths of the Michelson Morley apparatus. He showed that it took longer for light to go to the far mirror and back if it were parallel to the direction the whole...

On a episode of "PBS Spacetime" (fantastic youtube series, go check it out), the host mentioned that Bohr believed that reality doesn't exist until a quantum system is observed. Einstein believed that the universe still runs independently outside of a conscious observers mind. What is the actual...

E=mc^2 states that when you speed up matter to the speed of light, it becomes pure energy, of mc^2 joules. Now, if that is true, can you reverse the equation? Wouldn't energy speed up to the negative speed of light(-c^2), turn into matter? Or is that the wrong balance?

Homework Statement If someone on a spaceship looked at a clock on Earth traveling at 99.5% the speed of light what would they notice? Homework EquationsThe Attempt at a Solution Would they notice that time is faster on earth? Is my assumption correct

I'm not used to Einstein notation and I'm struggling a bit with the more complex examples of it. I got the general gist of it and can follow the basic cases but get sometimes a bit lost when there are a lot of indexes and calculus is involved. All primers I've found online for now only give the...

Hello dear friends, today's question is: In a non static and spherically simetric solution for Einstein field equation, will i get a non diagonal term on Ricci tensor ? A R[r][/t] term ? I'm getting it, but not sure if it is right. Thanks.

I have read that Albert Einstein was quite (pleasantly) surprised to read Schwarzschild's solution to his field equation because he did not think that any complete analytic solution existed. However, of all the possible scenarios to consider, a point mass in a spherically symmetric field (ie, a...

Homework Statement [/B] List two postulates of special relativity and then in your own words explain how these two statements are synthesized in Einstein's theory. Homework Equations 1. The laws of physics are the same in all inertial reference frames. 2. Light propagates through a vacuum...

Hi all - I am trying to follow a derivation of the above. At some point I need to find gαβ for gαβ = ηαβ + hαβ with |hαβ|<<1 I am stuck. The text says gαβ = ηαβ - hαβ but I cannot figure out why. Can anybody help?

I have read this paper http://www.sciencedirect.com/science/article/pii/S1355219813000695 that the author try to said that einstein not believe that gravity is not cause the space time curvature. I want to know that this is true or not. Because when I have read about general relativity I always...

The main reason for this post is because I want to know what other fellow physics lovers are like. I'm interested in knowing each and every one of you and your approach to science! Reading some things here I see that a lot of you care a lot about your brain and your career in science. Some even...

Hi, I'm a CAD student, writing a research paper for my English Comp. class on interstellar travel. I wan't to quote Einstein but can't find were he stated this exactly: Because space and time are relative, the faster you move through space the slower you move through time relative to someone...

How is this done in practice? I know that in GR the gravity is believed to curve not only space, but also time, and this prediction has been confirmed somehow in practice. How can we measure that? Because as far as i know, there is no device that actually measures time, but instead measures a...

I am confused about Einstein's thinking. I understand when he formulated his general theory of relativity, he wanted to incorporate 3 foundations for his theory: The relativity principle, the equivalence principle, and Mach's Principle. He believed that inertia and weight were essentially the...

Homework Statement Assume a two level laser system with no degeneracy (g1 = g2 = 1). If [tex]N_2 + N1 = \text{constant}[\tex], show that [tex]B12 = B21[\tex]. Homework Equations [tex]\frac{\partial N_1}{\partial t}=-B_{12}\rho(v_{21}N_1[\tex] [tex]\frac{\partial N_2}{\partial...

I recently calculated the Einstein tensor for the exterior Schwarzschild solution. Here it is: G00 = 0 G11 = [-2GM/(r3c2 - 2GMr2)] - G2M2/[r2(rc2 - 2GM)2] - [-G2M2/(r4c4 - 2GMr3c2)] - (-2GM)/(r3c2) - (-2G3M3)/[r3c2(rc2 - 2GM)2] G22 = (2G2M2rc2 - 2G3M3) / (r3c6 - 2GMr2c4) G33 = G22sin2(θ)...

Can one shed light on the velocity of the photon through the fourth dimension x4 using limits? To begin with, please study the mathematics from Brian Greene’s book An Elegant Universe. The upshot is that the faster an object moves through space, the slower it moves through the fourth...

I'm a big fan of Einstein and I'm guessing many of you are also. I thought I'd start a thread where people who have researched Einstein's life and science can corroborate or dispel myths about the legend. I'll start with a couple unanswered questions I have after doing some research and...

Homework Statement Okay, in Carrol's Intro to Spacetime and Geometry, Chapter 4, Eq. 4.63 to 4.65 require a derivation of a difference between Christoffel Symbol. I did the calculation and found my answer to be somewhat correct in form, but the indices doesn't match up Homework Equations So...

Hello I've been have been done some research about Einstein Field Equations and I want to get great perspective of Ricci tensor so can somebody explain me what Ricci tensor does and what's the mathmatical value of Ricci tensor.

hi, when I see the einstein hilbert action I really started to be curious about that equation $$S=\int{\sqrt{g}d^4xR}$$. How is this action derived?? Is there a any proof using action integral involving the lagrangian density ? If there is not a derivation from lagrangian action, What is the...

I am studying the history of Quantum Mechanics and was reading about particle entanglement. What I would like to know is how did Einstein see that particle Entanglement meant that particles would be affected by spooky action at a distance. I guess that spooky action at a distance may also be...

Dear PF Forum, I have a question regarding Einstein Elevator, which I believe there are many topics about this. But I haven't got the answer. I've watched some youtube video or read about it, I forgot. That our head is wiser than our foot, because time slow for our foot. Okay..., this could have...

How many Einstein rings have been found to date, i mean galaxies lensed by gravity?

Homework Statement Homework EquationsThe Attempt at a Solution Very confused by this problem. For one thing, it doesn't specify if there is or isn't any light present to drive the stimulated emission/absorbtion. I guess there's no reason to assume that there is no light - but since the...

In Einstein’s book Relativity – the special and the general Theory (authorized translation by Robert W. Lawson, University of Sheffield) in chapter XI (the Lorentz Transformation), he gives us these formulas as the transforms: x’ = (x-vt)/sqr(1-(v^2/c^2)) y’ = y z’ = z t’ = t-(v/c^2) ∙x /...

How could it be tested that there exists true randomness in the universe? One could simply argue that the is information that we do not posses that causes the outcome of a measurement to occur, right?

In this http://web.stanford.edu/~oas/SI/SRGR/notes/SRGRLect6_2007.pdf, it is stated: Likewise, objects in spacetime all move at constant speed c in spacetime but if you change its direction, say by moving at speed v in the x direction, then spatial speed will change and so will the speed along...