Einstein Definition and 811 Threads

If the laws of physics say that nothing can move faster than the speed of light, how can we square it in Einsteins equation? It dosent make synce to me. How does Einsteins equation work can someone break it down for me and explain it in layman’s terms please. How can we warp spacetime just by...

So let me ask a question about the speed of light. Why can't we go faster than the speed of light? I understand the idea with the photon clock — the clock slows down as you move faster because the photon has to travel a longer distance. But theoretically, if we throw a rock at a wall, it would...

Einstein's equations in general relativity indicate that the universe is expanding. Einstein himself believed that the universe should be stable so he introduced a correction to his equations which made for a static universe. He later admitted that was his biggest blunder. Hubble proved by...

Hi All I just finished the following course on Einstein and Relativity: https://www.edx.org/learn/humanities/harvard-university-the-einstein-revolution It is especially interesting as it goes into the details of how he differed from Poincare. I was fascinated by some of Poincare's...

How did you find PF?: Google search I encountered a problem in the equations for Einstein's Special Theory of Relativity back when I was in high school in 1964. With the invention of the internet, I tried to discuss this with scientists in sci.physics.relativity, but most of the responses...

Einstein was awarded the Nobel prize "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect" which is a bit of a waffle. Does anyone know of any instances where the award could be considered “brave”?

I'm wondering what are in people's opinions the "must read" papers of Einstein. I concentrate more on general relativity but also other stuff. Reviews by Einstein and maybe other important contemporary papers would also be welcome, as well as maybe modern commentary on them.

Hello, Has anyone here used software to solve the Einstein field equations? If so, what software have you used, or what software do you recommend? Is it possible to use something like MATLAB to play around with the field equations?

Here is a screenshot from Einstein's 1905 ELECTRODYNAMICS OF MOVING BODIES:My understanding is that here Einstein says that the rod, the 2 observers and the 2 clocks are in the moving system, one observer & clock at each end of the rod. From their point of view they are not moving. They can very...

In Appendix 4 of the book "Relativity, The Special and General Theory", Einstein describes the evolution of the cosmological implications of general relativity as follows: My original considerations on the subject were based on two hypotheses: (1)There exists an average density of matter in the...

I'll set out by saying that I have no real formal training in physics or maths. However, I have been keen to try to understand what exactly convinced Einstein that spacetime must be curved. As I understand it, the bending of star light was already explained by Newtonian physics, although of...

Hi, I've recently developed an interest for the history of the development of cosmology and find it very interesting. The key events I have been reading up on are: 1915 - Einstein's theory of General Relativity was published. 1923 - Hubble discovered a Cepheid variable in the Andromeda...

Just preordered a “Black Hole” version of the watch. It tries to mimic what it would look like to travel through a wormhole, in celebration of Einstein’s theory of relativity.

I calculated the speed using the information provided through the above equation and finding V' = 1.2 m/s. However, the first solution must be -1,2 m/s. I don't know how to reach it, any suggestion?

Okay I’m assuming I have to use √1- v^2/c^2 multiplied by some coefficient of length but I don’t understand any of this and could really use help understanding the process and/or reference material that might point me in the right direction

Hi, I've just calculated the orbital precession for the earth using the sigma formula of general relativity. $$ \sigma=\frac{24 \pi^{3} R^{2}}{T^{2} c^{2}\left(1-e^{2}\right)}=\frac{24\pi^3×1.5×10^{11}}{3×10^7×3×10^8(1-0.0034^2)}=0.012 $$ What is the unit of the result? Degrees per century or...

So, I have recently been trying to learn how to work with tensors. In doing this, I have come across Einstein Notation. Below is my question. $$(a_i x_i)_{e}= (\sum_{i=1}^3 a_i x_i)_r=(a_1 x_1+a_2 x_2+a_3 x_3)_r$$; note that the following expression is in three dimensions, and I use the...

In the textbook: Electrochemical Systems by Newman and Alyea, 3rd edition, chapter 11.9: Moderately Dilute Solutions, equation for the mole flux of the component ##i## is given by: $$ N_i = - \frac {u_i c_i} {z_i F} \nabla \bar\mu_i\ + c_i v \tag {1}$$ where ##u_i## is the ionic mobility...

I know that if ##\eta_{\alpha'\beta'}=\Lambda^\mu_{\alpha'} \Lambda^\nu_{\beta'} \eta_{\alpha\beta}## then the matrix equation is $$ (\eta) = (\Lambda)^T\eta\Lambda $$ I have painstakingly verified that this is indeed true, but I am not sure why, and what the rules are (e.g. the ##(\eta)## is in...

I tried to solve it considering the canonical ensemble (since the system is at the equilibrium with temperature T) and started finding the partition function:The problem is I am not sure if I have done it correctly and need help because I don't really know where to check.

I am wondering if I am using Einstein notation correctly in the following example. For a matrix ##R## diagonal in ##1##, except for one entry ##-1##, such as ##R = [1,-1,1]##, is it proper to write the following in Einstein notation: ##R_{\alpha} R_{\beta} = \mathbb{1}_{\alpha \beta} ##, such...

Hi For an operator A we have Aψn = anψn ; the matrix elements of the operator A are given by Amn= anδmn My question is : is this an abuse of Einstein summation convention or is that convention not used in QM ? Thanks

Hi, reading this old thread Second postulate of SR quiz question I'd like to ask for a clarification on the following: Here the Einstein definition of simultaneity to a given event on the Langevin observer's worldline locally means take the events on the 3D spacelike orthogonal complement to...

What do you think?

Hello , I was trying to vary Einstein Hilbert action in Mathematica , but the syntax failed me badly. I have derived the result by hand , but I want to present the topic with nb.file . Nevertheless, as I said, the syntax is my major concern now. any help will be appreciated! thank you

In Gravitation by Misner, Thorne and Wheeler (p.139), stress-energy tensor for a single type of particles with uniform mass m and uniform momentum p (and E = p2 +m2) ½ ) can be written as a product of two 4-vectors,T(E,p) = (E,p)×(E,p)/[V(E2 – p2 )½ ] Since Einstein equation is G = 8πGT, I am...

Alright, this is my idea of an experiment that could distinguish between the examples of the EP. Now, obviously I'm wrong (I don't say this because of your acceptance, i say this because I've tried with other ideas but they were wrong). The thing here is that i don't see where I'm wrong, and i...

What would be the consequences of such thing? How it will affect physics theories and the world?

[Moderator's Note: Thread spin off due to topic and level change.] For a spherically symmetric solution, if SET components were written in terms a single one of 4 coordinates, in a way plausible for a radial coordinate, the I believe solving the EFE would require spherical symmetry of the...

What is the difference between the approaches of Einstein, Debye and Peierls regarding the heat transfer?!

In Chandrasekhar's book, The Mathematical Theory of Black Holes. The sign of Einstein equations is minus "-" , Eq. (1-236). However, the sign of Riemann and Ricci tensor are the same as MTW's book. The sign of Einstein equations in MTW's book are "+"! Is there a error?

Let's say I want to describe a massive box in spacetime as described by the Einstein Field Equations. If one were to construct a metric in cartesian coordinates from the Minkowski metric, would it be reasonable to use a piecewise Stress-Energy Tensor to find our metric? (For example, having...

About a week ago I was reading about Cartan's geometric interpretation of the Einstein Field Equation Gij + Λgij = κTij According to Cartan, this equation expresses the idea (sum of moments of rotation for the faces of a little 3-cube) = 8π * (amount of energy-momentum within that 3-cube) As...

Are there any experiments either already performed or even simply proposed that could be used to distinguish Einstein Cartan gravity from GR? My current understanding is that they are the same in vacuum, and only differ in matter. In matter the Einstein Cartan metric can have torsion, unlike...

There are two parts to my question. The first is concerns the variation of the Reimann tensor. I am trying to show $$\delta...

Hi If i have a vector r = ( x1 , x2 , x3) then i can write r2 as xixi where the i is summed over because it occurs twice. Now is xixi the same as xi2 ? I have come across an example where they are used as equivalent but i am confused because xi2 seems to be the square of just one component of r...

In the famous book, Gravitation, by Misner, Thorne and Wheeler, it talks about the stress-energy tensor of a swarm of particles (p.138). The total stress-energy is summed up from all categories of particles. Is summation meaningful in the non-linear theory of Einstein gravitation? Thanks.

Short, probably stupid, question; what does this left-right arrow ##a \leftrightarrow b## at the bottom-right mean? [It's this paper for ref.] Does it just mean the last term repeated, except this time with ##a## and ##b## indices exchanged? Thanks.

Does anybody know why Einstein never pursued the idea of wormholes beyond his very short 1935 paper? If he did does anybody know of any of his papers that go into this idea in more detail. I know recently there was the proposal of EPR=ER mainly put forth by Susskind and Maldecena. The ER=EPR...

Good day. I have read many books, forums, and articles, and watched many youtube videos, all in an effort to understand special relativity and time dilation. Or rather, more precisely, trying to find a valid explanation that does not result in contradictions and paradoxes, and if it does, one...

This is probably just a coincidence, but I happened to notice while looking at Einstein crosses an unusual pattern common to these four images. I was looking for more but it turns out there may not be as many crosses as I originally thought. Must be rare. The pattern is that of the 4...

Others are telling me the Einstein Field Equations can work in other dimensions other than 4D (3D space + 1D time). How true is it? So I'd like to ask for clarifications. I googled about it and found one reference for example: Kaluza–Klein theory - Wikipedia I assume the Einstein equations is...

Can be Einstein equation rewrited into some simpler form, when suppose only spherically symmetric (but not necessarily stationary) distribution of mass-energy ? If yes, is there some source to learn more about it ? Thank you. edit: by simpler form I mean something with rather expressed...

I have listening to talks come across the terms"Einstein frame" and "String frame" but am not at all clear what they mean. Can anyone give a layman's explanation as to what is theses phrases mean in the context of cosmology ?

When I learned about Einstein solids in thermal physics, we assumed the fundamental assumption of statistical mechanics. For two interacting Einstein solids, I completely understand why this is valid after a considerable amount of time has passed. But, how can we model these solids as they get...

Quantum mechanics has argued for years that space is not a vacuum. Arguments attempting to brush aside quantum mechanics vacuum theory claiming, it's 'just a quantum mathematical theory' can now put to rest. In this article, laboratory experimentation demonstrates that the Casimir Effect can...

I read this paper where if you take the alcubierre metric calaculations while including torsion in GR you get positive energy spin requirements instead of exotic matter. Here is the link: https://arxiv.org/abs/1807.09745 Could it be because a spinning quantum vacuum will be less stiff like a...

Hi All To the general public there are all these myths that Einstein failed math, was a poor student, and all sorts of other misconceptions. Most people on this forum know it is poppycock and I, and I have no doubt other posters, have had to explain its just a myth a number of times. Well...