General Definition and 1000 Threads

Spacetime is the foundation of General Relativity, describing how mass and energy influence the curvature of space and the flow of time. However, an important question arises: Is spacetime a physical entity, or is it merely a mathematical framework? Physics relies on measurable quantities and...

I was always big with watches, and I just have stumbled on a few that are masterpieces. Unfortunately they cost $500,000. What do you think?

I am trying to imporove my general maths and revisting my pre-college text books. For the above example question, my answer was 4 which is not correct as it is -4. The only difference I can see in my working is the first operation 3a^2. Here I simply did 3 x -2^2 which is -12 but in the answer...

Hi All Would it be possible to introduce some exercises in general relativity at the high school level? Exercises that would at least help to raise students' awareness of the aspects that will be studied in greater depth at university or in post-doctorate studies? If so, what examples of...

https://www.amazon.com/General-Relativity-Robert-M-Wald/dp/0226870332?tag=pfamazon01-20

We are working with series currently, and some of the problems ask you to create a general term and write it in series summation form. Some of it is a no-brainer, but other ones, I'm at a loss as to how they expect us to get the answer without a ton of trial and error. For example, there is...

I’ve been self studying some of the concepts related to General Relativity, by trying to model Geodesics and calculate distances on curved surfaces. I found that I seem to understand some of the concepts related to the math, but not others as when I try to make some calculations I find that my...

For part one, my energy conservation equation is nhf0 + mc2 = nhf' + E my momentum conservation in x-axis is nhf0= nhf' cos(theta) + c𝒑 cos(fi) My momentum conservation in y-axis is nhf' sin(theta) = c𝒑 sin(fi) For part 2 I understand that I am supposed to get a qudratic equation in terms of...

How do you derive the position vector in a general local basis? For example, in spherical coordinates, it's ##\vec r =r \hat {\mathbf e_r}##, not an expression that involves that involves the vectors ## {\hat {\mathbf e_{\theta}}}## and ## \hat {{\mathbf e_{\phi}}}##. But how would you show this?

Fire, Gravity, Electromagnetism, Atoms, DNA, Steam power, Nuclear, Quarks. All of these things have one thing in common. They are fundamental aspects of the universe that humans have uncovered and given names. However, all of these great discoveries occured quite some time ago and as a science...

Im looking for a general formula for the partial sum of a series where the nth term is in the form of a_n = 1/(c+kn), where c and k are arbitrary constants. it "looks" like a harmonic series but not in the form I'm capable of figuring out. help.

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For this, Does someone please know how do we derive equation 9.9 from 9.8? Do we take the limits as t approach's zero for both sides? Why not take limit as momentum goes to zero? Many thanks!

I have been learning a little Differential Geometry lately and recently came across the Hodge Star. So far I have been unable to find an explanation for its calculation that I can understand. I believe some ways of computing it were only valid in an orthonormal basis, but I would like to be able...

I bought a copy of Adler's new book on relativity. Is there a misprint on page 16 regarding the Lorentz metric = diag (-1,-1,-1,-1) or am I missing something? The text itself after the equation suggests it is the same metric as on the earlier page so that index placement, two lower indices vs...

TL;DR Summary: I have to find an equivalent resistance of the circuit below, dependent on the amount of ##R_3## - resistors. Here is the circuit: I think there is no general solution. When I want to calculate it, I have to do...

I have the following question to solve:Use the metric:$$ds^2 = -dt^2 +dx^2 +2a^2(t)dxdy + dy^2 +dz^2$$ Test bodies are arranged in a circle on the metric at rest at ##t=0##. The circle define as $$x^2 +y^2 \leq R^2$$ The bodies start to move on geodesic when we have $$a(0)=0$$ a. we have to...

I am studying metrics that exhibit CTCs. I was looking at a few different metrics... Tipler's solution Godel metric Kerr metric For starters to compare them, I am trying to convert said metrics into cylindrical coordinates. Thanks in advance for any help😃

Hi, I am looking to study general relativity at my own steam (currently finishing 1st year physics at Warwick) during the summer. What textbook(s) would you recommend? I've heard good things about A. Zee's 'Einstein Gravity in a Nutshell'- is that worth it, and would it be suitable for someone...

For this, Dose anybody please know of a better way to derive the formula without having ##c = \frac{\Delta Q}{m \Delta T}## then taking the limit of both sides at ##\Delta T## approaches zero? I thought ##\Delta Q## like ##\Delta W## was not physically meaningful since by definition ##Q## is...

I know nothing about physics, to be clear. My friend was saying due to general relativity, the faster you move through space, the slower you move through time. Objects with a heavy mass (like a blackhole) can distort the fabric of space time and being near its gravitational pull means that you...

Wasn't sure where to categorize this thread, but thought chemistry would be the most appropriate (mods: feel free to move as you see fit). I have some questions on the science of water evaporation - first in general terms and then within the context of something that happened to me. General...

In sect. 2.3.2 "Ideal Clock", p. 33, of É. Gourgoulhon's text book on "Special Relativity in General Frames" $$ \tau_C [ \, \text{tick}_{j}, \text{tick}_{(j + N)} \, ] = K_C \, N. $$ (equation (2.11); notation adapted.) The only other reference to this "constant K" is on the following page...

Hi, I am currently trying to do a project related to this engine and I am trying to find information about it. I am looking for technical papers, journals or overall description of the inner workings of the engine. I am looking forward for something more in depth than wikipedia. Also...

I have some questions regarding the expected exchange particles for gravitation. From my understanding the following was valid: We can linearize the equations of GTR for weak fields "Quantum mechanics" (Schrödinger, Dirac equations) are linear Those linear equations allow eigenstates and...

This time with General Relativity: https://www.amazon.com/dp/1541601777/?tag=pfamazon01-20 I got a copy as soon as I noticed it. And it is good - as all his books are. Notice - number one best seller. Lenny deserves a medal. There is a genuine thirst for science beyond banal...

Hello, everyone I am now working on this project quite a while now and I just wanted to share it with this forum, which I was a member for a long time. I am working on a python application about GR and I believe I managed to create a very user-friendly layout. It's called GTRPy, and it allows...

Here is the video: [link deleted by moderators] His basic idea is to take the spacetime interval and add a 5th term for the 5th dimension he is describing so it looks like: $$\Delta S^2 = c^2\Delta t^2 + c^2\Delta w^2 - \Delta x^2 - \Delta y^2 - \Delta z^2 $$ where w is the difference in time...

Modeling the time evolution of the sun and earth orbiting each other using ##F = \frac{GMm}{r^2}## is straightforward. However, it appears that modeling the time evolution of the same 2 body system using general relativity seems to be a hard/intractable problem? There was in depth discussion by...

So, I've been watching eigenchris's video series "Tensors for Beginners" on YouTube. I am currently on video 14. I, in the position of a complete beginner, am taking notes on it, and I just wanted to make sure I wasn't misinterpreting anything. At about 5:50, he states that "The array for Q is...

So, I've been watching eigenchris's video series "Tensors for Beginners" on YouTube. I am currently on video 14. I am a complete beginner and just want some clarification on if I'm truly understanding the material. Basically, is everything below this correct? In summary of the derivation of the...

My take; ##ξ=-4x+6y## and ##η=6x+4y## it follows that, ##52u_ξ +10u=e^{x+2y}## for the homogenous part; we shall have the general solution; $$u_h=e^{\frac{-5}{26} ξ} f{η }$$ now we note that $$e^{x+2y}=e^{\frac{8ξ+η}{26}}$$ that is from solving the simultaneous equation; ##ξ=-4x+6y##...

I'm wondering is I'm missing something, or this should be " a non-zero component"?

Does anyone know of a comprehensive list of solutions to GR, their developmental history, and the viability for serving as a practical model for the observable universe?

Once having converted the FLRW metric from comoving coordinates ##ds^2=-dt^2+a^2(t)(dr^2+r^2d\phi^2)## to "conformal" coordinates ##ds^2=a^2(n)(-dn^2+dr^2+r^2d\phi^2)##, is there a way to facilitate solving for general geodesics that would otherwise be difficult, such as cases with motion in...

General relativity permits some exact solutions that allow for time travel. Some of these exact solutions describe universes that contain closed timlike curves, or world lines that lead back to the same point in spacetime. I wondered if these solutions also permits Causal loops? Such as the one...

I was glancing through https://arxiv.org/abs/1605.07458 I don't fully get why scale invariance kicks in below a certain acceleration. Is this because the centripetal force becomes constant? I do see that Newton's second law with the centripetal force included is scale invariant. This symmetry...

I’m in need of recommendation of a general science book (‘general’ means just a bit of introduction and its application, not going into its detailed theoretical and technical workings) which contains the following topics (though not exhaustive) Space Technology: the basic concept of launching...

In texts on General Relativity, the proper time ##d\tau^2 = -ds^2## (with an appropriate choice of metric signature) is commonly said that the time measured by a timelike observer traveling along a path is given by the integral of ##d\tau## along this path. Of course it's possible to construct a...

For the 1 dimensional wave equation, $$\frac{\partial^2 u}{\partial x ^2} - \frac{1}{c^2}\frac{\partial ^2 u }{\partial t^2} = 0$$ ##u## is of the form ##u(x \pm ct)## For the 3 dimensional wave equation however, $$\nabla ^2 u - \frac{1}{c^2}\frac{\partial ^2 u }{\partial t^2} = 0$$It appears...

In Newtonian mechanics, G is simply a proportionality constant or the force with which two bodies of unit mass attract each other. However, GR doesn't treat gravity as a force. So how is G defined in GR? Is it a property of spacetime or just some useless mathematical artefact? What does G...

hello I'm korean high school student and sorry for my poor English. I saw ## t_0=t_f\sqrt{1 -\frac{ 2GM}{rc^2}} ## in wikipedia. does ## \sqrt{1 -\frac{ 2GM}{rc^2}} ## of this equation have name like lorentz factor ## \frac{1}{\sqrt{1 -\frac{v^2}{c^2}}} ##of ## t=\frac{t_0}{\sqrt{1...

Hello everyone, In trying to better understand how sailboats work, how they can sail upwind (not directly), how the go faster than the wind speed, I have been thinking about the magnitude of the wind force and its equation: $$F_{wind}= \frac {1}{2} \rho_{air} A v_{wind}^2$$ Instead of ##...

Hi PFs, I am reading this paper written by carlo Rovelli: https://arxiv.org/abs/1010.1939 there are many things that i fail to understand, but i would like to begin with a simple thing. Rovelli write that: It is locally Lorentz invariant at each vertex, in the sense that the vertex amplitude...

Additional/Optional Subject: Space and Defence technology. Began a week ago, they taught a whole week, for 2.5 hours per day on space technology: Orbiter, Rover, Ramjet, Scramjet, Air-breathing engine, Reusable Launching Vehicle and et cetra ... et cetra... Thought, I, could absorb and...

Hello guys I hope you all are doing well. :) I found below question in a book by Martin Braun "Differential Equations and Their Applications An Introduction to Applied Mathematics (Fourth Edition)" The question : The Bernoulli differential equation is (dy/dt)+a(t)y=b(t)y^n. Multiplying through...

If we insert the values from (2.9), (2.10), (2.11) into (2.5) & (2.6) how can we get (2.13) & (2.14) ?? I need to see the calculations step by step.

In a recent thread about Bell tests etc. it has been claimed my point of view of "locality" where "non-mainstream physics". Of course, I cannot give a complete summary of the foundations in a forum posting, as demanded by @DrChinese there. The most clear treatment, particularly emphasizing the...

Hope this question can be quickly clarified: There was a statement that the General Relativity can be interpreted by speaking of an ether whose state varies from point to point. Is this correct?!

We have a matrix ##M = \ket{\psi^{\perp}}\bra{\psi^{\perp}} + \ket{\varphi^{\perp}}\bra{\varphi^{\perp}}## The claim is that the eigenvalues of such a matrix are ##\lambda_{\pm}= 1\pm |\bra{\psi}\ket{\varphi}|## Can someone proof this claim? I have been told it is self-evident but I've been...