Relativity Definition and 998 Threads

In both Wald and Carroll, a type (k,l) tensor has k dual vectors and l vectors, yet a (1,0) tensor is a vector and a (0,1) tensor is a dual vector. I must be missing something simple. Please explain.

<Moderator’s note: a reference to an article published in a predatory journal has been removed. References on PF should be from the professional scientific literature or from other sources consistent with the professional scientific literature> I read through many posting on various threads in...

In case you haven't heard, there is a new textbook on relativity to be published by Cambridge UP in 2022. It is compiled and edited by Coleman's three students Griffiths, Derbes, and Sohn who took Physics 210 relativity course at Harvard in the late 60's when Sidney was teaching it. The book...

Initial observer is at rest. So ##x\prime=0##, and according to question they are 10 meter apart. So lorentz transformation becomes ##vt=x## ##v=\frac{x}{t}## ##=\frac{10 \\ \mathrm m}{13\times10^{-9} \mathrm s}## But I don't get the expected answer. I believe if I had took ##\beta c## instead...

Hi, I´m trying to solve a special relativity problem, and I think I need some help. There are two inertial frames of reference, ##O## and ##O'##, the last one moving with relative velocity ##v## in the ##x## direction. There's a rod with length ##L'## fixed to frame ##O'##, such that front end...

I'm a female neurobiologist in my 60s with a lifelong passion for physics (but my math was not strong enough). I have a special interest in special relativity and a decent grasp of the basics. I can solve Lorenz calculations 'til the cows come home'. I don't need help with homework of any type...

> A particle of mass M at rest decays into two particles of masses m1 and m2 traveling in opposite directions at velocity v1 and v2 respectively. Express v2 in terms of v1, m1, m2, and M. Since both objects are from a single object that's why I took relativistic mass of both objects are same. I...

This set of videos by eigenchris (separate playlists on Relativity and on Tensors) also looks interesting and can help anyone interested in learning about these topics. A while back I watched some of them and thought they could be helpful. I like his presentation of one-forms. (I've been...

I was browsing YouTube (again) and stumbled upon this set of lectures by Ta-Pei Cheng. (I've seen the cover of the textbooks... but I'm not familiar with the author-lecturer or the details of the texts... but this looks interesting.) http://www.umsl.edu/~chengt/...

Summary:: Special relativity and Lorentz Transformations - I got this problem from a first-semester course at university. I have been struggling for a few days and decided to get some help. A rocket sets out from x = x' = 0 at t = t' = 0 and moves with speed u in the negative x'-direction, as...

Andrzej Dragan ( https://www.fuw.edu.pl/~dragan/ ) has a "Course on relativity" on YouTube. https://www.youtube.com/c/relaTVty/playlists I'm not familiar with Dragan... but the videos display some flair and personality. (...

I am new here, so pardon my ignorance. First of all, I am aware of the impossibility to distinguish experimentally between SR (Special Relativity) and LET (Lorentz Ether Theory). I know there is a PF policy article on LET and the Block Universe. I must admit though that LET is more appealing...

I recently noticed that "General Relativity: The Essentials" by Carlo Rovelli has been published. Based on the description, table of contents, and the Amazon reviews, it seems to me that it might be a spiritual successor to Dirac's "General Theory of Relativity." Is that an accurate assessment...

In a stressful situation, when you're thinking rapidly, time really does seem to slow down. Like "that was the longest 30 seconds of my life." Since thinking is made up of the firing of action potentials in neurons, could those events, in the brain, work with relativity to slow down personal...

How to Judge original time and original length of special relativity

I was starting out some problems on force and motion at 10+2 level. I was told you don’t need to know about frame of reference. But I want to. So which books are there to understand frames? Is it a part of relativity? If yes then which books? Thank you guys.

Considering an atom within a rigid body, does the angular momentum of an electron within the atom vary when the body is put in motion? My intuition is that, whether considered in a classical sense or quantum sense, the speed of a given electron in its motion within an atom will be constant and...

In a recent thread, I said that if there was interest, I would post in a separate thread the calculations for the kinematic decomposition of the congruence of worldlines describing the rod in the "rod and hole" relativity paradox discussed in that thread. Since there was interest, I am posting...

I am confused by the concept of space-time in special relativity, I have 3 spatial dimensions and 1 time dimensions. In Newtonian physics don't I also have 3 spatial dimensions and 1 time dimension? Then why call it space time in special relativity and not in Newtonian physics?

Einstein says ' we cannot whether it is true that only one line goes through two points' ' We can only say Euclidean Geometry deals with things called straight lines to each of which is ascribed the property of being uniquely determined by two points situated on it, - What does he mean? and...

A rigid rod with length ## l_0## slides on a smooth and flat tabletop along the length at speed of ## ~\frac {\sqrt{3}}{2}c~ ##, there is a hole of width ##~l_0~##on the table. The observer who is stationary relative to the desktop thinks that the length of the rigid rod ##~ l=l_o...

From the section[5.1] of 'Homogeneity and Isotropy' from General Relativity by Robert M. Wald (pages 91-92, edition 1984) whatever I have understood is that - ##\Sigma_t## is a spacelike hypersurface for some fixed time ##t##. The hypersurface is homogeneous. The metric of whole space is ##g##...

The way I was doing is that I list events 1. lightning hits x=0 this is (x_1=0,t_1) 2. lightning hits x=12 (x_2=12,t_2) 3. left lightning reaches "me" (x_3=9,t_3) 4. right lightning reaches "me" (x_4=9,t_4=t_3) t_4=t_3 since "I" see the lightning at the same time Then the...

The twin paradox can be explained by changing reference frames. But I’m really curious how this paradox can be explained. In the situation below there are three observers: A: Standing at a moving train platform moving at a speed of c/2 relative to “the ground”. B: Standing at a moving train...

I saw a book that uses special relativity to solve the twin paradox, the inference process is roughly as follows. Suppose a spacecraft sets off from the Earth to travel to a distance black hole and then return to the earth. We divide this process into three stages, that is, the process of...

I believe this does not belong to the homework category. I hope I won't be mistaken. I am reading a book to self-study special relativity, the following is an example mentioned in the book. When clock C' and clock C1 meet at times t'=t1=0, both clocks read zero. The Observer in reference frame...

Posed question is that a comment plunges into Jupiter. Same time as my physics class starts on Earth. My friend is traveling towards Jupiter at a significant percentage of c. Would the person in spaceship say that the comment collision occurred before, after or as class started? My answer: same...

I was discussing in another page this topic with someone. He said it's relative in everything, meaning that energy and force doesn't count. This is obviously wrong because the fact that today we can't (maybe tomorrow we can) know which thing is moving towards the other and which not, doesn't...

Dear readers, Maybe someone can enlighten me on the understanding of the proof given by the Michelson–Morley experiment on the special relativity. Just as introduction to detail the setting: There are 2 coordinate systems A and B. A stands still and B moves with the velocity v along one of...

Does time dilation in Special Relativity relate to the Doppler effect? If you move near the speed of light you experience time differently and the sound is stretched. Are these similar phenomenon?

Hi all, What I notice is that there's a significant difference in style between the GR texts and the other textbooks. In particular, GR texts very much try hard to read like a math textbooks, emphasizing theorems and abstract definitions, which I'm not sure are practically useful (though...

Some introduction books on Lagrangian and Hamiltonian mechanics use classical mechanics as the theoretical framework, and when it come to special relativity it goes back to the basics and force language again. I would like to ask for some recommendations on good books that introduces Lagrangian...

I'd like to get some help on checking my understanding of special relativity, specifically I'm trying to clarify the idea of coordinates. Any comment is really appreciated! The spacetime is an affine space ##M^4##, which is associated with a 4 dimensional real vector space ##\mathbb{R}^4##...

I hear these massless and hypothetical particles could travel faster than light, would that prove relativity wrong?

Hello everyone, I am preparing to write an exam project in college about special relativity, however i am missing the critical experiment to prove that it is true. I thought about using the life time of muons, but i don't have a scintillator to detect them, so unless a standard geiger counter...

I made an exercise whose question is like that: A spacecraft moves with speed v at the axis x. There are two target at the axis x, in which the distance between them is L at the ground frame. Suppose that the spacecraft shoot the target simultaneously when it passes by the target. A|so...

My answer is (A) since I think the motion of the spacecraft will alter the length of the spacecraft (length contraction) but not changing the orientation so the angle will stay the same But my teacher said my answer is wrong. What is my mistake? Thanks

I was doing a exercise which considerst he time it takes for light travels a glass with thickness proper D and velocity v. The speed of light is c/n inside the glass. Now, my approach was to go to the glass frame, take the relative speed between the glass and the light using the trivial formula...

I want to learn General Relativity so I am looking for a good beginners book with low amounts of math and clear explanations. Any suggestions?

Ok, so basically: There is a frase with a particle moving horizontally with velocity v and a rod parallel to the ground, with rest length L, falling with speed u vertical constant. The rod bounces off on the ground. Describe what happens in the particle frame and find the angle the rod makes...

I am an amateur in physics and I have a question. How does speed of an object affect time?

hello it is well known that gravitationl force is actually a fictitious force generally speaking,are fictitious forces still necessary in general relativity ? the fictitious forces which we experience on a bus or on a car can also be understood as due to the spacetime distortion ?

I want to learn special relativity.I have read a tiny bit of 2nd edition of Spacetime Physics: Introduction to Special Relativity and am liking it. Is it a good book? I also want problems to solve. I tried Special Relativity: For the Enthusiastic Beginner but found it to difficult. Does anyone...

i am having some hard time thinking about this problem: It is basically this: Imagine a bulb and a receptor distant L from each other (at the same axis x) inside a room, the roof of the room is at a height d from the bulb and receptor. Now you are at a train moving horizontally, parallel to...

Consider a far-away galaxy that is considered to be currently receding from Earth at 2x the speed of light. (With this 2x c recession velocity, we are speaking of the Vnow, the imputed relative velocity of the galaxy compared to Earth now, not the velocity of the galaxy relative to Earth at the...

I found an interesting list of "must-read" papers in the field of general relativity compiled by Emanuele Berti: https://pages.jh.edu/eberti2/posts/must-read-paper-list/ Are there any notable exceptions, or other "classic" papers that - in your view - every relativist ought to have read?

While learning about Special Relativity I learned that we use the Transformation matrix to alter the space .This matrix differs for Contravariant and Covariant vectors.Why does it happen?,Why one kind of matrix (Jacobian) for basis vectors and other kind(Inverse Jacobian) for gradient...

Assume that space is a three-dimensional torus ( a 3D donut) . If there is a clock traveling at a CONSTANT speed in a direction parallel to the torus (inside out of the hole) and one clock that is still. Which clock ticks faster and why? I know that the clock rotating will tick slower, but I...

I'm watching this minutephysics video on Lorentz transformations (part starting from 2:13 and ending at 4:10). In my spacetime diagram, my worldline will be along the ##ct## axis and the worldline of an observer moving relative to me will be at some angle w.r.t. the ##y## axis. When we switch...

Which is the mathematical procedure to obtain ##\delta r = \frac{GM}{3c^2}## from ##\nabla^2 V = R_{00} = 4\pi G\rho## where ##\nabla^2 V## is volume contraction of a spherical mass of density ##\rho## and ##R_{00}## is the 00 component of Ricci tensor ##R_{ij}##?