Relaitivity Definition and 88 Threads

Consider the curve (thanks to SE) in flat spacetime, given in Cartesian coordinates by$$x^μ(λ)=\left(λ , R\cos\frac{\lambda⁡}{R} , R\sin\frac{\lambda}{⁡R} ,0\right)$$where ##~R~## is a positive constant. At each point$$\dot x^\mu \dot x_\mu=0$$so it is a null curve but not a geodesic (not a...

Hello, I was thinking 🤔, Einstein's brilliant theory of relativity is an observation of time/space and how it alters with speed. If for example an object were to oscillate at such a speed to produce a very noticeable difference to its progression in time to its surroundings environment, say...

it requires less energy to impart acceleration to an object than to the entirety of the universe, This would break the principle of relativity since the amount of energy to move an object should be the same as the amount of energy to move the rest of the universe. This observation implies a...

As some of you know I have been coding a 2+1D relativistic simulator that can handle (constant proper) acceleration in any direction on a plane. So far it is going quite well. I have now decided to simulate a Sagnac gyroscope inside the simulation by sending signals in opposite directions...

Greetings. I registered to this forum because of a particular issue regarding Gravity. I'm no astrophysicist or mathematician, i searched to find an answer, but the terminology and equations are a little much for me. I feel the best direct way is to ask people with the right expertise. It is...

d(ɣmv)/dt = qvB (dɣ/dt)mv + ɣm(dv/dt) = qvB Substituting gamma in and using the chain rule, it ends up simplifying to the following: ɣ^3*m(dv/dt) = qvB Now, I am confused on how to solve for v.

Hi, I'm Dutch, not any kind of Quark ;-) (so excuse me for any bad English) and I'm very curious about "how the universe works". Cosmology/astrophysics and modern physics (quantum, relativity). I find it all mighty intersting. Actually all physics and also how it's all developed and "evolved"...

According to @vanhees71 and his notes at https://itp.uni-frankfurt.de/~hees/pf-faq/srt.pdf under certain conditions one can choose ##\tau## as the parameter to parametrize the Lagrangian in special relativity. For instance if we have, $$A[x^{\mu}]=\int d\lambda...

I am reading pretty much everywhere that LET (Lorentz Ether Theory, or call it Neo-Lorentzian Relativity, or whatever theory that involves a preferred undetectable frame with some yet unknown properties that make all the moving objects with respect to this frame length contact and time dilate)...

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##...

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...

I once naively think that the speed of light is also a constant in a medium in all inertial frames which is not the case. I tried to derive the result yet there is a discrepancy from the results I read in some articles. For example, from [Link to unpublished paper redacted by the Mentors], the...

In special relativity (especially relativistic collisions), is the center of mass frame as useful as Newtonian mechanics?

I started by finding the main events: Sending the first message Receipt the first message Sending the second message Receipt the second message Now, what we know is the time by ##S'## (comoving frame with the spaceship) ##T_1'## and ##T_2'## remaining to arrive to the Earth measured at...

So I understand that time is now part of the four vector, and so dividing delta X by delta t (time according to me), would produce just c as the first dimension of the vector, which gives us no intuition as to how fast time is moving for the observer, so is not useful. I understand why we...

My question: How do the values for the velocity, momentum and energy of an electron in a double-slit experiment are altered by the observation? Probably,energy is altered. Given that energy is a function of momentum and velocity, either or both of these must have been changed. However, I am...

I am reading this article now :http://www.cmp.caltech.edu/refael/league/thorne-morris.pdf. And i am a little bit confused about the Eq.(38a)and Eq.(38b), which means the time measured by traverller and people in the sataion, and I just think the time measured by traveller should be his proper...

In relativity, the speed of light in vacuum is a universal constant. Also, it has wave-particle duality. So if the speed of light slows down in a different media other than vacuum, what exactly is slowing down? Macroscopically speaking, the speed of light does slow down. What about in the...

Summary: At this point, I am thorough with single variable, multivariable calculus, differential equations, linear algebra and basic concepts of point-set topology and tensor analysis. To learn General Relativity along-with its mathematical rigor, what are the topics I should first be thorough...

Summarized: Which mathematical fields should you focus on if your goal is to gain a better understanding of relativity and related subjects? (My apologies if there are already other threads asking this question, but 'math' and 'relativity' aren't really useful search terms on this forum.) Hi...

Based on the exponential growth of time dilation 0.0 - 1.0 if given the radius of an object how do you calculate the mass of the object? Time dilation is a function of gravity. Which can be thought of as escape velocity from a gravitational field. So if you have to achieve .866 c to escape...

Hi, Do we obtain the same escape velocity equation: Ve = sqrt(2GM/r) using both Newtonian and Relativistic approach?

Background: I'm about to graduate with a mathematics degree(in the US), hence I have exposure to multivariable calculus, real analysis, abstract algebra, complex variables etc (no differential geometry however). I have also taken a class on QM(using Griffiths) and I saw some SR during a Modern...

I have come across a questions which reads "Why does even photon travel?". After reading special and general theory of relativity, this one bugs me all over. For a particle moving closer to speed of light, clock slows down and the space around it contracts. I see a photon travel and I see things...

In Newtonian mechanics, both gravitational mass and inertial mass is m. This principle is known as the principle of equivalence. However, I heard that in Relativity, gravitational mass is γm instead of m because total energy of the particle is γmc2. But in special relativity, it is widely known...

Sometimes I get so bored that I just try to calculate certain experiments I've heard without know the solution. Like using the basic formula to calculate the speed of the moon around the Earth. This time I tried to calculate the differences between 2 clocks, on put on the highest building in the...

If the speed of light would change in the universe without any other natural constant changing, would all clocks be affected in the same way by this? This is implied by Einstein in this paper on page 368 http://myweb.rz.uni-augsburg.de/~eckern/adp/history/einstein-papers/1912_38_355-369.pdf...

Hello I know that maxwells equations are consistent with relativity. The following thought experiment seems to imply otherwise so I am wondering where my mistake lies. Lets say we have some very large conductor loop(with a radius of many lightyears). At the center of the loop is some magnet...

I have learned about the electric fields of static charges and those of moving charges. From what I gather(although I have not really learned the specifics) when charges are accelerated they emit electromagntic waves which are essentialy an electromagnetic field progagating through space. My...

This is a question I was looking at based on Relativity and John Wheeler's one-electron universe theory. https://en.wikipedia.org/wiki/One-electron_universe My question is this. The faster you move towards the speed of light, wouldn't everything in the universe contract to a single particle...

Can anyone suggest a book from where I can learn the math used in relativity like Tensors,Minkowski spacetime metric ,etc ? A suggestion of pdfs would also be appreciated?

Homework Statement There are 2 particles(1,2) separated ∆x=L moving with the same velocity u_x in frame of reference S , there's an other reference S' moving at v . I have to calculate ∆x'. GAMMA(LORENTZ'S FACTOR) Homework EquationsThe Attempt at a Solution I have done x1=0 when t=0 So for...

Consider that we have a magnet and a magnetometer (a fluxgate magnetometer with a single coil), standing still as shown in fig 1. In fig 1, the magnetic field measured at the axis z1 of the magnetometer coil is B1. But if everything (magnet, magnetometer and the axes) was rotating together...

I was reading the paper entitled "The Rayleigh—Taylor instability in astrophysical fluids" by Allen & Hughes (1984), and they discuss relativistically hot plasmas in the context of weak magnetic fields which are presumed to have no dynamic influence, so they take a fluid approach. In this paper...

Can anyone briefly explain the difference between covariance and invariance in terms of special relativity? My understanding is that an invariant quantity is a value which does not change regardless of frame of reference it is being measured in. Covariance is a value which when measured in...

I'm having trouble understanding how the 4-wave vector is derived, and also how it is then used alongside the 4-momentum vector to formulate the relativistic de Broglie equation. The inner product of the 4-momentum vector with itself, is an invariant quantity. If we define the 4-momentum...

Homework Statement On the axis of an infinite wedge that moves with velocity ##\vec{V}##, the body decays with the formation of a lot of splinters that fly away uniformly in all directions with velocity ##\vec{u}##. What should be the angle of the wedge that half of the splinters fall on its...

Homework Statement The Michelson interferometer in the figure below can be used to study properties of light emitted by distant sources A source ##S_1##, when at rest, is known to emit light at wavelength ##632.8~ \rm nm##. In this case, if the movable mirror is translated through a...

One of the founding principles in GR is the principle of general relativity, which loosely states that all coordinate frames (inertial and non-inertial) are equivalent in the sense that the laws of physics are invariant. My question is, does the justification for this come from Einstein's...

I recently watched this Varitasium video where he explains the magnetic field due to a current carrying wire. In the video he explains how what we see and describe as the magnetic field produced by a current carrying wire is actually just a electric force caused by the an imbalance of charges...

I'm having this discussion with my engineering peers: A ball is sitting on top of a train traveling at, say, 10m/s. The ball has mass of 2kg, for simplicity. The ball's kinetic energy KE relative to ground zero is 1/2 m v^2, or 100J. A person riding on the train picks up the ball and tosses...

I know that absolute zero is impossible to achieve but we can get close. According to google the coldest temperature ever reached in a lab was 0.006K. Do you think this is because while the atoms are moving very slow relative to the observer they are still moving at the velocity of Earth's...

---I am not sure in which section i should post this question , so if it is wrong section kindly move it to the proper section ---- I am really confused to draw a clear line between what is science and what is not . I know science has some characteristics which differentiates it from...

I don't uderstand how, using special relativity theory (time dilatation and length contraction), one can explain why in the Michelson interferometer there is no delay between the two rays in the reference frame where the interferometer is moving. Consider the picture ##2.## Setting...

Let's assume that it is possible to teleport safely (in one piece, with same body structure) to different galaxy using something as wormhole. Then what would be acceleration that participating in such travel human experience? As I know solar system travels at 230 km/s around the galactic...

First, I am new to physics and only taking my first course in calculus based classical mechanics with topics covering thermodynamics and an introduction to general and special relativity. Everything here is pretty much a question, even if periods exist and not question marks. My teacher had...

In all the derivations of E2=p2c2+m2c4 ,that I've stumbled on, it's assumed that the rest mass energy is m*c2 just because kinetic energy is mc2λ-mc2. Was it originally assumed? If so, can someone explain me why is it a logical assumption? Are there any derivations without such assumptions?

So, I have been thinking about TRAPPIST-1 and how far away that system is from us. It is 40ly away from Earth, according to our frame of reference. This is often put in a way that makes one think that even at speeds close to that of light, it will take almost 40 years to get there. The muons in...

Hi, I was wondering, as in the Bachelor's degree curriculum there is no SR course, for one who is interested in theoretical physics (as me), would do it alone, perhaps with texts such as Rindler or Synge ...? Thank you in advance !

Homework Statement In a 2-body scattering event, A + B → C + D, it is convenient to introduce the Mandelstam variables, s ≡ −(PA + PB)2 , t ≡ −(PA − PC) 2 , u ≡ −(PA − PD) 2 , where PA,...,D are the 4-momenta of the particles A, . . . , D respectively, (· · ·) 2 = (· · ·) · (· · ·) denotes a...