Relativity Definition and 998 Threads

Homework Statement Special Relativity Question. Consider objects 1 and 2 moving in the lab frame; they both start at the origin, and #1 moves with a speed u and #2 moves with a speed v. They both move in straight lines, with an angle θ between their trajectories (again in the lab frame). What...

There are a pair of entangled particles moving in opposite directions. A measurement is done on particle A, the wavefunction collapses randomly, you observe either spin up or spin down, A does an action at a distance on B, particle B instantly collapses to the opposite spin state, a measurement...

Homework Statement A thin rod of proper length 4a is traveling along the x-axis of a frame S with a speed ##{\frac {\sqrt 3} 2}c## in the positive x-direction. A hollow cylinder CD of proper length 2a is placed with its axis along the x-axis, so that when the ends of the cylinder are open the...

I see this has been already discussed but the old threads are closed. EPR before EPR: a 1930 Einstein-Bohr thought experiment revisited "In this example, Einstein presents a paradox in QM suggesting that QM is inconsistent, while Bohr attempts to save consistency of QM by combining QM with the...

I had a bit of a thought experiment the other day, does relativity mean that technically you couldn’t travel faster than the speed of light to the observer. But if you were traveling from Earth to another planet, could you technically be traveling faster than the speed of light relative to the...

Homework Statement I'm stuck on part (d) but I've included the previous subquestions in case they're useful. The length of an asteroid is exactly 300 m = 1 µls (micro light-second) when at rest. Draw a carefully labelled space-time diagram to illustrate the following: (a) Depict the rest...

Sometimes experimental or observational evidence from credible physicists points to new physics and then turns out to be wrong due to statistical flukes, experimental error or a theoretical analysis mistake. What cases of this happening do you find most notable, what showed that the hints were...

What's the usefulness of a Lie Algebra? As I see on Wikipedia a Lie Algebra is a vector space with an operation on it called Lie Bracket.. This seems to be the formal definition. In Relativity, we have the Lie Algebra of the Lorentz group, the Lie Algebra of the Poincaré Group, which are those...

Homework Statement Question attached: Homework Equations see below The Attempt at a Solution [/B] my main question really is 1) what is meant by 'abstract tensors' as I have this for my definition: to part a) ##V^u\nabla_uV^a=0## but you do say that ##V^u=/dot{x^u}## ; x^u is a...

What is the deviation in the expansion of the universe exactly quantified, when I would assume general relativity and project it backwards? As a statistician I am asking for data, for either the backwards projected general relativity case and either the real expansion case, as it is...

Greg Bernhardt submitted a new PF Insights post Rindler Motion in Special Relativity, Part 2: Rindler Coordinates Continue reading the Original PF Insights Post.

Just for a bit of fun, which theory , relativity or quantum mechanics has the most accurate ( i.e to how many decimal places confirmation between theory and experiment) measurement ever made?

I am posting this paradox as a brain teaser If we drilled a tunnel through the earth, to the other side, and measured gravity in the tunnel, gravity would be zero in the center of mass. This is Newtonian gravity and is connected to the vector addition of the gravitational force; cancels in...

Homework Statement In an electromagnetic filed, the elctric field ##\vec{E}## forms an angle ##\theta## with the magnetic field ##\vec{B}##, and ##\theta## is invariant for all inertial observers. Finding the value of ##\theta##. Homework Equations Tranformations of fields perpendicular to the...

Homework Statement S and S' are in standard configuration with v=αc (0<α<1). If a rod at rest in S' makes an angle of 45o with Ox in S and 30o with O'x in S', then find α. Homework Equations We are in the world of Lorentz transformations so we have t'=(t-vx/c2)/(1-v2/c2)1/2...

I think mass as a form of potential energy and am always told that this is wrong. According to wiki: "In physics, potential energy is the energy possessed by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors." Why do this...

Homework Statement In an inertial reference frame ##S## is given the four-potential: $$A^\mu=(e^{-kz}, e^{-ky},0,0)$$ with ##k## a real constant. ##A^\mu## fullfills the Lorentz gauge? And the Coulomb gauge? Which is the four-potential ##A'^\mu## in a reference frame ##S'## which is moving...

Homework Statement Let's have a three-particle decay of equal mass ##m##; in the CM frame the three particles have equal energy ##E## and they form angles of ##\frac{2\pi}{3}## between each other. Which is the angle between two of the three particles in the rest frame of the other one. (The...

I always liked the idea of starting relativity discussions with the idea that your father could travel at a substantial fraction of the speed of light and return back at roughly the same age as you. This makes time dilation seem interesting, and drives curiosity in students. But I'm struggling...

A rocket is in constant velocity. The velocity of the rocket is 150Mm/s (or 0.5 of the speed light, or 150 million meters per second) relative to us (we as observer). We observe two lights, one moving in parallell with the rocket, another is moving in the opposite direction. Below I have made...

Homework Statement A photon hits a proton at rest in the laboratory frame and there is the process: $$\gamma + p \rightarrow n+\pi^+$$ The mass of the pion is ##m_\pi## and assuming that the masses of the proton and the neutron are the same (##m##): Finding the threshold energy of the foton...

Greg Bernhardt submitted a new PF Insights post Rindler Motion in Special Relativity: Hyperbolic Trajectories Continue reading the Original PF Insights Post.

Homework Statement a) Calculate the kinetic energy required to accelerate a single proton from a rest position to 0.9999c. The mass of a proton is 1.67*10^-27 kg. b) Find the ratio of the kinetic energy to the energy of a proton at rest. c) Explain why no particle accelerator will ever be able...

I’ve seen a few places, here is 1 such link: http://physics.weber.edu/schroeder/mrr/MRRtalk.html I have a problem with how they represent the charges in the frame where the free charge is stationary and the charges are moving in the wire. This seems wrong for 2 reasons: 1. They show additional...

According to various sources, the Moon is separating from Earth 4 cm every year. I’ve searched for the explanation and I’ve found the following: The friction the seas and oceans from the Earth make with it’s soil causes the Earth’s rotation to slow down. This causes the Moon to speed up...

Let us assume a "toy-metric" of the form $$ g=-c^2 \mathrm{d}t^2+\mathrm{d}x^2+\mathrm{d}y^2+\mathrm{d}z^2-\frac{4GJ}{c^3 r^3} (c \mathrm{d}t) \left( \frac{x\mathrm{d}y-y\mathrm{d}x}{r} \right)$$ where ##J## is the angular-momentum vector of the source. Consider the curve $$ \gamma(\tau)=(x^\mu...

Homework Statement This is more of a solution check than an actual problem, but I didn't see any other fitting thread to post this on. I'm starting to learn special relativity and have received 2 starting questions on the subjects, I solved them to the best of my abilities but have no actual...

Homework Statement A light-clock (a photon traveling between two mirrors) has proper length l and moves longitudinally through an inertial frame with proper acceleration ##\alpha## (ignore any variation of a along the rod). By looking at the time it takes the photon to make one to-and-fro...

https://www.forbes.com/sites/startswithabang/2018/02/14/black-holes-must-have-singularities-says-einsteins-relativity/amp/

So the first term of the Lagrangian is proportional to ##{F_{\mu \nu}}{F^{\mu \nu}}##. I wrote out the matrices for ##{F_{\mu \nu}}## and ##{F^{\mu \nu}}## and multiplied at the terms together and added them up, but some of the terms didn't cancel like they should have. Should I have used minus...

Hello All, I recently purchased a book on relativity called "Gravity in a Nutshell" by Zee. While it is interesting I find his conversational style to be too chatty. I prefer a little more of a "get to the point" conversational style. I'm going to be modeling the evolution of the...

I am a working professional trying to get back to some physics that I used to enjoy a couple of decades ago. I still do remember the basic calculus (integrals, partial derivatives, basic ODE) and am interested in studying General Relativity. I have a decent understanding and memory of Special...

Homework Statement Finding the maximum mass ##M_x## which can be made from a collision of identical particles with mass ##m##, in the laboratory frame, in which one particle is at rest and the other one has energy ##E##. The reaction is the following: ##a+b \rightarrow a+b+x##.The Attempt at a...

Homework Statement A rocket is flying away from the Earth with a costant acceleration ##a## in a frame in which the rocket is at rest. Finding the equation of motion (the relation between the distance from the Earth and the terrestrial time). Showing that there is a maximum time ##T## after the...

1. Homework Statement Why does the non-relative simultaneous frame have an additional term of ##v \Delta t## along with the contracted length ## L ## for ## \Delta x ##? 2. Homework Equations ## L + v \Delta t = \Delta x ## ---- (1) ## \Delta x = \gamma \Delta x' = \gamma L_{\star} ## ----...

Homework Statement In the inverse Compton scattering there is a particle, with energy ##E## in the laboratory frame and mass at rest ##m##, which collide head on with a photon with energy ##E_\gamma##. Finding the maximum energy the photon can have after being scattered. The Attempt at a...

Homework Statement P and M are each riding Ents while playing catch with two rings. P throws his gold ring with a speed relative himself that is twice the speed that M throws his silver ring relative to himself. P and M start off going with the same speed and direction, 30m apart with M in...

Homework Statement Finding the maximum scattering angle of a particle whose mass in ##m_1## which hits with relativistic velocity ##v## a particle at rest with mass ##m_2<m_1##. The Attempt at a Solution I've written the 4-momenta (p before the collision, k after the collision and the z-axis...

Hi everyone. Given: an asteroid with the mass of 50,000,000 kg, which is moving with the velocity of oh-my-god particle -- 99.99999999999999999999951% of c. Due to relativistic effects, its total kinetic energy will be 1.44 E+36 Joules (Lorentz factor = 3.2 E+11). A hypothetical particle...

Homework Statement In a reference frame ##S## there is a particle with mass ##m## and charge ##q## which is moving with velocity ##\vec{u}## in an electric field ##\vec{E}## and in a magnetic field ##\vec{B}##. Knowing the relativisitc laws of motion for a particle in an EM field, find the...

MinutePhysics is attempting to produce a series of video lessons on Special Relativity, using an approach, according to the video, that will be different and "simpler" than the traditional method that SR has been taught in schools. Since we often get questions on here about this topic...

Homework Statement In frame S particle 1 is at rest and particle 2 is moving to the right with velocity u. Now consider a frame S 0 which, relative to S, is moving to the right with velocity v. Determine the value of v such that the two particles appear in S' to be approaching each other with...

If I am wasting anyone's time, please advise so I can leave and find another source to assist me in my quest. I have been thinking about the theory of General and Special Relativity for most of my life. When I was 16 years old, I saw a documentary about Einstein and how he used his thoughts as...

Homework Statement In the inertial frame ##S'## the standard lattice clocks all emit a 'flash' at noon. Prove that in ##S##, this flash occurs on a plane orthogonal to the ##x##-axis and traveling in the positive ##x##-direction at speed ##\frac{c^2}{v}##. Homework Equations Lorentz...

Homework Statement A man is flying with a speed of 0.7c and at a height 1 km. During his flight, he measures the distance between Toronto and Montreal to be 450 km. What is the real distance between them. I don't think the answers are based on real life, they are just examples of places...

Homework Statement Find the length of a meter stick if in the laboratory frame it is angled at 60 degrees relative to the direction of motion, and it is traveling at .8 c. I have calculated gamma to be 1.667 Homework Equations Lorentz transformations The Attempt at a Solution a' = l' cos(x)...

Hello fellow physicists.Recently I imagined a particle far away from everything (infinitely away) such that there is no potential energy affecting the particle. Ep = 0 Ek = mc2δ : δ = (1-v2/c2)-1/2 L = EP- Ek = -mc2δ ∂L/∂v = vE0/c2 *δ^3 where E0 = mc2 d( ∂L/∂x)/dt = 0 ∴ vE0/c2 *δ^3 = 0 mvδ3...

Hi everyone, I'm struggling to grasp simultaneity in Special Relativity. Since I am struggling conceptually, I have posted my question here. But if you think this problem I made up modified should go to homework, I apologise (and feel free to move it). Suppose we have two light sources...

The question: If the max speed I can go in the universe is the speed of light measured from? Background: If there are three rocks in a vacuum along a line (the x axis), one is stationary (rock 1), one is moving 5 m/s in the x direction (rock 2) and one is move -5 m/s in the x...

Hi everyone, I am currently working on a project in Physics analyzing the possibility of magnetic fields protecting against radiation particles such as fully ionized nuclei or electrons. I wrote a code in Matlab that simulates a 3-D magnetic field based on a combination of wires and wire loops...