Special relativity Definition and 1000 Threads

Homework Statement An electric dipole instantaneously at rest at the origin in the frame K' has potentials \Phi'=\mathbf{p}\cdot\mathbf{r}'/r'^3 and \mathbf{A}'=0 (and thus only an electric field). The frame K' moves with uniform velocity \mathbf{v}=\vec{\beta }c in the frame K. Show that in...

Hi, If a particle is within 2 m/s of the speed of light (like at CERN) and then more energy is transferred to the particle, where does this energy go? Some sources I have read talk about relativistic mass getting bigger and approaching infinity as a particle approaches 'c'. However, this source...

I am having a hard time trying to understand this transformation from lorentz:https://imgur.com/a/WYWMO (You should ignore the spanish part and just focus on the math). I can’t understand well why they turn into what you can see in the second picture, when taking really small values of x...

Hello. I want to clear a doubt on Special Relativity, time dilation and clocks. If we get an accurate clock and make it orbit the, for example, Earth very, very fast, will the actual mechanical clock lag behind from the accurate clocks on Earth? The thing in this question is about the actual...

Homework Statement Anna and Bob are both born just as Anna's spaceship passes Earth at 0.9c. According to Bob on Earth, Planet Z is a fixed 30 ly away. As Anna passes Planet Z on her continuing outward journey, what will be (a) Bob's age according to Bob, (b) Bob's age according to Anna, (c)...

Hi, Can someone please anlayse the visual effects for light travel in the documentary 'Journey to edge of the universe' Especially around the 43:12 and the 1:02:20 mark. Can you also tell me if it is or is not an accurate depiction of what we should be seeing theoretically?

I try to find the formula of dilation of time between a reference frame (R') moving at a speed v and a fixed observer in (R). For this, I take the example that we often find as a demo : that of a train in which a light beam is emitted vertically (in the train): this vertical trajectory in the...

You are launched upward inside a railway coach in a horizontal position with respect to the surface of Earth, as shown in the figure. After the launch, but while the coach is still rising, you release two ball bearings at opposite ends of the train and at rest with respect to the train. a)...

A non-moving observer is looking at two different rockets in space. One rocket is moving at a steady velocity of 0.5c, and the other rocket is currently moving in 0.5c but has steadily accelerated from 0.3c and will continue accelerating until it gets to 0.7c. Assuming that there is no...

How can volumes and hypervolumes be related to Einstein's theory of special relativity and to quantum mechanics? Also, can volumes and hypervolumes of objects be used for modeling how different scenarios can change over time? Oh yeah, and hi my name is Sasha Jaffarove!

Homework Statement Homework EquationsThe Attempt at a Solution it is known that ##a_0 ##is the proper acceleration ## a= \frac{a_0}{\gamma^3} ## hence integrating it gets ## v = \frac{a_0t}{\sqrt{1 + (\frac{a_0 t}{c})^2}} ## but this is in terms of t how to make it in terms of t'

If a frame S' moves with velocity v in x direction wrt S, and you have v = 0.5c, u_x' = -0.9c and u_y' = 0.9c then it seems you find that u_y = 1.417c, greater than c. The relevant formula is: u_y = u_y'/(gamma * [1+v u_x' / c^2]) Apologies for formatting. Details: gamma = 1/sqrt(1-v^2/c^2)...

Homework Statement My textbook states: Since the number of particles of dust is conserved we also have the conservation equation $$\nabla_\mu (\rho u^\mu)=0$$ Where ##\rho=nm=N/(\mathrm{d}x \cdot \mathrm{d}y \cdot \mathrm{d}z) m## is the mass per infinitesimal volume and ## (u^\mu) ## is...

Hello, I'm self-studying Ta-Pei Cheng's Relativity, Gravitation and Cosmology. Problem 2.8 is the following: Two spaceships traveling in opposite directions pass one another at a relative speed of ##1.25 \times 10^8## m/s. The clock on one spaceship records a time duration of ##9.1 \times...

Let's assume that a and b charges are moving. now in our lab frame there will be a electric+magnetic force whereas in a rest frame of either of the charges, there will be only an electric force. So, two inertial observers will measure different forces?

I've commonly heard it said that Lorentz invariance is equivalent to saying that special relativity is obeyed, although I also recall discussions arguing that this is not precisely and technically correct, although the two concepts heavily overlap. I also understand that Lorentz invariance has...

In Schutz's A First Course in General Relativity (second edition, page 45, in the context of special relativity) he gives the scalar product of four basis vectors in a frame as follows: $$\vec{e}_{0}\cdot\vec{e}_{0}=-1,$$...

Homework Statement Our galaxy is about 10^5 light-years across, and the most energectic particles known have an energy of about 10^19 eV. How long would it take a proton with this energy to traverse the galaxy as measured from (a) the galaxy and (b) the particle? Homework Equations I...

Homework Statement Before the discovery of the neutron, it was proposed that the penetrating radiation produced when beryllium was bombarded with alpha particles consisted of high-energy &gamma rays (up to 50 MeV) produced in reactions such as α + 9Be --> 13C + γ a.) Calculate the Q value for...

Hi There, I've been spending some of my free time learning about Quantum Mechanics. This was all going somewhat smoothly, until I encountered something known as "Entanglement Swapping" while learning about loophole free bell tests, such as the one conducted by Hensen et al at TU Delft in 2015...

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...

Pardon me if this has been asked before, but I'm confused with the implication that SR makes, that there is no objective moment of present. Do the science still believe that the time flows (i don't mean the arrow of time, but the phenomena of flowing/passing, eq. flowing of a river)? I mean, how...

Homework Statement A visit to Regulus is on my bucket list. However, it is 77 light years away. Assuming I will live only another 40 years, can I make it to Regulus? How fast would I have to travel (at constant speed) to get there in 40 years? Homework Equations t1 = t0...

Let's assume that a light source is moving parralel to x-axis and is in point x,y,z in lab frame. Suppose it emits a light ray. In the rest frame that coincides with the lab frame, the light source is in point x',y and z. However, because of relativistic aberration the two light rays will make...

Hello, In my free time, I've been learning about an eclectic range of topics (ie. French History, Kinetic Theory etc.). Most recently I've been focused on Quantum Mechanics, which happens to be most complex topic I've ever looked at. Typically I write up summaries after reading from various...

Imagine yourself to be bat. You can't see anything. You don't have eyes. All you can do is echolocate, using ultrasound. Now imagine something is moving away from you faster than the speed of sound. Can you locate it ? Can you perceive its existence ? If the answer is yes, how ? If no , then...

Hello! If energy bends spacetime, then an object moving at high velocity will bend spacetime a lot around it due to its really big kinetic energy. It follows, that an object can become a black hole at extremely high enough velocities. But, since velocity is relative, we can find an observer for...

Is it fair to say that the photon does not follow the rules of Special Relativity? I ask this because the photon relative to all other frames of reference has zero mass even though it is traveling at the speed of light. If we increase the speed of any other particle to the speed of light its...

Hi all, I have a problem to fully understand how we can apply Special Relativity to a system where one observer is still in the center, and other one is moving in a circle around. For example, like a satellite orbiting Earth. In case of GPS, the clocks carried by satellite are running slower...

I'm working on semiconductor physics and cyclotrons. There's an article that I am trying to understand, but am having difficulties matching with experiment. I asked a question on an electronics site, but apparently the physics is too advanced. The relativity article which sparked my interest...

I have a random paradox I seem to have found with three colliding observers, though to explain it properly I'm going to use a bit of visual aid and a bit of abstracting it from the math (or setting the math so that it works according to my example). For anyone who wants the TLDR, read this...

Hi, I have yet another question in the field of the special relativity theory. I always thought that the derivation of the relativistic mass is trivial. But I discovered that there is some complexity due to the transverse and longitudinal relativistic mass derivation. I saw a thread where...

Let's assume that a disk is rotating with relativistic speed in a frame. We can find the velocity of a particle using v=rw formula. However, what is the r in this formula? is it the radius of the disk in rest frame or in the lab frame?? And Is the magnitude of velocity same for all points of...

Hello everyone, Reminder: The key of the explanation of the "twin paradox" resides in the acceleration. We know that the time runs slower for the twin in the spaceship (since it was accelerated)...

I am trying to get this idea of Time dilation understood. If there exists only two objects in a Universe and one object is stationary and the other object is moving at 99 % the speed of light. Their clocks were both synchronized when both objects were stationary relative to each other. Then the...

Homework Statement I have noticed that in some calculations they use $$ \vec{\nabla}\cdot\vec{u}=\frac{1}{V}\frac{dV}{d\tau}$$. I would like to derive it. Homework Equations ##\vec{u}=(\frac{dt}{d\tau},\frac{dx}{d\tau},\frac{dy}{d\tau},\frac{dz}{d\tau})## ##\vec{A}\cdot\vec{B}=A^{\mu}B_{\mu}##...

Problem statement: A rocket propels itself rectilinearly by giving portions of its mass a constant (backward) velocity ## u ## relative to its instantaneous rest frame. It continues to do so until it attains a velocity ## v ## relative to its initial rest frame. Prove that the ratio of the...

Homework Statement Special relativity: A rod traveling with the relativistic velocity of 0.866c moving towards a garage. The length of the rod is L, that of the garage is L/2. From the reference frame of the garage, we find the value of Lorentz factor = 2 we say that rod would fit inside garage...

Consider two bodies A &B are moving apart with a velocity V due to the expansion of space. According to an observer in A the body B is moving away and an observer in B feels the body A is moving apart. Can some one answer in which body the time dilates and why?. ( I am specifying once again that...

So, I am a newbie in quantum mechanics, took modern physics last fall for my physics minor. I know that Schrodinger based his equation based on the equation K + V = E, by using non-relativistic kinematic energy (P2/2m + V = E) p becoming the operator p= -iħ∇ for the wave equation eigenfunction...

Homework Statement A train of length L moves at speed 4c/5 eastward, and a train of length 3L moves at speed 3c/5 westward. How fast must someone run along the ground if he is to coincide with both the fronts-passing-each-other and backs-passingeach-other events? Homework Equations Velocity...

Suppose I'm an observer out in space and 30 km from me there's another observer, who is static with respect to me. Let's say my name is A and the other is B. We're both far far away from all the cosmical objects that might have a gravitational influence on us. We both notice a spaceship flying...

Dear All, I am doing the Special Relativity course at World Science U, and came across this question which I got wrong: When 100 nanoseconds have elapsed on traveling Gracie's watch, she immediately stops, turns around, and heads back toward George at the same speed of her outbound journey...

I am trying to understand why the special relativity is not suitable for describing the gravity. Consider a counterexample assuming it is the suitable and the space-time containing a gravitational mass is flat. Then one could describe the acceleration of a test particle from his inertial frame...

Dear All, Just wanted to share this excellent free Special Relativity online course I came across by Brian Greene, which I believe is one of the best around. Not sure if it's been shared before here. Special Relativity — World Science U, by Brian Greene...

Homework Statement A cone has half angle θ0 and lateral surface area S0 in the frame in which the cone is at rest. If someone moves at relative speed β=v/c along the cones symmetry axis, what surface area will they see for the cone? Homework Equations I believe the lateral surface area of a...

Two spaceships with their engines shut off and identical radio receiver-amplifier-reemitting devices are in the empty space, very far from each other and from any celestial body. The lag time from absorbing to reemitting in the device is vary small compared to the return time of the signal (2t)...

Context The following is from the book "Ideas and methods in supersymmetry and supergravity" by I.L. Buchbinder and S.M Kuzenko, pg 56-60. It is about realizing the irreducible massive representations of the Poincare group as spin tensor fields which transform under certain representations of...

I think special relativity would disallow our universe from having the structure similar to an ant on a sphere. What I mean is that it can't be possible to travel in a constant direction and to come back to your original location. Suppose there is an observer S on a planet and an observer S'...

This may seem like a stupid question, but i can't get my head around this so please bear with me. I just looked at the derivation of Dirac equation and my question is: do the solutions for a free particle obey special relativity? because if yes why? I mean I thought using E2=(mc2)2+(pc)2 would...