Special relativity Definition and 1000 Threads

We all know that in the lab frame observing a charge moving along x-axis, we see an electric field ##E = \frac{Q}{4\pi \epsilon_0 x^2\gamma^2}##, picking up an extra factor of ##\gamma^2## at the bottom. Assuming no external fields are present, what would the charge see in its own rest frame...

Homework Statement (a) Show ##a = \frac{a_0}{\gamma^3}##. (b) Find proper acceleration of rocket (c) Find speed as a function of time. (d) Find acceleration of second rocket. Homework EquationsThe Attempt at a Solution Part(a) 4-vector acceleration is given by ##\gamma^2 \left[...

Hi, This is not a question aimed at answering a homework problem, but since it is part of a course on Special Relativity, I believe I'm supposed to put my question here. The course itself, however, is a Dutch High School syllabus on SR, so I won't be able to link to source material. The...

Suppose there was a universe that was small, and flat, but globally it was connected like a torus. Basically, pac-man's universe (except special relativity is in effect). The space ##(\mathbb{R} \pmod{1})^3##. Does this assumed universe have a distinguished inertial frame where the...

Hi! First of all, sorry for my english, I'll try to do my best translating the exercise. I've been working on it this evening but I'm having some troubles: Problem: On the Star Wars film, there's a starship traveling at a velocity of 5c. This is nonsense, but we can assume this if we suppose...

Homework Statement A star travels in a direction transverse to the line of observation from Earth, with a speed 0.5c. It also emits light with wavelength ##\lambda_0## in the rest frame of the star. Calculate the wavelength of the light as observed on Earth, and also the angle at which the...

Time-like and light like separations between events make sense, because a particle or a light flash can travel between them. However, how can you have a space-like interval when even light cannot travel such an interval (because its velocity is not greater than c). Obviously the first event...

Homework Statement Two passenger trains A and B, each 240 m long, pass a 60 m long railroad platform in Winnepeg. The trains are moving in opposite directions at equal speeds of 0.665c with respect to the ground. Train A is traveling west and all tracks are perfectly straight. A) From the...

Has anyone ever seen KE derived this way? The only non-classical assumption is that mass = Energy/c^2 (I know, that's a big one) and that it accumulates as mass as the object is accelerated. (sorry for the plain text formatting, I need to learn how to do it right, I may reply with my first try)...

[Mentor's note: this post does not use the homework template because it was originally posted in a non-homework forum.] ----------------------------- A ship (attached to reference frame S') is passing us (standing in reference frame S) with velocity v= 0.933c. A proton is fired at speed...

I'm looking for an introduction level books on special relativity. My goal is to get familiar with Dirac equation as I'm into atomic physics in this semester. My background on the subject is that I have taken a course in the past which was designed to be kind of introductory to modern physics in...

I'm reading An Intro to GR, Hughston and Tod, it says that in GR the idea is that the geometry of st varies from point to point, represented by allowing the metric to vary over space-time. It uses a (+,-,-,-) signature and so ##proper time=ds^{2}##. It then makes the comment that proper time...

Homework Statement 1. You observe two events to occur simultaneously. A friend is moving with respect to you. The friend will see : The event the friend is moving towards occurs first, in their perspective The order of the events is random and cannot be predicted The events occur...

Lorentz transformation. Time separation between two events in system S and system S' is given by Lorentz transformations \Delta t'=\frac{\Delta t-\frac{u \Delta x}{c^2}}{\sqrt{1-\frac{u^2}{c^2}}} If event 2 is caused by event 1 in system S then ##\Delta t=t_2-t_1##. But it is possible to choose...

s2 = t2 - x2 - y2 - z2 This equation is covariant (Lorentz covariance). The interval "s" is invariant (Lorentz invariance). Can you derive everything in special relativity from these facts? Or am I mistaken about that?

Assume a light was emitted from the origins of two frames in relative motion. Assume the light acquired some position (x,y,z,t) in an F frame. Then map that point using the lorentz transformations to (x',y',z',t') in a F' frame. Can anyone prove under all conditions that the the light...

Suppose frame ##S^\prime## moves in the positive ##x## direction at ##v## with respect to frame ##S##, and frame ##S^"## moves in the positive ##y## direction at ##v^\prime## with respect to frame ##S^\prime##. Then, ##E^\prime_x=E_x## ##E^\prime_y=\gamma(E_y - vB_z)## ##E^\prime_z=\gamma(E_z...

How to combine special relativity and maxwell equation as simple as possible without going into qed? Sorry for such a absurd request as I am not smart at all.

I want to prove that the transformation equation for electric field holds, namely Ex = Ex', where Ex is the x component of E field in S frame and Ex' is that in S' frame, for the special case in which the charged particle has a vertical velocity Uy' in the S' frame (Ux' = Uz' = 0). It is already...

While trying to understand special relativity, i came across the following explanation several times: Imagine a train moving at c/4 from left to right. If a person A, inside the train standing near the back of the train, flashes a light, the light is supposed to travel in the direction of the...

In the light of this policy https://www.physicsforums.com/threads/what-is-the-pfs-policy-on-lorentz-ether-theory-and-block-universe.772224/ , is it now considered acceptable to teach relativity by starting out with Lorentz Ether Theory (LET) and its Newtonian time which appears to be...

Homework Statement This is a relativity problem: [/B] A tree and a pole are 3000 m apart. Each is hit by a bolt of lightning. Mark, who is standing at rest midway between the two, sees the two lightning bolts at the same instant of time. Nancy is flying her rocket at v = 0.5c in the direction...

I seem to be missing something fundamental about length contraction in SR. I would be grateful if someone can point out the error in the following logic. Suppose I have a method to measure lengths of objects in the following manner: I place a mirror at the right end of the object, send a light...

Are the general principles of string theory “the properties of fundamental particles are due to their unique vibrational pattern of strings in 10 or 11 or 26 dimensions” incompatible with both general and special relativity? due to an observer would be able to detect changes in properties of...

Hi everybody, I'm learning Special Relativity, and probably ok with four vectors, the metric equation, the Lorentz Transform, and the Doppler shift, etc., but enough about me. I'm still a little confused about time dilation. In several hypothetical examples of SR that I have seen, two...

I have been asked about time dilation which I thought I understood, but maybe you can help me provide an answer? If a spaceship is traveling at 0.866c then time will slow by a factor of 2 due to the speed the spaceship has. Why? If it is alone in space, light years away from any other body...

wiki says "Experiments that attempted to directly probe the one-way speed of light independent of synchronization have been proposed, but none has succeeded in doing so" Here's a proposed experiment which I could not find any evidence of this being performed before.. Central light source...

Homework Statement A train is traveling in the x direction at a speed of v. On the train, a passenger is playing darts and fires a dart in the y direction with a speed of Uy. The dart hits the target and stops abruptly. What is the difference in the mass of the dart as observed by a person on...

Can we just combine special relativity and Newtonian gravity? If cannot, why is it intuitively not possible? If can, why is the intuition behind it? Because if can, there seems to be a need for a mediator of force for gravity which can only travel at light speed.

Homework Statement The new earth-Pluto SuperShuttle line boast that it can take you between the two planets (which are about 5.0 h apart in distance) in 2.5 h according to your watch on board the shuttle. Assume that the shuttle travels at a constant velocity. a.) What time interval must the...

Homework Statement [/B] 1.) A muon is created by a cosmic ray interaction at an altitude of 60km. Imagine that after its creation, the muon hurtles downward at a speed of 0.998, as measure by a ground-based observer. After the muon’s “internal clock” registers 2.0μs , the muon decays? a.) If...

Homework Statement A particle of rest mass m0 collides elastically with a stationary particle of equal mass and scatters at angle θ. The incident particle has kinetic energy T0 before the collision and T1 after the collision. (a) Show that T12 (2m0c 2 + T0) 2 = p02 p12 c4 cos2 θ. (b) Using the...

Homework Statement A rocket, initially at rest, propels itself in a straight line by giving portions of its mass a constant (backward) speed vout relative to its instantaneous rest frame. (a) Is rest mass conserved in this process? (b) Show that m0du′ = −dm0 vout, where m0 is the rocket’s...

So my question arises from the whole time dilation thought experiment where one person stays on Earth the other speeds off in a rocket at near light speed. Upon return of course the one in the rocket is younger, etc. The reason I bring this up is how do we determine who is actually moving...

As I understand it, faster than light communication is not possible, but I have a specific example which concludes that it is and I'm trying to find the mistake. The scheme uses two things 1) An entangled Bell pair ## | \phi \rangle = | 0 0 \rangle + | 1 1 \rangle## ( neglecting normalization )...

I've already completed most of the question, it's an add on at the end that has stumped me. I've calculated using time dilation the difference in ages between the two twins, Joe traveled at v = 24/25 (c=1 units) to a planet for 7 years in HIS reference frame and returned at v = 12/25 The...

Homework Statement A particle and its anti-particle are directed toward each other, each with rest energy 1,000 MeV. We want to create a new particle with rest energy 10,000 MeV and total energy 100,000 MeV. What must the speed of the particle and antiparticle be before the collision. ERest0 =...

I'm on my first pass through special relativity and I can't remember the math that would take me from: (∂τ/∂x') + (ν/(c2-ν2))(∂τ/∂t) = 0 To τ = φ(ν)(t - (ν/(c2 - ν2))x') Any help would be appreciated. Also, sorry for the terrible format, but I haven't taken the time to figure out how to do...

If velocity is relative and dependent on an observer then how does an isolated object "approach the speed of light"? Approaching the speed of light relative to what? Does the ubiquitous constant velocity/closed compartment analogy break down at relativistic speeds? If one were traveling "near...

We know that when a rigid frame, say a rocket undergoes constant proper acceleration, its worldline is hyperbolic. The equation is given by: x^2 - c^2t^2 = \left( \frac{c^2}{a_0} \right)^2 Suppose P is such a worldline and worldine can also be written as: I understand how these are...

Homework Statement Suppose a constant force F acts on a particle of mass m initially at rest. (a) Integrate the formula for acceleration \vec{a} = \frac{\vec F}{\gamma m} - \frac{\vec v}{\gamma mc^2}(\vec F \cdot \vec v) where \gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} to show that the speed...

Homework Statement (a) Find matrix element ##M_{ij}## (b) Show that ##x^j## is an eigenvector of ##M_{ij}## (c) Show any vector orthogonal to ##x^j## is also an eigenvector of ##M_{ij}## Homework EquationsThe Attempt at a Solution Part(a) [/B] \frac{\partial^2 \Phi}{\partial x^i x^j} =...

Homework Statement Alphonse decides to go for a joy ride in his Astro-Scooter. He maintains a speed of 0.604 c and is gone for 6.53 years according to his ship's clock. His twin brother Carl says he is full of beans. According to Carl, how long has Alphonse been gone? To=? T=6.53 years...

Homework Statement Consider the usual two inertial frames S and S' in standard configuration. In 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 (de-Broglie-) speed...

Lets suppose we have a observer O and two objects A and B a speed is 0.5c and B speed is 0.3c than we can calculate other relative speed acoording to these informations.We know that (according this info B sees A going to 4/17c but we can pretty sure that's true because we can't ask. him How...

I hypothesize that I can measure an increase in background radiation due to cosmic rays from ground level in Utah to 10,000 ft altitude with a Geiger Muller set-up. I feel that I have enough information to order equipment now (a working knowledge of gm tubes, energy levels of & the special...

I have studied most of the concepts of Newtonian mechanics and understood the calculations and derivations involving the concerned formulae. I have a basic knowledge of calculus (differentiation of products along with differentiation of trigonometric, logarithmic, exponential and implicit...

I understand the theory of special relativity and the mathematics which support it. I even understand that the time dilation has been proven. Therefore I am going to ask a question which on first blush may appear that I disagree with it but that is not the case. The question I can not seem to...

In QM, the energy operator is proportional to the time derivative E ~ d/dt So higher energy particles have higher frequencies, i.e. their wave functions change more often per time than when at rest But in SR, higher energy particles seem to exist in slow motion, appearing to age little How...

Homework Statement An astronaut went to sun from Earth by a rocket. According to the clock in the rocket, the traveling time was 5 minute. What was the velocity of the rocket? ( Earth is 8 light minute away from sun) Homework Equations t = \frac {t_0}{\sqrt {1 - \frac{v^2}{c^2}}}The Attempt at...