Special relativity Definition and 1000 Threads

Homework Statement A particle of mass m is moving along the positive x direction with momentum p and energy E It collides with a particle of the same mass at rest to form a new particle of mass M. Show that M^2 = 2m/c^2 * (E + mc^2) 2. Homework Equations E^2= p^2c^2 + m^2c^4 The Attempt...

what makes the light moving and why it moves with this speed 299792458 mps?

Homework Statement i)A police spaceship P is chasing another spaceship A. Both ships have velocities βP = βA = 3c/5 as measured along the x-axis in the Solar System reference frame O. The police ship is a distance L = 1 light-second (i.e. the distance traveled by light in one second) behind...

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 !

In his little book for the layman, Seven Brief Lessons on Physics author Carlo Rovelli states: What is it about SR which is incompatible with gravity-as-a-force?

Its been a few years since I have done any special relativity so I am a bit rusty, need help with either my working/understanding or if correct, making sense of my answer. This is not CW, just a question from a past exam paper that I am using as preparation. 1. Homework Statement Street light...

Homework Statement Hi all, I'm given an electron with momentum 2.0*10-20kgm/s and was asked to convert the momentum into units of Mev/c then calculate the total energy of the electron, the lorentz factor and the speed of the electron, I did this successfully but then the question got confusing...

Can a sphere or disk rotating with uniform speed follow born condition of rigidity?

Two clocks A and B are orbiting a non-rotating planet. Each clock periodically transmits its current time value via a radio signal and the other can receive that value. Their orbits are in closely-spaced parallel planes and both orbits are the same distance from the planet. The two clocks are...

While studying about some physics things, I came to know a term Relativistic beaming. I looked up in wiki and found a pretty decent article which gives you an equation where the real and apparent luminosity are related by a factor of (Doppler factor)^3-a where a is spectral index. But where's...

I was reading about the Ehrenfest Paradox and it got me thinking about something (that I think is) similar: Suppose we take a large, flat, and rigid disk, and we attach to various parts of it a number of clocks (some very close to the center of the disk, some along the edge, others in between)...

I'm reading the book "Quantum Field Theory and the Standard Model" by Matthew Schwartz and I'm finding it quite hard to understand one derivation he does. It is actually short - two pages - so I find it instructive to post the pages here: The point is that the author is doing this derivation...

Homework Statement Einstein developed much of his understanding of relativity through the use of gedanken, or thought, experiments. In a gedanken experiment, Einstein would imagine an experiment that could not be performed because of technological limitations, and so he would perform the...

Homework Statement Consider the process of decay of a muon into one electron, one electron antineutrino and one muon neutrino using the Fermi theory. Assume the matrix element is, ignoring the electron's and the two neturino's masses, |\mathcal{M}|^2 = 32G_F^2(m^2-2mE)mE being E the electron...

Homework Statement Muons of Kinetic energy 'E' are produced in collision with a target in a laboratory. The mass of a muon is ##106MeV/c^2## and its half life in it's rest frame is ## 1.4 * 10^{-6}## in its rest frame. what should be the minimum KE such that more than half of the muons...

I know variations of these have probably been asked numerous times before, but I'm having trouble with this specific scenario. Imagine the classic Train Paradox, except instead of lighting strikes we have an observer at the centre of the train shooting laser pulses towards the rear (Event E1)...

Hello! I have a small problem with a task professor gave us. I tried many options (you will see below) but I cannot seem to get the right solution. Any advice or guideline how to solve this would be really helpful. In advance I thank you for helping me. Homework Statement Our professor of...

1. The problem statement, all variables, and given/known data A car of proper length 12m is being driven at 0.9c through a garage of proper length 6m. The garage has a front and back door. The garage owner, Joe, says that the car will fit inside the garage with no damage to it, albeit for a tiny...

Homework Statement Plane A flies with speed 0.6c chasing plane B which speed is 0.4c . Both speed is measured by observer on Earth. Then, plane B fires a small rocket which rest mass is 10 kg towards plane A. Rocket speed is 0.2c relative to plane B where c equals the speed of light in vacuum...

Homework Statement A spaceship moves away from Earth at 0.9c and fires a probe in the same direction as its motion at 0.7c. What is the probe's velocity relative to Earth? Homework EquationsThe Attempt at a Solution The Lorentz velocity transformation is ##v_x' = \frac{v_x -...

Hello, I read that satellites is effected by the time dilation caused by gravity and also by that one from special relativity. And so there is a need to prepare the onboard clock to ensure that the time is synchronized with a clock on Earth. But why is this effect not symmetric? The...

As far as I understand it, the Lorentz factor ##\gamma(\mathbf{v})## is constant when one transforms between two inertial reference frames, since the relative velocity ##\mathbf{v}## between them is constant. However, I'm slightly confused when one considers four acceleration. What is the...

Homework Statement You approach an enemy ship at a speed of 0.5c measured by you, and the ship fires a missile toward your ship at a speed of 0.7c relative to the enemy ship. What speed of the missile do you measure, and how much time do you have measured by you and the enemy ship before the...

Given a massive particle traveling freely. Also assume that it is in a momentum eigenstate - a pure unmodulated sine wave in position space. In non-relativistic quantum mechanics, the phase velocity for that particle would be greater than the velocity of light. Does the phase velocity for...

Homework Statement [/B] The problem is as follows: in a reference frame there is one electron at rest and one incoming positron which annihilates with the electron. The positron energy is E and two gamma rays are produced. Find first the energy of the photons in the center of mass frame as...

Special relativity states that the speed of light is constant for all the references, as long as they are not accelerating. For example, the speed of light would be c for a train moving linearly with a constant speed and would also be c for an observer who's not moving at all (I took the Earth...

Two chunks of rock, each having a mass of 1.00 kg, collide in space. Just before the collision, an observer at rest in the reference frame of a nearby star determines that rock A is moving toward the star at 0.800 c and rock B is moving away from the star at 0.750 c . If the rocks stick...

The Lorentz transformation matrix may be written in index form as Λμ ν. The transpose may be written (ΛT)μ ν=Λν μ. I want to apply this to convert the defining relation for a Lorentz transformation η=ΛTηΛ into index form. We have ηρσ=(ΛT)ρ μημνΛν σ The next step to obtain the correct...

Homework Statement (a) A spaceship at rest in a certain reference frame S is given a speed increment of 0.50c. Relative to its new frame, it is then given a further 0.50c increment.This process is continued until its speed with respect to its original frame S exceeds 0.999c. How many...

Homework Statement Homework Equations Gamma factor: $$\gamma = \frac{1}{\sqrt{1-\beta^2}} $$ Lorentz contraction $$l'=\frac{l}{\gamma}$$ Trig: $$ cos\theta = \frac{adjacent}{hypotenuse}$$ The Attempt at a Solution I have all the quantities but the algebra doesn't seem to work out...

Hi people, I have a question about the frame of references. Let's have an example: First case: Jill on rocket and Jack stationary on Earth. Jill moves relatives to Jack 0.6c (1.8*10^8m/s). The distance is 18*10^8m. At the zero time Jack and Jill synchronize their clocks. Then Jill starts to...

Consider at stationnary radar at the origin ##z=0## and a target (speed ##v##) moving along the ##z## axis and away from the radar. The radar is sending plane waves (frequency ##f_i##) to the target and they come back to the radar (the radar is then both an emitter and a receiver). I am...

I'm having some confusion about the creation of magnetic field lines. How I understand it so far, is that a magnetic field is basically an electric field viewed from a relative point. I don't have a great understanding so far, as I just started to learn about it, but I've learned that objects...

Hello all, I have a question that's been bothering me the last few days and wasn't sure where to turn. Recall the original Special Relativity thought experiment: A spaceship travels at constant velocity v, moving in the positive x direction. An observer on the spaceship emits a photon directly...

I just came across this recently released title by David Morin, "Special Relativity: For the Enthusiastic Beginner". If its anything like Morin's past books, it'll be excellent for self studiers. https://www.amazon.com/dp/1542323517/?tag=pfamazon01-20

In the context of General Relativity spacetime is a four-dimensional Lorentzian manifold M with metric tensor g, its Levi-Civita connection \nabla and a time orientation vector field T \in \Gamma(TM). In this context I've seem the following three definitions: A coordinate system is a chart...

Let's assume there are two observers. Observer B is at rest and observer A is in a spaceship which has transparent walls. A draws line of 1 meter. When A arrives near B, B draws a line of 1 meter. And sees that A's 1 meter is shorter than own 1 meter. before forget i should say that meter is...

In my infamous simulation of the twin paradox, i assume a near instantaneous acceleration, with the results being almost identical with the "real" thing sub some extremely small values which you could not see with the naked eye anyway. But i might want to take the simulation a step further, to...

I have some issues understanding the following thought experiment: Suppose you are standing still, and two balls are moving towards you from opposite direction. From your own reference frame, Ball A is ##10^5## m away from you, moving towards you from the left with speed ##0.8c##, and Ball B is...

I'm doing some special relativity exercises. I have to find $$x(t), v(t)$$ of a charged particle left at rest in $t=0$ in an external constant uniform electric field $$\vec{E}=E_{0} \hat{i}$$, then with that velocity I should find the Liénard–Wiechert radiated power. I will show you what I did...

This question based on the site located here: http://galileo.phys.virginia.edu/classes/252/srelwhat.html The question is: If the object (spaceship) moving close to the velocity of light and I'm as a static object. The time goes slower in the object moving with constant velocity (inertial frame)...

As per the above figure coil A is situated inside a magnetic field caused by small accelerating objects B which in turn are causing the larmor frequency in coil Object C or train of objects C have quadruple movement and are rotating around the coil A giving out gravitational waves. Objects C...

Homework Statement While not explicitly a homework question, I am having some trouble with deriving expressions for the center of mass energy in a fixed target experiment versus a collider experiment. The question is effectively, "Derive an expression for the center of mass energy in a fixed...

Let's assume that a system has zero total momentum. The following relationship between mass and energy should apply: E=mc^2. If a system is overall at rest, does that mean that any internal changes to that system, assuming they leave the system with non-negative mass, will not be able to...

Homework Statement (a) Light waves satisfy the wave equation ##u_{tt}-c^2u_{xx}## where ##c## is the speed of light. Consider change of coordinates $$x'=x-Vt$$ $$t'=t$$ where V is a constant. Use the chain rule to show that ##u_x=u_{x'}## and ##u_{tt}=-Vu_{x'}+u_{t'}## Find ##u_{xx},u_{tt},##...

Homework Statement Suppose that A', B', and C' are at rest in frame S', which moves with respect to S at speed v in the +x direction. Let B' be located exactly midway between A' and C'. At t' = 0, a light flash occurs at B' and expands outward as a spherical wave. (A', B', and C' are all on...

Homework Statement The rockets of the Goths and the Huns are each 1000 m long in their respective rest frame. The rockets pass each other, virtually touching, at relative speed of 0.8 c. The Huns have a laser cannon at the rear of their rocket that shoots a deadly laser beam at right angles to...

On the following link it is mentioned that this experiment tests special relativity. Can someone please explain how it does that? http://www.sciencemag.org/news/2016/12/deep-probe-antimatter-puts-einstein-s-special-relativity-test

Dear All, I am trying to find some good books that provide a comprehensive one-stop education for special and general relativity, with concise coverage of key fundamentals of the maths involved. It is intended for self study, and I do not have strong fundamentals on advanced physics / maths...

We know that while deriving the special theory of relativity formulas like Lorentz Transformation, Length contraction, Time dilation etc, we assume that there is an observer at each point of the space in a certain frame and all these observers contain synchronized clocks and scales. But what if...