Relativistic Definition and 1000 Threads

So the thing I have issues with in this problem is that it's about 2 particles traveling relative to each other. Been going though the basics of relativity, relativistic lengths, times, kinetic energy, work and force. But this problem states two particles and I'm not sure how to approach it. The...

Homework Statement find series expansion of relativistic energy formula, At what speed is there a 10% correlation to the non relativistic KE. Homework Equations $$ E=\frac{mc^2}{\sqrt(1- \frac{v^2}{c^2})} = mc^2 + \frac{1}{2}mv^2 + ... $$ The Attempt at a Solution I found the series above...

I suppose I am not the first to notice this, but if you are going at say, 0.999c you will have shrunk by a factor of about 20 and everything else on the craft. Suppose the spacecraft is 2000 meters long, at 0.999c it will shrink to about 100 meters long. So suppose a person 2 meters tall...

Hello, I want to know if energy added to moving objects is quantized. Kinetic energy of an moving object is given as KE = (γ - 1) mc2 , where γ is 1/√(1-v2/c2). And quantum theory talks about any energy always being quantized. So can the KE in moving objects be quantized?

Homework Statement : 1) Consider 3rd orbit of He+ (Helium), using non-relativistic approach, the speed of electron in this orbit will be [given K = 9 x 109 constant, Z = 2 and (hfPlanck's Constant) = 6.6 x 10-34 J s] A) 2.92xl06m/s B) 1.46xl06m/s C) 0.73xl06m/s D) 3.0xl06m/s[/B]Homework...

I have been coding a speed of light simulator and I am having a bit of trouble with a few aspects of the project. My first question is: Are the length contraction and relativistic aberration formulas BOTH needed in my calculations or does the relativistic aberration formula already account for...

Homework Statement Given that ##Q' = \int d^{3}x \bigg[ \rho \big( \frac{vx}{c^{2}},x,y,z \big) - \frac{v}{c^{2}} j^{x} \big( \frac{vx}{c^{2}},x,y,z \big) \bigg]##, show the following: ##\frac{dQ'}{dv} = \frac{1}{c^{2}} \int d^{3}x \bigg[ x \big( \frac{\partial \rho}{\partial t} -...

I'm interested in the derivation of relativistic Boltzmann equation from entropy after reading Scott Dodelson's wonderful cosmology book. Does anyone know of any good readings for this? The usual way of doing things in classical mechanics is to assume \frac{dN}{dt}= 0 and go from there; but...

1. A distant camera is taking an image of a bullet of proper length l_0 and velocity v. The bullet is moving on a straight line which is parallel to the ruler (a bit behind the bullet, when it is watched from the camera). An angle between the velocity vector and the line that connects the camera...

I haven't read these articles, but it seems that the claim is that there are spherically symmetric static space-times, which can describe compact isolated objects with arbitrarily large masses and arbitrarily small radi without being black holes. That doesn't seem right. What am I missing...

Homework Statement Find the observed frequency ##\nu## in terms of proper frequency ##\nu_0##, speed ##v## and radial velocity component ##v_r## for a source moving at velocity ##\vec v## with respect to the observer. Now consider an observer in frame S where the source is seen moving at...

Okay, I tried searching for this in the forums and didn't really find what I was looking for. So, I'll start a new thread and if anybody has seen this before, feel free to drop a link to an old thread or whatever. Many of our older space probes use/used thermoelectric radioisotope batteries to...

While linear accelerating an electron, with direction of acceleration being the ##z+## axis of the spherical coordinates, its radiation in angular distribution form is(according to this tutorial: http://farside.ph.utexas.edu/teaching/em/lectures/node132.html) ##\frac{dP(t')}{d\Omega} =...

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[...

Homework Statement If a mass of 1 kg has a velocity of 0.7c, what is the relativistic momentum? Homework Equations I don't know what equation to use...Please help..

From special relativity, we know that t=t0/(1-v2/c2)1/2 For the object moves as a circle with radius r, the velocity v = w r Therefore, time varying along radius r as t=t0/(1-w2 r2/c2)1/2 In this case ds2= dr2- c2 dt2 = dr2- c2 dt02 /(1-w2 r2/c2) Since object will move in shortest path in...

i need thee the derivation of relativistic doppler shift. i found its derivation in the book of Serway, but it is not in detail and step by step. in the book there is given that: can anyone give me the step after eq#1.13? how eq#1.13 converted in the form of eq#1.14?

While reading an online tutorial (http://www.phy.duke.edu/~rgb/Class/phy319/phy319/node146.html) about deriving the relativistic generalization of Larmor Formula, I got some problems with the steps. Basically with an assumption ##\beta \ll 1## the author gets ##Power = \frac{e^2}{6 \pi...

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)...

I understand that slower particles will be subject to the electric fields of the material for longer and lose energy, but why should relativistic particles also lose energy quickly? The only idea we have is that there is a lorentz contraction of the electric field, BUT why then would that...

There are plenty of examples where someone derives the magnetic force from a current carrying wire on a moving charged particle by looking at the frame of the particle and finding that the current has Lorentz contracted in such a way as to produce an electric field in an otherwise neutral wire...

I'm hoping that someone can help me understand a topic on page 86 of Feynman's "Six Not-so-easy-pieces", in the "4-4 Relativistic mass" section. He says, "It is an interesting exercise to now check whether or not Eq.(4.9) is indeed true for arbitrary values of w, assuming that Eq.(4.10) is the...

Okay these are kind of layman questions but I appreciate the time and effort for answering. You've probably got the question like when a proton is in the LHC what do people mean by it gains mass as it reaches a faster speed I realize it gains acceleration mass in the way it's continually...

I considered a free falling object in the Schwarzschild metric at rest at infinity and found as approximation the acceleration : $$\frac{d^2 r}{dt^2}\approx -\frac{GM}{r^2}+\frac{3G^2M^2}{r^3c^2}$$ This would mean if there are no sign error in some sense that the force becomes repulsive at...

Hi there, I'm trying to get a better intuitive handle on the concept of rest mass and rest energy - the energy term associated with rest mass. Introductory Physics textbooks often give statements along the lines of "mass is a form of energy" or "mass can be converted to energy" to explain...

Relic neutrinos decoupled from matter around the time of nucleogenesis so had the same temperature as matter and photons at that time. Photons decoupled much later, after electron/positron annihilation which heated the photons slightly so thereafter neutrino temperature should be (4/11)^(1/3)...

Homework Statement A pion at rest (mπ = 273me) decays into a muon (mμ = 207me) and an antineutrino (mn ≈ 0). Find (a) the kinetic energy of the muon and (b) the energy of the antineutrino in electron volts. Homework Equations K = (γ-1)mc2 E = γmc2 ER = mc2 E2 = p2c2 + (mc2)2 I didn't...

Does anybody know a good read/primer that compares the observed cosmological redshift values to predictions made by the relativistic (gravitational) redshift? Thank you!

Hello there, I've been given the relativistic correction of the Schrödinger equation for a free particle: $$ - \frac{\hbar^2}{2m} \frac{\partial ^2\Psi}{\partial x^2} - \frac{\hbar^4}{8m^3c^2} \frac{\partial ^4\Psi}{\partial x^4} + E_0 \Psi = i \hbar \frac{\partial \Psi}{\partial t} $$ How we...

Homework Statement We have a particle mass ##m## with kinetic energy ##k## colliding with a stationary particle of mass ##2m##. The collision creates a composite mass of ##\sqrt{17}m##. Find the value of ##k## Homework EquationsThe Attempt at a Solution I have tried using mass-energy...

Problem statement, work done, relative equations: I am unsure if I got this problem right, especially part (e) A star is moving at 0.2c along the x axis. The star is moving away from observer A and toward observer B. The star emits light with a maximum intensity at wavelength 500nm. (a)...

How much energy would be required to accelerate something the size of the space station to the same speed as protons colliding at the LHC?

In classical physics E=Fd and F=ma so E=mad. a=d/t2 so E=md2/t2 Measurements of d and t will get complicated by Lorentz transformation, so, is E=Fd still a correct definition of energy, or is it a Newtonian approximation which is not accurate at relativistic velocities?

Homework Statement An Electron (rest mass=9.11*10^-31kg) is accelerated to an energy (mass energy+kinetic energy) of 30*10^6 eV (30 MeV). What is its kinetic energy? Its momentum? Its speed? (Note: 1 eV = 1.602*10^-19 Joules; c=2.998 * 10^8 ms^-1) Homework EquationsThe Attempt at a Solution...

Homework Statement A particle has charge e and masse m0. It is accelerated by a charge V to a relativistic velocity. Show that its de Broglie wavelength is: \lambda = \frac{h}{\sqrt{2m_0eV}} (1+\frac{eV}{2m_0c^2})^{-\frac{1}{2}} Homework Equations \lambda = \frac{h}{p} Conservation of...

1. The problem statement, equations, and work done: [A] Two identical spring and mass oscillators are set in motion in perpendicular directions. The masses are each 4.0 kg and the spring constants are 196 N/m. [1] Calculate the angular frequency and the period of the oscillators. ##\omega =...

In non-relativistic QM, the probability postulate works very well in position and momentum space. But, I have read that in relativistic QM (Dirac or QFT), the probability postulate in position space does not work because the corresponding probability density function is not Lorentz covariant...

I have limited physics knowledge, but I have always been interested in the physics and I am an industrial radiation safety officer with an engineering background.Have there been any experiments in respect to measuring half life with large variance in gravitational fields? Although half life may...

Suppose the molecules of an ideal gas move with a speed comparable to the speed of light. I am trying to adapt the kinetic theory to express the pressure of the gas in terms of m and the relativistic energy, but each time I try to derive the expression, I get: P = (1/3)(N/V)(v/c)√(E2 - m2c2)...

I know this topic has come up several times throughout the years, but after reviewing a good number of the threads, I’m still not clear as to whether any kind of consensus on the matter has been reached or not, or if there may be new developments in either theory or observation. If you review...

Homework Statement In a given inertial frame two particles are shot out simultaneously from a given point with equal speeds u at an angle of 60 degrees with respect to each other. Using the concept of 4-velocity or otherwise, show that the relative speed of the particles is given by ##u_R =...

Lets assume we have a starship which is flying from Earth to star XY which is in distance for example 100 lightyears. The computer of that ship is programmed that way, that it maintains acceleration 1 g. After some time the speed of ship reaches some significant part of speed of light and to...

I’m searching for an introduction to relativistic Boltzmann equation. (Sorry, I know this is a question about learning material) I’ve read an excellent script from David Tong about non-relativistic kinetic theory (from Liouville to Navier-Stokes using Boltzmann equation (see link below)...

Hello, I have tried to derive a relativistic formula for work using the E = ϒmc^2 equation and that work is equivalent to change in energy. But I have not gotten especially far and everything is messy. However, when looking at solutions to some harder problems I encountered the formula...

The reaction p→n+e++νe is common inside nucleus. But it not considered when we talk about free particle and reason is simply given mass of products being larger than reactants. Now my question is if there is a high energy proton having total energy in order of 2 GeV or let it to be 100 GeV (To...

My question concerns motion of relativistic Strings, as the reader with a great a mount of deductive skills can deduce :). The question is: How can I derive the P's. More acuratly speaking why is the numerator how it is. I am referring to Zwiebach chapter 6. Thanks for any clarifications and...

In a recent thread, I referred to what I thought was a well-known very simple way of describing how objects move in a gravitational field, in terms of the rate of change of their coordinate momentum in isotropic coordinates. It seems that this result is not widely known (and I can't see a...

Suppose an observer flies through our solar system at ##v \approx c## relative to the Sun, such that he sees each planet's (and the sun's) mass as greatly increased. What happens to the orbits of the planets? Since he sees the center of mass of the solar system as flying past him at ##v \approx...

Effects of a 150,000 kilogram object launched at Earth, just below the speed of light: 99.99999999999999 percent 'c' speed.The object weighing 150,000 kilograms gets a relativistic mass increase of 183,648,173,214,437,391 kilograms, therefore getting a relativistic energy of...

A convoy of spatial ships leaves the Earth at a speed v. Each ship is relativistically compressed in the direction of movement. What happens to the space between the ships? Is it compressed too?