Relativistic Definition and 1000 Threads

Show that, according to relativistic physics, the final velocity ##v## of a rocket accelerated by its rocket motor in empty space is given by ##\frac{M_i}{M} = \Big ( \frac{c+v}{c-v} \Big) ^ \frac{c}{2 v_{ex}}## where ##M_i## is the initial mass of the rocket at launch (including the fuel)...

The answer is required to be in terms of M,m and c only. But, I am not able to calculate the momentum of the m mass particle using the above two. Can anyone help me by telling me what I am missing?

If we have a plane wave, usually in Relativity notation it is written as ##A^\alpha = a^\alpha \exp(i x_\alpha k^\alpha)##. (I know we need to take the real part in the end). In cartesian coordinates, and two dimensions say, that ##x_\alpha k^\alpha## would be ##x^\alpha k_\alpha = x k_x + y...

I am intrigued by the special-relativity explanation of magnetic force discussed here (linked from the physicsforums FAQ): http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#Length_Contraction Naively, from this explanation, it seems that a test charge at rest in the lab...

q = 1.602e-19C mass_electron = 1.098e27 c = 3e8 Omega(Mag_flux_den) = 5GHz Lorentz factor = 100 synchrotron radiation at frequency v = 5GHz Mag_flux_den = (Omega(Mag_flux_den) * c * Mass_electron * Lorentz factor) / mass_electron Mag_flux_den = (5000 x 3e8 x 1.098e27 x 100 ) / 1.602e-19 =...

I came across a question that states What mass would a neutrino need to still be relativistic today (T = 2.37K) ? So for a particle to be relativistic we need ##pc \gg mc^2## Well Neutrino was relativistic in the early universe, so I took the time when the neutrino decoupled which is...

dv/dt is the acceleration, so I thought I could find the acceleration from F = qE = ma = dp/dt. But this is a relativistic case, so the proper acceleration is a = F/mγ3, where v in the gamma is the v of the electron and F = eE. However, I'm not sure if this is correct, because the constant τ...

Hi gentlemen. My model is simple. Imagine, I watch a body which approaches me with velocity of w which value I can measure . I know that this a body has velocity v in a some reference system which aproaches me with same velocity of v. This velocity needs to be calculated (I can not mesure it)...

Does this violate conservation of momentum or some other law? It claims to take advantage relativistic mass increases to achieve propulsion https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20190029657.pdf

We never learned how to use these formulas, so I'm pretty much grasping for straws. I got 2.04 kg/m^3. Can anyone check my work/teach me proper methods if I'm wrong? Thanks.

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Hi everyone, I'm interested in relativistic anisotropic hydrodynamics and often a "gradient Expansion" is mentioned in articles, but not how this works exactly. I gathered that this is some kind of expansion of the energy-momentum tensor. Can someone explain to me how this expansion is set up...

I wanted to re-do Egan's results for relativistic hoops with a different model, one with a relativistic hoop with a constant circumference. The idea is that by having the circumference not change as we spin up the hoop, we shouldn't be storing energy by "stretching" the material of the hoop...

Quick question about the relativistic energy of a rotating thin ring, hoop or cylinder. Is there any reason why the relativistic energy would be anything different than ##E=\gamma_t m_0 c^2## where ##\gamma_t## depends on the tangential velocity ##v_t## observed by someone at rest with the...

Problem Statement: It is possible to describe synchrotron radiation as caused by a loss of electrical charge of relativistic particles that are moving in a magnetic field? Relevant Equations: E = mc2 An Italian expert of black hole M87 (Elisabetta Liuzzo) explains that the expected axial...

I have to find pμ(τ) of a particle of mass m and charge q with v(0) = (vx(0), vy(0), vz(0)) in a electric field E parallel to the y-axis and a magnetic field B parallel to z axis, both constant and uniform, with E = B. Here follows what I have done (see pictures below): I wrote 4 differential...

A lecturer today told the class that relativistic QM for single particles is flawed by showing us that for a state centered at the origin, it was possible that ##Pr(\vec{x}>ct)>0##. He said that this was down to the fact that we should be considering multi-particle states in relativistic...

I first thought of this problem when I came across the "Ehrenfest Paradox", and realized that as velocity approaches c, the measured force must diverge to infinity as the velocity approaches c.

Summary: Why is there no contradiction between energy as a non relativistic scalar and Galilean invariance? If energy is a non relativistic scalar, doesn't it mean that there is a contradiction with Galilean invariance? What i mean is that if i try to accelerate an object within the Galilean...

I have a question about this picture: It shows matter traveling at relativistic velocities away from a black hole: "Figure 5.21: This VLA image of the radio-loud quasar 3C 175 shows the core, an apparently one-sided jet, and two radio lobes with hot spots of comparable flux densities. The jet...

Summary: Relativistic effects on the quantum states of electrons in Copper and Gold Hello. I am a new member. I have read that the explanation for the colors of copper(red) and gold(yellow) compared to other metals being silver or grey in color is due to relativistic effects on the valence...

I've been interested in relativistic spacecraft since news of the Breakthrough Starshot project announcement a few years ago. Breakthrough Starshot's method of laser propulsion still has many technical hurdles needed to be crossed. So I'm wondering what you guys think the first forms of...

I have read that relativistic jets emitted by black holes are thought to contain a mixture of matter and antimatter including positrons and electrons. Is there any mechanism known that would lead to matter or electron concentration in one of the two relativistic jets, and antimatter or positron...

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Does relativistic mass make a proportional gravitational effect on observer it flies by? Does 1 ton (resting 1 ton) of lead moving relatively observer at some speed close enough to C may appear as a micro black hole? What abort Hawking radiation in this case? Does it mean that we may convert any...

I was looking up stuff for relativistic two-body decay, and I came across this pdf: https://indico.cern.ch/event/391122/contributions/928962/attachments/782786/1073126/twoBodyDecay.pdf which says that because ##p_2^2=P^2−2P\cdot p_1+p_1^2## we apparently have ##m_2^2=M^2−2ME_1+m_1^2##. But this...

It is easy to derive E=1/2mv^2 from the Schroedinger equation for the nonrelativistic one dimensional case where e^ipx-iEt/\hbar is the free traveling wave function: i\hbar x -iE/\hbar x e^ipx-iEt/\hbar = - - \hbar^2/2m x p^2/2m x e^ipx-iEt/\hbar which reduces to E=1/2mv^2 Where should I start...

So I want to include near-light-speed travel in my fiction, but I'm getting bogged down by the implications of it! My understanding is: If something travels very fast (close to the speed of light) time dilation will cause it to experience time slower, meaning that the journey, as observed by...

Hello guys, i am currently studying for my msc thesis in theoretical physics and i need to find the derivation of relativistic Boltzmann equation, any suggestions ? Because i ve searched for papers/books for it and couldn't find anything. Any ideas? Thx in advance

I know I can get momentum in terms of kinetic energy in this way: K = .5mv^2 => p = sqrt(2mK) substitute into debroigles gives me: λ = h/(sqrt(2mk)) = hc/(sqrt(2mc^2K)) which would be the nonreletivistic equation but I need the reletivistic equation. I can plug in the equation for...

Hi! I'm trying to wrap my head around the idea of a spaceship - [let's just say it is "fusion-powered" very very efficiently :wink:] - under constant thrust, accelerating towards a distant star. It accelerates for the first half of the journey, then cuts its engines & turns around 180-degrees...

The Biot-Savart law which describes a magnetic field created by a displacement current: $$\frac{dB}{dV}=\frac{\mu_0\epsilon_0}{4\pi}\frac{\frac{∂E}{∂t}×r}{r^2}$$ What's the relativistically co-variant form of this equation? Is the introduction of speed of light propagation delays enough, or...

Homework Statement A charge q1 is at rest at the origin, and a charge q2 moves with speed βc in the x-direction, along the line z = b. For what angle θ shown in the figure will the horizontal component of the force on q1 be maximum? What is θ in the β ≈ 1 and β ≈ 0 limits? (see image) Homework...

In an inertial frame, consider that a particle's position and the time measured by a clock in this frame are respectively, ##(t,x)##. Suppose there's another frame, moving with constant speed ##v_R## with respect to the frame described above. The particle acceleration is given in the first...

Hello everyone, Any object has a gravitational potential energy as a function of the distance from the Earth (R). Does this energy depend only on the rest mass of the object; or one must take into account it's relativistic mass? In other words, if we imagine two identical bullets on the top...

Perhaps naively I assumed that for a relativistic particle the product of mass times velocity would be the same in both Newtonian and Einsteinian mechanics. The simplistic thinking was the mass increase in relativistic dynamics would balance out the non-real superluminal velocity of a particle...

Peeling this out into its own thread for clarity: How is time dilation of extreme reference frames (photons, black holes, intergalactic space-time) taken into account in Big Bang cosmology? Since from the POV of a singularity or a photon, their clocks have effectively stopped and any lower...

Does The Presence of Charge Add To Relativistic Mass-Energy, or does it take two particles attracting or repelling one another to generate charge-related mass-energy?

Thought you all might be interested in this article. It could just be hype, but there also might be something deeper to it. You hear of so many schemes of tying together quantum mechanics with a relativistic understanding of gravity, that it's easy to respond to yet another announcement like...

In his book, Landau mentioned varying the relativistic lagrangian However, I do not understand how he got from varying the integral of ds to varying only the contravariant components. Would the general procedure not be varying $$\delta S = -mc\delta\int_a^b\frac{dx_idx^i}{\sqrt{ds}}$$ and...

The action for a relativistic point particle is baffling simple, yet I don't really understand why it is written as, $$S = -m\int ds $$ I know it's right because we get the right equations of motion from it, but can one understand it in a more intuitive way?

It is my understanding that in both Classical Field Theory and QFT the Lagrangian must be Lorentz invariant in order for the fields to be considered relativistic. Buy what about the field itself (φ or ψ)? As complex-valued functions of space and time do they also have to be Lorentz invariant...

Hi everyone, I have a question that can't solve. Does exist a lagrangian for the relativistic angular momentum (AM)? I can't even understand the question because it has no sense for me... I mean, the lagrangian is a scalar function of the system(particle,field,...), it isn't a function FOR the...

Homework Statement Two images are attached. The first image details the problem. The second image has an x',y' coordinate system depiction of the problem. Homework Equations The total energy of a particle is defined as E = mc^2, with m = γ*m_0. The Attempt at a Solution If the x', y'...

Homework Statement Homework Equations (1) E2 = p2c2 + m02c4 (2) E = γm0c2 (3) E = Eγ1 - Eγ2 (4) p = E / c (5) E = hf (6) λ = c / f The Attempt at a Solution a) Using eqn (1), rearranged p = (E - m0c2) / c , I obtained 2.9 MeV c-1. Not sure if I have the right answer here as I...

Hello everyone and apologize if my questions seem a bit off, please have patience with me. I want to have the following, rather simple, thought experiment. Let's say that we have a moving object O with the proper length L, when at rest. Let's say that object O starts moving at 0.9c (90% the...

1. Homework Equations E=mc^2 Relativistic mass equation given in the question The first part of the question: I understand 200 MeV is the energy lost as it initially moves with 200MeV however is brought to rest and thus this total kinetic energy must have been transferred from the 'two...

<Moderator's note: Moved from New Member Introduction.> I am asking assistance in addressing several questions I have with the relativistic kinetic energy expressions given as {I am sorry for the format of the notations. It was inadvertently distorted.} KE=mc2 [1/sqrt(1-(v2/c2)) -1]...

Hi guys, I've been asked to check somebody's relativity logic and i'd love to get s second opinion as it's easy to slip up. There is a train, with an observer (A) in the middle, with a device that fires marbles simultaneously up the train and down the train. There is also a...

I noticed that the Schwarzschild Radius Formula and the Escape Velocity Formula are actually identical. The Schwarzschild Radius is supposed to be one of the great equations generated from Relativity, while the Escape Velocity is something that was generated just using Newtonian gravity. All you...