Relativistic Definition and 1000 Threads

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...

The problem goes: ‘One end of a rubber band is attached to a wall. The free end is stretched away from the wall at a rate v. At time zero the band is length L0 and a bug starts crawling along, from the wall, at rate u. How long until the bug reaches the free end?’ (Typically u << v for...

Would there have been any relativistic effects if there was no ultimate speed?

In Newtonian mechanics, both gravitational mass and inertial mass is m. This principle is known as the principle of equivalence. However, I heard that in Relativity, gravitational mass is γm instead of m because total energy of the particle is γmc2. But in special relativity, it is widely known...

Assuming equal mass billiard balls and elastic collisions, classical physics shows that after any collision the motion of the colliding balls will be orthogonal. How does that situation change under SR ? More generally for an elastic collision between objects m and M with m<M, is maximum angle...

Hello, According to Special Relativity, the mass of an object must increase as its speed approaches the speed of light. m=m0γ In the formula that allows us to calculate the kinetic energy of a body, KE=0.5mv2, should we take into consideration such increase in mass? Weam Abou Hamdan Wednesday...

Homework Statement A rocket moving with speed v passes a stationary observer. The observer waits a time T (according to his clock) after the rocket passes and send a pulse of light in the direction of the rocket. The rocket pilot notes that, according to her clocks, the time elapsed between the...

Hello, I am reading Griffith's "Introduction to Electrodynamics" 4ed. I'm in the chapter on relativistic electrodynamics where he develops the electromagnetic field tensor (contravariant matrix form) and then shows how to extract Maxwell's equations by permuting the index μ. I am able to...

Suppose a comet F ,at 1 AU distance, is traveling toward a massive body (a neutron star or other) with v= .99 c, suppose also that a = 3 km/s^2 and (to simplify calcs) that it is uniform from there to the star. It will hit the star after ca. 1000 seconds and its speed should equal C: 297*10^9...

Homework Statement An antiproton of energy 35 ##GeV## from a source outside the solar system interacts with a proton in the upper atmosphere traveling on a trajectory which is radial with respect to the centre of the Earth. The antiproton annihilates the proton with the final outcome that two...

Homework Statement A muon has a lifetime of 2.20 x10-6 s when at rest, after which time it decays into other particles. a) Ignore any effects of relativity discussed in this section. If the muon was moving at 0.99c, how far would it travel before decaying into other particles, according to...

In this super short video of the derivation of the relativistic kinetic energy, , I'm just stuck on one thing. Around 1:00 minute in, the constants of integration change from 0 to pv when the integration changes from dx to dv. Where does the pv come from? Thanks!

Homework Statement Homework Equations Conservation of linear momentum Conservation of energy Energy-momentum relationship: ##E^2-(m_0c^2)^2=c^2p^2## Lorentz transformation of energy: ##p=\gamma(v)(p'+vE'/c^2)## ##\mathbf{p}=\gamma(v)m_0v##, ##E=\gamma(v)m_0c^2## The Attempt at a Solution My...

In a solution to a problem we were given, it is written that a positron momentum with energy of 2mc2 (where γ=2) is √(γ2-1)*mc = √(4-1)*mc = √3*mc How did they get that P=√(γ2-1)*mc?

In particle phyisics four-momentum is used and De Broglie relation is used to understand what lenghts can be "seen" in an experiment. Here (page 6) https://people.phys.ethz.ch/~pheno/PPP/PPP2.pdf it is claimed Where ##Q^2## is not actually "momentum" but its the square of the four momentum...

Suppose Superman and Green Lantern are on an airless planet. Green Lantern whips up a spring and puts a mass on the end, and the spring extends some amount due to the gravitational pull on the mass. Superman then goes off with the spring and mass, and gets up to 0.9c and flies past Green...

Homework Statement A muon has a lifetime of 2.20 x10-6 s when at rest, after which time it decays into other particles. a) Ignore any effects of relativity discussed in this section. If the muon was moving at 0.99c, how far would it travel before decaying into other particles, according...

Homework Statement Exact spin symmetry in the Dirac equation occurs when there is both a scalar and a vector potential, and they are equal to each other. What physical effect is absent in this case, that does exist in the Dirac solution for the hydrogen atom (vector potential = Coulomb and...

I'm reading modern physics, Tipler 5th edition, pages 21 and 22, and I'm not understanding how the differentiation was done from the position to find the velocity. Equation for position: x'= y(x - vt) y is the gamma constant. Then in the first step to find the velocity, a derivative was done...

Homework Statement The proper length of spaceship A is 60.0m and the proper length of spaceship B is 120.0m. The proper mass of spaceship A is 15000 kg. An observer on Earth watches the two spaceships fly past at a constant speed and determines that they have the same length. If the speed of...

So, if kinematics is the study of motion without reference to its causes (which is how it seems to be defined in many places), then here is my attempt to come up with a complete picture of motion without reference to its causes. This is just a summary to help me organize my thoughts (it is NOT...

For a relativistic fluid, the equation of state is given by: $$\rho = \rho_0 + 3p/c^2 $$ The above expression is nicely derived in Weinberg (1972). Although I was told that for a compressible fluid that is relativistically hot (i.e. ##p \gg \rho_0 c^2)## under a constant acceleration, ##g##...

I just came across the following paper: Gisin, N. (2011). Impossibility of covariant deterministic nonlocal hidden-variable extensions of quantum theory. Physical Review A, 83(2), 020102. proving that, under sensible hypotheses, nonlocal hidden variable theories for relativistic quantum...

Hi everyone. I have some questions related to relativistic mass: Does atoms and molecules are affected by this relativistic effects? and does relativistic mass affects the way we weigh things? What I mean is; (and based on my limited knowledge of Special and General Relativity ) atoms an...

Observer A measures B moving east at .8c and measures C moving west at .8c . Then wouldn't the impact of the two will be a result of relative motion greater than c in frame A. I understand B and C frame will not see any object speed greater than c. So the impact in frame A and frame B will not...

Homework Statement We know the momentum of an electron, which is: 1,48*10^-21. Momentum is m*v (mass*speed) If we divide the momentum by the mass of the electron to find electron's speed, it'll give a value where v> 3*10^8 m/s. Since speed can't be above speed of light, we have to calculate...

Homework Statement Two spaceships pass each other. Spaceship A moves relative to nearby planet at velocity v1 , while spaceship B moves at velocity v2 relative to the planet . How fast does spaceship A moves relative to spaceship B. Homework Equations Velocity Transformation : v* =...

Homework Statement A Sigma^+ decays at rest into a neutron and a pion^+ meson, i.e. according to the reaction $$\Sigma \rightarrow n + \pi$$ The n and π masses are assumed known. The kinetic energy of the π + is measured to be 92 MeV. Determine the momentum of the pion. Homework Equations...

I'm having trouble understanding how the 4-wave vector is derived, and also how it is then used alongside the 4-momentum vector to formulate the relativistic de Broglie equation. The inner product of the 4-momentum vector with itself, is an invariant quantity. If we define the 4-momentum...

I try to calculate the speed curve of a relativistic rocket driven by a 100% efficient engine with constant thrust, when traveling to a distant star. All equations I can find consider constant acceleration, which of course is not working, since the ships mass decreases when the fuel is used...

Hello! I've been reading about relativistic mass for last few days and it leads me to even more confusion. Supposing, we are assuming SR. 1. Why some people say that relativistic mass leads to confusion? As far as I learned, relativistic mass tells me the mass of an object, that is moving...

Looking for existing examples of or guidance on building computer simulations of simple N-bodies in relativist situations. Of particular interest is the simulation of a planet orbiting a star whilst that trivial solar system is caught in a dark flow of relativist velocity; maybe .8 or .9 C. Not...

[Moderator's note: This thread was spun off from a previous thread in the Quantum Physics forum. It was moved here since this specific subject is more on topic in this forum.] I didn't say that somebody who uses the relativistic mass doesn't understand relativity. It's just an unneeded...

Hi guys, thanks for helping with this! I'm a little stuck with this question about the derivation for relativistic mass. 1. Homework Statement By considering the inelastic collision of two balls as perceived in different reference frames show that the relativistic mass is equal to the rest...

Regarding the expansion of space... In one book I've read the diameter of the universe is more than 100B light years across, even though the age of the universe is only roughly 14B years old. This is due to accelerated expansion of space. In another book it says that space is expanding in a...

Homework Statement According to the standard assumptions, there are three species of (massless) neutrinos. In the temperature range of 1MeV < T < 100MeV, the density of the universe is believed to have been dominated by the black-body radiation of photons, electron-positron pairs, and three...

Homework Statement Considering 2 scattering particles with momenta ##p_{1}, p_{2}##, where ##p_{2} = 0## in the Lab reference. The momenta of these 2 particles after elastic collision are ##p_{1}', p_{2}'##, respectively. Due to the 4-momentum relation, we have ##p_{1i}p_{1}^{'i} = e_{1}e_{1}'...

I'm in the process of learning special relativity (SR), and I'm a bit confused as to why the relativistic energy dispersion relation ##E^{2}=m^{2}c^{4}+p^{2}c^{2}## gives the energy for a free particle? I get that it is the sum of (relativistic) kinetic energy plus the rest mass term (a...

If I were able to accelerate a particle to relativistic speeds, then capture that particle in a box in such a way that it kept its speed, then weighed that box, would it weigh more than the box + rest weight of the particle? Would it exert a gravitational field greater than that of the box with...

Homework Statement I am given the Hamiltonian of the relativistic free particle. H(q,p)=sqrt(p^2c^2+m^2c^4) Assume c=1 1: Find Ham-1 and Ham-2 for m=0 2: Show L(q,q(dot))=-msqrt(1-(q(dot))^2/c^2) 3: Consider m=0, what does it mean? Homework Equations Ham-1: q(dot)=dH/dp Ham-2: p(dot)=-dH/dq...

I am observing the speed of an object whose acceleration is about 1000G to 10000G (10000-10000m/s^2), both with a laser sensor and a high speed camera in very short time But the results keep coming out in a way that the laser sensor sees the velocity about 10-20% faster than the high speed...

Homework Statement Consider an inertial laboratory frame S with coordinates (##\lambda##; ##x##). The Lagrangian for the relativistic harmonic oscillator in that frame is given by ##L =-mc\sqrt{\dot x^{\mu} \dot x_{\mu}} -\frac {1}{2} k(\Delta x)^2 \frac{\dot x^{0}}{c}## where ##x^0...

Hi everyone. Given: an asteroid with the mass of 50,000,000 kg, which is moving with the velocity of oh-my-god particle -- 99.99999999999999999999951% of c. Due to relativistic effects, its total kinetic energy will be 1.44 E+36 Joules (Lorentz factor = 3.2 E+11). A hypothetical particle...

Just wanted any books / pdfs which introduce special relativistic calculus.

Hello fellow physicists.Recently I imagined a particle far away from everything (infinitely away) such that there is no potential energy affecting the particle. Ep = 0 Ek = mc2δ : δ = (1-v2/c2)-1/2 L = EP- Ek = -mc2δ ∂L/∂v = vE0/c2 *δ^3 where E0 = mc2 d( ∂L/∂x)/dt = 0 ∴ vE0/c2 *δ^3 = 0 mvδ3...

This is not a homework question, but I read elsewhere that questions for self-study were required to be placed in this section. I had a question that pertains to the non-instantaneous transfer of information (limited at the speed of light, c) and how it would work in a thought-experiment...

Hi everyone, I am currently working on a project in Physics analyzing the possibility of magnetic fields protecting against radiation particles such as fully ionized nuclei or electrons. I wrote a code in Matlab that simulates a 3-D magnetic field based on a combination of wires and wire loops...

Homework Statement If a spacecraft is traveling to a star which is located at a distance of 1 lightyear and it would take the spacecraft 1 year to reach the star in its own frame, how fast would the spacecraft actually fly? Also, how long would the journey take for an observer on Earth...

After a few recent discussions I have realized that I don’t know anything about a relativistic theory of materials. Does anyone have a good link for a reference about Hooke’s law in relativity, or something similar. Homogeneous isotropic linear media is fine.

Homework Statement so i read morin's derivation of rocket equation propelled by photons now i want to try for relativistic mass ejection but i am having some problems let subscript e denote quantities of ejected material and subscript of r denote quantities of rocket Homework Equations ## P =...