Relativistic Definition and 1000 Threads

Hi, I am stuck with the following task I have developed a Taylor expansion for ##L[\gamma]=\sqrt{c^2-v^2}## up to the third order for the position ##a=0##, for this I have rewritten ##L[\gamma]## as follows: $$L[\gamma]=\sqrt{c^2-v^2}=c \sqrt{1-\frac{v^2}{c^2}}$$ Then I did the following...

Classics ! James D. Bjorken, Sidney D. Drell - Relativistic Quantum Mechanics (1964) James D. Bjorken, Sidney D. Drell - Relativistic Quantum Fields (1965) Sold as a pair (reasonable infraction on the 1 book/thread guideline) Mint condition

I figured since ## dr/dt ## is simply the velocity of the target mass, the velocity ##u_x## would simply have to be changed by the Lorentz transformation. Since the rest mass doesn't change, I think this should be as simple as taking the Lorentz transformation for velocity, and substituting the...

Recently, I spent some time trying to get an intuitive understanding of special relativity. (I am not a physicist, only took a few physics lectures in the mid-90s) It all went well until I tried to imagine accelerating objects with non-zero length. Specifically, I tried to imagine what a...

Under the RELATIVISTIC definition of Action, is the Action for a beam of light always zero? Thanks in advance.

Obviously it'd add up to somewhere between 99% and 100% light speed. So how do you figure that out? In the scenario, you reach 99% light speed in one direction, then without slowing, you start to accelerate into an either directly left or right direction (say the engine can rotate without...

I'm following the derivation in Lancaster and Blundell. First, the Lagrangian for the free particle is ##L=-\frac {mc^2} {\gamma}## and the action ##S=\int -\frac {mc^2} {\gamma} \, dt##. Then, EM is "turned on" with the potential energy ##-qA_{\mu}dx^{\mu}##. Then, they say, the action becomes...

Hello! My question is related to going from Eq. 32 to Eq. 33 in this paper (however I have seen this in other papers, too). In summary, starting with: $$H \propto \bar{e}\gamma_\mu\gamma_5 e \bar{q}\gamma^\mu q$$ where we have the gamma matrices, e is the electron field and q is the...

Hi, I am trying to learn relativistic classical field theory as a preparation for studying quantum field theory. I am currently reading chapter 13 i Herbert Goldstein's Classical Mechanics edition 3, but I think that this book is a bit too brief and does not fully derive and explain the...

I thought of this description recently and I think it's pretty intuitive, but I've gotten some side eye telling it to friends and family (maybe because relativity is screwy, maybe because I'm confused, maybe both?) so I want to get some confirmation that it's reasonable. Here goes: If you're in...

Hello friends of the Forum. I want to ask you why the inertial acceleration in free fall in the relativistic geodesic equations is assumed equal to zero in free fall and equal to 9.8 m/s at rest on the earth's surface. On the other hand, assuming that zero acceleration in free fall, what would...

Question: With maximum do they mean that the speed of the pions is the same as the proton and an antiproton? Otherwise there will be two unknowns, and if I use both relativistic-energy and momentum conservation equations I get difficult equations.

It is often argued that Dirac Equation is not valid as relativistic quantum mechanics requires the creation of antiparticles. But, there are also some arguments that suggest otherwise. For example, I saw Arnold Neumaier's website on this that there are multiparticle relativistic quantum...

Would the force (as predicted by Coulomb’s law) exerted on two charged particles q1 and q2, separated by distance r, and at rest relative to frame S change, if q1 and q2, began moving relative to S but we’re still at rest relative to each other?

I feel like this should be pretty straightforward knowing all the equations involved but my brain seems be stalling for some reason.

I was watching this video by Brian Green about relativistic velocity addition when he said something at the end that I wondered about. https://www.britannica.com/video/222286/Your-Daily-Equation-07-Relativistic-Velocity-Combination It was along the lines of the formula will always result in...

Body 1 travels 48 light years from point A to point B at 82% of light speed. Body 2 leaves point A 33 years after Body 1 and travels the 48 light years to point B at 99.99995% of light speed. What I think I know: Body 1 takes 58 years to reach point B according to an earth observer. Body 1...

I am aware of the Newtonian model of Gravitation and I am interested in Relativistic Mechanics. I do not know anything about relativistic mechanics other than its more "accurate" at modelling gravitation and that it "reduces" to the classical formulation in some cases. I only want to be able...

Hello! I have a question. If there is a wooden rod which burns certain time, and an astronaut inside rocket lights two such rods: one oriented along the rocket's length and the other goes across the rocket, and an observer see the rocket passing by with a relativistic speed. Will the observer...

Let us consider relativistic particle (electron) which moves with relativistic speed ##v## in the Coulomb field (in the field of a fixed heavy nucleus). The main question is what is the potential energy of a particle in such a static field? Landau and Lifshitz in their book "Field Theory"...

How does this end up +? Can't work out steps.

I'm trying to understand this paper (equation 2.16 specifically): Bini, D., Carini, P., & Jantzen, R. T. (1995). Relative observer kinematics in general relativity. Classical and Quantum Gravity. Am I correct in reading there is no way to express the relativistic relative velocity composition...

Hi all experts! I would like to read about the Lagrangian of a classical (non-quantum), real, scalar, relativistic field and how it is derived. What is the best book for that purpose?Sten Edebäck

Hi, I am reading Robert D Klauber's book "Student Friendly Quantum Field Theory" volume 1 "Basic...". On page 48, bottom line, there is a formula for the classical Lagrangian density for a free (no forces), real, scalar, relativistic field, see the attached file. I like to understand formulas...

Was curious at the upper limit for neutron stars, found this article stating one was found at around 700 / s https://www.newscientist.com/article/dn8576-fast-spinning-neutron-star-smashes-speed-limit/ did not see the size, the article is behind a paywall, but it would have taken a radius of...

I am reading Andy Weir's Hail Mary. There was a part about relativity: it wrote, that a relativistic interstellar ship had lots of spare fuel, because the mission planners actually ignored relativity, and thought travel will be Newtonian. Am i wrong to think, that is nonsense, and the opposite...

d(ɣmv)/dt = qvB (dɣ/dt)mv + ɣm(dv/dt) = qvB Substituting gamma in and using the chain rule, it ends up simplifying to the following: ɣ^3*m(dv/dt) = qvB Now, I am confused on how to solve for v.

I found out about this interesting paper through a Tweet by Steven Thomson. https://arxiv.org/abs/2108.05169 https://www.nature.com/articles/s41467-022-31608-6 Relativistic Bohmian trajectories of photons via weak measurements Joshua Foo, Estelle Asmodelle, Austin P. Lund, Timothy C. Ralph...

If we imagine launching an electron wave in a reference frame S with speed v, should someone viewing the electron from frame S1, which is in inertial motion referring to S, use the relativistic velocity addition to calculate the speed of the electron?

Hello. Could anyone help me with some insight in an extra term appearing in the motion equations of a relativistic fluid? I say extra term, because it's not present on the motion for a test particle, as it follows: Let's propose Minkowski space-time, the motion equations for a fluid with zero...

In a recent thread about Bell tests etc. it has been claimed my point of view of "locality" where "non-mainstream physics". Of course, I cannot give a complete summary of the foundations in a forum posting, as demanded by @DrChinese there. The most clear treatment, particularly emphasizing the...

My solution was as follows: $$\frac {d\overrightarrow p} {dt}=q \frac {\overrightarrow v} {c}\times \overrightarrow B_0$$ The movement is in the ##[yz]## plane so ##|\overrightarrow v\times \overrightarrow B_0|=vB_0##, therefore: $$\biggr |\frac {dp} {dt}\biggr |= \frac {qvB_0} {c}.$$ On the...

$$ds^2 = dt^2 - r^2 d\theta^2 = d\theta^2((dt/d\theta)^2-r^2) = d\theta^2((1/w)^2-r^2)$$ $$C = \Delta S = \int ds = \int \sqrt{(1/w^2-r^2)}d\theta = 2\pi \sqrt{(1/w^2-r^2)} $$ $$C/2r = \frac{\pi \sqrt{(1/w^2-r^2)}}{r} = \pi \sqrt{\frac{1}{(wr)^2}-1}$$ But this answer is wrong. And i don't know...

Global Newtonian mechanics seems to be compatible with 1) Hubble's law, and 2) the cosmological principle: take a vector space, set the velocity of a galaxy at x to be v=x, where x is the position vector. Then from any galaxy, the other galaxies seem to go away with velocity v2-v1 = x2-x1. That...

In non relativistic quantum mechanics, the expectation value of an operator ##\hat{O}## in state ##\psi## is defined as $$<\psi |\hat{O}|\psi>=\int\psi^* \hat{O} \psi dx$$. Since the scalar product in relativistic quantum has been altered into $$|\psi|^2=i\int\left(\psi^*\frac{\partial...

I was reading an article, and I saw this expression. $$ 1+z=\frac{(g_{\mu\nu}k^{\mu}u^{\nu})_e}{(g_{\mu\nu}k^{\mu}u^{\nu})_o} $$ Where ##e## represents the emitter frame, ##o## the observer frame, ##g_{\mu\nu}## is the metric, ##k^{\mu}## is the photon four-momentum and ##u^{\nu}## is the...

In non-relativity then there is QM, but in relativistic regime then there is QFT. Then what is useful role of Relativistics QM nowaday, or it is only has a historical meaning?Does non-existance wave function in relativistic regime make RQM meaningless?

I have derived the Coulombian potential as an effective potential between two spinless charged particle taking the non-relativitic approach on the scattering amplitude obtained in terms of the Feynman rules in SQED. The scattering amplitudes are: I'm using the gauge in which xi = 1. How could...

Does mechanical watch ticks slower when move fast, due to relativistic effects? To make watch tick slower you must change oscillation of balance wheel inside watch, so if answer is yes, what myster "force" change balance wheel oscillation in mechanical watch to ticks slower?

Comments please Is there good sobriquet to use for relativistic length ? Just a thought to aid the struggling college frosh STEM students

Hey everyone, if I were to view a shining person rotating near a black hole at near the speed of light there would be 2 kinds of redshifts: gravitational redshift and relativistic doppler effect redshift. Right? But, say at some point, the person is traveling towards me, then the doppler effect...

If it were possible to obtain absolute zero, could relativistic matter exist when classical momentum would be zero? Would a particle cease to exist? I can't do the math. Thank you for reading my question.

I've been noodling around with derivations of the relativistic energy and momentum, and I almost got it down to just a few lines. But not quite. I'm going to work in one spatial dimension, for simplicity (even though some derivations require a second spatial dimension) Let's assume that there...

Let's say a small object orbits around massive object at some distance in perfectly circular orbit. In Newtonian physics the force acted upon orbiting body is: Force = m1 * orbital_speed^2 / distance = G * (m1*m2) / r^2 for an object of 1kg orbiting a body of 2*30^kg at the distance of 1.521 *...

edit: I had a sign error that is now corrected, no further help needed. Consider in the laboratory frame one second passing. Let ##(t,x)## be the coordinates of various events in a spacetime diagram. Both particles are released at ##(0,0)## Then after one second the left moving particle is at...

In most experiments of SR, we look at atomic and subatomic particles or the frequency of EM radiation. The Haefele-Keating experiment looked at the resonance of cesium atoms stimulated by a certain EM frequency https://en.wikipedia.org/wiki/Hafele–Keating_experiment The Ives-Stillwell...

Hi guys. I am studying the relativistic implementation of the standard Tsiolkosvky rocket equation, but ran into some doubts. Doesn't special relativity apply only to inertial frames of reference(non-accelerated)? Then, how could it be used for the rocket equation, which speaks of a ##\Delta...

I am studying through online resources some principles of spacecraft propulsion, since it really fascinates me, and makes me want to know a bit more about it :) For rockets, thruster, I found the Tsiolkovsky rocket equation: $$\Delta v=v_e ln(\frac{m_0}{m_f})$$ Of course, rockets can travel...

I found the observed frequency from the energy. Then I used the receding Doppler shift formula to find, the source frequency but after that when i tried to use the Rydberg equation I got a value for the energy level less than one. and I'm pretty sure my work is right, any help is greatly...

Hi guys, a special relativity problem requested to choose the right graph representing relativistic momentum ##p## as a function of rel. kinetic energy ##K##, from these four: At first, I tried writing ##p## as a function of ##K##, in order to then analyze the function's graph and see if it...