Relativistic Definition and 1000 Threads

I have some difficulties in viewing the literature on the topic. In textbooks on analytical mechnics the procedure given for Special relativistic motion is to write the kinetic term relativistically and attach the unchanged potential term. So, for a harmonic oscillator the Lagrangian is ##L =...

Homework Statement Question attached: Hi, To me this looks like a classical, continuous system, as a pose to a quantum, discrete system, so I am confused as to how to work the system in the grand canonical ensemble since , in my notes it has only been introduced as a quantum...

Consider a spring-mass oscillator on a train moving at relativistic speed. According to SR, to a stationary observer, both the mass and the period will appear to have increased by a factor of γ. But the period is supposed to be proportional to the square root of the mass. Something is wrong...

Hi, If a particle is within 2 m/s of the speed of light (like at CERN) and then more energy is transferred to the particle, where does this energy go? Some sources I have read talk about relativistic mass getting bigger and approaching infinity as a particle approaches 'c'. However, this source...

Hello! I am reading a derivation for Fermi pressure and the author assumes that the electrons in a box are cooled so much that they occupy all the states in the momentum space from p=0 up to a maximum value of p. Then after he obtains a formula for the pressure, he simplifies the formula...

The gravitational field of some massive body appears one way to a nearby stationary particle. But does the field appear to be distorted to a particle traveling at relativistic speeds?

I have a pressing question, but I don't exactly know how best to articulate, or where. I am a wafer fab operator in the semiconductor industry. I usually operate ion implanters. The highest energy ion beams we use are a little over 3.5 MeV. As an aside, I am looking for a way, given that, to...

Hi people! First of all, sorry for my poor english. I read in many places and I did the calculus and I agree that the field of a moving charge have this aspect: (Taked from Feynman´s Lectures on Physics chapter 26th.) But my problem is in that my intuition says me that it must be something...

I have a sample problem : Photon, with energy E, is absorbed by m. Then, mass m becomes m' (i think it's relativistic mass). Calculate the new mass. My teacher solved the problem as follows; P1=( E/c, P3dphoton); // momentum of the photon P2=(mc, 0); // momentum of the stationary mass...

Homework Statement A body emits photons of frequency ##\omega_*## at equal rates in all direction in its rest frame. An observer is moving with speed V relative to the body in the x direction. Find the rate at which the photons are received per unit solid angle ##dN/dt'd\Omega'## a large...

"It is impossible to "weigh" a stationary electron, and so all practical measurements must be carried out on moving electrons. The same is true with any other sub-atomic particle. For particles like photons or gluons the situation is even more problematic since the very concept of a stationary...

In Quantum Mechanics Concepts and Applications by Zettili the following formulas are used for phase and group velocities. {\rm{ }}{v_{ph}} = \frac{w}{k} = \frac{{E\left( p \right)}}{{p}}{\rm{ }}\\ {\rm{ }}{v_g} = \frac{{dw}}{{dk}}{\rm{ = }}\frac{{dE\left( p \right)}}{{dp}}{\rm{ }} In...

Homework Statement A sodium light source moves in a horizontal circle at a constant speed of 0.100c while emitting light at the proper wavelength of λ0=589 nm. Wavelength l is measured for that light by a detector fixed at the center of the circle. What is the wavelength shift λ-λ0? Homework...

Homework Statement A stationary excited nucleus decays to its grpund state by emitting a γ-ray photon of energy Eγ. The grpund state nucleus recoils in the opposite direction at speed v. Show that when v<<c the change of mass of the nucleus is approximately: me - mg = Eγ/c2 [1+ 1/2(v/c)]...

Based on my limited understanding of special relativity, as an object's velocity increases with respect to an observer the object undergoes spatial contraction (making it appear to the observer to get thinner in the direction of travel) and time dilation (so the observer would view the object's...

I loved Modern Quantum Mechanics by Sakurai, where Quantum Mechanics is presented and worked out. Now I would like to proceed further, and learn about Relativistic Quantum Mechanics and Quantum Field Theory. I started by reading Sakurai's Advanced Quantum Mechanics, but later I found that the...

The rays of light from a moving source are tilted towards the direction of the source's motion. It is as if light emitted by a moving object is concentrated conically, towards its direction of motion. This effect is called relativistic beaming. For example, if a source is emitting light...

Does the concept of relativistic mass make any wrong predictions? One of the most senior professor of the best university here wrote a note on false predictions of relativistic mass trying to disprove it. However, I have seen criticism of it. But I didn't get most part of those counter...

I don't uderstand how, using special relativity theory (time dilatation and length contraction), one can explain why in the Michelson interferometer there is no delay between the two rays in the reference frame where the interferometer is moving. Consider the picture ##2.## Setting...

1. Homework Statement ( This question is from the textbook of Introduction to Elementary Particle Physics, written by Griffiths, on the problem set of Chapter 3 ) Particle A (energy E) hits particle B (at rest), producing particles C1, C2, ...: A + B → C1 + C2 + ... + CN. Calculate the...

When constructing a relativistic quantum mechanical equation, namely Dirac equation, what would happen if we choose the Hamiltonian so that it's not linear in the momentum operator and the rest energy? You could say, why don't try it yourself and see what happens? That's because my knowledge is...

Let's assume that a light source is moving parralel to x-axis and is in point x,y,z in lab frame. Suppose it emits a light ray. In the rest frame that coincides with the lab frame, the light source is in point x',y and z. However, because of relativistic aberration the two light rays will make...

Hello, I am trying to work through attached paper, deriving from equation 2.2 to 2.4. I am not familiar with the notation. If I try and get the integral of inside the <> brackets, I end up with a different eqn 2.4. I need some maths help here :) Any help would be greatly appreciated...

What's the difference between relativistic quantum mechanics and quantum field theory? In principle, my guess is that to do the former, one needs to express the Hamiltonian in a relativistic, Lorentz invariant, form, because it seems to be the only frame-related term in the wave equation. (Is...

I'm working on semiconductor physics and cyclotrons. There's an article that I am trying to understand, but am having difficulties matching with experiment. I asked a question on an electronics site, but apparently the physics is too advanced. The relativity article which sparked my interest...

Hi, I have yet another question in the field of the special relativity theory. I always thought that the derivation of the relativistic mass is trivial. But I discovered that there is some complexity due to the transverse and longitudinal relativistic mass derivation. I saw a thread where...

Homework Statement In Newtonian theory the gravitational potential Φ exerts a force F = dp/dt = −m∇Φ on a particle with mass m and momentum p. Before Einstein formulated general relativity, some physicists constructed relativistic theories of gravity in which a Newtonian-like scalar...

Let's assume that a disk is rotating with relativistic speed in a frame. We can find the velocity of a particle using v=rw formula. However, what is the r in this formula? is it the radius of the disk in rest frame or in the lab frame?? And Is the magnitude of velocity same for all points of...

If we move towards a source of EM waves, in our reference frame the frequency appears (and it is) higher than what a stationary observer will see due to Doppler effect. The field transformations show that these two observers will se static fields differently so I would also expect that the peak...

Hi. I want to know about relativistic Landau levels (especially about massless Dirac fermion in a uniform magnetic field), but I cannot find textbooks. Does anyone know textbooks or articles about it? Thanks.

Homework Statement A train of length L moves at speed 4c/5 eastward, and a train of length 3L moves at speed 3c/5 westward. How fast must someone run along the ground if he is to coincide with both the fronts-passing-each-other and backs-passingeach-other events? Homework Equations Velocity...

Let's assume there is a device that can hold fresh meat in a stationary position, and this device can spin at relatively high speeds. Would this allow fresh meat to last longer without freezing?

Does anyone have an equation that -- given energy applied to a mass over a distance -- will give me an (ideal) final velocity of the mass? If I direct a gigajoule to accelerate a gram over a distance of a meter, I obviously get into real trouble with c using conventional equations. I've found...

A rocket flies past the me with velocity ##0,866## c, therefore ##\gamma=2##. Its length in rest is 10 m. When I am parallel with the last part of the rocket, the rocket stops immediately. The last part stays parralel with me, but the beginning of the rocket jumps for factor 2, therefore jumps...

Homework Statement A high-energy photon collides with a proton at rest. A neutral pi meson is produced according to the reaction ##\gamma + p \to p + \pi^{0}##. What is the minimum energy the photon must have for this reaction to occur? (The rest mass of a proton is ##938\ \text{MeV/c}^{2}##...

Can you please direct me to ref that shows the derivation of the escape velocity from a spherical object that moves in velocity v~c with respect to rest frame? I suspect the escape velocity is increasing (intuitively since the mass increases). Please comment and suggest alternatives.

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...

In two papers of Terrel and Penrose, the concept of Terrel effect were presented. Both of the papers say that "the plane of projection is expanded by a certain factor, which is equal to Doppler factor for certain cases." Now does it mean the area of the projected plane is expanded by that...

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'll start with link describing the phenomenon: https://books.google.com/books?id=WTfnBwAAQBAJ&pg=PA43&lpg=PA43&dq=relativity+twist+rotating+cylinder&source=bl&ots=C2SDJNPF2K&sig=ImFDYGm_0qK7JoDU0ulsxLk3sMU&hl=en&sa=X#v=onepage&q=relativity%20twist%20rotating%20cylinder&f=false Quote: "A...

If I were to have an object that is floating in space, with a radius of 100 m , that is going to crash unto Earth from a distance of 94,725,000 m and a speed of 299,792,455 m/s, how will it affect earth?(in terms of recoil or rebound.)

this wiki link is down. does anyone know the title of the Okun paper or have a link? "For many years it was conventional to enter the discussion of dynamics through derivation of the relativistic mass, that is the mass–velocity relation, and this is probably still the dominant mode in...

Lets suppose there is an observer at a certain distance from a planet that is moving at 0.9c as seen by the observer. We take as a reference, a frame where the observer is at rest. A spaceship leaves the planet and begins accelerating relative to the planet in the oposite direction. The observer...

When would I use the equation ##E = \gamma mc^2## and when would I use ##E^2 = (mc^2)^2 + (pc)^2##? I'm a little confused because my textbook calls them both total energy equations. I know that for a particle at rest it has energy ##E=mc^2##. It can't be at rest for the equation ##E = \gamma...

Wasn't sure whether to post this in SR or QP here, but chose the latter. Assuming: 1. The results of a quantum measurement are random, and that Alice and Bob (performing simultaneous measurements on widely separated, entangled particles) end up with measurements that are perfectly correlated...

I tried to get a relativistically correct expression of ##\int_0^t\frac{dp}{ds}dt## similar to the derivation of relativistic energy expression but I got a result which is not defined: $$\int_0^t\frac{dp}{ds}dt=\int_0^v\frac{d\left(\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}}\right)}{v}$$...

How would a physicists expect a perfect relativist quantum particles simulation to look like? Can anyone give a description of its functionality? Let's say for example, someone would program a simulation, composed of a 4D space-time diagram. Within this simulation are a large amount of quantum...

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...

Homework Statement How much energy does it take to accelerate an object of mass 20,000 kg from rest to 0.9965c? m = 20,000 kg v0 = 0 m/s vf = 0.9965c Homework Equations ## E^{2} = \sqrt{(pc)^{2}+(mc^{2})^2} \\ E_{KE} = (\gamma - 1)mc^{2} \\ \gamma = \sqrt{\frac{1}{1-(v/c)^{2}}} \\ p = \gamma...

If we are considering a problem involving generic photon emitters and detectors that are moving at various relativistic velocities with respect to each other, do we need to move outside of non-relativistic quantum optics? I'd like to stress that this question is not about any definite species...