Relativistic Definition and 1000 Threads

Homework Statement Unstable particles cannot live very long. Their mean life time t is defined by N(t) = N0e−t/τ , i.e., after a time of t, the number of particles left is N0/e. (For muons, τ=2.2µs.) Due to time dilation and length contraction, unstable particles can still travel far if their...

Homework Statement Unstable particles cannot live very long. Their mean life time t is defined by N(t) = N0e−t/τ , i.e., after a time of t, the number of particles left is N0/e. (For muons, τ=2.2µs.) Due to time dilation and length contraction, unstable particles can still travel far if their...

I'm trying to render the sky as it would appear from a starship moving at some large part of the speed of light. Geometry was straightforward, but colors are the problem. How would the doppler effect change the color of a star? The expectation is that the stars behind are red and the ones ahead...

I'm doing a research project on time, the title being "Is our perception of time an illusion?" I have essentially established two main viewpoints, being the relativistic view of time and the quantum view. They both clash of course like in every other way, so I am interested to see if anyone has...

Bell's theorem states that super-luminal communication exists between particles that are separated by space-like separation viz. faster than light transmission of information. There is spontaneity in this. Relativistically this would amount to going back in time. The state of creation of...

[Note from mentor: this thread was originally posted in a non-homework forum, therefore it does not use the homework template.] I have been given an equation for the relativistic doppler effect but I'm struggling to see this as a function and then give a first order Taylor expansion. Any help...

For a highly relativistic rocket powered by an external laser such that the thrust is 2*Power/c, the efficiency is dismal at the start when v is low yet approaches 100% as v approaches c. I take efficiency to mean the ability to convert the energy of the beam into usable kinetic energy. Does the...

Homework Statement Find the speed of a particle whose total energy is twice its rest energy. Homework Equations E2 = p2c2 +m2c4 The Attempt at a Solution 4m2c4 = p2c2 +m2c4 3m2c4 = p2c2 SQRT(3)mc2 = pc SQRT(3)mc = p SQRT(3)mc = mv SQRT(3)c = v I know I can use E = gamma*mc2 to get the...

Is the relativistic Snell's law : $$\frac {sin\theta_1}{sin\theta_2}=\frac {c_2}{c_1}\sqrt {\frac {c^2-c_2^2}{c^2-c_1^2}} $$ ? OR where could I check this ?

Authors: George F. R. Ellis, Roy Maartens, Malcolm A. H. MacCallum Title: Relativistic Cosmology Google Books Link: https://books.google.com/books?id=FPRFi3L0h9kC&printsec=frontcover#v=onepage&q&f=false

I have a simple question on the relativistic view point with regard to light. From wiki, "All inertial frames are in a state of constant, rectilinear motion with respect to one another; an accelerometer moving with any of them would detect zero acceleration." Simply I understand if a physical...

I'm trying to understand the relativistically spinning disk within the framework of SR (if that is even possible). I thought to first simplify the problem by considering a spinning ring/annulus, but I don't know if my analysis is correct. I imagined a spinning ring of radius R, spinning at an...

By classical E&M I mean the general basics. I understand that even classical EM has clear relativistic undertones, but is anything taught classically actually wrong under the context of relativistic EM? For example, does Faraday's law continue to hold etc. I know this is kind of a broad...

I think the relativity provides the Doppler shift (in a radar - double version) in a form: ##\frac{1-v}{1+v}## which is quite simple, as a square of a single Doppler: ##f' = f\sqrt{\frac{1-v}{1+v}}## But I never seen what is a classical version of this - what is a formula for a radar shift in...

I was told in special relavity that f=ma does not always hold true so using the f=delta p/delta t is better. So why is that? They said it had something to do with relativistic mass, at least when traveling at 99.9% of the speed of light.

Hello, I am an electrical engineer rather than a physicist, however, I am trying to understand the physics of a twin wire transmission line in terms of the charge and current density. Let's say we have a lossless, infinite length, twin wire transmission line, a step current is induced into the...

I was trying to understand how the electric & magnetic forces are related. I was going through the equations & the simple explanation of relativistic magnetic field given everywhere. Which goes like this... There is a current carrying conductor & a charge capable of moving outside it. The...

Homework Statement A resting electron was sped up to 0.5 of the speed of light. Find: A. relativistic mass of the electron, B. total energy of the electron, C. kinetic energy of the electron. Homework Equations K = mv^2/2 E=mc^2 The Attempt at a Solution Let’s first find the kinetic energy...

Hello, Question: If Sgr A were to emit relativistic jets, say... to a 90 degree angle from what we see as the Milky Way, how visible would that be to us on Earth? The pictures I see on the internet suggest that the jets are about twice as long as galaxies themselves. This makes me think that...

Hello, I am trying to solve a problem and I have trouble with almost every part of it. Homework Statement For the Lagrangian L=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu} show that \Pi^{\sigma\rho} = \frac{\partial L}{\partial(\partial_{\sigma}A_{\rho})}=-F^{\sigma\rho} Hence show that the...

Hello, It kind of bothers me that the derivation for the Lorentz transformation relies on two dimensions of space. (Here I am referring to the standard derivation where one person is using a vertical light clock in a trolley traveling horizontally at speed v, and an observer outside is...

Homework Statement I am watching a course on Relativistic Quantum Mechanics to freshen up, and I have found to have some issues regarding simple operator algebra. This particular issue on the Pauli Equation (generalization of the Schrodinger equation that includes spin corrections) in an...

Hello all. In Morin's classical mechanics book, chapter 12 (relativistic dynamics), in the axample about the relativistic rocket, we have a rocket that propels itself converting mass into photons and firing them back. Here Morin takes dm as a negative quantity, so the instantaneous mass of the...

Given the relativistic equation for energy E2 = (pc)2 + (mc2)2 I want to find the non-relativistic approximation for kinetic energy in non-relativistic terms, Knr = p2/2m I start off with subtracting the rest energy E0=mc2 from the above equation. So K = E - E0 and assume that c is very...

I'm interested how was measured the famous Mercury's precession: 43'' / cy. How it has been measured? where is the angle 43'' - in this image: http://en.wikibooks.org/wiki/Astrodynamics/Classical_Orbit_Elements The preccesion is about the periapse, so it's defined wrt the node: therefore...

Say there is a theoretical sphere of radius r, at rest, then if it's velocity changes then I assume that the radius is subject to length contraction and thus it's volume would decrease from a stationary observer. Is this assumption true?

I am trying to understand magnetism and its relation to electricity: Suppose there are two electrons traveling side by side in deep space at 1 cm distance at .99 c In this article http://academic.mu.edu/phys/matthysd/web004/l0220.htm it is said that the ratio $F_B/F_E$ is $v^2/c^2$ for v <<...

Homework Statement Hi I've been modelling a particle traveling in a particle detector that has a momentum vector Px, Py, Pz which we've conveniently been using Pperpendicular (i.e. in the xy plane) and Pz. I can calculate the distance traveled in the xy plane and I need to calculate the...

Homework Statement An astronomer sees two objects moving along the same line of sight away from each other. The first object moves away from the Earth with a velocity of 2.5×108 m/s, and the second object moves towards the Earth with a velocity of 1.8×108 m/s. According to this astronomer how...

According to the wiki page: http://en.wikipedia.org/wiki/Matter_wave the generalised form for the de Broglie wave is simply: \lambda = h/p I suppose this not correct, because there is no trasform which can change only one side of the equation. In this case we have two variables: 1. a momentum...

I'm looking at George Smoot's derivation on pp. 2-3 here: http://aether.lbl.gov/www/classes/p139/homework/five.pdf It's elegant and succinct, but I'm having trouble understanding the very last step. Using the Lorentz transformation, he gets this relationship: ##dt = dt^\prime \gamma (1 +...

Homework Statement This is not homework. I am trying to figure out a simple and quick way to find the speed that correspond to a given energy can you tell me if it is correct? . At LHC they had experiments that give protons 7 Tera eV: we know that a proton is .938272 Gev , so...

So I was wondering... for no particular reason: Say you have a proton and your right arm is a particle accelerator. You throw the proton at about 90% the speed o' light. The you take your left arm which also happens to be a particle accelerator and you shoot an electron out right next to it...

It is said many times, from the days of Einstein, Minkowski and Poincaré, that Classic or Newtonian Mechanics are not consistent with motion at relativistic speeds, that a new relativistic mechanics is needed, viz. Albert Einstein: … the apparent incompatibility of the law of propagation of...

Hello, I tried a different route to derive relativistic kinetic energy and I cannot see why it doesn't work. Here is my work: 8.00000000000000E+01 RM, Rest mass of object 7.50000000000000E+05 v, velocity of object 6.00001877636573E+07 Momentum, p,= RM/Sqrt(1-(v^2/c^2))*v...

Let a mass oscillate with relativistic acceleration (sinusoidal) by means which are irrelevant. What does the gravitational field look like a distance R away?

I am trying to find the DeBroglie wavelength of an electron moving at .8c. I have never learned special relativity but I believe the momentum is affected (mass change). I used the formula p= (mv)/(1-v^2/c^2) and got a momentum of p = 2.733 E-22 and a wavelength of lamda = 2.4149 E-12. Did I...

Homework Statement Massive particles are relativistic when their kinetic energy is comparable to or greater than the energy corresponding to their rest mass. (This condition implies that their speed is close to the speed of light.) But what does the comparable mean? Is it that the particle...

Homework Statement In a thought experiment, a train is moving at a speed of 0.95c relative to the ground. A pendulum attached to the ceiling of the train is set into oscillation. An observer T on the train and an observer G on the ground measure the period of oscillation of the pendulum. State...

What would happen if I were to fly toward a gravitational wave pulse at relativistic speed? Would I be destroyed by the Doppler-shifted pulse? Would the wave become visible?

Hi! Yes, I know that faster-than-light travel is impossible. But please stay with me for a while to help me understand this. Let's imagine we take some unobtainium and build a 12-km-radius propeller, attached to an engine able to accelerate it up to 250,000 rpm (like a turbocharger, or not a few...

If you put everything in a rest frame, it seems as if it's impossible to tell an isolated system from a closed system (globally in SR, locally in GR). Am I off my rocker to think so? There's at least one catch I've thought of so far: light. I can't say for sure that it satisfies either...

Homework Statement 2-body, COM frame collision a+b ---> c+d E = Ea+Eb = Ec+Ed Show that dE/dPf = Vc+Vd Show that the answer is the same when the velocities are relativistic I don''t know how to work out the relativistic aspect of the question. Homework EquationsThe Attempt at a Solution E =...

Quote from the wikipedia article of relativistic quantum chemistry: "... These corrections affect the electrons differently depending on the electron speed relative to the speed of light. Relativistic effects are more prominent in heavy elements because only in these elements do electrons attain...

Homework Statement Homework Equations The Attempt at a Solution

Hey, folks. I, on a whim today, started taking a MOOC quantum mechanics course that I have the functional math skills necessary to do but have virtually no background knowledge of quantum to start with and am incredibly rusty on stuff like PDE's; Quite frankly I'm out of my league, but the...

A : If a relativistic particle hit something, does its kinetic energy derived from base mass, or relativistic mass? B : Do we have any data, how it affects a gravity based interaction between two relativistic objects? C : Let's suppose a relativistic isotope emits two particles, one in the...

Homework Statement The given problem is that we have a rocket ship, accelerating at a constant rate of 1g (in its own instantaneous inertial rest frame) for 40 years. We must find the distance it travels in that time, as measured by an observer on earth. Homework Equations dx'=gamma*(dx-vdt)...

Homework Statement This problem comes from an intermediate step in the textbook's derivation of relativistic energy. It states that E_k\:=\:\int _0^u\frac{d\left(\gamma mu\right)}{dt}dx then leaves the following intermediate calculation as an exercise to the reader: Show that...

Do effects like velocity time dilation and gravitational time dilation occur in probabilistic QM, are SR and GR compatible with QM?