Tagged Questions
3
votes
3answers
165 views
Energy conserved… or not? Confused!
I am confused. Could someone kindly explain what's going on in this question?
A particle of mass $m$ and charge $e$ moves in the $x,y-$ plane. There is a constant magnetic field $B$ that points in ...
0
votes
0answers
56 views
Relativistic canonical transformation
What is relativistic canonical transformation? I need every piece of information about it.
Does anyone know a reference or an article about relativistic canonical transformation?
For example, in ...
-1
votes
1answer
44 views
Organic Proliferation In Terms of Speed [closed]
OK for 5 stars...Dealing with Einsteins theory of special relativity:
Here is the question:
As observed on earth, a certain type of bacterium is known to double in number every 24.0 hours. Two ...
1
vote
2answers
123 views
Relativistic Doppler effect derivation
This is about a step in a derivation of the expression for the relativistic Doppler effect.
Consider a source receding from an observer at a velocity $v$ along the line joining the two. Light is ...
2
votes
1answer
93 views
Proton-proton collisions
I have a question about proton-proton collisions at the LHC. Firstly, the 4-momentum $p^\mu=(E/c,\vec{p})$ can be represented as $p^\mu =(m_T \cosh \Psi, p_T \cos \phi , p_T \sin \phi, m_T c \sinh ...
1
vote
1answer
63 views
$\frac{dt}{d\tau}=\gamma$ in special relativity
I hope this is not too silly a question: We often see
$$\frac{dt}{d\tau}=\gamma=\frac{1}{\sqrt{1-v^2}},$$ taking $c=1$.
Problem:
I don't understand why...
In the Minkowski metric, using the ...
0
votes
0answers
35 views
Inelastic relativistic collision [closed]
I have to solve the following problem:
A particle of rest mass, $m_1$, and velocity $v_1$ collides with a stationary particle of mass $m_2$. Find the rest mass $m$ and velocity $v$ of the resultant ...
0
votes
2answers
56 views
Minimum $E$ of $p\bar{p}$-collision for $q\bar{q}$ pair with mass $m_q$
I am currently working out the energy required to create a particle anti-particle pair from a collision of a proton travelling along the x-direction with an anti-proton which is at rest. The particle ...
1
vote
3answers
156 views
Integration by parts to derive relativistic kinetic energy
I have come across a weird integration during derivation of relativistic kinetic energy. Our professor states that i can get RHS out of LHS using integration by parts:
$$
\int\limits_0^x \! ...
0
votes
2answers
279 views
Generating artificial gravity by using rotation
If I want to design for futuristic space stations and I want to use rotation to produce
artificial gravity. One of such designs consists of a giant ring that is rotated about its centre. If it were ...
2
votes
1answer
96 views
Lorentz invariance of the wave equation
I want to show that the 2-d wave equation is invariant under a boost, so, the starting point is the wave equation
$$\frac{\partial^2\phi}{\partial x^2}=\frac{1}{c^2}\frac{\partial^2\phi}{\partial ...
0
votes
1answer
77 views
Developments originating from $E=mc^2$
What kind of significant impacts have originated from $E=mc^2$.
Generally, it is regarded as the most famous equation of all time. Except for nuclear energy (fission and fusion) I do not know any ...
1
vote
2answers
118 views
Lorentz boost matrix for an arbitrary direction in terms of rapidity
We have derived the Lorentz boost matrix for a boost in the x-direction in class, in terms of rapidity which from Wikipedia is:
Assume boost is along a direction $\hat{n}=n_x \hat{i}+n_y \hat{j}+n_z ...
0
votes
0answers
34 views
Special relativity: Related speed [closed]
If a sheep is moving in a velocity of 2mph related to a train, and the train is moving in a velocity of 2mph related to the ground what is the velocity of the SHEEP related to the ground.Is there an ...
0
votes
1answer
78 views
Senior High School work on Doppler measurements
Sorry this question is really vague- as a result I'm very confused. Perhaps you can help me make sense of it.
"Radar measurements: Construct a space-time diagram of the radar tracking of an asteroid ...
3
votes
2answers
125 views
Metric coefficients in rotating coordinates
Let $(t,x,y,z)$ be the standard coordinates on $\mathbb{R}^4$ and consider the Minkowski metric
$$ds^2 = -dt^2+dx^2+dy^2+dz^2.$$
I am trying to compute the metric coefficients under the change of ...
0
votes
0answers
77 views
Sequence of events in special relativity [closed]
I am taking a general education course on special relativity, and get quite confused by problems asking about which event happens first according to different observers. Is there an effective way to ...
0
votes
1answer
72 views
Lorentz Transformations and Aberration
Why does the azimuthal angle, $\phi$, remain unchanged between reference frames in special relativity?
Edit: Here is a link from "Radiative Processes in Astrophysics": ...
0
votes
4answers
179 views
Find total energy and momentum of an moving electron in a rest frame
I have an electron moving with speed $u'$ in a frame $S'$ moving with speed $v'$ relative to a rest frame $S$.
How do I find the total energy and momentum of the electron in the rest frame $S$?
I ...
1
vote
2answers
63 views
Does the sign of $\Delta x$ matter in this time dilation calculation?
I cannot for the life of me figure out what I am doing wrong with this problem:
If a high speed particle travels a distance of 39 Km with a half life of 1 micro sec, what must its speed be to travel ...
1
vote
1answer
113 views
Lorentz transformations for sine wave in random direction
Hello i have been struggling to derive Lorentz transformations for a sine wave, which is traveling at random direction. I started by prooving that phase $\phi$ is invariant for relativity and that ...
5
votes
2answers
285 views
relativistic acceleration equation
A Starship is going to accelerate from 0 to some final four-velocity, but it cannot accelerate faster than $g_M$, otherwise it will crush the astronauts.
what is the appropiate equation to constraint ...
1
vote
0answers
88 views
maximum distance between accelerating objects started at different times [closed]
Let there be two objects that have zero relative velocity with respect to each other in an inertial frame. If they both undergo identical accelerations, but one starts the acceleration at t = T1 and ...
1
vote
1answer
194 views
Why can't this speed be measured?
Superman and Supergirl were playing catch. When Superman is moving with a speed of 0.800c relative to Supergirl, he threw a ball to Supergirl with a speed of 0.600c relative to him.
a. ...
0
votes
1answer
130 views
Decay of particle (for example $\pi^+$); Find energy
I don't understand how to solve this:
A $\pi^+$ decays into a muon and neutrino. Find the pion's energy if
max $E_\nu$ / min $E_\nu$ = 100/1;
$m_\nu = 0$
$m_\pi*c^2 = 140\text{ peta-eV}$
0
votes
3answers
520 views
Getting from $E^2 - p^2c^2 = m^2c^4$ to $E = \gamma mc^2$
What is each mathematical step (in detail) that one would take to get from:
$E^2 - p^2c^2 = m^2c^4$
to
$E = \gamma mc^2$,
where $\gamma$ is the relativistic dilation factor.
This is for an ...
0
votes
0answers
50 views
Taylor approximation of e(v) [closed]
Relativistic mass $\displaystyle m(v)=\frac{m_o}{\sqrt{(1-(v/c)^2}}$
$m_o$ = mass of object measured at rest
$c$ = speed of light ($3\times 10^8\;m/s$)
$v$ = speed
If the total relativistic energy ...
1
vote
1answer
67 views
Perpendicular Fields and Equations of Motion
I have the following problem to solve:
A particle of mass $m$ and charge $e$ moves in the laboratory in crossed, static, uniform, electric and magnetic fields. $\mathbf{E}$ is parallel to the ...
0
votes
1answer
265 views
Special Relativity - Relativistic Dynamics
I've been wrestling with this problem but to no avail. I'm hoping that someone here can give me a little nod in the right direction.
Problem statement:
A thrust-beam space vehicle works bearing a ...
0
votes
0answers
63 views
Relativity Scenario [closed]
Does anyone have any ideas about this scenario? I'm having trouble comparing what happens at the different speeds. It has to do with simultaneity
Suppose Al is at rest standing in between two sets ...
0
votes
0answers
58 views
Which velocity must a particle achieve to triple the relativistic mass of an idle particle [closed]
We have this question in our homework. I have the solution, but I don't know how to get to it. So, I was hoping some of you could shed some light on it.
Solution: $$\frac{2\sqrt{2}}{3}c$$
Thanks in ...
1
vote
1answer
184 views
Knowing the mass and force acting on a particle, how do we derive the relativistic function for velocity with respect to time?
Use this scenario:
An electron gains speed in the Stanford Linear Accelerator (SLA) across 3000 meters, reaching a final velocity of 0.95c due to a constant force pushing on the electron. Given the ...
7
votes
2answers
843 views
Transformation of angles in special relativity
My question is about the problem below
Depicted are two space ships (the USS Voyager and the USS Enterprise), each with velocity $v=c/2$ relative to the space station (Babylon 5).
At the exact ...
1
vote
0answers
111 views
Show that the electric field E in the system at rest is $E=\frac{Q}{4 \pi \epsilon_0 \sqrt{(x^2+y^2+z^2)^3}} (x,y,z)$ [closed]
A body point charge $Q$ moves in relation to the reference system $\Sigma$ according to the law of motion $x(t)=v_0 t$, $y(t)=0$, $z(t)=0$.
