All Questions
36 questions
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1
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How to determine particle energies in center of momentum frame? [closed]
I want to show for the following process that, except for the angle $\theta$, all momenta and energies are fixed by energy-momentum conservation.
Namely:
$$p_A=\frac{1}{2\sqrt{s}}(s+m^2_A-m^2_B\space,...
CommunityBot
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1
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0
answers
94
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Feynman physics relativistic mass
Here is the page I read from Feynman physics. My question is when we ride along in a car moving with horizontal speed of the particle one then we get situation in fig 16-3a, according to last section ...
- 213k
1
vote
2
answers
480
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How important is the concept of rapidity in relativity?
After studying the concept of rapidity and the associated formulation of special relativity in terms of hyperbolic trigonometric functions of rapidity, I've come to understand the elegance of this ...
- 213k
2
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2
answers
423
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Transformation of the Lorentz factor when a relativistic particle partially absorbs energy from a photon?
I came across this paper (on arXiv) that says when a particle with high Lorentz factor $\Gamma$ meets a radiation beam and absorbs some energy $\epsilon$, it's Lorentz factor transforms like so (Eq. (...
- 213k
2
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3
answers
511
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Four-vector of a proton as seen from the rest frame of another [closed]
I have a question regarding the four-vector of two protons. My task is to determine the four-vector of one proton as seen from the rest frame of the other.
I'm having a hard time understanding ...
- 12.4k
1
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1
answer
64
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Why does light change its path in different frames of reference?
A similar question has previously appeared on this site:
Light in Different Reference Frames
But my question is slightly different in nature. The difference would be clear after a read of this ...
- 28.4k
0
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3
answers
137
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Do relativity and frame of reference contradict each other? [closed]
Relativity states that nature doesn't depend on how we look at things, and a physical process is the same no matter what perspective we choose to think about it in, and frame of reference is a set of ...
- 15.5k
3
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1
answer
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Proof of Lorentz invariant phase space factor
I was going through the following proof of Lorentz invariant Phase space (in Modern Particle Physics by Mark Thomson).
Could someone please help me understand how the equation in the box is valid? If ...
CommunityBot
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0
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65
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Definition of acceleration and inertial frames of reference
Sorry for my math lacks, I hope you'll be patient even if this question will probably not be clear.
How can we define acceleration in special relativity (and in Newtonian mechanics were we apply ...
- 213k
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1
answer
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Special relativity - Center of mass frames vs Laboratory frames
In the reaction where particle A hits particle B, which is at rest. This produces
particles C and D. For the minimum energy of particle A for the reaction to take
place I have two calculations. I don'...
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1
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1
answer
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To prove: the integration measure is Lorentz invariant (Schwartz's problem 2.6b)
I am stuck on Schwartz's ("Quantum Field Theory and the Standard Model") problem 2.6b, and would be grateful for clarification. (I'm aware that this question has been asked and answered elsewhere (...
0
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3
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Is there any explanation from special relativity regarding the speed of a fly inside a car?
I have faced a scenario mentioned in this Question.
There was a fly inside my car and I was travelling so fast. shutters are opened in the car. I observe that when I slow down and accelerate, there ...
- 14.1k
1
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1
answer
62
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Interpretation of a basic Special Relativity problem using tensors
I'm solving a problem in which a muon with a half life of $\tau=10^{-6}s$, generated at 30km of altitude, travels at an unknown velocity. I'm asked to calculate its velocity and then the distance in ...
- 213k
0
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1
answer
83
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How to find the coordinates for a worldline with $y=z=0$ that experiences constant acceleration?
I'm studying some lecture notes on special relativity and at some point one considers an inertial system in which a particle has $4$-velocity and $4$-acceleration given by
$$U = (c\frac{dt}{ds}, \frac{...
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votes
1
answer
51
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A question about the Lorentz transformation of "infinitesimals"
Notations conventions: $p$ stands for the momentum (so $d^3p$ is the differential element according to which we integrate, for the $3$ space coordinates). A Lorentz transformation is denoted by $\...
- 213k
0
votes
2
answers
313
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Dependence of Lorentz factor on only a component of velocity
In cases of two- or three-dimensional space, why doesn't the Lorentz factor of a component of 3-space momentum depend on only the corresponding component of velocity? That is, why isn't there, for ...
- 213k
1
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0
answers
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General 2D equations of motion in non-inertial relativistic frame of reference
Let's assume that there is inertial frame of reference $S$, and the observer is at the origin of this frame at time (associated with this inertial frame) $t = 0$. The observer has own frame of ...
- 213k
0
votes
1
answer
467
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Partial derivative of a 4-velocity
Trying to do some basic manipulations with 4-vectors and I have a question about the proper (no pun intended) approach. It's probably easiest if we look at a simple example. So let's define a 4-...
- 213k
1
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3
answers
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How to prove the relativistic momentum? [duplicate]
As far as I know, the relativistic momentum of a particle is given by the equation: $$p=\frac{m_0v}{\sqrt{1-\frac{v^2}{c^2}}}$$
where $m_0$ is the mass of the particle and $v$ is the velocity of the ...
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0
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53
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Energy and momentum conservation equations for frame moving at speed $v$
A particle of rest mass $M$, while at rest in the laboratory, decays into a particle of mass $m$ and speed $v$, and a photon of frequency $f$ moving in opposite direction.
I want to look at this ...
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votes
1
answer
2k
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Lorentz transformation four momentum to to lab frame
I would like to know how to transform from a generic four momentum of the form:
$(E, p_x, p_y,p_z)$
to the frame where the $y$-component is zero:
$(E^\prime, p\sin\theta, 0, p\cos\theta)$
What is ...
- 52.2k
0
votes
1
answer
193
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Derivation of simple Lorentz boost identity, $dp'_z/dp_z$
Given a Lorentz boost in the $z$-direction, in natural units we can write
$$p'_z = \gamma(p_z+\beta E)\,,\;\;\;\;\;E' = \gamma(E+\beta p_z)\,.$$
In Peskins & Schroeder's Introduction to QFT, p. ...
- 145
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votes
0
answers
40
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Calculating center-of-mass enegies for processes/reactions
Let's take any arbitrary process: $d\overline{d}\rightarrow g$.
Let's say I am interested in the center-of-mass energy at which the process can take place. How can I calculate it for any given ...
- 213k
0
votes
2
answers
1k
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Special Relativity; 3 Momentum Conservation
In SR, I understand you can use 4 momentum conservation, but what are the special cases where you can use 3 momentum/energy conservation?
An example I have seen is with
$$P_1=(M_1, 0) \\ P_2=(M_2,0) \...
- 213k
3
votes
2
answers
1k
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Factorising a 4D Dirac delta function in a rest frame
I'm working through a QFT problem and at one stage in the solutions we have this step:
$$\delta^{(4)}(p - q_1 - q_2) = \delta(E_1 +E_2 - M)\delta^{(3)}(\bf{q_1} - \bf{q_2}).$$
We are working in the ...
- 213k
3
votes
1
answer
3k
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Transformation of $4-$velocity
Notation: a greek index indicates four labels; spacetime coordinates $\mu = (0,1,2,3)$. A latin index indicates three labels; spatial coordinates $i = (1,2,3)$.
$$* * *$$
A quantity, to be ...
- 16.4k
1
vote
2
answers
336
views
Rocket faster than light?
In this article, wikipedia describes a constantly accelerated rocket, assuming special relativity :
$$ x(\tau) \;=\; \frac{c^2}{a} \left(\cosh \frac{a \ \tau}{c} -1 \right) $$
The proper time $\tau$ ...
- 20.8k
0
votes
2
answers
573
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Momentum in the rest frame
I am a little confused over the terminology of the rest frame. Say a photon collides with a massive particle then from the rest frame of the massive particle would it be the photon or the particle ...
- 26.6k
1
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1
answer
167
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Writing source four velocity for Lorentz boosted frame
I am trying to derive the source four velocity for Lorentz boosted frame. If the source four velocity for rest frame is denoted as $U^{\alpha} = (1, \bar 0)$, then how do I write this $U^{\alpha}$ for ...
- 16.4k
0
votes
2
answers
1k
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Lorentz Boost of the Lab Momentums
Lets assume we have a two body scattering like;
$$a + b = c+d$$
In the lab frame particle $a$ is moving with a certain beam energy $E_a$, and hits stationary particle $b$. Before the collision, ...
- 12.4k
2
votes
2
answers
6k
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Energy in the Relativistic COM Frame
I have been taught that in Classical Mechanics, the total energy of a system of two particles in the Centre of Mass Frame is given by
$$
E_\mathrm{total} = \frac{1}{2}MV^2 + \frac{1}{2}\mu v_r^2
$$
...
1
vote
1
answer
105
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Change in frequency of light clock due to to acceleration
The problem statement:
A light-clock (a photon travelling between two mirrors) has proper length l and moves longitudinally through an inertial frame with proper acceleration $\alpha$ (ignore any ...
- 2,145
0
votes
1
answer
4k
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Finding the total energy in centre of mass frame
I'm working through a problem in a special relativity textbook (Woodhouse) and I'm having some difficulty.
I have to show that if I have a particle of rest mass $M$, total energy $E$ colliding with a ...
CommunityBot
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1
vote
1
answer
392
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A fast object (0.8c) getting overtaken by another fast object (0.9c): why don't times agree?
I'm trying to work on an exercise in Wolfgang Rindler's book "Introduction to Special Relativity" and I'm stuck on the following exercise:
Two particles move along the x-axis of S at velocities 0....
- 213k
0
votes
1
answer
768
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Problem conserving 4-momentum at CoM frame in an inelastic collision [closed]
I am confused about the case where mass is not conserved in a collision (not due to relativistic factors). The center of momentum (CoM) frame is not the same before and after the collision.
Let's ...
- 10.4k
3
votes
1
answer
216
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Special relativity kinematics problem [closed]
I have this problem in SR kinematics.
a spaceship travels near earth at c/2. it shoots off a light-ray at 45deg to its direction of travel (measured in its own ref frame). What is this angle in the ...
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