Questions tagged [special-relativity]
The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.
1
vote
0answers
14 views
Converting a general QFT state to another inertial of light-cone reference frame
Assume, in a certain reference frame, a relativistic QFT at time $t=0$ is in the state
$$
\hat{\Psi}(t=0) |vac\rangle \quad,
$$
where
$$
\hat{\Psi}(t) = \operatorname{e}^{-i\hat{H}t} \sum \limits_{n=1}...
0
votes
0answers
17 views
Angular momentum of a circualr polarized EM wave
In an exercise, I am being asked to compute the angular momentum of a circularly polarized wave.
The wave is defined by the four potential:
$$\Phi^\mu(x^\nu) = \text{Re} \left\{ \varepsilon^\mu e^{...
0
votes
2answers
39 views
Relativistic Mass when Viewed from Different Frames of Reference
I understand relativistic mass and the equations underpinning it. My question deals with how to calculate relativistic mass when an object is viewed from different frames of reference.
Consider a ...
2
votes
0answers
32 views
Can the Dirac Hamiltonian accommodate a variable speed of light?
The Dirac Hamiltonian has the form1
$$\left[\beta m c^2+c\sum_{n=1}^3\alpha_np_n\right]$$
where $\alpha_n$ and $\beta$ are Hermitian matrices, and $c$ is the speed of light.
My question: Is there a ...
0
votes
2answers
60 views
Another objection to Feynman's moving infinite sheet of charge “radiator”
In The Feynman Lectures on Physics Vol II 18-4, A travelling field we are provided the thought experiment of two uniformly and oppositely electrically charged planar sheets of infinite extent lying in ...
0
votes
3answers
56 views
How are these two definitions of energy related/derive from each other?
How are these two definitions of energy related/derive from each other:
$$E = \frac{mc^2} {\sqrt{(1 - v^2/c^2)}}$$
vs.
$$E = \sqrt{m^2c^4 + p^2c^2}~?$$
Both equations express the relation between ...
5
votes
0answers
62 views
Consider two electrons released from rest at a distance $d$. How much energy is radiated?
Abraham-Lorentz?
Two electrons d apart have potential energy. Release them, they will be repelled according to Coulomb's law.
I could make an assumption about the associated vector potential, but I ...
0
votes
1answer
28 views
Can the Hermitian conjugate of a column vector still be column vector?
From what I understand, contravariant vectors are represented by column vectors, and covariant vectors are row vectors. So for a QED current, say $j ^ { \mu } = \overline { \psi } \gamma ^ { \mu } \...
1
vote
1answer
57 views
$(1,1)$ representation of $SL(2,\mathbb{C})$
How do you prove that the $(1,1)$ representation of the $SL(2,\mathbb{C})$ group acts on symmetric, traceless tensors of rank 2?
0
votes
0answers
43 views
Showing the Lorentz-Fitzgerald length contraction
I'm trying to show that if we have a rod of length $L$ that is at rest wrt the inertial frame $K$, and we have a observer $K'$ moving wrt $K$ with speed $v_0$ in the direction along the length of the ...
0
votes
2answers
169 views
Is the acceleration of two objects with different temperature same with the same force? [on hold]
$F=ma$ is not the case at relativistic speeds. But what is the total energy including mass which resists against force?
0
votes
0answers
101 views
A Non-Velocity Dependent 4-Vector Transformed as Velocity Dependent 4-Vector
I would appreciate it if someone could explain the following:
It is understandable that the Minkowski space Gauss' and Ampère-Maxwell equations in index notations
\begin{equation}
\partial_{\nu} F^{\...
1
vote
1answer
97 views
What if a spaceship going half the speed of light turned on its headlights in both directions?
If the spaceship, travelling at c/2 were to turn on only its forward facing headlights, then after one second (relative to us, the stationary external observers) we would see that the ship has moved ...
1
vote
0answers
24 views
information theory and energy mass relationship (E=mc2) - just a hunch … [on hold]
I was walking on the street the other day and thought to myself, maybe E=mc2 can be derived from information theoretic principles.
I did not do too much work on this, just want to brainstorm a bit.
...
-1
votes
0answers
19 views
Is Time a relative quantity if yes, How? [duplicate]
According to the theory of relativity, time dilation is a difference in the elapsed time measured by two observers, either due to a velocity difference relative to each other, or by being differently ...
2
votes
2answers
60 views
Do lengths contract or expand due to relativity?
Ok I have a simple question.
We consider two frames, one is $F$ which is at rest and one is $F'$ which is moving with $v_0$ in the $+X$ direction with respect to $F$. Suppose a rod is at rest in $F$ ...
0
votes
0answers
23 views
Would massless (infinitely) rigid rods have inertia in Special Relativity? [on hold]
It is known that infinitely rigid rod cannot be accelerated in Special Relativity: if two particles accelerated with the same acceleration, the distance between them changes.
So, if the rod is ...
0
votes
1answer
60 views
Space time diagrams : Length contraction
I am trying to get a better understanding for length contraction in a geometric sense and came across this diagram:
but what I am having trouble with is why in the ref frame of the blue vector ...
-1
votes
1answer
55 views
Action and reaction [on hold]
If Plank's constant h physical meaning action can be related with the Action of Sir Issac Newton's third law of motion.
Secondly, In Newton's third law of motion if actions represent force only , not ...
0
votes
0answers
17 views
What happens to a uniform electric field when a point charge is sent moving in a direction neither parallel nor perpendicular to the field?
If you have two reference frames, one where a charged particle is stationary but in a uniform electric field, and another where the system is moving at speed $\vec v$ in a general direction (neither ...
1
vote
1answer
93 views
Surjectivity of momentum mapping
I have to show that the following mapping of momenta is surjective. The mapping $\{p_i^{\mu},p_j^{\mu},p_k^{\mu}\}\rightarrow\{\tilde{p}_{ij}^{\mu},\tilde{p}_k^{\mu}\}$ is given by
$$
\tilde{p}_k^{\...
1
vote
0answers
31 views
3-particle phase space in $d$ dimensions
recently I came across a problem concerning the 3-particle phase space. I am trying to show, that the 3-particle phase space for massless particles with momenta $p_1$, $p_2$ and $k$ is given by
$$
d\...
0
votes
0answers
23 views
A bus and a ditch - an extension of the barn ladder paradox [duplicate]
Suppose, a bus is travelling with constant velocity in a straight road, and there is a ditch in front of it.
Suppose, the rest length of the bus and the ditch are equal.
Suppose the speed of the bus ...
2
votes
2answers
77 views
How do we know that light cannot travel faster than it does?
We assume the speed of light in vacuum is its maximum speed but can we not assume that it could be faster, or slower?
1
vote
1answer
36 views
Lorentz transformation of intensity
I have come up with an expression for the way intensity transforms, however it is different to the book, and I cannot seee where I have gone wrong.
So we both start the same way:
$$
\frac{I}{I_0}=\...
-1
votes
0answers
18 views
Time dialation in General realtivity and Special relativity are same? [duplicate]
I came across a thought experiment .Consider two persons A and B both have a very accurate and synchronized clocks now if A moves with a velocity compareable to c then its his clock will run slower ...
-1
votes
1answer
70 views
Is speed of light is the only way to measure time [on hold]
After reading up on special relativity, I understood that because of Einstein's postulates
-the speed of light in free space is a universal constant
Everytime we measure time for an event, directly ...
3
votes
1answer
90 views
Special relativity: I arrive at a contradiction regarding the Lorentz invariance of certain quantity
I want to show the Lorentz invariance of $d^3 p/E$ (Eq. 8.11 of Mandl-Shaw), where $E$ is the relativistic energy. Peskin-Schroeder gives sort-of, a proof in section 2.3 which I am convinced of. But ...
0
votes
1answer
36 views
Relation of the Lorentz group to $O(1,3)$
Let $\Lambda$ be an element of the Lorentz group. It satisfies the identity:$${\Lambda}^T\eta\Lambda=\eta$$ where $\eta$ is the Minkowskii metric. Hence by the usual definition of orthogonality, $\...
2
votes
0answers
54 views
Can spherical harmonics be used in relativity equations?
I have a neutral pion of mass $m_{\pi}$, and it decays into two photons. In it's reference frame the decay is isotropic. One of the photons has a helicity of $+\hbar$ and the other $-\hbar$. In ...
-3
votes
1answer
68 views
What are the relativistic arguments for existence of space? [duplicate]
One of the interpretation of special relativity states that the time is an illusion and does not really exist. This interpretation promoted Einstein himself in his condolence letter after the death of ...
-1
votes
0answers
26 views
How to define events in special relativity [duplicate]
See my answer to this question:
What is an event in Special Relativity?
I'm not actually sure of this answer. What I do know is that: equations of motion (dynamical laws of physics), the minkowski ...
0
votes
0answers
51 views
Why am I not getting the right values for the time it takes a spaceship to get to 0.9c? [duplicate]
I'm attempting this problem:
Rocket undergoes constant acceleration from rest until it reaches a speed of 0.9c. The astronaut in the rocket feels a constant "induced gravity" of 1g. How long does it ...
-1
votes
0answers
66 views
Rod ring paradox in special relativity
We have a ring and a rod whose centres lie in the x,z plane. The plane of the ring is perpendicular to the z axis, and the rod is parallel to the x axis. The rod is slightly larger than the ring at ...
0
votes
2answers
42 views
Question about derivation of four-velocity vector
In order to describe a notion of rate of change of positon, in four-dimensional spacetime, we have to introduce the concept of four-velocity.
So, consider the following:
For a massive particle ...
1
vote
1answer
27 views
Relativistic Doppler Effect - calculate frequency $f'$ and $f$ in references $S'$ and $S$
Considering that $S$ (fixed) and $S'$ are inertial references which coincides when $t=t'=0$ and their coordinates $(ct,x,y,z)$ and $(ct',x',y',z')$ are related by Lorentz's transformations, calculate ...
0
votes
0answers
42 views
If I walk and you stand still, do you get older than me faster?
I was watching a video from Aurelien Barrau about relativity and time.
As he was talking to the audience, he said that since he was walking on stage, he was ageing slower than people sitting in the ...
1
vote
2answers
43 views
Magnetic force under change of reference: Do Maxwell's equations hold?
Suppose I have a uniform magnetic field through all of space
$$\textbf{B}(x,y,z)=\hat{\textbf{z}}$$
and a charge $q$ moving at a velocity of $v\hat{\textbf{x}}$. In this frame of reference, a magnetic ...
1
vote
3answers
80 views
Speed vs Velocity of light in Light clock thought experiment
A related question has been asked multiple times (like here, here and here). But none of those answers are clearing my doubt. In fact they're furthering my confusion. My specific doubt is regarding ...
3
votes
1answer
84 views
Is this geometric argument enough to show that special relativity assumes flat spacetime?
I am preparing myself to teach a class about special relativity a few weeks from now. To make sure they'll understand that spacetime must be flat for special relativity to work, I came up with the ...
3
votes
1answer
51 views
Are there other processes theoretically out there that can cause time dilation besides gravity and velocity?
I am just wondering if there is anything else besides gravity or velocity that causes time dilation in regards to special relativity or other theoretical models of our universe.
3
votes
0answers
43 views
Rindler Coordinates Derivation
In my GR lectures we've derived Rindler coordinates by first showing that the four velocity, which we defined as $$u^{\mu} = (\gamma c, 0, 0, \gamma u),$$ as a function of proper time can be written ...
2
votes
2answers
64 views
Is it possible to speed up time using Special Relativity?
I know that with special relativity when having more velocity than a stationary observer your time relative to the observer slows down. Is it possible using special relativity to increase your time ...
1
vote
0answers
98 views
Lagrangian method for finding Lorentz transformation [closed]
Consider a very general case: one reference system (x', y', z') is moving away from another fixed system (x, y, z) with constant speed $v$ (like in the fig. a little bit below).
Normally, using the ...
2
votes
3answers
98 views
A twisted triple paradox
As far as I know when a person travels with some velocity relative to other person time runs slower to him relative to the other person (Because the velocity of light is constant in all frame of ...
-2
votes
1answer
74 views
Speed of light question [closed]
Is this true?
1) c + 25 = c
Also how was the speed of light measured?
Did they use a black body to capture the excessive light back then?
3
votes
1answer
55 views
(Apparent) Paradoxes in General Relativity [closed]
I find that studying the paradoxes of special relativity, such as the twin paradox, ladder paradox, and Ehrenfest paradox, and their resolutions, helps me to understand it.
Are there any similarly ...
2
votes
2answers
87 views
How does inertia work at the particle level?
I've read recently that the mass of a proton is mostly not given by the Higgs mechanism. But rather it's given by the energy of quarks moving around inside the proton and gluons and other internal ...
1
vote
1answer
94 views
Minkowski metric under coordinate change
We are given the Minkowski metric $g_{ab}=\textbf{diag}(-1,1,1,1)$ and want to calculate $\tilde g_{ab}$ in the coordinates
\begin{align}
\tilde x^0 &= t-z \\
\tilde x^1 &= r\\
\tilde x^2 &...
1
vote
6answers
119 views
Thought experiment - faster than speed of light travel [closed]
I came up with a thought experiment and it has been on my mind for quite some time now. Would like to hear the thoughts of others as my wife has no clue what I'm talking about.
Given two points of ...
