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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.

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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}...
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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^{...
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2answers
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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 ...
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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 ...
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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 ...
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3answers
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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 ...
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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 ...
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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 } \...
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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?
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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 ...
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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?
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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^{\...
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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 ...
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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. ...
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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 ...
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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 $F$ ...
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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 ...
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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 ...
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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 ...
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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 ...
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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^{\...
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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\...
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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 ...
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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?
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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}=\...
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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 ...
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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 ...
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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 ...
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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, $\...
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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 ...
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1answer
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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.
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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 ...
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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 ...
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0answers
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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 ...
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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 ...
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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?
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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 ...
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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 ...
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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 &...
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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 ...