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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Is the cross section of a relativistic water hose or string always a perfect circle?

Given is a very long tube, such as a water hose or a tubular string with finite thickness, that has a constant circular cross section of radius $r$ along the length and that is at rest in an inertial ...
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110 views

Deriving the relativistic Larmor equation

I have derived the Larmor equation as $$P = \frac{q^2}{6\pi \epsilon_0 c^3} |\ddot{r}|^2.$$ How do I make this relativistic? Apparently, I have to consider the acceleration parallel and ...
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374 views

microcausality and locality

There is this thing I got confused: Microcausality is the statement that spacelike separated local field variables commute so that we can specify field variables on a spatial slice as a complete ...
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86 views

Relativity addition and signs

I have just covered a very brief module on special relativity as a part of my physics course. I have also done some extra reading mostly; Morrin's Classical Mechanics. While I found the book really ...
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172 views

Relativistic Transverse Doppler Effect

In Minkowski spacetime, two observers, A and B, are moving at uniform speeds u and v, respectively, along different trajectories, each parallel to the y-axis of some inertial frame S. Observer A emits ...
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99 views

About the speed of light

If Mr. E is aboard a spaceship traveling near the speed of light the usual reason for the spaceship not going faster than $c$ is the (relativistic) mass of the ship increases without bound, I think. ...
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127 views

Hidden momentum

I'm trying to learn about hidden momentum. After reading what I could find with a google search, I understand that it is equal to the momentum carried by radiation, calculated with the Poynting ...
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202 views

Translational and Rotational Energy in Special Relativity

In non-relativistic classical mechanics: $$\tag{1} \begin{eqnarray} \text{KE}&=&\frac{1}{2}\sum_i m_i v_i^2=\frac{1}{2}\sum_i m_i (\vec{v}_{cm}+\vec{v}_{i,rel})^2 \\ ...
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What speed should have an alone planet to have a habitable zone due to relic radiation?

What speed should have an alone planet to have a habitable zone due to relic radiation, without any star involvement? How much time the planet will be able to remain in the habitable zone before the ...
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129 views

Majorana equation and non-invariance of spinor representation under discrete Lorentz transformations

Here I asked about getting an equation for two-component spinor as the alternative for Dirac equation. It was found that it is called Majorana equation. It may be easily derived by using historical ...
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82 views

(References) Study of Asymptotically Flat spacetimes

I am interested in studying the asymptotic structure of Minkowski spacetime in General Relativity. I believe most of the work in this area concerns the asymptotic structure of Minkowski space at null ...
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47 views

Does FTL signaling allow signaling in the past at the cost of arbitrary precision?

In a recent paper (http://link.springer.com/chapter/10.1007/978-3-642-30870-3_53#page-1), G. Szekely and P.Nemeti wrote the following. Let us consider two reference frames A and B initially, at event ...
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94 views

Consistency of equation with special relativity?

The following is the equation which, I want to know, if it is valid in relativistic domain. Consider two equal charges moving in same direction with velocity $v$ and charge $q$ at a separation of ...
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192 views

Charge above a conductor; effects due to Lorentz force law for moving charges

Currently working through a practice preliminary examination problem. I have your standard charge situated a distance d from a infinite conductor(lets say in the $\hat{z}$ direction and neglecting ...
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77 views

Manipulating a formula for a relativistic Doppler shift

Lets say we take the standard configuration when $x'y'$ is moving away from system $xy$ (image 1). By knowing that the phase is constant in all frames $\phi=\phi'$ we can derive the Lorenz ...
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62 views

minimal proper time curves bounded on acceleration

Assuming Minkowski spacetime, we know that the longest proper time curve joining two points is the rect joinining both events, While the shortest time-like curve is not a compact set (because there ...
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572 views

The definition of Lorentz transformation

I know that the Lorentz transform, when two frames $\mathcal{S}$ and $\mathcal{S}'$ are in standard configuration (the axes are all parallel to their counterparts in the other inertial frame) is ...
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213 views

Solving the equation of relativistic motion

How does one solve the tensor differential equation for the relativistic motion of a partilcle of charge $e$ and mass $m$, with 4-momentum $p^a$ and electromagnetic field tensor $F_{ab}$ of a constant ...
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104 views

Car parking special-relavity puzzle

Hi I read the following puzzle from an old text book long time ago. However it doesn't provide the answer. So what is the solution? Let's suppose a car is going to park to a garage and the garage is ...
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190 views

How do I extend the Lorentz transformation metric to dimensions>4?

How do I extend the general Lorentz transformation matrix (not just a boost along an axis, but in directions where the dx1/dt, dx2/dt, dx3/dt, components are all not zero. For eg. as on the Wikipedia ...
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Are objects like $a^{\mu \nu} a_{\mu \nu} b^{\mu \nu}$ consistent with Einstein summation?

I'm familiar with Einstein' summation notation and I understand objects like $a^{\mu \nu} a_{\mu \nu}$ just fine. But I'm wondering why I've never come across objects like this: $a^{\mu \nu} a_{\mu ...
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55 views

QFT: Ground State Momentum - Normalisation of States

In my notes I have, $$ \left\langle \mathbf{p} \left| \mathbf{q} \right.\right\rangle = \left\langle 0 \left| {a(\mathbf{p})}\ {a(\mathbf{q})}^{\dagger} \right| 0 \right\rangle $$ I am not sure how ...
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Classical Fermion and Grassmann number

In the theory of relativistic wave equations, we derive the Dirac equation and Klein-Gordon equation by using representation theory of Poincare algebra. For example, in this paper ...
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25 views

How much is the maximum posible information travel speed in medium?

Light has slower speed in medium. Should we consider this when we use special relativity in atmosferic(or any other type of medium) motions? If we should use vacuum light speed, does it mean photons ...
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22 views

Spin of a gauge field

I was wondering what is the simplest way to understand the reduction of the Wigner's little group from $SO(d-1)$ to $SO(d-2)$ when one considers massive and massless fields respectively (in a $d$ ...
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73 views

Confusion about reading of clock as seen from different inertial systems

Suppose a clock, located at point $x'$ in the inertial frame $S'$, registers two events $t_1'$ and $t_2'$. Let $\Delta t'=t_2'-t_1'$. The same two events will be registered by two different ...
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39 views

Spacetime as a coset of a symmetry group

In the introduction to his nice PNAS paper on symmetry, David Gross said Einstein’s great advance in 1905 was to put symmetry first, to regard the symmetry principle as the primary feature of ...
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28 views

Fixed background theories which feature lorentz invariance?

Are there fixed background theories that also display lorentz invariance? Could be with lorentz invariance being true only approximately at some limit... Realized we can still arrive at time-dilation ...
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40 views

Calculus/Vector Calculus and so on in special relativity book recommandation

I want to learn calculus 1,2,3 vector calculus, analysis and so on in special relativity. But I never found a good and clear book/source on it. Can someone recommend an easy book or internet source on ...
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48 views

What is the relationship between the “mass” of QFT and that of Newtonian mechanics?

In QFT we work with Lagrangians which contain terms $m$ such that the relativistic relation $E^2 = p^2 + m^2$ is satisfied. By classical analogy $m$ is called the 'mass'. We note that due to the ...
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27 views

Why does inter-electron distance in wire grow with acceleration?

When you have an electrically neutral wire, and apply a voltage across it, free electrons (provided by source) flow through the wire and thus an electric current is created. Assuming an ideal ...
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40 views

Are relativistic spacecraft slowed down by oncoming gamma ray photons?

I recently read that a proton having an energy of ten billion GeV can travel across our galaxy in about 5 minutes from the frame of the proton. From the Earths frame we would see it take roughly ...
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invariant angles in Minkowski space

Invariant intervals are fundamental in relativity. But if you make a triangle in space-time from 3 invariant intervals, then it will also have 3 invariant angles, by the cosine law which can easily be ...
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Is Lorentz Transformation about the difference of coordinates or coordinates of itself?

I have seen different authorities talking about different interpretation of Lorentz transformation. In his book 'Introduction to Classical Mechanics', David Morin states We always talk about eh ...
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55 views

The derivation of the irreducible representations of the Lorentz group

I took the way of classification of Lorentz group representations from Sexl, Urbantke, Relativity, groups and particles (Germ. ed. 1975). But I don't understand it as I outline in the following: In ...
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Would magnetic charge (i.e., magnetic monopoles) be Lorentz invariant if it existed?

Would magnetic charge (i.e., magnetic monopoles) be Lorentz invariant if it existed? It is clear that Maxwell's equations in themselves permit magnetic charges but what would their relativistic ...
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53 views

Total cross section of particle decay

Suppose a particle A travelling along the $z$-axis and decays into particles B and C. The cross section is given by $$\frac{d\sigma}{d\cos\theta^*} = k(1+\cos\theta^*)^2$$ where $k$ is a constant ...
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Taking a 'relative' limit

I am looking at Hamiltonians for specific physical situations. I have taken a given Hamiltonian $\vec{H}(\vec{p}, \vec{x})$ and have found the following Hamiltonian equations: $$\frac{d\vec{x}}{dt} = ...
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33 views

How to find the generators of a deformed boost?

I'm reading the paper arXiv:gr-qc/0012051 on doubly special relativity. In page 7, the author wants to find the generators of a deformed boost that preserves $$E^2 = p^2 + m^2 - l_p p^2 E$$ ($l_p$ is ...
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53 views

Travelling twin's clock in twin paradox on the way back

Suppose the situation of the twin paradox: twin A stays on Earth, the other (B) goes to a star with velocity $v$, and at the beginning of the journey their clocks were synhronized. We know that when A ...
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30 views

What does it mean to perturb the electromagnetic energy with respect to a change in a Lorentz frame?

I am perturbing the energy of an electromagnetic field using \begin{align} \dfrac{\partial U}{\partial \zeta} = \dfrac{1}{\mu} \boldsymbol{H}\cdot \dfrac{\partial \boldsymbol{H}}{\partial \zeta} + ...
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36 views

How to add together non-parallel rapidities?

How to add together non-parallel rapidities? The Lorentz transformation is essentially a hyperbolic rotation, which rotation can be described by a hyperbolic angle, which is called the rapidity. I ...
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64 views

Space and time variant? But together invariant?

I admit I'm having difficulty with spacetime. I don't understand how unifying space and time, seemingly variant quantities, results in an invariant spacetime. All texts and references talk about using ...
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51 views

Are reversible and irreversible processes frame dependent?

since it is all about time. If I have a look at an irreversible process from a frame where time runs really slow. is there a possibility of considering that process reversible from that frame?
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Two spaceships are accelerating equally, uniformly on exactly parallel tracks. Does a rope suspended between them eventually rip?

This question is a variant of "Bell's spaceships problem". Rather than one spaceship following the other "on the same track", let the two spaceships accelerate "side by side", on exactly parallel ...
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34 views

Homogeneity of the Lorentz Transformation

The standard Lorentz transformation is linear and homogeneous. This fact implies the following: $\Delta t'= \gamma\ (\Delta t - \frac{v \Delta x}{c^2}),\ \Delta x'= \gamma\ (\Delta x - v \Delta t),\ ...
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Two particle collision - excited particle emits photon absorbed by the other particle

Part (a) Doing everything in the lab frame: 4-vector before collision: $(Mc,0)$ Let $E$ be energy of photon emitted, p be momentum of de-excited particle. 4-vector after collision: ...
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What does the temperature of the early universe tell me?

I am re-reading Weinberg's book "The First Three Minutes". In the Introduction he makes this statement: "At about one-hundreth of a second, the earliest time about which we can speak with any ...
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Compatibility of twin paradox with the time-dependent Hubble constant

The universe is currently expanding with a speed of about 70 km/sec/Mpc which is today's Hubble constant. As this expression includes two length units, it is also possible to use the unit: $sec^{-1}$, ...