The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.

learn more… | top users | synonyms (5)

2
votes
0answers
60 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 ...
2
votes
0answers
421 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 ...
2
votes
0answers
183 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 ...
2
votes
0answers
100 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 ...
2
votes
0answers
177 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 ...
1
vote
0answers
26 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 ...
1
vote
0answers
46 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 ...
1
vote
0answers
21 views

Is macroscopic causality an issue in the context of certain quantum experiments?

In order to formulate my question properly I need to explain a few things. Cramer_Herbert Zych_Brukner Reference 1. - John Cramer, Nick Herbert, "An Inquiry into the Possibility of Nonlocal Quantum ...
1
vote
0answers
26 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} + ...
1
vote
0answers
28 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 ...
1
vote
0answers
32 views

Polarization vector identity in Minkowski space?

Playing around with numerical light-like momenta $p^\mu_1,p^\mu_2$ (light-like meaning ${p_1}^\mu {p_1}_\mu={p_2}^\mu {p_2}_\mu=0$) and corresponding circular polarization vectors ...
1
vote
0answers
43 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 ...
1
vote
0answers
41 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?
1
vote
0answers
51 views

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 ...
1
vote
0answers
26 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),\ ...
1
vote
0answers
30 views

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: ...
1
vote
0answers
45 views

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 ...
1
vote
0answers
36 views

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: $sec^{-1}$, ...
1
vote
0answers
57 views

Perceived direction of light emitted in moving reference frame

I was thinking the other day about the simple example used to demonstrate time dilation effects and to derive the Lorrentz factor - where the time it takes for a light pulse to be emitted, bounce of a ...
1
vote
0answers
58 views

2 questions on 4-velocity

Firstly 4-velocity is defined by $u^\mu=\frac{dx^\mu}{d\tau}$ let us consider the component $x_i$ of $x^\mu$ then this derivative can be written as: ...
1
vote
0answers
34 views

Clock synchronazation in special relativity using signal other than light

I'm reading Taylor & Wheeler "Spacetime Physics" and have a question about possibility of correct clock synch using signal other then light. For example, we choose reference clock(A) and at ...
1
vote
0answers
75 views

Spin in relativity

Mass and spin of the particle are used in classification of elementary particles. The mass is defined to be a Lorentz invariant quantity. On the other hand, the spin is a spacelike 4-vector and cannot ...
1
vote
0answers
283 views

Why does Coulomb's law not hold for fast moving charges?

We all remember calculating the electric force of interaction between a stationary nucleus and a revolving electron using Coulomb's law. The electron in this case is moving. Here's what I think about ...
1
vote
0answers
45 views

Since “coordinate time” has a very specific meaning, how to call more general parametrizations?

Recently I've learned that "coordinate time" assigned to a particular time-like spacetime path is not only required (1) to be monotonous and continuous and even differentiable wrt. the "proper time" ...
1
vote
0answers
173 views

A question on an exercise from Gravitation by Misner, Thorne and Wheeler

My question is on problem 4.1 of Gravitation. In a generic case of electric field and magnetic field(i.e not $E=0$ or $B=0$ or $E$ and $B$ perpendicular), define the direction $\hat{n}$ unit vector , ...
1
vote
0answers
26 views

Explain polarization in RF in which the conductor is stationary

Consider a metal rod parallel to $x$-axis moving with velocity $\vec v =(0,v,0)$ perpendicular to magnetic field $\vec B=(0,0,B)$. Lorentz force will give rise to the electric field $\vec E = - ...
1
vote
0answers
24 views

4-acceleration of rotating frame

Consider the 3-dimensional Minkowski space $$ ds^2=dt'^2-dr'^2-r'^2d\phi'^2 $$ Now we transform it into a rotating frame: $$ t'=t,r'=r,\phi'=\phi+\omega t $$ Then the metric becomes $$ ...
1
vote
0answers
94 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 ...
1
vote
0answers
82 views

Hyperbolic Cosine and Sine in Terms of 3-D Velocity

Intuitively, why are $\cosh(\theta) = \frac{1}{\sqrt{1-(v/c)^2}}$ and $\sinh(\theta) = \frac{v/c}{\sqrt{1-(v/c)^2}}$ true in special relativity? Is there some picture I can draw in Minkowski space ...
1
vote
0answers
80 views

Are there 'special' cases for when special relativity can be applied for accelerating bodies?

I have the following theoretical situation: A space station modeled as a ring in free space is rotating about its centre point at a high speed. I am trying to work out where time flows slower. From ...
1
vote
0answers
138 views

Including special relativistic effects in momentum in Heisenberg's Uncertainty Principle

I've been told that an electron is somewhere within the space of $10^{-10}m$ and am supposed to find the uncertainty in its velocity. Simply applying $m\Delta x \Delta v \geq \frac{h}{4\pi}$ results ...
1
vote
0answers
79 views

Integral of energy-momentum tensor

On Weinberg's Gravitation and Cosmology section 8 chapter 2, he introduced the energy-momentum tensor of a system of $n$ particals: $$ ...
1
vote
0answers
172 views

Twin Paradox - different approaches

What was the difference between Langevin's approach to the twin paradox and Max Von Laue's? I don't understand how Langevin tried to use the idea of absolute acceleration to explain the distinction in ...
1
vote
0answers
56 views

Moving Clocks Time Problem

http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Special_relativity_rel_sim/index.html Talking about the situation of clocks shown on this page. Clocks A&B. Now suppose clock B is moving ...
1
vote
0answers
94 views

Time-Independent Gravitational Equation?

Is it possible to calculate gravitational induced position change without requiring the use of time (and therefore, acceleration) anywhere in the equation? If such an equation were to be discovered, ...
1
vote
0answers
117 views

Quantum Eraser under Lorentz Boost

Suppose I am conducting the Quantum Eraser experiment. The results of this experiment are easy to understand with the traditional quantum mechanical interpretation of a pair of entangled photons. ...
1
vote
0answers
120 views

Space contraction: what do we see

This is my opinion about what we will see. When the pipe arrive at the bar, we will be unable to see some part of it anymore (the pipe will absorb the light emitted by the bar), even if the pipe and ...
1
vote
0answers
203 views

Non-zero charge density due to Lorentz contraction in current carrying wires

In trying to answer this question I came across the following problem. The original question relates to the idea that what looks like a magnetic field in one reference frame, ends up as an ...
1
vote
0answers
49 views

Do two synchronous clocks have simultaneous indications?

Considering two clocks, $C$ and $D$, which were at rest to each other throughout a sufficiently extended trial, and given their time parametrizations $t_C : {\text{ ordered set of}}C{\text{'s ...
1
vote
0answers
63 views

Time reversal invariance and statistics

To what extend does the behaviour of time reversal invariance depend on the statistics of the particle under consideration? More explicitly: To what extend does the action of the time reversal ...
1
vote
0answers
89 views

Direct sum of the spinors and EM field tensor

EM field tensor refer to the direct sum of $(1, 0), (0, 1)$ spinor representation of the Lorentz group. How to show it? Each of these spinor representations corresponds to the symmetrical spinor ...
1
vote
0answers
176 views

Relations between fields transforming by Lorentz and Poincare groups

We can analyze fields transforming by the Lorentz group as $(m, n)$ representations, where $m,n$ are the max eigenvalues of two SU(2) operators, which generate the irreducible representation of the ...
1
vote
0answers
62 views

Transformation of $t=0$ line in moving frame of reference

How does $t=0$ transform into $t - vx/c^2 = 0$ if a frame of reference is moving as given in here? It seems that the relativistic transformation is given by $$ \begin{bmatrix} x' \\ ct' ...
1
vote
0answers
91 views

Wick rotation and special relativity

CMIIW, but as I understand it, Wick rotation replaces the Minkowski basis (t,x,y,z) with the Euclidean basis (it,x,y,z). Suppose that $t_2=t_1 \cosh \beta+x_1 \sinh \beta$ and $x_2=t_1 \sinh \beta+x_1 ...
1
vote
0answers
42 views

Calculate the acceleration of the trailing muon bunch

Two separate suitably short but intense bunches of muons, "A" and "B", are both supposed to be constantly accelerating (in an otherwise sufficiently flat region) with constant proper acceleration ...
1
vote
0answers
216 views

Does Mansuripur's Paradox involve fictitious charges?

Mansuripur's Paradox involves a magnet moving at relativistic speeds in an external electric field. Additional: thanks to Retarded Potential, who found the original paper. If I understand correctly, ...
1
vote
0answers
224 views

Matrix manipulation for Dirac matrices

From the Dirac equation in gamma matrices, we know that $$\gamma^i=\begin{pmatrix} 0 & \sigma^i \\ -\sigma^i & 0 \end{pmatrix}$$ and $$\gamma^0=\begin{pmatrix} I & 0 \\ 0 & -I ...
1
vote
0answers
296 views

Newton's gravitational constant $G$, the reduced Planck constant $\hbar$, the speed of light $c$: the Dream Team of moderators?

The three great constants of Nature are well known: the speed of light $c$ (special relativity), the reduced Planck constant $\hbar$ (quantum mechanics), Newton's ...
1
vote
0answers
270 views

Could one transmit a signal with equally-tuned casimir plates across the quantum field?

It seems, one could exploit the Casimir effect to send messages across arbitrarily-large distances with carefully-tuned Casimir plates. Obviously, relativity would preclude FTL information transfer, ...
1
vote
0answers
475 views

How equivalent are heat energy and work energy in connection with a spinning flywheel?

Let's say we have two identical spinning flywheels, that have arbitrary geometry, and are made of copper. Now we apply some heat energy at the center point of flywheel A, causing it to slow down a ...