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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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 ...
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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 ...
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Fate of largest scale structures?

In $\Lambda\mathrm{CDM}$, structures form "bottom up" with larger structures forming later. Structures are generally speaking supported by the velocity dispersion of their constituent objects (e.g. ...
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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: $$ ...
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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 ...
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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 ...
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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, ...
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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. ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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' ...
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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 ...
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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 ...
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284 views

The definition of Lorentz transformation

I know that the Lorentz transformation, 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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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, ...
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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 ...
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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 ...
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260 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, ...
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371 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 ...
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Conserved charge from conserved current associated with translational invariance

(c.f Di Francesco, 'Conformal Field Theory' P.45) Di Francesco calls the conserved charge arising from the conserved current associated with a translation invariant theory the 'four momentum'. While ...
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Why don't we experience dilatations in Minkowski spacetime?

The question This question follows on from the use of projective coords for spacetime in Notation for Translation Group Generators . Under Felix Klein's Erlangen Program, Minkowski spacetime starts ...
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Macroscopic Bose condensate in Special Relativity

I remember from an experiment about the Josephson effect the state of each of the super conductors is fully described by a phase factor. From there I assume that is true for any Bose-Einstein ...
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Twin Paradox Without Acceleration

So I've been doing a lot of reading about the twin paradox and have encountered several different explanations that strive to resolve it. First off let me start by saying general relativity is not an ...
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what about doing the laser beam in a moving reference frame but with a ball

I realize the situation where a laser beam moves vertically in a moving vehicle but what if the laser beam was a normal ball If we do the same steps of the proof considering that the velocity of the ...
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thrust-bursting towards a destination in space

<--burst of thrust------|ME in a ship>----->>--<<--laser radar--<<---->>---||destination In the above, I imagine myself in a ship, marking my speed to a far off destination with laser ...
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48 views

Conditions that the coordinate must satisfy in order to become local inertial

Consider the coordinate transformation $$ \tilde x^a=x^a+\frac{1}{2}\Gamma^a_{bc}x^bx^c $$ I have shown that at the origin $O=(0,0,0,0)$, $$ \frac{\partial\tilde g_{ab}}{\partial\tilde x^c}=0 $$ ...
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(Special Relativity) Points that can be seen by an observer

Let the metric be $$ ds^2=(1+gz)^2dt^2-dx^2-dy^2-dz^2 $$ where $g$ is a positive constant. Let an observer be stationary at $x=y=0$ on the surface $z=0$ and look upwards at an angle $\theta$, how ...
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Exercise Lorentz Transformations

I have 2 inertial frames, both are in relative motion along the x axis moving with constant velocity $v_x$. It is called with Standard figuration where the Lorentz transformations relate the ...
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Derivation of proper acceleration in terms of rapidity

In the Wikipedia page for proper acceleration, an equation for proper acceleration in terms of rapidity is given as $\alpha = \frac{\Delta \eta}{\Delta \tau}$, where $\eta$ is the rapidity of the ...
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179 views

Compton Scattering: Klein-Nishina formula derivation

I'm following a derivation of the Klein-Nishina formula from scratch and this is what I have so far: $P_{e,i} = m_0\gamma_u[1,u]$ and $P_{\gamma,i} = [\frac{\hbar\omega_i}{c^2}, ...
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Realtivistic explanation of forces between two conducting wires

The formula for the force between two infinite conducting wires per unit of length, $F_l = \frac{\mu_0}{2\pi} \frac{I_1 I_2}{r}$, is quite well known. It was used for definition of ampere and was ...
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What is the age of the Universe from the big-bang light perspective?

What is the age of the Universe from the big-bang light perspective? We all agree that the universe is around 14 billion years, from the perspective of a hypothetical observer moving in a galaxy, ...
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Ultrarelativistic limit of helicity values

Let's have helicity operator: $$ \hat {h} = \frac{(\hat {\mathbf S} \cdot \hat {\mathbf p})}{|\mathbf p|}. $$ For massive case spin $s$ representation it has $2s + 1$ eigenvalues $s, s - 1,..., -s$, ...
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Angles between axes after Lorentz transformations

Consider frame $K_1, K_2, K_3$ such that $K_1$ moves along the $y$ axis of $K_2$ with speed $v$ and $K_2$ moves along the $x$ axis of $K_3$ with speed $u$. Find the angle between the $x$ axis of $K_1$ ...
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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 ...
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does an object travelling close to the speed of light in an inertial frame of reference behave Relativistically

The two tenants of Special Relativity are: The laws of physics are the same in all inertial frames of reference. The speed of light in free space has the same value $c$ in all inertial frames of ...
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Theoretically if you passed the speed of light, would there be a sonic boom equivalent?

I know that it is technically impossible to reach the speed of light since the mass of the object traveling would reach infinity. Despite this if it were possible, would there be some sort of ...
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Why is radiation at the relativistic limit characterized by 1/gamma angle?

Trying to think of a reason as to why? Also, the factor that radiation is zero on axis? I haven't been able to resolve these two fundamental principles in my head :(
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How to find the speed of free tachyon after emission the light?

Let's have the model in which free tachyon emits the light. We have $$ E = E_{1} + E_{\omega}, \quad \mathbf p = \mathbf p_{1} + \frac{E_{\omega}}{c}\mathbf n , \quad cos(\mathbf p_{1} , \mathbf n ) = ...
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How to interpret Lenz's law in STR?

By the Lenz's law, when a charged particle goes through a coil it generates a magnetic field. This field generates a current in the coil, slowing down the particle. But by Special Relativity (STR), ...
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When do wave function collapse in this case?

In relativity, an event A can occur before another event B in one frame while A may occur after event B in another. In quantum mechanics, we may measure the spin of two entangled electrons: If you ...
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Clock synchronization and dilation

This is a question on the synchronization of clocks. If a girl on a train has the same clock that a guy has on the platform and they synchronize their clocks at 12am together when the train and the ...
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Field of moving charge / Lorentz;Lienard-Wiechert

First question here. I'm really confused at the moment. An electron moves at constant velocity, no acceleration Wikipedia says here Lorentz: Which yields something like this: Wheras here, ...
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Relativistic elastic head-on collision: The momentum just reverses direction

Consider a relativistic elastic head-on collision between a projectile, with mass $m_a$ and velocity $\mathbf{v}_a$, and a stationary target of mass $m_b$. Here "head-on" means that the two particles ...
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Action-reaction principle in special relativity

Consider a relativistic train of weight $W_t$ in its rest frame. Force transformation equations say that in the planet's frame its weight is reduced to $W_p=\frac{W}{\gamma}$. My question is: what is ...
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Possible values of energies and impulses of virtual photon emitted by real electron

I need to find the possible values of energies and impulses of virtual photon emitted by real electron. I don't understand how to compute it (look to the text below). Let's introduce the free ...