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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Horizon and Unruh radiation for a finite period of acceleration

It's a well known fact that an observer that accelerates at a constant rate from $-c$ at past infinity to $+c$ at future infinity sees a horizon in flat Minkowski spacetime. This is easy to see from a ...
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534 views

What is the formula for the relativistic ellipse?

If an astronomer moves at relativistic speed, the stars and constellations are distorted. He sees the stars towards which he is moving blue shifted, while the ones he's moving away from are red ...
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What if the binding energy becomes larger than the rest mass?

Looking at the equation for binding energy and mass defect, $$ B = m_{\text{free}} - m_{\text{bound}} \\ \Rightarrow m_{\text{bound}} = m_{\text{free}} - B, $$ my question is the following. Suppose ...
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What's the purpose of the arbitary additive constants in Einstein's Inertia of Energy Paper?

In Einstein's paper: Does the Inertia of a Body Depend upon its Energy content? he introduces arbitary additive constants whose purpose I'm confused about. The paper has a frame $(x,y,z)$ where a ...
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240 views

Can a spinor be defined as any quantity which transforms linearly under Lorentz transformations?

Recently I’ve come across a few papers from China (e.g. Xiang-Yao Wu et al., arXiv:1212.4028v1 14 Dec 2012) that make the following statement: ...any quantity which transforms linearly under ...
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Do velocity and acceleration time dilation factors add?

For a spinning space station such as in 2001, A Space Odyssey, what would be the time slowing in the perimeter of the spinning space station with respect to the center axis of the station? The ...
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What does a relativistically moving capacitor “look” like? [duplicate]

Suppose I have a parallel plate capacitor with a vacuum between the plates, a voltage $V$ across them and a capacitance of $C$. What will this arrangement look like to an observer in a uniformly ...
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620 views

Classical vs. Quantum use of the spin 4-vector

I have a few basic questions about the Pauli-Lubanski spin 4-vector S. I've used it in quantum mechanical calculations as an operator, that is to say each of the components of S is a matrix operator ...
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680 views

Relativistic drift velocity of electrons in a superconductor?

Is there a formula for the effective speed of electron currents inside superconductors? The formula for normal conductors is: $$ V = \frac{I}{nAq}$$ I wonder if there are any changes to this ...
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321 views

Disk spinning at the speed of light [duplicate]

Of course, I mean that the edge of the disk is traveling at the speed of light. This is a question that popped into my head a few years ago when I was learning about some basic relativity in high ...
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Does the “Andromeda Paradox” (Rietdijk–Putnam-Penrose) imply a completely deterministic universe?

Wikipedia article: http://en.wikipedia.org/wiki/Rietdijk–Putnam_argument Abstract of 1966 Rietdijk paper: A proof is given that there does not exist an event, that is not already in the past for ...
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Relativistic equivalent of a spring-force?

Usually what helps me understand a concept better in physics is to write a simulation of it. I've got to the point where I'm competent in the basics of special relativity, but, I can't figure out how ...
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$E=mc^2$ resembles kinetic energy formula?

The simplest equation expressing mass–energy equivalence is the famous $E=mc^2$ where $c$ represents the speed of light. Compare this with $E_K = \frac{1}{2}mv^2$. Since $E=mc^2$ can be applied to ...
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Derive $\frac{\mathrm{d}}{\mathrm{d}t}(\gamma m\mathbf{v}) = e\mathbf{E}$ from elementary principles?

It is experimentally known that the equation of motion for a charge $e$ moving in a static electric field $\mathbf{E}$ is given by: $$\frac{\mathrm{d}}{\mathrm{d}t} (\gamma m\mathbf{v}) = ...
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What is $c + (-c)$?

If object A is moving at velocity $v$ (normalized so that $c=1$) relative to a ground observer emits object B at velocity $w$ relative to A, the velocity of B relative to the ground observer is $$ v ...
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What does $\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ mean with respect to special relativity?

What does the following mean with respect to special relativity? $$\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$$
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Extended Rigid Bodies in Special Relativity

I was reading Landau & Lifshitz's Classical Theory of Fields and I noticed that they mention that an extended rigid body isn't "relativistically correct". For example, if you consider a rigid ...
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Special Relativity and $E = mc^2$

I read somewhere that $E=mc^2$ shows that if something was to travel faster than the speed of light then they would have infinite mass and would have used infinite energy. How does the equation show ...
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The reference frame of $c$

I don't have a lot of knowledge of special relativity and associated topics; some of the few things I know are that "all motion is relative" (that is, there is no 'stationary reference frame'), and ...
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Can special relativity distort the relative order in which events occur?

Pretend you are throwing darts at a dart board. You throw dart $d_1$ at time $t_1$. After you throw your first dart, you throw your second dart $d_2$ at time $t_2$. Given that $t_2 > t_1$ in a ...
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Why proper acceleration is $du/dt$ and not $du/d\tau$?

Wikipedia says: In relativity theory, proper acceleration[1] is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. and says: In the ...
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Does the general topology of Minkowski space-time change under a Lorentz transformation?

Does the general topology of Minkowski space-time change under a Lorentz transformation? Open balls in $\mathbb{R}^{4}$ (with the standard topology) are not invariant under Lorentz transformations. ...
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Does entanglement not immediately contradict the theory of special relativity?

Does entanglement not immediately contradict the theory of special relativity? Why are people still so convinced nothing can travel faster than light when we are perfectly aware of something that ...
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Relative Motion

I read the following: http://www.feynmanlectures.caltech.edu/I_15.html#Ch15-S4 "Now let us see what happens to the moving clock. Before the man took it aboard, he agreed that it was a nice, ...
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Bound State of Only Massless Particles? Follows a Time-Like Trajectory?

Is there any way in which a bound state could consist only of massless particles? If yes, would this "atom" of massless particles travel on a light-like trajectory, or would the interaction energy ...
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Velocity Time Dilation

In Wikipedia article about time dilation, it says: "Hafele and Keating, in 1971, flew caesium atomic clocks east and west around the Earth in commercial airliners...the moving clocks were expected ...
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Generators of Poincare Groups

How can I determine the generators of the Poincare Group, $P(1,3)$ explicitly? Here $P(1,3)$ means a matrix Lie group.
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What is a Lorentz boost and how to calculate it?

I know very little special relativity. I never leaned it properly, but every time I read someone saying: "if you boost in the x-direction, you get such and such" my mind goes blank! I tried ...
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Does magnetic propagation follow the speed of light?

Does magnetic propagation follow the speed of light? E.g. if you had some magnet of incredible strength and attached an iron wire that is one light year long to it, would the other end of the iron ...
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Infinitesimal Lorentz transformation is antisymmetric

The Minkowski metric transforms under Lorentz transformations as \begin{align*}\eta_{\rho\sigma} = \eta_{\mu\nu}\Lambda^\mu_{\ \ \ \rho} \Lambda^\nu_{\ \ \ \sigma} \end{align*} I want to show that ...
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Why is the Dirac equation not used for calculations?

From what I understand the Dirac equation is supposed to be an improvement on the Schrödinger equation in that it is consistent with relativity theory. Yet all methods I have encountered for doing ...
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Would travelling at relativistic speeds have any impact on human biology?

If a person was sitting on a craft that has accelerated to near light speed speed from Earth (e.g. 99.999% of light speed) would there be any impact on his or her human biology due to relativistic ...
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Calculating the commutator of Pauli-Lubanski operator and generators of Lorentz group

The Pauli-Lubanski operator is defined as $${W^\alpha } = \frac{1}{2}{\varepsilon ^{\alpha \beta \mu \nu }}{P_\beta}{M_{\mu \nu }},\qquad ({\varepsilon ^{0123}} = + 1,\;{\varepsilon _{0123}} = - ...
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Lorentz transformation of the Spinor Field

I'm reading chapter 3 of Peskin and Schroeder and am stuck on page 43 of P&S. They have defined the Lorentz generators in the spinor representation as: \begin{equation} S^{\mu \nu} = ...
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The notion called aether

I am trying to learn relativity theory and going through an introductory text on special relativity. I stumbled on the Michelson-Morley experiment. The book claims (accounts) that the result of this ...
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Darwin term and Zitterbewegung

I've noticed that in the discussion of the fine structure of Hydrogen atom standard QM texts claim that the Darwin term, which corrects energy of $\ell=0$ (or $s$-) states only, is related to the ...
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Frequency of cosmic microwave background

Some people refer to cosmic microwave background's (CMB) frame of reference as an absolute one. If I understand correctly, we can measure 'absolute' velocity in this frame by using the Doppler effect. ...
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How can photons interact with anything?

I read photons do not age because they move at the speed of light. So when a photon interacts with my eyes, aren't they apart in space-time by the difference of the time in the frame of reference of ...
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What is the real meaning of length contraction?

Suppose one inertial observer measures a rod at rest w.r.t. him and another observer is moving w.r.t. rod. We then say that length will be shorter for moving observer but at the instants the first ...
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How is the speed of light constant in all directions for all observers?

Please imagine the following thought-experiment: Order of Events: Pulse - A single pulse of light is emitted from the light towards the mirror Reflect - The pulse hits the mirror and is ...
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The Dual Cloud Chamber Paradox

2012-04-07 Addendum: The Dual Cloud Chamber Paradox Two 10m diameter spheres $A$ and $B$ of very cold, thin gas have average atomic separations of 1nm. Their atoms are neutral, but ionize easily and ...
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Help Me Gain an Intuitive Understanding of Lorentz Contraction

I'm having a hard time getting an intuitive understanding of Lorentz Contraction. I understand what it is by definition but I don't 'get it.' I'm not a physicist, just an amateur, so sorry if this ...
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Why does Minkowski space provide an accurate description of flat spacetime?

What is the chain of reasoning (beginning, of course, from observations about the universe) that leads one to predict that Minkowski space provides an accurate description of space-time in the ...
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Number of the Generators of Poincare Group

It is said that the Poincare group, $P(3,1)$ has $10$ generators. $6$ of them are the generators of the Lorentz group, $O(3,1)$ and the other $4$ generators are the generators of $4D$ translational ...
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What axiomatizations exist for special relativity?

Einstein 1905 gives the following axiomatization of special relativity (Perrett and Jeffery's translation): The laws by which the states of physical systems undergo change are not affected, whether ...
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Meaning of spin

I'm pretty astounded that I did not hear about this sooner, but in my course on QFT our professor told us that the concept of spin can be used to mean three things: Mechanical spin (apparently a ...
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Is there a relativistic generalization of the Maxwell-Boltzmann velocity distribution?

The Maxwell-Boltzmann velocity distribution in 3D space is $$ f(v)dv = 4\pi \left(\frac{m}{2\pi k_B T}\right)^{3/2} v^2 \exp\left(-\frac{m v^2}{2k_B T}\right)dv$$ It gives the probability for a ...
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Calculate the electric field of a moving infinite magnet, without boosting

Consider a rectangular slab of permanently magnetized material. The slab's dimensions are $L_x$, $L_y$, and $L_z$, and the slab is uniformly magnetized in the $\hat{x}$-direction. The slab is not ...
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Peskin & Schroeder Chapter 3.1 EoM Lorentz Invariant under Lorentz Invariant Lagrangian

From Peskin & Schroeder QFT page 35: The Lagrangian formulation of field theory makes it especially easy to discuss Lorentz invariance. And equation of motion is automatically Lorentz ...
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Relativity and Current in Wire

If an observer is stationary relative to a current-carrying wire in which electrons are moving, why does the observer measure the density of moving electrons to be the same as the density of electrons ...