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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Status of experimental searches for tachyons?

Now that the dust has settled on the 2011 superluminal neutrino debacle at OPERA, I'm interested in understanding the current status of experimental searches for neutrinos. Although the OPERA claim ...
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213 views

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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348 views

Gravity's Rainbow

What is it? I've seen it in context of a few research papers such as Absence of black holes at LHC due to gravity's rainbow and Thermodynamics of black holes in gravity’s rainbow formalisms My best ...
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321 views

What does Weinberg–Witten theorem want to express?

Weinberg-Witten theorem states that massless particles (either composite or elementary) with spin $j > 1/2$ cannot carry a Lorentz-covariant current, while massless particles with spin $j > 1$ ...
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118 views

Perfect fluid and Cauchy momentum equation

The stress-energy tensor of a perfect fluid is given by $$T^{\mu\nu}=\left(\rho+pc^{-2}\right)u^\mu u^\nu+pg^{\mu\nu}$$ The divergence of the stress-energy tensor is zero: $\nabla_\mu T^{\mu\nu}=0$. ...
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57 views

Is there a time dilation between my left and right arms?

Is there a time dilation between my left and right arms when walking? due to special relativity I guess Thanks
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56 views

Time changing potential gives rise to “force”?

Imagine a charged particle inside a Faraday cage (i.e. charge on outside, zero electric field inside, but non-zero electric potential on the inside). Suppose the charge distributed on the outside of ...
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77 views

If tachyons existed, would we notice them?

In special relativity the space-time can be seen as a static four-dimensional picture that contains the entire past and the future of a flat universe. And the patterns in it are subject to several ...
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43 views

Subluminal speed when going in a circle around someone

Some time ago I thought about such situation: There are two people in the room. Both have synchronized watches on their wirsts. Then the person A starts running around person B with the speed of ...
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1answer
99 views

How can the 'choice' of a photon said to be delayed?

My question arises from two ideas that seem to be contradictory. Idea One: Wheeler's Delayed Choice experiment is an interesting variation of the double slit experiment. Idea Two: In the "reference ...
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67 views

Hafele-Keating revisited with a gravity clock

Most modern clocks use electromagnetic phenomena to measure time. There are perhaps some older clocks that involve gravity to some degree (hour glass, pendulum), but I believe they still have a ...
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52 views

Invariance in Euclidean and Minkowski spaces

Consider Wick's rotation from Minkowski to Euclidean space in QFT. What is the connection between O(4) invariance in Euclidean space and Lorentz invariance in Minkowski space? If we define a quantity ...
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36 views

The norm of the vector sum of two 4-momentum vectors before and after pair production

Two photons traveling along the x-axis (in a lab frame of reference) of different frequencies are about to collide. Their 4-momentum vectors are (h$\nu_1$/c , h$\nu_1$/c , 0, 0) and (h$\nu_2$/c , ...
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49 views

Is there a name for the linear quantity corresponding to the (quadratic) “interval $\Delta s^2$”?

Recently it has been affirmed here (again) that the quantity called "interval (also 'spacetime interval' or 'invariant interval')" is referring to two (in general distinct) events as arguments, such ...
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60 views

Representations of Lorentz algebra

It is well known that the Lorentz algebra can be written as two $SU(2)$ algebras. By defining $$N_i=\frac{1}{2}(J_i+iK_i), \qquad N^{\dagger}_i=\frac{1}{2}(J_i-iK_i)$$ we have ...
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1answer
43 views

Time for two relativistic objects to meet

How do you prove that the time for two objects traveling towards each other at relativistic velocities is still d/(v1+v2). Answer seems to have something to do with velocity addition but I'm ...
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71 views

Relativistic momentum of an electron

Suppose we have some interaction between a photon and an (initially) stationary electron, and we wished to find the final momentum of the electron. Should we solve this using conservation of momentum, ...
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49 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 polarization vectors ...
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108 views

Physical interpretation of distances

Suppose we have a universe with only two distinguishable particles, neglecting gravitation. These particles start off next to each-other, ostensibly "touching" each-other and at rest. If it takes ...
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1answer
165 views

Time-reversed twin paradox

This started with wondering about the nature of certain physical quantities under time-reversal - chiefly, that acceleration retains its magnitude and direction at a given time regardless of the ...
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1answer
46 views

Rotating Observers in Special Relativity: Coriolis-like effect?

Do any noninertial "forces" [terms in the metric] (like Coriolis in Newtonian mechanics) appear to a rotating observer (reference frame) in special relativity? Is the resulting spacetime after ...
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1answer
177 views

Doppler shift for a uniformly accelerating observer

This was given in textbook as an example. An observer on a spaceship with a four velocity $u$ is approaching from $x = +\infty$ a star at rest in the reference frame $S$ while undergoing constant ...
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1answer
333 views

Theoretically if you passed the speed of light in a medium, would there be a sonic boom equivalent?

I know that it is technically impossible to reach the speed of light in vacuum since the mass of the object traveling would reach infinity. However in a medium, would there be some sort of theoretical ...
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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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388 views

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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50 views

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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55 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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103 views

Paradox - Laws of physics are the same in all inertial reference frames vs Equivalence Principle (Pictures Added)

According to the equivalence principle, no experiment should exist that one can perform to determine whether one is in an accelerating elevator, or in a gravitational field. I will outline two ...
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64 views

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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99 views

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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63 views

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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55 views

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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418 views

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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76 views

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 ...
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127 views

At near light speeds, are small objects in your path a problem?

A mental exercise: A space ship is accelerating toward me from far away. As it approaches me, I can observe its acceleration. This high speed ship keeps accelerating faster toward the speed of light. ...
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88 views

Transformation of a time-dependent acceleration to another frame

How do I transform a time-dependent acceleration between to rest frames? I was given a particular problem and while I found possibilities [1] [2] for acceleration-transformations when the acceleration ...
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95 views

What is wrong in following arguments about connection of local gauge invariance and causality?

There is a question and corresponding downvoting of my answer, so I decided to ask this question. There is my answer on it: "...The most theories of free fields are invariant under global gauge ...
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148 views

does light beam bend when moving with a constant velocity?

I'm studding special relativity and there is a famous example where there is a moving train witch has a light source on its floor and a mirror attached to its roof. an observer in the train sees a ...
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71 views

Gravitational Behavior of Rotating Body

Consider a stick with a (ball-shaped) weight at the end of it. Let's say this stick is in a state of rotation (it's floating in vacuum) and is also in a state of translational motion. Consider a ...
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103 views

positron / electron annihilation - where is the invariant?

Electron and a positron are headed towards each other with same kinetic energies - observed from center of mass (COM) system. After the colission two photons are emitted and are headed in opposite ...
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57 views

Kaon spontaneously splits into two pions (just need an confirmation)

I just need a confirmation on a problem that I am dealing. In my problem I have a statioary kaon which spontaenously splits into two pions which are headed in different directions. Is it possible to ...
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relativity - equivalent frames do not have equivalent clocks and rods

In problems about relativity we have a stationary frame S and a moving frame M and two observers initially at the same reference point. Then the two frames pass each other and we measure the distance ...
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accelerating a gravitational field

Newton's equation for gravity calculates gravitational force between two bodies $F= GMm/r^2$ My question is: How does the force change as these two bodies accelerate together through the universe and ...
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Where does the transformation of $\gamma$ come from?

I was reading Tipler, and in his book he says that in order to transform energy, we must write gamma in terms of quantities in the non-primed frame. However his derivation makes no sense to me, it's ...
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514 views

Collision of 2 particles - calculating the mass and a speed after the collision

Lets say we have a particle of mass $m_1$ which has a kinetic energy $W_{k1}$. This particle collides with another same particle. How can i calculate mass $m_2$ and the speed $v_2$ of the particle ...
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88 views

Relativistic canonical transformation

What is relativistic canonical transformation? I need every piece of information about it. Does anyone know a reference or an article about relativistic canonical transformation? For example, in ...
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Help identifying an expression for the action

I found the following expression for the action of a (free, I think) relativistic particle in my notes but I can't remember from what it came from: $$ S = \int_{0}^{N} \left [ ...
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380 views

Lorentz transformations of the polarization vector

Let $\bf{n}'$ be a unit vector in the direction of a wavevector in the plasma rest frame and $\bf{B'}$ be a unit vector along the magnetic field in the plasma rest frame. The electric field of a ...
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Comparing Lagrangian in Special Relativity vs General Relativity for a weak gravitational field

This is a sequel to this question. Who knows a difference between the Lagrangian in SR and GR for a weak gravitational field in non-relativistic case? What is the reason of this difference?