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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Mass of particle near light speed in a medium

I am trying to get a common understanding from these two previous questions: Why does the mass of an object increase when its speed approaches that of light? What happens if light/particles exceeded ...
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Doppler redshift in special relativity

I came across this exercise in Elementary General Relativity by Alan MacDonald: A source of light pulses moves with speed v directly away from an observer at rest in an inertial frame. Let $ \Delta ...
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Inertial frames of reference

I'm struggling with the notion of an inertial frame of reference. I suspect my difficulty lies with the difference between Newtonian and relativistic inertial frames, but I can't see it. I've read ...
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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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reflection at speed of light when both mirror and viewer is travelling at the speed of light [duplicate]

consider me sitting on the top of a train which is travelling close to the speed of light, will I be able to see my image on a mirror which I'm holding in my hand??
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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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How to derive the Time Dilation formula given: [closed]

Since I do not have 10 reputation I will fit this all in one image: If you have any questions please dont hesitate to ask. EDIT: http://img16.imageshack.us/img16/8604/myquestion2.png
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1answer
399 views

Neumann boundary condition and the open string

In string theory, If an open string obeys the Neumann boundary condition, then in the static gauge, one can show that the end points move at the speed of light. The derivation is straightforward, but ...
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257 views

Question about negative mass [duplicate]

How is it possible to have negative mass for negative mass means something that has less mass even than nothing ? Does nothing has mass? And how is nothing a reference.
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1answer
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Nonlinear combination of velocities implies no absolute time?

Landau 1961 begins with a brief presentation of special relativity. This question is about the validity of a certain argument that they use in building up the foundations of the subject from scratch, ...
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369 views

Does it matter in which direction I travel in relativity theory?

I'm not a physicist, but I'm still very interested in the relativity theory, especially in how the twin paradox is explained. Actually, it does not make sense to me and I hope you can answer my ...
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3answers
369 views

Why geometrically four acceleration is a curvature vector of a world line? And what is proper acceleration?

Why geometrically four acceleration is a curvature vector of a world line? Geometrically, four-acceleration is a curvature vector of a world line. Therefore, the magnitude of the ...
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How to compute the speed of sound in relativistic hydrodynamic?

In Weinberg: Gravitation and Cosmology chapter 2.10 (Relativistic Hydrodynamics) the speed of sound is derived as $v_s^2 = \left(\frac{\partial p}{\partial \rho}\right)$ and the equation of state ...
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236 views

Measurements and simultaneity [duplicate]

Picture a situation where we have two observers, $A$ and $B$, and a system in a certain quantum state. If $B$ makes a measurement of some observable, say energy for example, the state will collapse to ...
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Which causal structures are absent from any “nice” patch of Minkowski space?

Which "causal separation structures" (or "interval structures") can not be found among the events in "any nice patch ($P$) of Minkowski space"?, where "causal separation structure" ($s$) should be ...
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1answer
121 views

What's the relativistic energy of a moving strained spring as $k\to\infty$ [closed]

Suppose a spring with stiffness $k$, is strained by constant forces on each end. In a frame where the strained spring moves at a constant velocity, what's the total relativistic energy of the moving ...
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5answers
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Why define four-vectors to be quantities that transform only like the position vector transforms?

A four-vector is defined to be a four component quantity $A^\nu$ which transforms under a Lorentz transformation as $A^{\mu'} = L_\nu^{\mu'} A^\nu$, where $L_\nu^{\mu'}$ is the Lorentz transformation ...
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Deriving the action and the Lagrangian for a free point particle in Special Relativity

My question relates to Landau & Lifshitz, Classical Theory of Field, Chapter 2: Relativistic Mechanics, Paragraph 8: The principle of least action. As stated there, to determine the action ...
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1answer
197 views

The Speed of Light [duplicate]

I know that the speed of light is constant for some reason. But why is it that when shining light from a spacecraft that is moving at (almost) the speed of this light, the speed of this light ...
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2answers
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Generalizing a relativistic kinematics formula for spatial-acceleration dependence

I'm starting from this expression $$ \alpha dt = \gamma^3 dv $$ where $\alpha$ is proper acceleration of a point particle, $dv$ and $dt$ are coordinate differentials of velocity and time, and ...
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300 views

Velocity of an object undergoing homogenous acceleration

So I was considering the following problem within the context of Special Relativity: Given an object O, with initial velocity v, undergoing constant acceleration at a rate of a, I want to express the ...
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2answers
131 views

Relative to the speed of light

Einstein's relativity tells us that light always travels at the speed of light relative to me, no matter how fast I'm going. Right? This really confuses me though. If light travels from A to B in one ...
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417 views

Special Theory of relativity on electromagnetic waves

Since time slows down and length contracts, when we travel almost at speed of light, if the speed of light (or EM waves) remains same and the wavelength of light remains same, do we measure the ...
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1answer
137 views

How can we observe lights properties if it travels at the speed of light, or can we? [duplicate]

Special relativity says that anything moving (almost) at the speed of light will look like its internal clock has (almost) stopped from the perspective of a stationary observer. How do we see light as ...
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1answer
213 views

Can a pushed plank beat light and break the laws of physics? [duplicate]

Imagine you are one lightyear away from a photon sensitive (light sensitive) switch. So it is obvious that light would take one year to reach to the switch. Now I have a one lightyear long plank. I ...
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What is the time component of velocity of a light ray?

If we have a light ray $x^\mu$ with velocity $c$, what is $c^0$ (the time component)?
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346 views

How to add a potential term to the Dirac Equation?

I've read that if you have a Hamiltonian for the Dirac Equation, you can add a potential term to it simply by adjusting the momentum operator so that $p^\mu \rightarrow p^\mu-A^\mu$, where $A^\mu$ is ...
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1answer
285 views

What has $E = mc^2$ to do with nuclear powerplants?

In life, when you talk about nuclear energy, there always happens to be a guy who says that famous Einstein's equation. "Yeah, they just convert mass to energy, $E = mc^2$ ya know?" When I think ...
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Synchronization of clocks and observations of time in special relativity

I have thought up a situation that I cannot understand with my understanding of special relativity. I don't know general relativity, but as the situation doesn't involve gravity or acceleration, I'm ...
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Does the stress-energy tensor contain the equations of motion?

Derivatives $\nabla_i T^{ik}=0$ of a stress-energy tensor of physical system express conservation laws. Whether contains a stress-energy tensor also the information on the equations of motion of ...
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Quantum Mechanical Effects of an object accelerating near speed of light $c$?

Consider a space ship, undergoing constant acceleration (which for our purposes means that the same amount of energy is being used per second to increase its speed). According to special relativity ...
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791 views

Formulas for kinetic energy

I was reading ABC of relativity from Bertrand Russell and some formulas about kinetic energy caused me some problems. Here is the extract : The kinetic energy is, in the usual form ...
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210 views

Relativistic Lagrangian transformations

I need to study the relativistic lagrangian of a free particle. It's $\ L= - m c^2 \sqrt[2]{1- \frac{|u|^2}{c^2}} $ I need to study the translation, boost and rotation symmetry. I say it doesn't ...
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If angular momentum corresponds to linear momentum, what corresponds to energy?

Angular momentum is defined from linear momentum via $\vec L = \vec r\times\vec p$, and is conserved in a closed system. Since energy is the time part of the linear four-momentum, is there a quantity ...
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What if EM or QCD was spontaneously broken?

Suppose that Standard Model Higgs mechanism broke electromagnetism, by e.g. veving the charged component of the doublet, so that the photon was massive with $m_\gamma\sim v$. Could such a Universe ...
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1answer
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If time stops at the speed of light is a photon 'everywhere' at once? [duplicate]

I am not a physicist so excuse my question if it's paticularly stupid. As a particle gets closer to the speed of light time slows down as for that particle as compared to a reference from the ...
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1answer
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Explicit form of $\gamma^\mu \partial_\mu$ in the Dirac equation

I'm in an introductory particle physics class, and in performing manipulations on the Dirac equation, my instructor expands the $\gamma^\mu \partial_\mu$ term as: $$\gamma^\mu \partial_\mu = \gamma^0 ...
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Spin-Statistics Theorem (SST)

Please can you help me understand the Spin-Statistics Theorem (SST)? How can I prove it from a QFT point of view? How rigorous one can get? Pauli's proof is in the case of non-interacting fields, how ...
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Why do we identify symmetric 2nd rank tensors with spin-2 particles in string theory?

I am going through Tong's lecture notes on String Theory and came across the following irrep decomposition (Chap 2, p.43) of the bosonic string first excited states: $$\text{traceless symmetric} ...
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Violation of Newton's 3rd law

I'm just expressing my guess. Let two particles A and B experiences forces $F_1$ and -$F_2$ between them and let guess also there are two observer, one is stationary and other is moving with ...
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1answer
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can be exist the negative mass? [duplicate]

I'm not sure about this but I guess there must be negative masses in the universe because of the symmetry. If the gravity is one of the main forces in nature it must has negatives mass to be able to ...
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1answer
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Volume element $\mathrm{d}^4k =\mathrm{d}k^0 \,|\mathbf{k}|^2\,\mathrm{d}|\mathbf{k}| \,\mathrm{d}(\cos\theta) \,\mathrm{d}\phi$ in Minkowski space?

Suppose we have an integral $$\int \mathrm{d}^4k \,\ f(k)$$ we want to evaluate and that we're in Minkowski space with some metric $(+,-,-,-)$. Is it true that: $$\mathrm{d}^4k = \mathrm{d}k^0\ ...
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Energy conserved… or not? Confused!

I am confused. Could someone kindly explain what's going on in this question? A particle of mass $m$ and charge $e$ moves in the $x,y-$ plane. There is a constant magnetic field $B$ that points in ...
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2answers
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Does inertia increase with speed?

I have heard that when the speed of the object increase, the mass of the object also increase. (Why does an object with higher speed gain more (relativistic) mass?) So inertia which is related to ...
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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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225 views

Is period of rotation relative?

My question is inspired by the following answer by voix to another problem: "There is a real object with relativistic speed of surface - millisecond pulsar. The swiftest spinning pulsar currently ...
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1answer
146 views

Neutrinos and Speed of light

Einstein's Special Theory of relativity postulates that the speed of light is same for all frames. Suppose a neutrino is there moving at the speed of light. Then will that neutrino also be flowing ...
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Speed of Light and Information

Einstein in his thought experiment(?) for the constancy of speed of light in vacuum in all frames reasoned , that if speed of light of vacuum isn't constant than you'll be able to perceive effect ...
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How to keep the clock of a spaceship synchronised to the clock of an observer? [duplicate]

I read that the clocks of GPS satellites seem to run slower than the clock of stationary observer, because of their speed (special relativity) and seem to run faster than the clock of stationary ...
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Doubts concerning Wigner's classification

Wigner classified particles in function of the eigenvalues of $P_\mu P^\mu$ and $W_\mu W^\mu$. Then, it can be proved that for massless particles spin values can be only $\pm s_{max}$. But for a ...